Gravity Dams

UNITED STATES DEPARTMENT OF THE INTERIOR

BUREAU OF RECLAMATION

DESIGNOF

GRAVITYDAMS

DESIGN MANUAL FOR CONCRETE GRAVITY DAMS

A Water Resources Technical Publication

Denver, Colorado

1976

As the Nation’s principal conservation agency, the Department of theInterior has responsibility for most of our nationally owned publiclands and natural resources.

This includes fostering the wisest use of our land and waterresources, protecting our fish and wildlife, preserving the environmentaland cultural values of our national parks and historical places, andproviding for the enjoyment of life through outdoor recreation.

The Department assesses our energy and mineral resources and worksto assure that their development is in the best interests of all ourpeople.

The Department also has a major responsibility for American Indianreservation communities and for people who live in Island Territoriesunder U.S. administration.

UNITED STATES GOVERNMENT PRINTING OFFICE

DENVER : 1976

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, U.C. 20402.and the Bureau of Reclamation, Engineering and Kesearch Center, Attention: 922, P.O. Box 25007,

Denver F‘ederal Center, Denver, Colorado 80225.Stock Number 024-003-00102-3

Frontispiece.-Grand Coulee Dam and Powerplants.-CN 222-l 17-14091-July 22, 1975

This manual presents instructions, examples,procedures, and standards for use in the designof concrete gravity dams. It serves as a guide tosound engineering practices in the design ofconcrete gravity dams and provides thetechnically trained, qualified design engineerwith specialized and technical information thatcan be readily used in the design of such a dam.

The manual came into being because of thenumerous requests made to the Bureau for itslatest concepts on the design of concrete dams.A companion Bureau manual “Design of ArchDams” is also being prepared and will soon bepublished.

“Design of Gravity Dams” was prepared tocover all heights of concrete gravity damsexcept small dams under 50 feet which arec o v e r e d i n “Design of Small Dams.”Foundations for the design of dams discussedin this book are assumed to be rock.

The material used in this book from “Designof Small Dams” has been revised to make itapplicable to larger concrete gravity dams.Although most of this text is relatede x c l u s i v e l y t o t h e d e s i g n o f d a m s a n dappurtenant structures, it is important that thedesigner be familiar with the purpose of theproject of whicll the dam is a part , theconsiderations ilzj7uencing its justificatioq andthe mamxr of arriving at the size and type ofstructure to be built. Factors which affect theselection of the type of dam and its locationa r e d i s c u s s e d i n c h a p t e r I I , “ D e s i g nConsiderations.” Chapter XV discusses the

ecological and environmental considerationsrequired in constructing a dam. The integrityo f t h e s t r u c t u r a l d e s i g n requires strictadherence to specifications for the concreteand to the practice of good workmanship inconcrete production. Therefore, a summary ofBureau of Reclamation concrete constructionpractices or methods is included in chapterXIV, “Concrete Construction.”

The manual should be of service to allconcerned with the plamring and designing ofwater storage projects, but it cannot relieve theagency or person using it of the responsibilityfor a safe and adequate design. The limitationsstated in the design procedures should beheeded.

This book was prepared by engineers of theBureau of Reclamation, U.S. Department ofthe Interior, at the Engineering and ResearchCenter, Denver, Colorado, under the directionof H. G. Arthur, Director of Design andConstruction, and Dr. J. W. Hilf,* Chief,Division of Design. The text was written bymembers of the Concrete Dams Section,Hydraulic Structures Branch, Division ofDesign, except for Appendix G “Inflow DesignFlood Studies,” which was written by D. L.Miller, * of the Flood and SedimenationSection, Water and Management PlanningBranch, Division of Planning Coordination.Members of the Concrete Dams Section whomade substantial contributions to the texti n c l u d e : M . D . Copen,” J . Legas, E . A .Lindholm, G. S. Tarbox, F. D. Reed,* C. L.

*Retired

V

VI PREFACE

Townsend,* J. S. Conrad,* R. 0. Atkinson, R.R. Jones, M. A. Kramer, C. W. Jones,* J. L.Von Thun , G. F. Bowles, and J. T.R i c h a r d s o n . * T h e m a j o r e d i t i n g a n dcoordinating of the test was done by E. H.Larson,* and the final preparation of the textfor printing was done by R. E. Haefele and J.M. Tilsley, all of the Publications Section,Technical Services and Publications Branch,Division of Engineering Support. The authorsand editors wish to express their appreciationto the personnel in the General Services Branchfor their contributions and to the techniciansof Concrete Dams Section and Drafting Branchwho prepared charts, tables, and drawings foruse in the text.

The methods of design and analysis weredeveloped through the efforts of dedicatedBureau engineers during the many years theBureau of Reclamation has been designing andconstructing concrete gravity dams. Theirefforts are gratefully acknowledged.

T h e r e a r e occasional references toproprietary materials or products in thispublication. These must not be construed inany way as an endorsement of the Bureau ofReclamation since such endorsement cannot bemade for proprietary products or processes ofmanufacturers or the services of commercialfirms for advertising, publicity, sales, or otherpurposes.

C o n t e n t s

PREFACE . . . . . . . . . . . .

Chapter I-IntroductionSection

l-l. scope . . . . . . . . .1-2. Classifications . . . . . .l-3. General dimensions . . . . .l-4. Gravity dam definitions . . .I-5. Bibliography . . . . . . .

Chapter I I-DesignConsiderations

A. LOCAL CONDITIONS

2- 1. General . . . . . . .2-2. Data to be submitted’ . . .

6. MAPS AND PHOTOGRAPHS

2-3. General . . . . . . . . .2-4. Survey control . . . . . .2-5. Data to be submitted . . .

C. HYDROLOGIC DATA

2-6. Data to be submitted . . . .2-7. Hydrologic investigations . .

D. RESERVOIR CAPACITY ANDOPERATION

2-8. General _ . . _ . _ . .2-9. Reservoir allocation

definitions . . . . . . .(a) General(b) Water surface elevation’ ’ ’

definitions . . . . . .(c) Capacity definitions . . .

2-10. Data to be submitted . . . .

Page

V

11122

33

334

45

7

77

79

10

Chapter I I-DesignConsiderations-Continued

Section

2-l 1.2-12.

E. CLIMATIC EFFECTS

Page

General . . . . . . . . . 10Data to be submitted . . . . 10

F. CONSTRUCTION MATERIALS

2-13.2-14.

2-15.

Concrete aggregates .Water for construction

purposes . . . . .Data to be submitted .

G. SITE SELECTION

. . . 1 1

. . . 11

. . . 1 1

2-16. General . . . . . .2-l 7. Factors in site selection

H. CONFIGURATION OF

. . . 1 1

. , . 12

DAM

2-18. Nonoverflow section . . . . 122-19. O v e r f l o w s e c t i o n . . . * . 12

I. FOUNDATION INVESTIGATIONS

2-20. Purpose . . . . . . .2-21. Field investigations . .

(a) Appraisal invcsti-gation . . . .

(b) Feasibility investigation(c) Final design data . .

2-22. Construction geology . .2-23. Foundation analysis

methods . . . . . .2-24. In situ testing . . . .2-25. Laboratory testing . . .2-26. Consistency of presentation

of data . . . . . . .

1313

13131515

151616

16

VII

VIII CONTENTS

Chapter I I-Design Chapter lll-Design Data andConsiderations-Continued Cri ter ia-Cont inued

J. CONSTRUCTION ASPECTS D. LOADS-Continued

Section Pa&!

2-27. General . . . . . . . . . 1’72-28. Construction schedule . . . . 17

SeCtiOn Page

3-10. Deadload . . . . . . . . 283-11. Ice . . . . . . . . . . 283-12. Silt . . . . . . . . . . 293-13. Earthquake . . . . . . . 29K. MISCELLANEOUS CONSIDERATIONS

2-29. Data to be submitted . . . . 172-30. Other considerations . . . . 18

L. BIBLIOGRAPHY

2-3 1. Bibliography . . . . . . . 20

Chapter Ill- Design Data andCriteria

A. INTRODUCTION

3-l Basic assumptions . . . . . 2

B. CONCRETE

3-2 Concrete properties .(a) Strength(b) Elastic propkrties’ :(c) Thermal properties(d) Dynamic properties(e) Other properties .(f) Average concrete

properties . . .

. . . 21

. . . 21

. . . 22

. . . 22

. . . 22

. . . 22

. . . 22

C. FOUNDATION

3-33-4

Introduction . . . . . . . 23Foundation deformation . . . 23

3-5. Foundation strength . . . . 243 - 6 . F o u n d a t i o n p e r m e a b i l i t y . . 2 6

D. LOADS

3-7. Reservoir and tailwater . . . 263-8. Temperature . . . . . . . 263-9. In ternal hydrostatic

pressures . . . . . . . . 27

E. LOADING COMBINATIONS

3-14. General . . . . . . . . 303-l 5. Usual loading combination . . 303- 16. Unusual and extreme loading

combinations . . _ . . . 303-17. Other studies and investi-

gations . . . . . . . . . 30

F. FACTORS OF SAFETY

3-18. General _ . . . . . . . . 303-19. Allowable stresses . . . . . 313-20. Sliding stability . . . . . . 3 13-21. Cracking , . . . . . . 323-22. Foundation stability . . . . 33

G. BIBLIOGRAPHY

3-23. Bibliography . . . . . . . 33

Chapter IV--Layout andAna I ysis

4-l. Introduction . . . . . . . 35(a) Level of design . . . . , 36

A. LAYOUT

4-2. Nonoverflow section . . . , 364-3. Spillway section . . . . . . 364-4. Freeboard . . . . . . . . 36

B. THE GRAVITY METHOD OF STRESSAND STABILITY ANALYSIS

4-5. Description and use . . . . 374-6. Assumptions . . . . . . . 37

CONTENTS

Chapter W-layout andAnalysis-Cont inued

B. THE GRAVITY METHOD OF STRESSAND STABILITY ANALYSIS-Continued

Section Page

4-7. Notations for normalreservoir loading . . .

4-8. Notations for horizontalearthquake . . . . .

4-9. Forces and moments actingon cantilever elements .

4- 10. Stress and stabilityequations . . . . . .

37

39

40

40

C. TRIAL-LOAD METHODS OF ANALYSIS

1. Trial-Load Twist Method of Arlalysis,Joints Ungrouted

4- 11. Introduction . . . . . . . 434-12. Theory . . . , . . . 444-13. Notations . . . . . . . 454-14. Foundation constants . . . . 474-1.5. Selection of elements . . . . 544- 16. Loads, forces, and

moments . . . . . . . . 544-17. Initial and unit deflections

of cantilevers . . . . . . 544- 18. Unit rotations of vertical

elements of twistedstructure due to unittwisting couple , . . . . 54

4 19. Unit deflections of horizontalelements of twistedstructure . . . , . . . . 57

4-20. Trial loads . . . . . . . . 584-2 1. Angular rotation of vertical

twisted elements due totrial loads on horizontalelements . . . . . . . . 60

4-22. Deflections of twistedstructure . . . . . . . . 60

4-23. Deflections of cantileverstructure . . . . . . . 60

4-24. Stresses and stabilityfactors . . . . . . . . . 60

iX

Chapter W-layout andAnalysis-Cont inued

C. TRIAL-LOAD METHODS OFANALYSIS-Continued

Section Pa&p

2. Trial-Load Twist Method of Analysis,Joints Grouted

4-25, Description of method . . . 614-26. Assumptions . . . . . . . 644-27. Horizontal beam elements . . 644-28. Notations . . . . . . . . 644-29. Equations . . . . . . . . 64

(a) Triangular load . . . . . 65(b) Uniform load . . . . . 66(c) Concentrated moment at

free end of beam(d) Concentrated normal load .

67

at free end of beam . . 67

3. Alzalysis of Curved Gravity Dams

4-30. Method of analysis . . . . . 68

D. DYNAMIC ANALYSIS

4-3 1. Introduction . . . . .4-32. Natural frequencies and

mode shapes . . , . .4-33. Response to an earthquake4-34. Loads due to horizontal

earthquake acceleration .4-35. Effects of vertical earth-

quake accelerations . .

68

6869

70

70

E. THE FINITE ELEMENT METHOD

4-36. Introduction . . . . . . . 70

1. Two-Dimensional Finite ElementProgram

4-37. Purpose . . . . . . . . . 724-38. Method . . . . . . . . . 724-39. Input . . . . . . . . . . 734-40. o u t p u t . . . . . . . . . 734-41. Capabilities . . . . . . . 73

X

Chapter IV-Layout andAnalysis-Cont inued

E. THE FINITE ELEMENT METHOD-Continued

Section

4-42.4-43.4-44.

P a g e

Limitations . . . . . . . 73Approximations . . . . . . 73Application to gravity

dams . . . . . . . . . 74

2. Three-Dimensional Finite ElementProgram

4-45. Application . . . . . . . 744-46. Capabilities and limitations . . 744-47. Input . . . . . . . . . . 754-48. output . . . . . . . . . 75

F. FOUNDATION ANALYSIS

4-49. Purpose . . . . . . . . . 76

I. Stability Analyses

4-50. Methods available . . . . . 76(a) Two-dimensional

methods( 1) Rigid section ’ ’ f ’

76

4-51.

method . . . . 76(2) Finite element

method . . . . . 76(b) Three-dimensional

methods . . . . . . . 76(1) Rigid block method . 76(2) Partition method . . 76(3) Finite element

method . . . . . 76Two-dimensionalmethods

(a) Rigid section ’ ’ ’ ’ * ’76

4-52.

method . . . . . . . 76(b) Finite element

method . . . . . . . 76Three-dimensional

methods . . . . . . . . 77(a) Rigid block method . . . 77(b) Partition method . . . . 78

CONTENTS

Chapter IV-Layout andAnalysis-Cont inued

F. FOUNDATION ANALYSIS-Continued

Sec t i on Page

(c) Finite elementmethod . . . . . . . 79

2. 0 tlzer Analyses

4-53. Differential displacementanalysis . . . . . . . . 79

4-54. Analysis of stress concen-trations due to bridging . . . 80

G. BIBLIOGRAPHY

4-55. Bibliography . . . . . . . 80

Chapter V-River Diversion

5-l.5-2.

5-3.

5-4.

5-5.

General . . . . . . . . . 83Characteristics of stream-

flow . . . . . . . . . 83Selection of diversion

flood . . . . . . . . . 83Regulation by an existing

upstream dam . . . . . . 84Turbidity and water

pollution control . . . . . 84

B. METHODS OF DIVERSION

5-6. ’ General . . . . . . . . . 855-7. Tunnels . . . . . . . . . 855-8. Conduits through dam . . . 885-9. Flumes . . . . . . . . . 885-10. Multiple-stage diversion . . . 925-l 1. Cofferdams . . . . . . . 92

A. DIVERSION REQUIREMENTS

C. SPECIFICATIONS REQUIREMENTS

5-l 2. Contractor’s responsibilities . . 955-l 3. Designer’s responsibilities . . 95

CONTENTS

Chapter VI-FoundationTreatmentA. EXCAVATION

Section Page

6-l. General . . . . . . . . . 976-2. Shaping . . . . . . . . . 976-3. Dental treatment . . . . . 976-4. Protection against piping . . . 100

B. GROUTING

6-5. General . . . . . . . . . 1016-6. Consolidation grouting . . . 1016-7. Curtain grouting . . . . . . 104

C. DRAINAGE

6-8. Foundation drainage . . . . 105

D. BIBLIOGRAPHY

6-9. Bibliography . . . . . . . 106

Chapter VII-Temperature

7-l. Purposes . . . I . . . . 1077-2. Volumetric changes . . . . 1077-3. Factors to be considered . . . 1087-4. Design data . . . . . . . 1087-5. Cracking . . . . . . . . 109

B. METHODS OF TEMPERATURECONTROL

7-6. Precooling . . _ _ . _ . . 1117-7. Postcooling . . . . . . . 1127-8. Amount and type of

7-9.cement . . . . . . . . 112

Use of pozzolans . . . . . 113

Control of ConcreteA. INTRODUCTION

7-l 0. Miscellaneous measures . . . 113(a) Shallow construction

lifts 113(b) Water curing . : : : : : 113(c) Retarding agents . . . . 113(d) Surface treatments . . . 113

Xi

Chapter VII - Tempera tu reControl of Concrete-

ContinuedB. METHODS OF TEMPERATURE

SectionCONTROL-Continued

Page(e) Rate of temperature

drop . . . . . . . . 114

C. TEMPERATURE STUDIES

7-l 1.7-12.

7-13.7-14.7-15.7-16.

General scope of studies . . . 114Range of concrete tempera-

tures . . . . . . . . . 114(a) Ambient air temperatures . 115(b) Reservoir water tempera-

tures . . . . . . . + 115(c) Solar radiation effect . . 115(d) Amplitudes of concrete

temperatures . . . . . 116Temperature gradients . . . 116Temperature rise . . . . . 118Artificial cooling . . . . . 120Miscellaneous studies . . . . 125

D. DESIGN CONSIDERATIONS

7-17. Placing temperatures . . . . 1257-18. Closure temperature . . . . 1257-19. Size of construction

7-20.7-21.7-22.7-23.7-24.

block . . . . . . . . . 126(a) Length of construction

block . . . . . . . 126(b) Width of construction

block . . . . . . . 127Concrete cooling systems . . 127Height differentials , . . I , 130Lift thickness . . . . . . , 130Delays between placements . . 13 1Closure slots . . . . . . . 13 1

E. CONSTRUCTION OPERATIONS

7-25. Temperature controloperations . . . . . . . 131

(a) Initial cooling

7-26.

(b) Intermediate and’final . ’ .132

cooling . . . . . . . 133(c) Warming operations . . . 133Foundation irregularities . . . 134

XII CONTENTS

Chapter VII - Tempera tu re Chapter IX-Spillways-Control of Concrete-

ContinuedE. CONSTRUCTION OPERATIONS-Continued

Section P a g e

7-27. Openings in dam . . . . . 1347-28. Forms and form removal . . . 1347-29. Curing . . . . . . . . . 1357-30. Insulation . . . . . . , . 135

F. BIBLIOGRAPHY

7-3 1. Bibliography . . . . . . . 13 5

Chapter VI I I-Joints in

8-l.8-2.8-3.8-4.8-5.8-6.8-7.

8-8.8-9.8-10.

StructuresPurpose . . . . . . .Contraction joints . . .Expansion joints . . . .Construction joints . . .Spacing of joints . . . .Keys . . . . . . . .Seals . . . . . . . .(a) Metal seals(b) Polyvinyl chloride seals(c) Other seals . . . .Joint drains . . . . .Grouting systems . . .Grouting operations . .

. . 137

. . 137

. . 138

. . 138

. . 138

. . 141

. . 143

. . 143

. . 143

. . 143

. . 145

. . 145

. . 146

Chapter IX-Spi l lwaysA. GENERAL DESIGN CONSIDERATIONS

9-l. Function . . . . . . . . 1499-2. Selection of inflow design

flood . . . . . . . . . 149(a) General considerations . . 149(b) Inflow design flood

hydrograph . . . . . 1.519-3 Relation of surcharge

storage to spillwaycapacity . . . . . . . . 151

9-4. Flood routing . . . . . . . 15 19-5. Selection of spillway size

and type . . . . . . . . 154

ContinuedA. GENERAL DESIGN CONSlDERA-

TIONS-Continued

Section P a g e

(a) General considerations . . 154(b) Combined service and aux-

iliary spillways . . . . 156B. DESCRIPTION OF SPILLWAYS

9-6. Selection of spillway layout . . 1569-7. Spillway components . . . . 157

(a) Control structure . . . . 157(b) Discharge channel . . . . 157(c) Terminal structure . . . 158(d) Entrance and outlet

channels . . . ...1589-8. Spillway types . . . . . . 159

Free fall spillways . . . . 159Ogee (overflow)

spillways . . . . . . 159Side channel spillways . . 160Chute spillways . . . . 160Tunnel spillways . . . . 161Morning glory spillways . . 161

9-9. Controls for crests . . .(a) Flashboards and

stoplogs . . . . .(b) Rectangular lift gates(c) Radial gates . . . .(d) Drum gates . . . .(e) Ring gates . . . .

C. CONTROL STRUCTURES

. 162

. 163

. 163

. 164

. 164

. 164

9- 10. Shape for uncontrolledogce crest . . . . . . . . 164

9-l 1. Discharge over an uncon-trolled overflow ogeecrest 165

(a) Coefficient of discharge : : 165(b) Effect of depth of

approach(c) Effect of upstream ’ ’ ’ ’

168

face slope(d) Effect of downstream ’ . ’

169

apron interference anddownstream submer-gence . . , . . . . 169

CONTENTS

Chapter IX-Spillways-Continued

C. CONTROL STRUCTURES-Continued

S e c t i o n Page

(e) Effect of heads dif-fering from designhead . . . . . . . . 171

(f) Pier and abutmenteffects . . . . . . . 17 1

9- 12. Uncontrolled ogee crestsdesigned for less thanmaximum head . . . . . . 174

9- 13. Gate-controlled ogeecrests . . . . . . . . . 174

9- 14. Discharge over gate-controlled ogeecrests . . . . . . . . . 174

9-15. Orifice control structures . . . 17.5(a) Shape 175(b) Hydraulics * : : : : : : 175

9-l 6. Side channel controlstructures . . . . . . . 176

(a) Layout 176(b) Hydraulics : : : : : : 178

D. HYDRAULICS OF DISCHARGECHANNELS

9-17. General . . . . . . . . . 1809-18. Open channels . . . . . . 181

(a) Profile . . . . . . . . 181(b) Convergence and diver-

gence . . . . . . . 183(c) Channel freeboard . . . 183

9- 19. Tunnel channels . . . . . . 185(a) Profile . . . . . . . . 185(b) Tunnel cross section . . . 185

9-20. Cavitation erosion ofconcrete surfaces . . . . . 186

E. HYDRAULICS OF TERMINALSTRUCTURES

9-2 1. Hydraulic jump stillingbasins

(a) Hydraulic design ’. . . . 186

of stillingbasins . . . . . . . 187

XIII

Chapter IX-Spillways-Continued

E. HYDRAULICS OF TERMINALSTRUCTURES-Continued

S e c t i o n Page

(b) Rectangular versustrapezoidal stillingbasin . . . . . . . . 192

(c) Basin depths by approxi-mate methods . . . . 195

(d) Tailwater considera-tions . . . . . . . . 195

(e) Stilling basin freeboard . . 1989-22. Deflector buckets . . . . . 1989-23. Submerged bucket energy

dissipators . . . . . . . 1999-24. Plunge pools . . . . . . . 201

F. HYDRAULICS OF MORNING GLORY( D R O P INLET) SPILLWAYS

9-25. General characteristics . . . . 2019-26. Crest discharge . . . . . . 2039-27. Crest profiles . . . . . . . 2069-28. Orifice control . . . . . . 2079-29. Tunnel design . . . . . . . 213

G. STRUCTURAL DESIGN

9-30. Genera1 . . . . . . . . . 2 14

H. BIBLIOGRAPHY

9-3 1. Bibliography . . . . . . . 2 15

Chapter X-Outlet Worksand Power Outlets

A. INTRODUCTION

10-l. Typesand purposes . . . . 217

B. OUTLET WORKS OTHER THANPOWER OUTLETS

10-2. General . . . . . . . . . 21810-3. Layout . . . . . . . . . 21810-4. Intake structures . . . . . 220

XIV

Chapter X-Outlet Worksand Power Outlets-

ContinuedB. OUTLET WORKS OTHER THAN

POWER OUTLETS-Continued

Set tion Page

(a) Trashrack . . . . 220(b) Entrance and transition : : 221

10-5. Conduits . . . . . . . . 22110-6. Gates and outlet controls . . 221

(a) Location of controldevices

(b) Types of gates’anh * * ’ ’224

valves . . . . . . . 22510-7. Energy dissipating devices . . 225

1. Hydraulic Design ofOutlet Works

10-8. General considerations . . . . 22610-9. Pressure flow in outlet

conduits . . . . . . . . 226lo- 10. Pressure flow losses in

conduits . . . . . . . . 228(a) Friction losses . . . . . 228(b) Trashrack losses . . . . 229(c) Entrance losses . . . . . 229(d) Bend losses . . . . . . 231(e) Transition losses 231(f) Gate and valve losses’ : : : 231(g) Exit losses . . . . . . 232

10-l 1. Transition shapes . . . . . 232(a) Entrances . . . . . . . 232(b) Contractions and

expansions . . . . . . 23310-l 2. Energy dissipating devices . . 233

(a) Hydraulic jump basins . . 233(b) Plunge pools . . . . . 234

10-13. Open channel flow inoutlet works . . . . . . . 234

2. Structural Design ofOutlet Works

10-14. General . . . . . . . . . 23410-15. Trashrack . . . . . . . . 23510-16. Conduit . . . . . . . . . 235

ChapCONTENTS

ter X-Outlet Worksand Power Outlets-

ContinuedB. OUTLET WORKS OTHER THAN

POWER OUTLETS-Continued

Section Page

10-17. Valve or gate house . . . . . 235lo- 18. Energy dissipating

devices . . . . . . . . . 235

C. POWER OUTLETS

10-19. General . . . . . . . . . 23610-20. Layout . . . . . . . . . 23610-21. Intake structures . . . . . 236

(a) Trashracks 237(b) Bellmouth entrance. : : : 240(c) Transition . . . . . . 240

10-22. Penstocks . . . . . . . . 2401 O-23. Gates or valves . . . . . . 24010-24. Hydraulic design of

power outlets . . . . . . 240(a) Size determination of

penstock 241(b) Intake structure * : : : : 241

1 O-25. Structural design ofpower outlets . . . . . . 242

(a) Trashrack . . . . . . . 242(b) Penstocks . . . . . . 242

D. BIBLIOGRAPHY

1 O-26. Bibliography . . . . . . . 242

Chapter Xl-Galleries andAdits

1 l-l. General . . . . . . . . . 24311-2. Purpose . . . . . . . . . 24311-3. Location and size . . . . . 243

(a) Foundation gallery . . . 243(b) Drainage gallery . . . . 243(c) Gate galleries and

chambers 243(d) Grouting galleries : : : : 247(e) Visitors’ galleries . . . . 247(f) Cable galleries . . . . . 247

CONTENTS

Chapter XI-Galleries andAdits-Cont inued

Section P a g e

(g) Inspection galleries . . . 2471 l-4. Drainage gutter . . . . . . 2471 l-5. Formed drains . . . . . . 2471 l-6. Reinforcement . . . . . . 2471 l-7. Services and utilities . . . . 2481 l-8. Miscellaneous details . . . . 248

Chapter XII-MiscellaneousAppurtenances

12-l. Elevator tower and shaft . . . 249(a) Design of shaft . . . . . 249(b) Design of tower . . . . 251

12-2. Bridges . . . . . . . . . 25 112-3. Top of dam . . . . . . . 25412-4. Fishways . . . . . . . . 25512-5. Restrooms . . . . . . . . 25512-6. Service installations . . . . 255

(a) Electrical services . . . . 257(b) Mechanical services . . . 258(c) Other service instal-

lations . . . . . . . 258

Chapter XI I I-StructuralBehavior Measurements

13-1. Scope and purpose . . . . . 259(a) Development of

methods . . . . . . . 259(b) Two general methods . . 259

13-2. Planning . . . . . . . . 26013-3. Measurement systems . . . . 260

(a) Embedded instrumentmeasurements

(b) Deformation measure-. . ’260

ments . . . . . . . 26213-4. Embedded instrumenta-

tion . . . . . . . . . . 26313-5. Supplementary laboratory

tests . . . . . . . . . 27013-6. Deformation instrumenta-

tion . . . . . . . . . . 27013-7. Other measurements . . . . 274

xvChapter XI I I-Structural

Behavior Measurements-Continued

section

13-8.

13-9.13-10.13-11.

page

(a) Uplift pressuremeasurements . . . . 275

(b) Drainage flow measure-ments . . . . . . . 275

Measurement programmanagement . . . . . . . 276

Data processing . . . . . . 279Results . . . . . . . . . 279Bibliography . . . . . . . 280

Chapter XIV-ConcreteConstruction

14 1. General . . . . . . . . . 28114-2. Design requirements . . . . 28114-3. Composition of concrete . . . 28214-4. Batching and mixing . . . . 28314-5. Preparations for placing . . . 28314-6. Placing . . . . . . . . . 28414-7. Curing and protection . . . . 28414-8. Finishes and finishing . . . . 28414-9. Tolerances . . . . . . . . 28514-10. Repair of concrete . . . . . 285

Chapter XV-Ecological andEnvironmentalConsiderations

A. INTRODUCTION

15-1. General considerations . . . 28715-2. Planning operations . . . . 288

B. FISH AND WILDLIFECONSIDERATIONS

15-3. General . . . . . . . . . 28815-4. Ecological and environ-

mental considerationsfor fish . . . . . . . . 288

15-5. Environmental considera-tions for wildlife . . . . . 291

X V I CONTENTS

Chapter XV-Ecological andEnvironmental

Considerations-Continued

Appendix B-Tr ial- loadTwist Analysis-JointsGrouted-Cont inued

C. RECREATIONAL CONSIDERATIONS

Section Page

15-6. General . . . . . . . . . 29315-7. Recreational development . . 293


15-8. General . . . . . . . . . 29315-9. Landscape considerations . . 29515-10. Protective considerations . . . 29615- 11. Construction considera-

tions . . . , . . . . . 296

section Page

B-6. Trial-load distribution . . . . 323B-7. Canti lever deflections . . . . 323B-8. Twisted-structure deflec-

tions . . . . . . . . . 335B-9. Beam-structure deflec-

tions . . . . . . . . . 335B-10. Total deflections . . . . . 340B- 11. Moment and shear due to

trial loads on beams . . . . 340B-l 2. Beam stresses . . . . . . . 340B- 13. Cantilever stresses . . . . . 340B- 14. Final results . . . . . . . 343

E. BIBLIOGRAPHY Appendix C-Finite Element15-l 2. Bibliography . . . . . . . 297

Appendix A-The GravityMethod of Stress and

Stability Analysis

Method of AnalysisA. TWO-DIMENSIONAL FINITE

ELEMENT ANALYSIS

A-l. Example of gravity anal-ysis-Friant Dam . . . . . 299

A-2. List of conditionsstudied . . . . . . . . 299

A-3. Computations and forms . . . 302A-4. Final results . . . . . . . 302A-5. Summary and conclusions . . 302

C-l.c-2.c-3.

c-4.c-5.

Introduction . . . . . . . 3 5 1Description of problem . . . 35 1Grid and numbering

system . . . . . . . . . 351Input . . . . . . . . . . 351output . . . . . . . . . 351

B. THREE-DIMENSIONAL FINITEELEMENT ANALYSIS

Appendix B-Tr ial-LoadTwist Analysis-Joints

Grouted

C-6. Introduction . . . . . . . 358c-7. Layout and numbering

C-8.c-9.

system . . . . . . . . . 358Input . . . . . . . . . . 358Output . . . . . . . . . 361

B-l. Example of twist anal-ysis, joints grouted-Canyon Ferry Dam . . . . 321

B-2. Design data . . . . . . . 321B-3. Abutment constants . . . . 321B-4. Deflections and slopes

due to unit loads . . . . . 321B-5. Deflections of canti-

levers due to initial

Appendix D-SpecialMethods of Nonlinear Stress

AnalysisD-l. Introduction . . . . . . . 37 1D-2. Slab analogy method . . . . 371D-3. Lattice analogy metnod . . . 372

(a) Conditions to beloads . . . . . . . . . 323 satisfied . . . . . . . 372

CONTENTS

Appendix D-SpecialMethods of Nonlinear Stress

Analysis-Cont inued

XVII

Appendix F-Hydraulic Dataand Tables-Cont inued

Set tion

(b) Solution . . . .(c) Equations(d) Boundary conditi’ons(e) Stresses(f) Applications and * *

limitations . . .D-4. Experimental models .

(a) Three-dimensionalmodels . . . .

(b) Two-dimensional dis-placement models

D-5. Photoelastic models .

Page

. . . 374

. . . 374. . 374

. . . 375

. . . 376

. . . 376

. . . 376

. . . 377

. . . 377

Appendix E-Comparison ofResults by Gravity and Trial-

Load MethodsE-l. Stresses and stability

factors . . . . . . . . . 381E-2. Structural characteristics

of dams and maximumstresses calculatedby the gravity andtrial-load methods . . . . . 381

Appendix F-Hydraulic Dataand Tables

F-l. Lists of symbols andconversion factors . . .

F-2. Flow in open channels .(a) Energy and head . .(b) Critical flow . . . .(c) Manning formula . .(d) Bernoulli theorem .(e) Hydraulic and energy

gradients . . . .(f) Chart for approximating

friction losses inchutes . . . . .

F-3. Flow in closed conduits .(a) Partly full flow in

conduits . . . .

. . 415

. . 417

. . 417

. . 420

. . 423

. . 425

. . 425

. . 426

. . 426

. . 426

Section Page

(b) Pressure flow inconduits . . . . . . 429

(c) Energy and pressuregradients . . . ...431

(d) Friction losses . . . . . 431F-4. Hydraulic jump . . . . . . 431F-5. Bibliography . . . . . . . 432

Appendix G-Inf low DesignFlood Studies

G-l. Introduction 435(a) Items to be &lu&ed ’ : : 435(b) Discussions in this

text . . . . . . . . 436

A. COLLECTION OF HYDROLOGICDATA FOR USE IN

ESTIMATING FLOODFLOWS

G-2. General . . . . . . . . . 43 7G-3. Streamflow data . . . . . . 437G-4. Precipitation data . . . . . 438G-5. Watershed data . . . . . . 439

B. ANALYSES OF BASICHYDROLOGIC DATA

G-6. General . . . . . . .G-7. Estimating runoff from

rainfall . . . . . . .(a) General . . . . .(b) Analysis of observed

rainfall data . . .(1) Mass curves of

rainfall(2) Isohyetal maps’ :(3) Average rainfall

by Thiessenpolygons

(4) Determination bf ’rainfall excess .

(5) Discussion ofobserved rain-fall analysesprocedures . .

. 439

. 440

. 440

. 441

. 441

. 441

. 443

. 444

. 445

XVIII

Appendix G-Inflow DesignFlood Studies-Continued

B. ANALYSES OF BASICHYDROLOGIC DATA-Continued

SeCtiOn

(6) Method of esti-mating retentionlosses . . . . .(I) Hydrologic soil

groups . .(II) Land use and

treatmentclasses

(III) Hydrologic’ *soil-covercomplexes .

(IV) Rainfall-runoffcurves forestimatingdirect runoffa m o u n t s .

(V) Antecedentmoistureconditions .

G-8. Analyses of streamflowdata . . . . . . . . .

(a) Unit hydrograph (unit-graph) principles . .

(b) Selection of hydro-graphs to analyze

(c) Hydrograph analyses- ’.

base flow separation .(d) Hydrograph analysis

of direct runoff-need for syntheticu n i t h y d r o g r a p h s . .

(e) Hydrograph analysisof direct runoff-dimensionless-graphcomputations andlag-time estimates . .

(1) Procedures(2) Lag-time curves 1 1

Page

. 446

. 446

. 447

. 448

. 448

. 448

. 450

. 453

. 455

. 455

, 455

. 457. 458. 459

C. SYNTHETIC UNIT HYDROGRAPH

G-9. Synthetic unitgraphs bylag-time dimensionless-graph method . . . . . . 462

CONTENTS

Appendix G-Inflow DesignFlood Studies-Continued

C. SYNTHETIC UNIT HYDRO-GRAPH-Continued

Section Pa&?

G-1 0. Trial reconstruction ofpast floods . . . . . . . 464

G 11. Synthetic unitgraphs byother methods . . . . . . 464

D. STREAMFLOW ROUTING

G-l 2. General . . . . . . . . . 464G-l 3. Practical methods of

streamflow routingcomputations 465

(a) Tatum’s method . : : : : 465(b) Translation and storage

method . . . . . . . 466(c) Comparison of

methods . . . . . . . 468E. DESIGN STORM STUDIES

G-14. General . . . . . . . . . 468(a) Probably maximum

p r e c i p i t a t i o n ( P M P ) . 4 6 8(b) Probable maximum

storm (PMS) . . . . . 468(c) Design storm 469(d) Additional references ’ : : 469

G 15. Probable maximum stormconsiderations . . . . . . 470

G- 16. Procedure for stormmaximization, plains-type terrain . . . . . . . 47 1

(a) Maximization of astorm in place ofoccurrence . . . . . . 471

(b) Maximization oftransposed storm . . . 472

G- 17. Design storm-probablemaximum precipitation(PMP) or probablemaximum storm (PMS)estimates for awatershed . . . . . . 473

(a) Example of a designstorm study . . . . . 473

CONTENTS X I X

Appendix G-Inflow Design Appendix G-Inflow DesignFlood Studies-Continued

E. DESIGN STORM STUDIES-Continued

Section Page

(b) Generalized precipita-tion charts . . . . . . 477

F. PRELIMINARY INFLOW DESIGNFLOOD, RAINFALL ONLY

G-1 8. General . . . . . . . . . 480G- 19. Example-preliminary

inflow design floodhydrographs, watershedseast of 105O meridian . . . 481

(a) Basin description . . . . 481(b) Dimensionless-graph

selection . . . . . . 486(c) Lag-times . . . . . . . 486(d) Preliminary design

storm values . . . . . 488(e) Arrangement of design

storm rainfall incre-ments and computationof increments ofrainfall excess

(f) Computation of prelk . .488

inary inflow designflood hydrographs . . . 492

G-20. Preliminary inflow designflood estimates,watersheds west of105O meridian

(a) Preliminary design . ’ . ’496

storm values, water-sheds west of 105Omeridian . . . . . . 498

(b) Arrangement of designstorm increments ofrainfall

(c) Assignment of-runoff ’ ’. 499

curve number, CN,and computationof increments ofexcess rainfall

(d) Floods from design * . . ’499

thunderstorm rainfall . . 499

Flood Studies-ContinuedF. PRELIMINARY INFLOW DESIGNFLOOD, RAINFALL ONLY-Continued

Section Page

G-2 1. Recommendations forrouting preliminaryinflow design floodsthrough a proposedreservoir . . . . . . . . 499

G. SNOWMELT RUNOFF CONTRIBUTIONSTO INFLOW DESIGN FLOODS

G-22. General . . . . , . .G-23. Major snowmelt runoff

during seasonal meltperiod for combinationwith probable maximumstorm runoff . . . .

(a) Damsites for reservoirswith no flood controlcapacity proposed .

(b) Damsites for reservoirswith proposed jointuse flood controlcapacity . . . .

G-24. Probable maximum snow-melt floods to becombined with majorrain floods . . . . .

(a) General . . . . .(b) Considerations for

estimates of probablemaximum snowmeltfloods . . . . .

(c) Springtime seasonal

. 499

. 500

. 500

. 502

. 502. 502

. . 502

probable maximum snow-melt flood estimates . . 503

(d) Major rain-flood esti-mates for combinationwith probable maximumsnowmelt runoff . . . 504

G-25. Probable maximumrain-on-snow IDFestimates . . . . . . . . 504

G-26. Special situations . . . . . 505

xx

Appendix G-Inflow DesignFlood Studies-ContinuedG. SNOWMELT RUNOFF CONTRIBUTIONSTO INFLOW DESIGN FLOODS-Continued

Section Page

(a) Frozen ground . . . . . 505(b) Snowmelt in the Great

Plains region ofthe United States . . . 505

H. ENVELOPE CURVES

G-27. General . . . . . . . . . 505

I. STATISTICAL ANALYSES-ESTIMATESOF FREQUENCY OF OCCURRENCE

OF FLOODS

G-28. General . . . . . . . . . 506G-29. Hydrographs for esti-

mating diversionrequirements duringconstruction . . . . . . . 506

J. FINAL-TYPE INFLOW DESIGNFLOOD STUDIES

G-30. General . . . . . . . . . 507G-31. Flood routing criteria . . . . 507

(a) Preceding storms . . . . 507(b) Seasonal flood

hydrograph 507(c) Operational criteria ’ 1 1 1 507

K. BIBLIOGRAPHY

G-32. Bibliography . . . . . . . 508

Appendix H-SampleSpecifications for Concrete

H- 1. Introduction . . . . . . . 5 11H-2. Contractor’s plants,

equipment, and con-struction procedures . . . . 511

H-3. Composition . . . . . . . 5 12(a) General . . . . . . . 512

CONTENTS

Appendix H-SampleSpecifications for Concrete-

ContinuedSection

H-4.

H-5.

H-6.

H-7.H-8.

H-9.

H-10.

H-l 1.

H-12.

(b) Maximum size ofaggregate . . . .

(c) Mix proportions . .(d) Consistency . . . .(e) Tests . . . . . .Cement . . . . . . .(a) General . . . . .(b) Inspection . . . .(c) Measurement and pay-

ment . . . . . .Pozzolan . . . . . .(a) General . . . . .(b) Inspection . . . .(c) Measurement and pay-

ment . . . . . .Admixtures(a) Accelerator. : : : :(b) Air-entraining agents .(c) Water-reducing, set-

controlling admixture(d) Furnishing admixturesWater . . . . . . .Sand . . . . . . . .(a) General . . . . .(b) Quality . . . . .(c) Grading . . . . .Coarse Aggregate . . .(a) General . . . . .(b) Quality . . . . .(c) Separation . . . .Production of sand and

coarse aggregate . . .(a) Source of aggregate .(b) Developing aggregate

deposit . . . . .(c) Processing raw

materials . . . .(d) Furnishing aggregatesBatching . . . . . .(a) General . . . . .(b) Equipment . . . .Mixing . . . . . . .(a) General . . . . .

Page

. . 513

. . 513

. . 514

. . 514

. . 514

. . 514

. . 515

. . 515

. . 516

. . 516

. . 516

. . 517

. . 517

. . 517

. . 517

. . 518. . 518. . 519. . 519. . 519. . 519. . 519. . 519. . 519. . 519. . 520

. . 520

. . 520

. . 521

. . 521

. . 521

. . 522

. . 522

. . 522

. . 524

. . 524(b) Central mixers . . . . . 524

CONTENTS

Appendix H-SampleSpecifications for Concrete-

ContinuedSection Page

(c) Truck mixers . . . . . 524H-13. Temperature of concrete . . . 525H-14. Forms . . . . . . . . . 525

(a) General . . . . . . . 525(b) Form sheathing and

lining . . . . . . . 526(c) Form ties . . . . . . . 527(d) Cleaning and oiling of

forms . . . . . . . 527(e) Removal of forms . . . . 527

H- 15. Tolerances for concreteconstruction . . . . . . . 527

(a) General(b) Tolerances for’dam . ’ . ’

527

structures . . . . . . 528(c) Tolerances for tunnel

lining(d) Tolerances for placing . ’ ’

529

reinforcing bars andfabric . . . . . . . 529

H- 16. Reinforcing bars andfabric . . . . . . . . . 529

(a) Furnishing . . . . . . 529(b) Placing . . . . . . . 529(c) Reinforcement drawings

to be prepared bythe contractor . . . . 530

(d) Measurement and pay-ment . . . . . . . . 530

H-l 7. Preparations for placing . . . 53 1(a) General . . . . . . . 531(b) Foundation surfaces . . . 531(c) Surfaces of construction

and contraction joints . . 531H-18. Placing . . . . . . . . . 532

(a) Transporting . . . . . 532(b) Placing . . . . . . . 532(c) Consolidation . . . . . 534

H-19. Repair of concrete . . . . . 534H-20. Finishes and finishing . . . . 535

(a) General . . . . . . . 535(b) Formed surfaces . . . . 535(c) Unformed surfaces . . . 536

H-21. Protection . . . . . . . . 536

xxiAppendix H-Sample

Specifications for Concrete-Continued

Section

(a) Mass concrete _ . .(b) Concrete other than

mass concrete . .(c) Use of unventcd heaters

H-22. Curing . . . . . . .(a) General(b) Water curing . : : :(c) Wax base curing

compound . . . .(d) Costs . . . . . .

H-23. Measurement of concreteH-24. Payment for concrete . .H-25. Bibliography . . . . .

Page

. . 536

. . 537. 537

. . 537

. . 537

. . 537

. . 538

. . 538

. . 538

. . 539

. . 539

Appendix I-SampleSpecifications for

Water and AirI-l. Scope . . . .

ControllingPollution. . . . . 541

A. PREVENTION OF WATERPOLLUTION

I-2.I-3.I-4.

I-5.

General . . . . . . . . . 54 1Control of turbidity . . . . 542Turbidity control methods . . 542(a) General . _ . . . . . 542(b) Requirements for

turbidity controlduring constructionat the damsite . . . . 542

(c) Bureau’s methods ofturbidity controlat the damsite

(d) Sampling and testing * ’ ’543

of water quality . . . . 543Payment . . . . . . . . 543

B. ABATEMENT OF AIR POLLUTION

I-6. General . . . . . . . . . 544I-7. Dust abatement . . . . . . 544INDEX . . . . . . . . . . . . . 545

XXIJ CONTENTS

TABLESTable Page

7-l. Thermal properties of concrete for various dams . . . . . . . . . . . . 1107-2. Computation of temperature stress . . . . . . . . . . . . . . . . 12 17-3. Values of D, D2, and 1t2f for pipe cooling . . . . . . . . . . . . . . 1247-4. Temperature treatment versus block length . . . . . . . . . . . . . 1279-l. Flood routing computations . . . . . . . . . . . . . . . . . . . 154

9-2.Hs

Coordinates of lower nappe surface for different values of x

when;=2 . . . . . . . . . . . . . . . . . . . . . . .

Coordinates of lower nappe surface for different values of %

when$=0.30 . . . . . . . . . . . . . . . . . . . . . .

Coordinates of lower nappe surface for different values of+

when$=0.15 . . . . . . . . . . . . . . . . . . . . . .

9-3.

9-4.

208

209

210

10-l. Coefficients of discharge and loss coefficients for conduitentrances . . . . . . . . . . . . . . . . . . . . . . . . 231

TABLES IN APPENDICESTable

A-l.

D-l.E-l.E-2.

F-l.F-2.

F-3.F-4.

F-S.G-1.G-2.G-3.G-4.G-5.G-6.G-7.G-8.G 9 .G-10.

Friant Dam, nonoverflow and spillway sections (revised design-maximumstresses, sliding factors, and minimum shear-friction factors . . . . . . . 3 19

Maximum nonlinear stress effects in sections of various dams . . . . . . . 373Comparison of stresses and stability factors for 12 dams . . . . . . . . . 411Maximum effects of twist action in some gravity dams with principal

dimensions of twisted structure . . . . . . . . . . . . . . . . . 4 13Conversion factors and formulas . . . . . . . . . . . . . . . . . 4 18Velocity head and discharge at critical depths and static pressures in

circular conduits partly fullUniform flow in circular sections flowing partly’full . : 1

. . . . . . . . 427

. . . . . . . . 428Velocity head and discharge at critical depths and static pressures in

horseshoe conduits partly full . . . . . . . . . . . . . . . . . . 429Uniform flow in horseshoe sections flowing partly full . . . . . . . . . 430Computation of rainfall increments . . . . . . . . . . . . . . . . 444Computation of rainfall excess . . . . . . . . . . . . . . . . . . 445Hydrologic soil-cover complexes and respective curve numbers (CN) . . . . . 449Curve numbers, constants, and seasonal rainfall limits . . . . . . . . . . 452Hydrograph analysis computations . . . . . . . . . . . . . . . . 460Coefficients for floodrouting by Tatum’s method . . . . . . . . . . . 466Illustrative example of streamflow routing by Tatum’s method . . . . . . 467Translation and storage method of streamflow routing . . . . . . . . . 469Example of design storm derivation for area east of 105’ meridian . . . . . 478Design storm depth-duration values, inches . . . . . . . . . . . . . . 480

CONTENTS XXIII

Table

G-1 1.

G-12.

G-13.

G-14.G-15.

G-16.

G-17.

G-18.

G-19.

Figure

2-1.2-2.2-3.2-4.2-5.3-l.3-2.

3-3.4-l.

Reservoir capacity allocation sheet used by Bureau of Reclamation . . .A typical geologic map of a gravity damsite . . . . . . . . . . .A typical geologic profile of a damsiteTypical construction schedule using Critical Path Method (CPM)’ 1 1 1 :Typical construction schedule using a bar diagram . . . . . . . . .Shear resistance on an existing joint in rock . . . . . . . . . . .Comparison of assumed and uplift pressures on a gravity dam (Shasta

Dam in California) . . . . . . . . . . . . . . . . . . . .Foundation base pressures for a gravity dam . . . . . . . . . . .Cross section of a parallel-side cantilever showing usual loading

combination . . . . . . . . . . . . . . . . . . . . . .Derivation of stress formulae for a concrete gravity dam . . . . . . .Stresses in straight gravity dams . . . . . . . . . . . . . . . .Schematic view simulating partial construction of a gravity dam in

vertical blocks . . . . . . . . . . . . . . . . . . . . .Cantilever and twisted-structure systems-joints ungrouted . . . . . .Direction of positive movements, forces, moments, and loads; and

direction of forces, moments, and movements due to positive loads . .Foundation deformation-values of kr in equation (1) . . . . . . .Foundation deformation-values of k3 in equation (3) . . . . . . .Foundation deformation-values of k4 in equation (4) . . . . . . .Foundation deformation-values of k5 in equation (2) . . . . . . .Loaded area of a foundation surface . . . . . . . . . . . . . .

Page

8. 14

. 14. 18. 19. 24

. 28

. 33

4-2.4-3.4-4.

. 38

. 41

. 42

4-5.4-6.

. 44

. 46

. 48

. 49

. 50

. 51

. 52

. 534-l 2. Unit normal loads on a cantilever . . . . . . . . . . . . . . . . 55

4-7.4 8 .4-9.4-10.4-l 1.

Constants for extending 6-hour general-type design-storm values west of105’ meridian to longer duration periods . . . . . . . . . .

Preliminary design storm estimate for hypothetical watershed, east of105’ meridian . . . . . . . . . . . . . . . . . . .

Preliminary design storm east of 105o meridian-arrangement ofincremental rainfall; computation of incremental excesses,AP,,forsubareasAandB . . . . . . . . . . . . . . . .

Minimum retention rates for hydrologic soil groups . . . . . . . .Simulated automatic data processing printout-preliminary inflow design

flood (IDF) contribution, subarea A . . . . . . . . . . . .Simulated automatic data processing printout-preliminary inflow design

flood (IDF) contribution, subarea B . . . . . . . . . . .Preliminary inflow design flood hydrograph, east of 105o meridian-same

lag-time curve for both subareas . . . . . . . . . , . . . .Preliminary inflow design flood, east of 105’ meridian-computation of

incremental excesses, AP,, considering basin as a whole, and usingan area1 weighted CN and minimum loss rate . . . . . . . . .

Preliminary inflow design flood hydrograph east of 105’ meridian-different lag-time curve for each subarea . . . . . . . . . . .

FIGURES

Page

. . . 485

. . . 488

. . . 490

. . . 491

. . . 493

. . . 493

. # . 494

. . . 496

. . . 498

XXIV CONTENTS

Figure

4-13.4-14.

4-l 5.4-16.4-17.4-18.

4-19.4-20.4-21.4-22.

4-23.4-24.4-25.5-l.

5-2.

5-3.

5-4.5-5.

5-6.

5-7.5-8.

5-9.

6-l.

6-2.7-1.

7-2.7-3.7-4.7-5.7-6.7-7.7-8.7-9.7-10.7-l 1.7-12.7-13.

Page

Unit twist loads on a cantilever . . . . . . . . . . . . . . . . . . 56Graph for determining J factor due to twist of a shaft of

rectangular cross section . . . . . . . . . . . . . . . . . . . 58Loads on a horizontal element . . . . . . . . . . . . . . . . . . 59Trial-load twist analysis for a straight gravity dam-joints grouted . . . . . . 62Twisted-structure loads . . . . . . . . . . . . . . . . . . . . . 63Hydrodynamic pressures upon the sloping face of a dam due to horizontal

earthquake effect . . . . . . . . . . . . . . . . . . . . . . 7 1A finite element with nodal point numbers and coordinate axes . . . . . . 75Sketch illustrating the two-dimensional stability problem . . . . . . . . 77Four-sided failure wedge for three-dimensional stability analysis . . . . . . 78Section through a sliding mass normal to the intersection line of two

planes . . . . . . . . . . . . . . . . . . . . . . . . . . 78Partition method of determining shear resistance of a block . . . . . . . . 79Partition method extended to multifaced blocks . . . . . . . . . . . . 80Stress distribution near a low-modulus zone . . . . . . . . . . . . . 80View from right abutment of partially completed Monticello Dam in

California, showing water flowing over low blocks . . . . . . . . . . 84Diversion of the river during construction of Folsom Dam and Powerplant

in California . . . . . . . . . . . . . . . . . . . . . . . . 86Diversion tunnel for Flaming Gorge Dam, a large concrete dam in

Utah-plan, profile, and sections . . . . . . . . . . . . . . . . . 87Typical arrangement of diversion tunnel with spillway tunnel . . . . . . . 89Diversion tunnel closure structure for a large concrete dam (Flaming

Gorge Dam in Utah) . . . . . . . . . . . . . . . . . . . . . 90Diversion conduit through Morrow Point Dam, a thin arch structure in

Colorado-plan and sections . . . . . . . . . . . . . . . . . . 9 1Completed diversion flume at Canyon Ferry damsite in Montana . . . . . . 92Completed diversion flume at Canyon Ferry damsite in use for

first-stage diversion . . . . . . . . . . . . . . . . . . . . . 93Flows passing through diversion opening and over low blocks of a

concrete and earth dam (Olympus Dam in Colorado) . . . . . . . . . 94Excavation layout for Pueblo Dam and spillway in Colorado-a concrete

buttress-type structure . . . . . . . . . . . . . . . . . . . . 98Foundation treatment for Grand Coulee Forebay Dam in Washington . . . . 102Temperature variations of flat slabs exposed to sinusoidal temperature

variations on both faces . . . . . . . . . . . . . . . . . . . . 117Computation form, sheet 1 of 2-range of mean concrete temperatures . . . . 118Computation form, sheet 2 of 2-range of mean concrete temperatures . . . . 119Temperature variations with depth in semi-infinite solid . . . . . . . . . 120Temperature rise in mass concrete for various types of cement . . . . . . . 120Pipe cooling of concrete-values of X . . . . . . . . . . . . . . . . 122Pipe cooling of concrete-values of Y . . . . . . . . . . . . . . . . 123Artificial cooling of concrete-effect of cooling water temperature . . . . . 124Artificial cooling of concrete-effect of coil length . . . . . . . . . . . 124Artificial cooling of concrete-effect of horizontal spacing of pipe . . . . . 124Glen Canyon Dam-cooling pipe layout . . . . . . . . . . . . . . . 128Glen Canyon Dam-concrete cooling details . . . . . . . . . . . . . 129Temperature history of artificially cooled concrete . . . . . . . . . . . 132

CONTENTS x x v

Figure

8-1.

8-2.

8-3.

8-4.8-5.9-l.

9-2.9-3.9-4.9-5.9-6.9-7.

9-8.

9-9.9-10.9-l 1.9-12.9-13.

9-14.

9-15.9-16.9-17.9-18.9-19.9-20.9-21.9-22.9-23.9-24.9-25.9-26.

9-27.9-28.9-29.9-3 0.9-3 1.9-32.9-33.9-34.

Page

Typical keyed transverse contraction joint for a concrete gravity dam(Friant Dam in California) . . . . . . . . . . . . . . . . . . . 139

Typical unkeyed transverse contraction joint (Grand Coulee Forebay Damin Washington) . . . . . . . . . . . . . . . . . . . . . . . 140

Typical longitudinal contraction joint for a concrete gravity dam(Grand Coulee Dam in Washington) . . . . . . . . . . . . . . . 142

Metal seals and connections at contraction joints . . . . . . . . . . . 144Grouting system details . . . . . . . . . . . . . . . . . . . . . 147Drumgate-controlled ogee-type overflow spillway in operation at Grand

Coulee Dam in Washington . . . . . . . . . . . . . . . . . . . 150Typical inflow and outflow hydrographs . . . . . . . . . . . . . . 152Typical reservoir capacity curve . . . . . . . . . . . . . . . . . . 153Typical spillway discharge curve . . . . . . . . . . . . . . . . . 153Spillway capacity-surcharge relationship . . . . . . . . . . . . . . 155Comparative cost of spillway-dam combinations . . . . . . . . . . . . 155Circular crest for morning glory spillway at Hungry Horse Dam in

Montana . . . . . . . . . . . . . . . . . . . . . . . . . 157Drumgate-controlled side channel spillway in operation at Hoover Dam on

the Colorado River . . . . . . . . . . . . . . . . . . . . . 160Chute type spillway (left) at Elephant Butte Dam in New Mexico . . . . . . 162A simple ogee crest shape with a vertical upstream face . . . . . . . . . 165Factors for definition of nappe-shaped crest profiles . . . . . . . . . . 166Ogee crest shape defined by compound curves . . . . . . . . . . . . 168Coefficient of discharge for ogee-shaped crest with vertical upstream

face . . . . . . . . . . . . . . . . . . . . . . . . . . . 170Coefficient of discharge for ogee-shaped crest with sloping upstream

face . . . . . . . . . . . . . . . . . . . . . . . . . . . 170Effects of downstream influences on flow over weir crests . . . . . . . . 171Ratio of discharge coefficients due to apron effect . . . . . . . . . . . 172Ratio of discharge coefficients due to tailwater effect . . . . . . . . . . 172Coefficient of discharge for other than the design head . . . . . . . . . 173Subatmospheric crest pressures for a 0.75 ratio ofH, to He . . . . . . . . 175Subatmospheric crest pressures for undershot gate flow . . . . . . . . . 175Coefficient of discharge for flow under a gate (orifice flow) . . . . . . . . 176Typical orifice control structures . . . . . . . . . . . . . . . . . 177Comparison of side channel cross sections . . . . . . . . . . . . . . 178Side charmel flow characteristics . . . . . . . . . . . . . . . . . 179Sketch illustrating flow in open channels . . . . . . . . . . . . . . 18 1Approximate losses in chutes for various values of water surface drop

and channel length . . . . . . . . . . . . . . . . . . . . . 182Flare angle for divergent or convergent channels . . . . . . . . . . . . 184Profile of typical tunnel spillway channel . . . . . . . . . . . . . . 185Overflow gate-controlled spillway on Canyon Ferry Dam in Montana . . . . 187Characteristic forms of hydraulic jump related to the Froude number . . . . 188Relations between variables in hydraulic jumps for rectangular channels . . . 189Type I stilling basin characteristics . . . . . . . . . . . . . . . . . 190Stilling basin characteristics for Froude numbers between 2.5 and 4.5 . . . . 191Stilling basin characteristics for Froude numbers above 4.5 where

incoming velocity does not exceed 50 feet per second . . . . . . . . . 193

XXVI CONTENTS

Figure

9-35.9-36.9-37.9-38.

Page

9-39.9-40.9-41.9-42.9-43.9-44.9-45.

9-46.

9-47.

9-48.

9-49.

9-50.9-51.

9-52.10-l.1 o-2.10-3.1 o-4.10-5.10-6.10-7.1 O-8.1 o-9.

Stilling basin characteristics for Froude numbers above 4.5 . . . . . . . . 194Stilling basin depths versus hydraulic heads for various channel losses . . . . 196Relationships of conjugate depth curves to tailwater rating curves . . . . . 197Deflector bucket in operation for the spillway at Hungry Horse Dam in

Montana . . . . . . . . . . . . . . . . . . . . . . . . . 200Submerged bucket energy dissipators . . . . . . . . . . . . . . . . 200Hydraulic action in solid and slotted buckets . . . . . . . . . . . . . 200Flow characteristics in a slotted bucket . . . . . . . . . . . . . . . 201Limiting criteria for slotted bucket design . . . . . . . . . . . . . . 202Definition of symbols-submerged bucket . . . . . . . . . . . . . . 203Flow and discharge characteristics of a morning glory spillway . . . . . . . 204Elements of nappe-shaped profile for a circular crest . . . . . . . . . . 205

Relationship of circular crest coefficient C, to: for differents

approach depths (aerated nappe) . . . . . . . . . . . . . . . . 206Circular crest coefficient of discharge for other than design head . . . . . . 207

HRelationship of g to -$ for circular sharp-crested weirs . . . . . . . . 211

Upper and lower nlppe pr:files for a circular weir (aerated nappe andnegligible approach velocity) . . . . . . . . . . . . . . . . . . 2 12

Comparison of lower nappe shapes for a circular weir for different heads . . . 2 12Increased circular crest radius needed to minimize subatmospheric

pressure along crest . . . . . . . . . . . . . . . . . . . . . 2 12Comparison of crest profile shape with theoretical jet profile . . . . . . . 213Typical river outlet works with stilling basin . . . . . . . . . . . . . 2 17Typical power outlet and canal outlet works . . . . . . . . . . . . . 2 17River outlet trashrack structure-plans and sections . . . . . . . . . . . 222Typical trashrack installations . . . . . . . . . . . . . . . . . . 224Pictorial representation of typical head losses in outlet under pressure . . . . 227Relationship between Darcy’sfand Manning’s y1 for flow in pipes . . . . . 230Coefficient for bend losses in a closed conduit . . . . . . . . . . . . 232A river outlet works with open channel flow . . . . . . . . . . . . . 235Typical penstock installations . . . . . . . . . . . . . . . . . . 237

lo- 10. Embedded penstock in abutment tunnel . . . . . . . . . . . . .IO- 11. Typical concrete trashrack structure for a penstock . . . . . . . . . .IO- 12. Typical fixed-wheel gate installation at upstream face of dam . . . . . .1 l-l. Galleries and shafts in Grand Coulee Forebay Dam-plans, elevations,

section . . . . . . . . . . . . . . . . . . . . . . . . .1 l-2. Galleries and shafts in Grand Coulee Forebay Dam-sections . . . . . .12-1. Architectural layout of elevator tower in Grand Coulee Forebay Dam . . .12-2. Structural layout of elevator shaft and tower in Grand Coulee Forebay

Dam . . . . . . . . . . . . . . . . . . . . . . . . . .12-3. Typical arrangement at top of a gravity dam (Grand Coulee Forebay Dam) .13-1. Locations of instrumentation installed in a gravity dam-plan and

elevation . . . . . . . . . . . . . . . . . . . . . . . .13-2. Locations of instrumentation installed in a gravity dam-maximum

section . . . . . . . . . . . . . . . . . . . . . . . . .

237238241

244246250

252256

261

261

CONTENTS X X V I I

Figure Page

13-3. Typical plumbline well in a concrete dam with reading stations atseveral elevations . . . . . . . . . . . . . . . . . . . . . . 263

13-4. A cluster of strain meters supported on a “spider” and ready forembedment in concrete . . . . . . . . . . . . . . . . . . . . 264

13-5. A stress meter partially embedded in concrete . . . . . . . . . . . . 26413-6. A joint meter in position at a contraction joint . . . . . . . . . . . . 26513-7. An instrument terminal board and cover box . . . . . . . . . . . . . 26513-8. A special portable wheatstone bridge test set for reading strain meters . . . . 26513-9. “No-stress” strain meter installation . . . . . . . . . . . . . . . . 26613-10. Meter group comprising strain meters and stress meters . . . . . . . . . 26713- 11. Trios of mutually perpendicular strain meters installed near face of dam . . . 26813-l 2. Penstock and reinforcement strain meters . . . . . . . . . . . . . . 26813-13. Pore pressure meter installed on a penstock . . . . . . . . . . . . . 26813- 14. Pore pressure meters installed in mass concrete . . . . . . . . . . . . 26813-15. Resistance thermometer installed at upstream face of a dam . . . . . . . 26813- 16. Deformation meter installed in cased well under dam to measure

deformation of foundation rock . . . . . . . . . . . . . . . . . 26913-17. Micrometer-type reading head for use with foundation deformation gage . . . 26913- 18. Micrometer reading head and invar tape used with horizontal tape gage in

abutment tunnel . . . . . . . . . . . . . . . . . . . . . . 27013-19. Creep tests in progress on 18- by 36-inch mass concrete cylinders . . . . . . 27013-20. Components of equipment for weighted plumbline installation . . . . . . 27113-21. Tank and float for use with float-suspended plumbline . . . . . . . . . 27113-22. Anchorage for float-suspended plumbline . . . . . . . . . . . . . . 27213-23. Typical plumbline reading station and reading devices . . . . . . . . . . 27213-24. Foundation deformation well, optical plummet, and reference grid . . . . . 27213-25. An instrument pier for use with collimation or triangulation systems . . . . 27313-26. A reference sighting target for use in obtaining collimation

measurements . . . . . . . . . . . . . . . . . . . . . . . 27313-27. A movable collimation target at a measuring station on top of a dam . . . . 27413-28. A collimation system layout for a gravity dam . . . . . . . . . . . . 27413-29. A triangulation system layout for a gravity dam . . . . . . . . . . . . 27413-30. A tensioning device used with a tape for precise baseline measurements . . . 27513-3 1. A pier plate, pier targets, and dam deformation targets . . . . . . . . . 27513-32. An uplift pressure measurement system for a gravity dam . . . . . . . . 27613-33. A pore pressure meter installation for determining uplift pressure . . . . . . 27713-34. Details of pore pressure meter installation illustrated on figure 13-33 . . . . 27815-1. Selective withdrawal outlet at Pueblo Dam in Colorado . . . . . . . . . 28915-2. Selective withdrawal outlet at Folsom Dam in California . . . . . . . . . 29015-3. Fish ladder used on the left abutment of Red Bluff Diversion Dam in

California . . . . . . . . . . . . . . . . . . . . . . . . . 29015-4. An aerial view of a small reservoir with trees left at the water’s edge

to provide a fish habitat . . . . . . . . . . . . . . . . . . . . 29115-5. Fish hatchery at Nimbus Dam in California . . . . . . . . . . . . . 29215-6. An artist’s conception of the gravel cleaner to be used at a salmon

spawning area on the Tehama-Colusa Canal in California . . . . . . . . 29215-7. Boat docking facilities at Canyon Ferry Reservoir in Montana . . . . . . . 29415-8. Viewing area at Glen Canyon Dam in Arizona . . . . . . . . . . . . . 29515-9. Chipping operations at Pueblo Dam in Colorado . . . . . . . . . . . . 297

X X V I I I CONTENTS

FIGURES IN APPENDICESFigure

A-l.A-2.

A-3.A-4.A-5.A-4.A-7.A-8.A-9.A-10.A-l 1.

A-12.

A-13.

A-14.

A-15.

A-16.

A-17.

A-18.

B-l.B-2.B-3.

B-4.

B-5.

B-6.B-7.

B-8.B-9.B-10.B-l 1.B-12.B-13.B-14.

Friant Dam-plan and sections . . . . . . . . . . . . . . . . . .Curves for coefficient KE for computing change in pressure due to

earthquake shock . . . . . . . . . . . . . . . . . . . . . .Friant Dam study-values and powers of y . . . . . . . . . . . . . .Friant Dam study-normal stresses on horizontal planes . . . . . . . . .Friant Dam study-shear stresses on horizontal and vertical planes . . . . .Friant Dam study-partial derivatives for obtaining uy . . . . . . . . . .Friant Dam study-intermediate computations for obtaining stresses . . . .Friant Dam study-normal stresses on vertical planes . . . . . . . . . .Friant Dam study-principal stresses . . . . . . . . . . . . . . . .Friant Dam study-gravity analyses for normal conditions . . . . . . . .Friant Dam Study-gravity analyses with horizontal earthquake

acceleration . . . . . . . . . . . . . . . . . . . . . . . .Friant Dam study-gravity analyses with vertical earthquake

acceleration . . . . . . . . . . . . . . . . . . . . . . . .Friant Dam study-gravity analyses with horizontal and vertical

earthquake effects, vertical acceleration upward . . . . . . . . . . .Friant Dam study-gravity analyses with horizontal and vertical

earthquake effects, vertical acceleration downward . . . . . . . . . .Friant Dam study-principal stresses on the maximum nonoverflow section,

normal conditions . . . . . . . . . . . . . . . . . . . . . .Friant Dam study-principal stresses on the maximum nonoverflow section,

horizontal and vertical earthquake accelerations included . . . . . . . .Friant Dam study-principal stresses on the spillway section for normal

conditions . . . . . . . . . . . . . . . . . . . . . . . .Friant Dam study-principal stresses on the spillway section, horizontal

and vertical earthquake accelerations included . . . . . . . . . . . .Canyon Ferry Dam study-plan, elevation, and maximum sections . . . . .Canyon Ferry Dam study-deflection of a beam due to unit normal loads . .Canyon Ferry Dam study-deflection of a horizontal element due to unit

shear loads . . . . . . . . . . . . . . . . . . . . . . . .Canyon Ferry Dam study-deflection of a cantilever due to unit shear

loads . . . . . . . . . . . . . . . . . . . . . . . . . .Canyon Ferry Dam study-deflection of a cantilever due to unit normal

loads . . . . . . . . . . . . . . . . . . . . . . . . . .Canyon Ferry Dam study-shears in twisted structure due to unit loads . . .Canyon Ferry Dam study-rotations of vertical twisted-structure elements

due to unit couple loads . . . . . . . . . . . . . . . . . . . .Canyon Ferry Dam study-deflection of cantilevers due to initial loads . . . .Canyon Ferry Dam Study-load ordinates at cantilever points . . . . . . .Canyon Ferry Dam study-trial-load distribution (trial No. 1) . . . . . . .Canyon Ferry Dam study-trial-load distribution (final) . . . . . . . . .Canyon Ferry Dam study--cantilever deflection components (final) . . . . .Canyon Ferry Dam study-total deflections (final) . . . . . . . . . . .Canyon Ferry Dam study-shears in horizontal elements and rotations of

vertical elements due to twisted-structure load (final) . . . . . . . . .

Page

300

301303304305306307308309310

311

312

313

314

315

316

317

318322324

325

326

327328

329330331332333334336

337

CONTENTS X X I X

Figure

B-15.

B-16.

B-17.

B-18.

B-19.B-20.

B-21.

B-22.

B-23.B-24.

B-25.

C-l.

c-2.c-3.

c-4.

c-5.C-6.c-7.C-8.c-9.

c-10.

c-11.

C-l 2.

c-13.

c-14.

c-15.C-16.

Page

Canyon Ferry Dam study-twisted-structure deflection due to rotations ofvertical element, and twisted-structure deflection due to beam loads(final) . . . . . . . . . . . . . . . . . . . . . . . . . . 338

Canyon Ferry Dam study-beam deflection due to beam loads and abutmentrotations, and deflection of horizontal elements due to twisted-structure loads (final) . . . . . . . . . . . . . . . . . . . . 339

Canyon Ferry Dam study-total beam and twisted-structure deflections(final) . . . .

Canyon Ferry Dam study-bending moments in’beam due to trial loads ’ . ’ ’341

(final), and total shear in horizontal elements due to trial loads(final) . . . . . . . . . . . . . . . . . . . . . . . . . 342

Force normal to an inclined abutment plane . . . . . . . . . . . . . 343Canyon Ferry Dam study-load distribution and adjustment on horizontal

elements . . . . . . . . . . . . . . . . . . . . . . . . . 344Canyon Ferry Dam study-load distribution and adjustment on cantilever

elements . . . . . . . . . . . . . . . . . . . . . . . . . 345Canyon Ferry Dam study-stresses in horizontal beam elements and in

cantilever elements . . . . . . . . . . . . . . . . . . . . . 346Canyon Ferry Dam study-principal stresses at upstream face of dam . . . . 347Canyon Ferry Dam study-principal stresses at downstream face of

dam . . . . . . . . . . . . . . . . . . . . . . . . . . . 348Canyon Ferry Dam study-sliding factors and shear-friction factors of

safety for trial-load and gravity analyses . . . . . . . . . . . . . . 349Grid layout for section DG of Grand Coulee Forebay Dam, including

excavated cut slope along canyon wall at right . . . . . . . . . . . . 352Two-dimensional input data-control data and material properties . . . . . 353Two-dimensional input data-loading and description of section by nodal

points . . . . . . . . . . . . . . . . . . . . . . . . . . 354Two-dimensional input data-elements defined by nodal points with

material . . . . . . . . . . . . . . . . . . . . . . . . . 355Nodal point displacements (no treatment) . . . . . . . . . . . . . . 356Nodal point displacements (25-foot treatment) . . . . . . . . . . . . 357Stresses in elements (no treatment) . . . . . . . . . . . . . . . 359Stresses in elements (25-foot treatment) . . . . . . . . . . . . . . . 360Grand Coulee Forebay Dam foundation study-microfilm printout showing

principal stresses (no treatment) . . . . . . . . . . . . . . . . . 36 1Grand Coulee Forebay Dam study-microfilm printout showing principal

stresses (25-foot treatment) . . . . . . . . . . . . . . .Grand Coulee Forebay Dam study-microfilm printout showing vertical

361

stresses (25-foot treatment) . . . . . . . . . . . . . . . . . . 362Grand Coulee Forebay Dam study-microfilm printout showing horizontal

stresses (25-foot treatment) . . . . . . . . . . . . . . . . . . 362Grand Coulee Forebay Dam study-microfilm printout showing shear stresses

(25-foot treatment) . . . . . . . . . . . . . . . . . . . . . 363Grand Coulee Forebay Dam study-three-dimensional finite element

grid . . . . . . . . . . . . . . . . . . . . . . . . . . . 364Three-dimensional input data-control data and material properties . . . . . 365Three-dimensional input data-description of section by nodal points . . . . 366

xxx CONTENTS

Figure

c-17.

C-18.c-19.D-l.D-2.

D-3.E-l.

E-2.

E-3.E-4.E-5.

E-6.E-7.E-8.

E-9.E-10.E-l 1.

E-12.

E-13.

E-14.

E-15.E-16.

E-17.E-18.E-19.E-20.

E-21.

E-22.E-23.

E-24.E-25.E-26.

E-27.

Page

Three-dimensional input data-elements defined by nodal points withmaterial . . . . . . . . . . . . . . . . . . . . . . . . . 367

Three-dimensional input data-load vectors . . . . . . . . . . . . . 368Grand Coulee Forebay Dam study-stresses at nodal points . . . . . . . . 369Lattice analogy-equations for displacement of joint 0 . . . . . . . . . 375Photoelastic study of foundation fault seam near downstream face of

Shasta Dam-reservoir full . . . . . . . . . . . . . . . . . . . 379Relation of stress at toe of dam to depth and location of fault zone . . . . . 380American Falls Dam gravity analyses of nonoverflow and spillway sections

including effects of earthquake accelerations . . . . . . . . . . . . 382American Falls Dam-gravity analyses of nonoverflow and spillway

sections, normal conditions with ice load . . . . . . . . . . . . . . 383Altus Dam-gravity analyses of maximum abutment and nonoverflow sections . 384Altus Dam-gravity analyses of spillway sections . . . . . . . . . . . . 385Keswick Powerplant Dam-gravity analyses of penstock section including

effects of earthquake accelerations . . . . . . . . . . . . . . . . 386East Park Dam-plan, elevation, and maximum section . . . . . . . . . 387East Park Dam-gravity analyses of maximum nonoverflow section . . . . . 388East Park Dam-stresses, load distribution, and radial deflections from

trial-load analysis . . . . . . . . . . . . . . . . . . . . . . 389Angostura Dam-plan, profile, and maximum section . . . . . . . . . . 390Angostura Dam-stresses from trial-load beam and cantilever analysis . . . . 391Angostura Dam-stability factors from trial-load beam and cantilever

analysis . . . . . . . . . . . . . . . . . . . . . . . . . 392Black Canyon Diversion Dam-stresses for normal conditions from gravity

analyses . . . . . . . . . . . . . . . . . . . . . . . . . 393Black Canyon Diversion Dam-gravity analyses including effects of

earthquake, vertical acceleration upward . . . . . . . . . . . . . . 394Black Canyon Diversion Dam-gravity analyses including effects of

earthquake, vertical acceleration downward . . . . . . . . . . . . . 395Kortes Dam-plan, elevation, and maximum section . . . . . . . . . . 396Kortes Dam-stresses and load distribution from trial-load twist

analysis . . . . . . . . . . . . . . . . . . . . . . . . . 397Kortes Dam-stability factors from trial-load twist analysis . . . . . . . . 398Marshall Ford Dam-plan, elevation, and maximum sections . . . . . . . 399Marshall Ford Dam-gravity analyses for normal conditions . . . . . . . . 400Marshall Ford Dam-gravity analyses including effects of earthquake,

vertical acceleration upward . . . . . . . . . . . . . . . . . . 40 1Marshall Ford Dam-gravity analyses including effects of earthquake,

vertical acceleration downward . . . . . . . . . . . . . . . . . 402Elephant Butte Dam-gravity analyses for maximum flood condition . . . . 403Elephant Butte Dam-gravity analyses including effects of earthquake

accelerations . . . . . . . . . . . . . . . . . . . . . . . . 404Grand Coulee Dam-plan, elevation, and maximum sections . . . . . . . . 405Grand Coulee Dam-stresses from trial-load twist and beam analysis . . . . . 406Grand Coulee Dam-stability factors from trial-load twist and beam

analysis . . . . . . . . . . . . . . . . . . . . . . . . . 407Shasta Dam-gravity analyses for normal conditions . . . . . . . . . . 408

CONTENTS xxx1

Fi&reE-28.

E-29.

F-l.F-2.

F-3.F-4.F-5.F-6.F-7.F-8.G-1.

G-2.

G-3.G-4.G-5.G-6.G-7.G-8.G-9.G-10.

G-11.

G-12.

G-13.

G-14.

G-15.G-16.c-17.

G-18.

Shasta Dam-gravity analyses including effects of earthquake, verticalacceleration upward . . . . . . . . . . . . . . . . .

Shasta Dam-gravity analyses including effects of earthquake, verticalacceleration downward . . . . . . . . . . . . . . . .

Characteristics of open-channel flow . . . . . . . . . . . .Depth of flow and specific energy for rectangular section in open

channel . . . . . . . . . . . . . . . . . . . . .Energy-depth curves for rectangular and trapezoidal channels . . .Critical depth in trapezoidal section . . . . . . . . . . . .Characteristics of pressure flow in conduits . . . . . . . . .Hydraulic jump symbols and characteristics . . . . . . . . .Hydraulic jump properties in relation to Froude number . . . . .Relation between variables in the hydraulic jump . . . . . . .Analysis of observed rainfall data . . . . . . . . . . . . .

Rainfall-runoff curves-solution of runoff equation, Q = (P - o.2s)2p + 0,8s

(U.S. Soil Conservation Service) . . . . . . . . . . . . . .Unit hydrograph principles . . . . . . . . . . . . . . . .Three common approaches for estimating base flow discharges . . . .Hydrograph analysis . . . . . . . . . . . . . . . . . . .Unitgraph derivation for ungaged area . . . . . . . . . . . .Comparison of results of streamflow routings . . . . . . . . . .Example of summary sheet, “Storm Rainfall in the U.S.” . . . . .Design storm-depth-duration values . . . . . . . . . . . . .Probable maximum precipitation (inches) east of the 105’ meridian for

an area of 10 square miles and 6 hours’ duration . . . . . . . .Depth-area-duration relationships-percentage to be applied to 10 square

miles, 6-hour probable maximum precipitation values . . . . . .Distribution of 6-hour rainfall for area west of 105’ meridian (see

fig. G- 13 for area included in each zone) . . . . . . . . . . .Probable maximum B-hour point precipitation values in inches for

general-type storms west of the 105’ meridian . . . . . . . . .General-type storm-conversion ratio from 6-hour point rainfall to area

rainfall for area west of 10.5’ meridian . . . . . . . . . . .Basin map-example of preliminary inflow design flood computation .Preliminary design storm-depth-duration curve . . . . . . . . .Example of preliminary inflow design flood hydrographs-same lag-time

curve for all unitgraphs . . . . . . . . . . . . . . . . .Example of preliminary inflow design flood hydrograph-different lag-time

curve for each subarea . . . . . . . . . . . . . . . . .

Page

. . . 409

. . . 410

. . . 420

. . . 421

. . . 422

. . . 424

. . . 432

. . . 433

. . . 433

. . . 434

. . . 442

. . 450

. . . 454

. . . 456

. . . 458

. . . 463

. . . 470

. . . 474

. . . 479

. . 481

. . 482

. . 483

. . , 484

. . , 485

. . . 486

. . 489

. . . 495

. . . 497

<<Chapter I

I ntroduct ion

l-l. Scope.-A concrete gravity dam, asdiscussed in this manual, is a solid concretestructure so designed and shaped that itsweight is sufficient to ensure stability againstthe effects of all imposed forces. Other typesof dams exist which also maintain theirstability through the principle of gravity, suchas buttress and hollow gravity dams, but theseare outside the scope of this book. Further,discussions in this manual are limited to damson rock foundations and do not include smallerdams generally less than 50 feet high which arediscussed in the Bureau of Reclamationpublication “Design of Small Dams”] 11 ’ .

The complete design of a concrete gravitydam includes not only the determination of themost efficient and economical proportions forthe water impounding structure, but also thedetermination of the most suitable appurtenantstructures for the control and release of theimpounded water consistent with the purposeor function of the project. This manualpresents the basic assumptions, designconsiderations, methods of analysis, andprocedures used by designers within theEngineering and Research Center, Bureau ofReclamation, for the design of a gravity damand its appurtenances.

1-2. Classifications. -Gravity dams may beclassified by plan as straight gravity dams andcurved gravity dams, depending upon the axisalinement. The principal difference in thesetwo classes is in the method of analysis.Whereas a straight gravity dam would beanalyzed by one of the gravity methodsdiscussed in this manual (ch. IV), a curved

‘Numbers in brackets refer to items in the bibliography, sec.l-5.

gravity dam would be analyzed as an arch damstructure, as discussed in the Bureau’s manual“Design of Arch Dams”[ 21 . For statisticalpurposes, gravity dams are classified withreference to their structural height. Dams up to100 feet high are generally considered as lowdams, dams from 100 to 300 feet high asmedium-height dams, and dams over 300 feethigh as high dams.

l-3. General Dimensions. -For uniformitywithin the Bureau of Reclamation, certaingeneral dimensions have been established andare defined as follows:

The structural height of a concrete gravitydam is defined as the difference in elevationbetween the top of the dam and the lowestpoint in the excavated foundation area,exclusive of such features as narrow faultzones. The top of the dam is the crown of theroadway if a roadway crosses the dam, or thelevel of the walkway if there is no roadway.Although curb and sidewalk may extend higherthan the roadway, the level of the crown of theroadway is considered to be the top of thedam.

The hydraulic height, or height to which thewater rises behind the structure, is thedifference in elevation between the lowestpoint of the original streambed at the axis ofthe dam and the maximum controllable watersurface.

The length of the dam is defined as thedistance measured along the axis of the dam atthe level of the top of the main body of thedam or of the roadway surf:iLs, on the crest,from abutment contact to sbutment contact,exclusive of abutment spillway; provided that,if the spillway lies wholly within the dam and

1

2 DESIGN OF GRAVITY DAMS

would appear if cut by a plane. A beam sectionis taken horizontally through the dam. Acantilever section is a vertical section takennormal to the axis and usually oriented withthe reservoir to the left.

A beum element, or beam, is a portion of agravity dam bounded by two horizontal planes1 foot apart. For purposes of analysis the edgesof the elements are assumed to be vertical.

A cantilever element, or cantilever, is aportion of a gravity dam bounded by twovertical planes normal to the axis and 1 footapart,

A twisted structure consists of verticalelements with the same structural properties asthe cantilevers, and of horizontal elements withthe same properties as the beams. The twistedstructure resists torsion in both the vertical andhorizontal planes.

The height of a cantilever is the verticaldistance between the base elevation of thecantilever section and the top of the dam.

The thickness of a dam at any point is thedistance between upstream and downstreamfaces along a line normal to the axis throughthe point.

The abutment of a beam element is thesurface, at either end of the beam, whichcontacts the rock of the canyon wall.

The crest of a dam is the top of the dam.l-5. Bibliography.

[I] “Design of Small Dams,” second edition, Bureau o fReclamation, 1973.

[2] “ D e s i g n o f A r c h D a m s , ” f i r s t e d i t i o n , B u r e a u o fReclamation, 1976.

not in any area especially excavated for thespillway, the length is measured along the axisextended through the spillway to the abutmentcontacts.

The volume of a concrete dam shouldinclude the main body of the dam and all massconcrete appurtenances not separated from thedam by construction or contraction joints.Where a powerplant is constructed on thedownstream toe of the dam, the limit ofconcrete in the dam should be taken as thedownstream face projected to the generalexcavated foundation surface.

l-4. Gravity Dam Definitions. -Terminologyrelating to the design and analysis of gravitydams and definitions of the parts of gravitydams as used in this manual are as follows:

A plan is an orthographic projection on ahorizontal plane, showing the main features ofa dam and its appurtenant works with respectto the topography and available geologicaldata. A plan should be oriented so that thedirection of streamflow is toward the top ortoward the right of the drawing.

A profile is a developed elevation of theintersection of a dam with the original groundsurface, rock surface, or excavation surfacealong the axis of the dam, the upstream face,the downstream face, or other designatedlocation.

The axis of the dam is a vertical referenceplane usually defined by the upstream edge ofthe top of the dam.

A section is a representation of a dam as it

<<Chapter II

D e s i g n C o n s i d e r a t i o n s

2-1. General. -Although not of immediateconcern to the designer of a dam and itsappurtenances, the early collection of data onlocal conditions which will eventually relate tothe design, specifications, and constructionstages is advisable. Local conditions are notonly needed to estimate construction costs, butmay be of benefit when considering alternativedesigns and methods of construction. Some ofthese local conditions will also be used todetermine the extent of the project designs,including such items as access roads, bridges,and construction camps.

2 - 2 . D a t a t o b e S u b m i t t e d . - L o c a lconditions should be described and submittedas part of the design data as follows:

(1) The approximate distance from thenearest railroad shipping terminal to thestructure site; load restrictions and physical

A. LOCAL CONDITIONS

inadequacies of existing roads and structuresa n d a n estimate o f i m p r o v e m e n t s t oa c c o m m o d a t e construction hauling; anestimate of length and major structures foraccess roads; and possible alternative means fordelivering c o n s t r u c t i o n materials andequipment to the site.

(2) Local freight or trucking facilities andrates.

(3) Availability of housing and otherfacilities in the nearest towns; requirements fora construction camp; and need for permanentbuildings for operating personnel.

(4) Availability or accessibility of publicfacilities or utilities such as water supply,sewage d i s p o s a l , e l e c t r i c p o w e r f o rconstruction purposes, and telephone service.

( 5 ) L o c a l l a b o r p o o l a n d g e n e r a loccupational fields existing in the area.

B. MAPS AND PHOTOGRAPHS

2-3. General.-Maps and photographs are ofprime importance in the planning and design ofa concrete dam and its appurtenant works.From these data an evaluation of alternativel a y o u t s c a n b e m a d e p r e p a r a t o r y t odetermining the final location of the dam, thetype and location of its appurtenant works,a n d t h e n e e d f o r r e s t o r a t i o n a n d / o rdevelopment of the area.

2-4. Survey Control. -Permanent horizontaland vertical survey c o n t r o l s h o u l d b eestablished at the earliest possible time. A grid

coordinate system for horizontal controlshould be established with the origin located sothat all of the features (including borrow areas)at d major structure will be in one quadrant.The coordinate system should be related to aState or National coordinate system, ifpracticable. All previous survey work, includingtopography and location and ground surfaceelevation of subsurface exploration holes,should be corrected to agree wi th thepermanent control system; and all subsequentsurvey work, including location and ground

3

4

surface elevations, should be based on thepermanent control,

2-5. Data to be Submitted. -A general areamap should be obtained locating the generalarea within the State, together with county andtownship lines. This location map should showexisting towns, highways, roads, railroads, andshipping points. A vicinity map should also beobtained using such a scale as to show detailson the following:

(1) The structure site and alternativesites.

(2) Public utilities.(3) Stream gaging stations.(4) Existing manmade works affected

by the proposed development.(5) Locations of potential construction

access roads, sites for a Government campand permanent housing area, and sites forthe contractor’s camp and constructionfacilities.

(6) Sources of natural constructionmaterials.

(7) Existing or potential areas orfeatures having a bearing on the design,construction, operation, or managementof project features such as recreationalareas, fish and wildlife areas, buildingareas, and areas of ecological interest.

The topography of the areas where the damand any of its appurtenant works are to belocated is of prime concern to the designer.

DESIGN OF GRAVITY DAMS

Topography should be submitted covering anarea sufficient to accommodate all possiblearrangements of dam, spillway, outlet works,diversion works, construction access, and otherfacilities; and should be based on thepermanently established horizontal and verticalsurvey control. A scale of 1 inch equals 50 feetand a contour interval of 5 feet will normallybe adequate. The topography should extend am i n i m u m o f 5 00 feet upstream anddownstream from the estimated positions ofthe heel and toe of the dam and a sufficientdistance beyond each end of the dam crest toinclude road approaches. The topographyshould also cover the areas for approach andexit channels for the spillway. The topographyshould extend to an elevation sufficiently highto permit layouts of access roads, spillwaystructures, and visitor facilities.

Ground and aerial photographs are beneficialand can be used in a number of ways. Theirprincipal value is to present the latest datarelating to the site in such detail as to showconditions affecting the designs. Close-upground photographs, for example, will oftengive an excellent presentation of local geologyt o s u p p l e m e n t t h a t o b t a i n e d f rom atopographic map. Where modifications are tobe made to a partially completed structure,such photographs will show as-constructeddetails which may not show on any drawings.

C. HYDROLOGIC DATA

2-6. Data to be Submitted.-In order todetermine the potential of a site for storingwater, generating power, or other beneficialuse, a thorough study of hydrologic conditionsmust be made. Necessary hydrologic data willinclude the following:

(1) Streamflow records, including dailyd i s cha rges , mon th ly vo lumes , andmomentary peaks.

(2) Streamflow and reservoir yield.( 3 ) P r o j e c t w a t e r r e q u i r e m e n t s ,

including allowances for irrigation andpower, conveyance losses, reuse of return

flows, and stream releases for fish; anddead storage requirements for power,recreation, fish and wildlife, etc.

(4) Flood studies, including inflowdesign floods and floods to be expectedduring periods of construction.

(5) Sedimentation and water qualitystudies, including sediment measurements,analysis of dissolved solids, etc.

(6) Data on ground-water tables in thevicinity of the reservoir and damsite.

(7) Water rights, including interstatecompacts and international treaty effects,

DESIGN CONSIDERATIONS-Sec. 2-7

and contractual agreements with locald i s t r i c t s , p o w e r c o m p a n i e s , a n dindividuals for subordination of rights,etc.

Past records should be used as a basis forpredicting conditions which will develop in thefuture. Data relating to streamflow may beobtained from the following sources:

( 1 ) W a t e r s u p p l y p a p e r s - U . S .Department of the Interior, GeologicalSurvey, Water Resources Division.

(2) Reports of state engineers.( 3 ) A n n u a l r e p o r t s - I n t e r n a t i o n a l

Boundary and Water Commission, UnitedStates and Mexico. .

(4) Annual reports-various interstatecompact commissions.

(5) Water right filings, permits-stateengineers, county recorders.

(6) Water right decrees-district courts.Data on sedimentation may be obtained

from:( 1 ) W a t e r s u p p l y p a p e r s - U . S .

Department of the Interior, GeologicalSurvey, Quality of Water Branch.

(2) Reports-U.S. Department of theInterior, Bureau of Reclamation; and U.S.Depa r tmen t o f A g r i c u l t u r e , SoilConservation Service.

Data for determining the quality of thewater may be obtained from:

( 1 ) W a t e r s u p p l y p a p e r s - U . S .Department of the Interior, GeologicalSurvey, Quality of Water Branch.

( 2 ) R e p o r t s - U . S . D e p a r t m e n t o fHealth, Education, and Welfare, PublicH e a l t h S e r v i c e , and EnvironmentalProtection Agency, Federal Water ControlAdministration.

( 3 ) R e p o r t s - s t a t e p u b l i c h e a l t hdepartments.

2-7. Hydrologic Investigations. -Hydrologicinvestigations which may be required forproject studies include the determination ofthe following: yield of streamflow, reservoiryield, water requirements for project purposes,sediment which will be deposited in thereservoir, f loodflows, and ground-waterconditions.

The most accurate estimate possible must be

5

prepared of the portion of the streamflow yieldthat is surplus to senior water rights, as thebasis of the justifiable storage. Reservoirstorage will supplement natural yield ofstreamflow during low-water periods. Safereservoir yield will be the quantity of waterwhich can be delivered on a firm basis througha critical low-water period with a givenreservoir capacity. Reservoir capacities and safereservoir yields may be prepared from masscurves of natural streamflow yield as related tofixed water demands or from detailed reservoiroperation studies, depending upon the studydetail which is justified. Reservoir evaporationand other incidental losses should be accountedfor before computation of net reservoir yields.

The critical low-water period may be onedrought year or a series of dry years during theperiod of recorded water history. Watershortages should not be contemplated whenconsidering municipal and industrial water use.For other uses, such as irrigation, it is usuallypermissible to assume tolerable water shortagesduring infrequent drought periods and therebyincrease water use during normal periods withconsequent greater project development. Whatwould constitute a tolerable irrigation watershortage will depend upon local conditions andthe crops to be irrigated. If the problem iscomplex , t h e c o n s u l t i n g a d v i c e o f a nexperienced hydrologist should be secured.

The annual rate at which sediment will bedeposited in the reservoir should be ascertainedto ensure that sufficient sediment storage isprovided in the reservoir so that the usefulfunctions of the reservoir will not be impairedby sediment deposition within the useful life ofthe project or the period of economic analysis,say 50 to 100 years. The expected elevation ofthe sediment deposition may also influence thedesign of the outlet works, necessitating a typeof design which will permit raising the intakeof the outlet works as the sediment isdeposited.

Water requirements should be determinedfor all purposes contemplated in the project.For irrigation, consideration should be given toclimatic conditions, soil types, type of crops,crop distribution, irrigation efficiency andconveyance losses, and reuse of return flows.

6 D E S I G N O F G R A V I T Y D A M S

evapotranspiration are also used in assessing thedisposition of water in an irrigation project,evaluating the irrigation water-managemente f f i c i e n c y , a n d p r o j e c t i n g d r a i n a g erequirements.

Reliable rational equations are available forestimating evapotranspiration when basicmeteorological parameters such 2lS netradiation, vapor pressure and temperaturegradients, wind speed at a prescribed elevationabove the crops or over a standard surface, andsoil heat flux are available. When informationon these parameters is not available, which isthe usual case, recourse is made to empiricalmethods. Numerous equations, both empiricaland partially based on theory, have beend e v e l o p e d f o r e s t i m a t i n g potentialevapotranspiration. Estimates f rom thesemethods are generally accepted as being ofsuitable accuracy for planning and developingwater resources. Probably the methods mostwidely used at this time are the BlaneyCriddlemethod shown in reference [ 11’ and the SoilConservation Service adaptation of theBlaney-Criddle method, shown in reference121.

A more recent method, nearly developeds u f f i c i e n t l y f o r g e n e r a l u s a g e , i s t h eJensen-Haise solar radiation method shown inreference [ 31 . In general terms, these methodsutilize climatic data to estimate a climaticindex. Then coefficients, reflecting the stage ofgrowth of individual crops and their actualwater requirement in relationship to theclimatic index, a r e u s e d t o e s t i m a t e theconsumptive use requirements for selectedcrops.

Project studies must include estimates offloodflows, as these are essential to thede termination of the spillway capacity.Consideration should also be given to annualminimum and mean discharges and to themagnitudes of relatively common floods having20-, lo-, and 4-percent chances of occurrence,as this knowledge is essential for constructionpurposes s u c h a s d i v e r t i n g t h e s t r e a m ,providing cofferdam protection, and scheduling

‘Numbers in brackets refer to items in the bibliography, sec.2-31.

For municipal and industrial water supplies,the anticipated growth of demand over the lifeof the project must be considered. For powergeneration, the factors to be considered areload requirements and anticipated load growth.

Knowledge of consumptive uses is importantin the design and operation of a large irrigationproject, and especially for river systems as awhole. However, of equal and perhaps moreimportance to an individual farm or project isthe efficiency wi th which the wa te r i sconveyed, distributed, and applied. The lossesincidental to application on the farm and theconveyance system losses and operationalwaste may, in many instances, exceed thewater required by the growing crops. In actualoperation, the amount of loss is largely amatter of economics. In areas where water isnot plentiful and high-value crops are grown,the use of pipe or lined conveyance systemsand costly land preparation or sprinklersystems can be afforded to reduce losses to aminimum. A part of the lost water may beconsumed nonbeneficially by nonproductiveareas adjacent to the irrigated land or indrainage channels. Usually most of this watereventually returns to a surface stream or drainand is referred to as return flow.

I n p l a n n i n g irrigation projects, twoconsumptive use values are developed. One,composed of monthly or seasonal values, isu s e d w i t h a n adjustment for effectiveprecipitation and anticipated losses mentionedabove to determine the total water requirementfor appraising the adequacy of the total watersupply and determining reservoir storagerequirements. The other, a peak use rate, isused for sizing the canal and lateral system.

E v a p o t r a n s p i r a t i o n , c o m m o n l y c a l l e dconsumptive use, is defined as the sum ofevaporation from plant and soil surfaces andtranspiration from plants and is usuallyexpressed in terms of depth (volume per unitarea). Crop consumptive use is equal toevapotranspiration plus water required forplant tissue, but the two are usually consideredt h e s a m e . P r e d i c t i o n s o r e s t i m a t e s o fevapotranspiration are basic parameters for theengineer or agronomist involved in planningand developing water resources. Estimates of


operations. Methods of arriving at estimates offloodflows are discussed in appendix G. If thefeasibility studies are relatively complete, theflood determination may be sufficient fordesign purposes. If, however, floodflows havebeen computed for purposes of the feasibilitystudy without making full use of all availabledata, these studies should be carefully reviewedand extended in detail before the actual designof the structure is undertaken. Frequently, newdata on storms, floods, and droughts becomeavailable between the time the feasibilitystudies are made and construction starts. Wheresuch changes are significant, the flood studiesshould be revised and brought up to date.

7

Project studies should also include aground-water study, which may be limitedlargely to determining the effect of groundwater on construction methods. However,some ground-water situations may have animportant bearing on the choice of the type ofdam to be constructed and on the estimates oft h e c o s t o f f o u n d a t i o n s . I m p o r t a n tground-water information sometimes can beo b t a i n e d i n connection with subsurfaceinvestigations of foundation conditions.

As soon as a project appears to be feasible,steps should be taken in accordance with Statewater laws to initiate a project water right.

D. RESERVOIR CAPACITY AND OPERATION

2-8. General. -Dam designs and reservoiroperating criteria are related to the reservoircapacity and anticipated reservoir operations.The loads and loading combinations to beapplied to the dam are derived from the severalstandard reservoir water surface elevations.R e s e r v o i r o p e r a t i o n s a r e a n i m p o r t a n tconsideration in the safety of the structure andshould not be overlooked in the design.Similarly, the reservoir capacity and reservoiroperations are used to properly size thespillway and outlet works. The reservoircapacity is a major factor in flood routings andmay determine the size and crest elevation ofthe spillway. The reservoir operation andreservoir capacity allocations will dctcrminethe location and size of outlet works for thecontrolled release of water for downstreamrequirements and flood control.

Reservoir area-capacity tables should bep r e p a r e d b e f o r e t h e f i n a l d e s i g n s a n dspecifications are c o m p l e t e d . Thesearea-capacity tables should be based upon thebest available topographic data and should bethe official document for final design andadministrative purposes until superseded by areservoir r e survey. Electronic computerprograms are an aid in preparation of reservoirarea and capacity data. These computers enablethe designer to quickly have the best results

obtainable from the original field data.2-9. Reservoir Allocation DefinitiompTo

ensure uniform reporting of data for design andc o n s t r u c t i o n , t h e f o l l o w i n g s t a n d a r ddesignations of water surface elevations andreservoir capacity allocations are used by theBureau of Reclamation:

(a) General. Dam design and reservoiroperation utilize reservoir capacity and watersurface elevation data. To ensure uniformity inthe establishment, use, and publication of thesedata, the following standard definitions ofwater surface elevations and reservoir capacitiesshall be used. Reservoir capacity as used here isexclusive of bank storage capacity.

(b) Water Surface Elevation Definitions.(Refer to fig. 2-l .)

(1) Maximum Water Surface is thehighest ‘acceptable water surface elevationwith all factors affecting the safety of thestructure considered. Normally, it is thehighest water surface elevation resultingfrom a computed routing of the inflowdesign flood through the reservoir on thebasis of established operating criteria. It isthe top of surcharge capacity.

(2) Top of Exclusive Flood ControlCapacity is the reservoir water surfaceelevation at the top of the reservoir capacityallocated to exclusive use for regulation of

8 DESIGN OF GRAVITY DAMSRESERVOIR CAPACITY ALLOCATIONS

PE OF DAM

ERATED B Y

EST LENGTH FT; CREST WIDTH

LUME OF DAM

NSTRUCTION PERIOD

REAM

S AREA ACRES AT EL

IGINATED BY:

1 REGION 1 STATE

RESERVOII

F T DA1

CU YD PROJECl

DIVISIOI

UNI-

STATUS OF DAI

APPROVED BY:

(Code) (Date) (Code) (Date)

FLOODCONTROL

A.F .

JOINT USE

A.F .

A .F .

A .F .

A .F .

b LOWEST POINT OF FOUNDATION EXCAVATION E L - - - - - -

0 Includes- _ _ _ _ _ _ _ _ _ _ a.f. allowance for- ._ _ _ _ year sediment deposition betweenstrearl,bed and EL _ _ _ _ _ _ _, of which- _ _ _ _ _ _ -a.f’. is above El- - - - _ - -.

@ Establishedby----- ----_ - - - - - - - - - - - ----_-----FERENCES AND COMMENTS:

Figure 2-1. Reservoir capacity allocation sheet used by Bureau of Reclamation.

DESIGN CONSIDERATIONS-Sec. 2-9 9

f l o o d i n f l o w s t o r e d u c e d a m a g edownstream.

(3) Maximum Controllable WaterSurface Elevation is the highest reservoirwater surface elevation at which gravityflows from the reservoir can be completelyshut off.

(4) Top of Joint Use Capacity is thereservoir water surface elevation at the topof the reservoir capacity allocated to jointuse, i.e., flood control and conservationpurposes.

(5) Top of Active ConservationCapacity is the reservoir water surfaceelevation at the top of the capacity allocatedto the storage of water for conservationpurposes only.

(6) Top of Inactive Capacity is thereservoir water surface elevation belowwhich the reservoir will not be evacuatedunder normal conditions.

(7) Top of Dead Capacity is the lowestelevation in the reservoir from which watercan bc drawn by gravity.

(8) Streambed at the Dam Axis is thee l e v a t i o n o f t h e l o w e s t p o i n t i n t h estreambed at the axis of the dam prior toconstruction. This elevation normallydefines the zero for the area-capacity tables.(c) Capacity Definitions.

(1) Surcharge Capacity is reservoircapacity provided for use in passing theinflow design flood through the reservoir. Itis the reservoir capacity between themaximum water surface elevation and thehighest of the following elevations:

a. Top of exclusive flood controlcapacity.

b. Top of joint use capacity.c . T o p o f a c t i v e c o n s e r v a t i o n

capacity.(2) Total Capacity is the reservoir

capacity below the highest of the elevationsrepresenting the top of exclusive floodcontrol capacity, the top of joint usecapacity, or the top of active conservationcapacity. In the case of a natural lake whichhas been enlarged, the total capacityincludes the dead capacity of the lake. If thedead capacity of the natural lake has not

been measured, specific mention of this factshould be made. Total capacity is used toexpress the total quantity of water whichcan be impounded and is exclusive ofsurcharge capacity.

(3) Live Capacity is that part of thetotal capacity from which water can bewithdrawn by gravity. It is equal to the totalcapacity less the dead capacity.

(4) Active Capacity is the reservoircapacity normally usable for storage andregulation of reservoir inflows to meetestablished reservoir operating requirements.Active capacity extends from the highest ofthe top of exclusive flood control capacity,the top of joint use capacity, or the top ofactive conservation capacity, to the top ofinactive capacity. It is the total capacity lessthe sum of the inactive and dead capacities.

(5) Exclusive Flood Control Capucityis the reservoir capacity assigned to the solepurpose of regulating flood inflows toreduce flood damage downstream. In someinstances the top of exclusive flood controlcapacity is above the maximum controllablewater surface elevation.

(6) Joint Use Capacity is the reservoircapacity assigned to flood control purposesduring certain periods of the year and toconservation purposes during other periodsof the year.

(7) Active Conservation Capacity is thereservoir capacity assigned to regulatereservoir inflow for irrigation, power,municipal and industrial use, fish andwildlife, navigation, recreation, waterquality, and other purposes. It does notinclude exclusive flood control or joint usecapacity. The active conservation capacityextends from the top of the activeconservation capacity to the top of theinactive capacity.

(8) Inactive Capacity is the reservoircapacity exclusive of and above the deadcapacity from which the stored water isnormally not available because of operatingagreements or physical restrictions. Underabnormal conditions, such as a shortage ofwater or a requirement for structural repairs,water may be evacuated from this space

10

after obtaining proper authorization. Thehighest applicable water surface elevationdescribed below usually determines the topof inactive capacity.

a . T h e l o w e s t w a t e r s u r f a c eelevation at which the planned minimumrate of release for water supply purposescan be made to canals, conduits, the river,or other downstream conveyance. Thiselevation is normally established duringthe planning and design phases and is theelevation at the end of extreme drawdownperiods.

b. The established minimum watersurface elevation for fish and wildlifepurposes.

c. The established minimum watersurface elevation for recreation purposes.

d. The minimum water surfaceelevation as set forth in compacts and/oragreements with political subdivisions.

e. The minimum water surfaceelevation at which the powerplant isdesigned to operate.

f . T h e m i n i m u m w a t e r s u r f a c eelevation to which the reservoir can bed r a w n u s i n g established operatingprocedures without endangering the dam,appurtenant structures, or reservoirshoreline.

g . T h e m i n i m u m w a t e r s u r f a c eelevation or the top of inactive capacityestablished by legislative action.

(9) Dead Capacity is the reservoircapacity from which stored water cannot beevacuated by gravity.2-10. Data to be Submitted.-To complete

D E S I G N O F G R A V I T Y D A M S

the designs of the dam and its appurtenantworks, the following reservoir design datashould be submitted:

( 1) Area-capacity curves and/or tablescomputed to an elevation high enough to allowfor storage of the spillway design flood.

(2) A topographic map of the reservoir siteprepared to an appropriate scale.

(3) Geological information pertinent toreservoir tightness, locations of mines ormining claims, locations of oil and natural gaswells.

(4) Completed reservoir storage allocationsand corresponding elevations.

(5) Required outlet capacities for respectivereservoir water surfaces and any required sillelevations. Give type and purpose of reservoirreleases and the time of year these must bemade. Include minimum releases required.

(6) Annual periodic fluctuations of reservoirlevels shown by tables or charts summarizingreservoir operation studies.

(7) Method of reservoir operation for floodcontrol and maximum permissible releasesconsistent with safe channel capacity.

(8) Physical, economic, or legal limitationsto maximum reservoir water surface.

(9) Anticipated occurrence and amounts ofice (thickness) and floating debris, and possibleeffect on reservoir outlets, spillway, and otherappurtenances.

(10) Extent of anticipated wave action,including a discussion of wind fetch.

(11) Where maintenance o f f l ow in toexisting canals is required, determine maximumand probable carrying capacity of such canal,and time of year when canals are used.

E. CLIMATIC EFFECTS

2- 1 1. General. -The climatic conditions since weather affects the rate of constructionwhich are to be encountered at the site affect a n d t h e o v e r a l l c o n s t r u c t i o n s c h e d u l e .the design and construction of the dam. Accessibility of the site during periods ofMeasures which should be employed during the inclement weather affects the constructionconstruction period to prevent cracking of schedule and should be investigated.concrete must be related to the ambient 2-12. Data to be Submitted.-The followingt e m p e r a t u r e s e n c o u n t e r e d a t t h e s i t e . d a t a o n c l i m a t i c c o n d i t i o n s s h o u l d b eConstruction methods and procedures may also submitted as part of the design data:be dependent upon the weather conditions, ( 1) Weather Service records of mean

DESIGN CONSIDERATIONS-Sec. 2-13 II

monthly maximum, mean monthly minimum, (3 ) Da i ly r ead ings o f max imum andand mean monthly air temperatures for the minimum river water temperatures should benearest station to the site. Data on river water submitted as soon as a station can betemperatures at various times of the year established at the site.should also be obtained. (4) Amount and annual variance in rainfall

( 2) Daily readings of max imum and and snowfall.minimum air temperatures should be submitted (5) Wind velocities and prevailing direction.as soon as a station can be established at thesite.

F. CONSTRUCTION MATERIALS

2- 1 3 . C o n c r e t e A g g r e g a t e s . - T h econstruction of a concrete dam requires theavailability of suitable aggregates in sufficientq u a n t i t y t o c o n s t r u c t t h e d a m a n d i t sappurtenant structures. Aggregates are usuallyprocessed from natural deposits of sand, gravel,and cobbles. However, if it is more practical,they may be crushed from suitable rock. Forsmall dams, the aggregates may be obtainedfrom existing commercial sources. If theaggregates are obtained from borrow pits orrock quarries, provisions should be made tolandscape and otherwise restore the areas tominimize adverse environmental effects. Ifaggregates are available from the reservoir area,particularly below minimum water surface,their adverse effects would be minimized.However, any early storage in the reservoir,prior to completion of the dam, may rule outthe use of aggregate sources in the reservoir.

2 - 1 4 . W a t e r f o r C o n s t r u c t i o nPurposes.-For large rivers, this i tem isrelatively unimportant except for quality ofthe water. For small streams and offstreamreservoirs, water for construction purposes maybe difficult to obtain. An adequate supply ofwater for construction purposes such as

washing aggregates and cooling and batchingconcrete should be assured to the contractor,and the water rights should be obtained forhim. If necessary to use ground water,information on probable sources and yieldsshould be obtained. Information on locationsand yields of existing wells in the vicinity,restrictions if any on use of ground water, andnecessary permits should also be obtained.

2-l 5. Data to be Submitted. -In addition tothe data on concrete aggregates and water forconstruction purposes, the following data onconstruction materials should be obtained:

(1) An earth materials report containinginformation on those potential sources of soils,sand, and gravel which could be used forbackfill and bedding materials.

(2) Information on riprap for protection ofslopes.

(3) Information on sources and character ofacceptable road surfacing materials, if required.

(4) References to results of sampling,testing, and analysis of construction materials.

(5) Photographs of sources of constructionmaterials.

(6) Stbtement of availability of lumber forstructural work.

G. SITE SELECTION

2 - 1 6 . G e n e r a l . - A w a t e r r e s o u r c e s Once the purpose and the service area aredevelopment project is designed to perform a defined, a preliminary site selection can becertain function and to serve a particular area. made.

12

Fo l lowing the de t e rmina t ion o f t headequacy of the water supply as discussed ins u b c h a p t e r C , t h e t w o m o s t i m p o r t a n tconsiderations in selecting a damsite are: (1)ilie site must be adequate to support the damand the appurtenant structures, and (2) thearea upstream from the site must be suitablefor a reservoir. There are often several suitablesites along a river where the dam can belocated.

The site finally selected should be thatwhere the dam and reservoir can be mosteconomically constructed with a minimum ofinterfcrencc with local conditions and stillserve their intended purpose. An experiencedengineer can usually eliminate some of the sitesfrom further consideration. Cost estimates mayb e r e q u i r e d t o d e t e r m i n e w h i c h o f t h eremaining sites w i l l p r o v i d e t h e m o s teconomical structure.

2-17. Factors in Site Selection. -In selectinga damsite the following should be considered:

Topography A narrow site will minimize theamount of material in the damthus reducing its cost, butsuch a site may be adaptableto an arch dam and this pos-sibility should be investi-gated.

Geology The foundation of the damshould be relatively free of


major faults and shears. Ifthese are present, they mayrequire expensive foundationtreatment to assure an ade-quate foundation.

Appurtenant While the cost of these struc-Structures tures is usually less than

the cost of the dam, economyin design may be obtained byconsidering their effect atthe time of site selection.For example, if a river hasa large flow, a large spill-way and diversion works willbe required. Selecting asite which will better accom-modate these appurtenanceswill reduce the overall cost.

Local Some sites may have roads, rail-Conditions roads, powerlines, canals,

etc., which have to be relo-cated, thus increasing theoverall costs.

Access Accessibility of the site hasa very definite effect on thetotal cost. Difficult accessmay require the constructionof expensive roads. An areasuitable for the contractor’splant and equipment near thesite will reduce the contrac-tor’s construe tion costs.

H. CONFIGURATION OF DAM

2-l 8. Nonoverflow Section. -A gravity damis a concrete structure designed so that itsweight and thickness insure stability against allthe imposed forces. The downstream face willusually be a uniform slope which, if extended,would intersect the vertical upstream face at ornear the maximum reservoir water level. Theupper portion of the dam must be thickenough to resist the shock of floating objectsand to provide space for a roadway or otherrequired access. The upstream face willnormally be vertical. This concentrates most ofthe concrete weight near the upstream face

where it will be most effective in overcomingtensile stresses due to the reservoir waterloading. The thickness is also an importantfactor in resistance to sliding and may dictatethe slope of the downstream face. Thicknessmay also be increased in the lower part of thedam by an upstream batter.

2-19. Overflow Section.-The spillway maybe located either in the abutment or on thedam. If it is located on a portion of the dam,the section should be similar to the abutments e c t i o n but modified at the top toaccommodate the crest and at the toe to


accommodate the energy dissipator. The may involve some changes from the theoreticalelevation of the crest and its shape will be hydraulic shapes. Hydraulic design of thedetermined by hydraulic requirements, and the overflow section is discussed fully in chaptershaping at the toe by the energy dissipator. IX. For structural design of the dam seeStability requirements for the overflow section chapters III and IV.

I. FOUNDATION INVESTIGATIONS

2 - 2 0 . P u r p o s e . - T h e p u r p o s e o f afoundation investigation is to provide the datanecessary to properly evaluate a foundation. Aproperly sequenced and organized foundationinvestigation will provide the data necessary toevaluate and analyze the foundation at anystage of investigation.

2-21. Field Investigations.-The collection,study, and evaluation of foundation data is acontinuing program from the time of theappraisal investigation to the completion ofconstruction. The data collection begins withan appraisal and continues on a more detailedbasis through the design phase. Data are alsocollected continuously during construction tocorrelate with previously obtained informationand to evaluate the need for possible designchanges.

(a) Appraisal Investigation.-The appraisalinvestigation includes a preliminary selection ofthe site and type of dam. All available geologicand topographic maps, photographs of the sitearea, and data from field examinations ofnatural outcrops, road cuts, and other surfaceconditions should be utilized in the selection ofthe site and preliminary evaluation of thefoundation.

The amount of investigation necessary forappraisal will vary with the anticipateddifficulty of the foundation. In general, theinvestigation should be sufficient to define themajor geologic conditions with emphasis onthose which will affect design. A typicalgeologic map and profile are shown on figures2-2 and 2-3.

The geologic history of a site should bethoroughly studied, particularly where thegeology is complex. Study of the history maya s s i s t i n recogn iz ing and adequately

investigating hidden but potentially dangerousfoundation conditions.

Diamond core drilling during appraisalinvestigations may be necessary in morecomplex foundations and for the foundationsfor larger dams. The number of drill holesrequired will depend upon the area1 extent andc o m p l e x i t y o f t he founda t i on . Somefoundations may require as few as three or fourdrill holes to define an uncertain feature.Others may require substantially more drillingto determine foundation treatment for apotentially dangerous foundation condition.

Basic data that should be obtained duringthe appraisal investigation, with refinementcontinuing until the construction is complete,are :

(1) Dip, strike, thickness, composition, andextent of faults and shears.

(2) Depth of overburden.(3) Depth of weathering.(4) Joint orientation and continuity.(5) Lithology throughout the foundation.( 6 ) P h y s i c a l p r o p e r t i e s t e s t s o f t h e

foundation rock. Tests performed on similarfoundation m a t e r i a l s m a y b e u s e d f o restimating the properties in the appraisalphase.

(b) Feasibility Investigation. -During thefeasibility phase, the location of the dam isusually finalized and the basic design data arefirmed up. The geologic mapping and sectionsare reviewed and supplemented by additionaldata such as new surveys and additional drillholes. The best possible topography should beused. In most cases, the topography is easilyobtained by aerial photogrammetry to almostany scale desired.

The drilling program is generally the means


Two Indicates strike and dip of fault -flOO Indicates strike and dip of joints

Figure 2-2. A typical geologic map of a gravity damsite.-288-D-2952

Orlginal g r o u n d s u r f a c e

-~Estlmated b e d r o c k

Figure 2-3. A typical geologic profile of a damsite.-288-D-2954


of obtaining the additional data required forthe feasibili ty stage. The program takesadvantage o f a n y k n o w l e d g e o f s p e c i a lconditions revealed during the appraisalinvestigation. The drill holes become morespecifically oriented and increased in numberto better define the foundation conditions anddetermine the amount of foundation treatmentrequired.

The rock specimens for laboratory testingduring the feasibility investigations are usuallynominal, as the actual decision for constructionof the dam has not yet been made. Testspecimens should be obtained to determinemore accurately physical properties of thef o u n d a t i o n r o c k a n d f o r p e t r o g r a p h i cexamination. Physical properties of joint orfault samples may be estimated by usingconservative values from past testing of similarmaterials. The similarity of materials can bejudged from the cores retrieved from thedrilling.

(c) Final Design Da&.-Final design dataare required prior to the preparation of thespecifications. A d e t a i l e d f o u n d a t i o ninvestigation is conducted to obtain the finaldesign data. This investigation involves as manydrill holes as are necessary to accurately definethe following items:

(1) Strike, dip, thickness, continuity,and composition of all faults and shears inthe foundation.

(2) Depth of overburden.(3) Depth of weathering throughout

the foundation.(4) Joint orientation and continuity.(5) Lithologic variability.( 6 ) P h y s i c a l p r o p e r t i e s o f t h e

foundation rock, including material in thefaults and shears.

The foundation investigation may involve,besides diamond core drilling, detailed mappingof surface geology and exploration of dozertrenches and exploratory openings such astunnels, drifts, and shafts. The exploratoryopenings can be excavated by contract prior toissuing final specifications. These openingsprovide the best possible means of examiningthe foundation. In addition, they provide

excellent in situ testing locations and areas fortest specimen collection.

I n a d d i t i o n t o t e s t s p e c i m e n s f o rdetermining the physical properties, specimensmay be required for final design for use indetermining the shear strength of the rocktypes, healed joints, and open joints. Thisinformation may be necessary to determine thestability of the foundation and is discussed asthe shear-friction factor in subchapter F ofchapter III.

Permeability tests should be performed as aroutine matter during the drilling program. Theinformation obtained can be util ized inestablishing flow nets which will aid instudying uplift conditions and establishingdrainage systems. The permeability testingmethods presently used by the Bureau ofReclamation are described in designation E-18o f t he Ea r th Manua l [4] a n d t h e r e p o r tentitled “Drill Hole Water Tests-TechnicalInstructions,” published by the Bureau ofReclamation in July 1972.

2-22. Construction Geology. -The geologyas encountered in the excavation should bedefined and compared with the preexcavationgeology. Geologists and engineers shouldconsider carefully any geologic change andcheck its relationship to the design of thestructure.

As-built geology drawings should bedeveloped even though revisions in design mayn o t b e r e q u i r e d by changed geologicconditions, since operation and maintenanceproblems may develop requiring de tailedfoundation information.

2-23. Foundation Analysis Methods. -Inmost instances, a gravity dam is keyed into thef o u n d a t i o n s o t h a t t h e f o u n d a t i o n w i l lnormally be adequate if it has enough bearingcapacity to resist the loads from the dam.However, a foundation may have faults, shears,seams, joints, or zones of inferior rock thatcould develop unstable rock masses when actedon by the loads of the dam and reservoir. Thesafety of the dam against sliding along a joint,fault, or seam in the foundation can bcdetermined by computing the shear-frictionfactor of safety. This method of analysis is


Manual [4] and the report entitled “Drill HoleW a t e r T e s t s - T e c h n i c a l I n s t r u c t i o n s , ”published by the Bureau of Reclamation inJuly 1972.

2-25. Laboratory Testing. -The followinglaboratory tests are standard and the methodsand test interpretations should not varysubstantially from one laboratory to another.A major problem involved with laboratorytesting is obtaining representative samples.Sample size is often dictated by the laboratoryequipment and is a primary consideration.Following is a list of laboratory tests:

explained in subchapter F of chapter III. Ifthere are several joints, faults, or seams alongwhich failure can occur, the potentiallyunstable rock mass can be analyzed by amethod called rigid block analysis. Thismethod is explained in detail in subchapter Fof chapter IV. These methods of analysis mayalso be applied to slope stability problems.

The data required for these two methods ofanalysis are :

(1) Physical properties.(2) Shearing and sliding strengths of

the discontinuities and the rock.(3) Dip and strike of the faults, shears,

seams, and joints.(4) Limits of the potentially unstable

rock mass.(5) Uplift pressures on the failure

surfaces.(6) Loads to be applied to the rock

mass.When a foundation is interspersed by many

faults, shears, joints, seams, and zones ofinferior rock, the finite element method ofanalysis can be used to determine the bearingcapacity and the amount of foundationtreatment required to reduce or eliminate areasof tension in the foundation. The descriptionof this method can be found in subchapter E ofchapter IV. In addition to the data required forthe rigid block analysis, the finite elementanalysis requires the deformation moduli of thevarious parts of the foundation.

2-24. In Situ Testing.-In situ shear tests[ 51 are more expensive than similar laboratorytests; consequently, comparatively few can berun. The advantage of a larger test surface mayrequire that a few in situ tests be supplementedby a greater number of laboratory tests. Theshearing strength relative to both horizontaland vertical movement should be obtained byeither one or a combination of both methods.

Foundation permeability tests may be run inconjunction with the drilling program or as aspecial program. The tests should be performedaccording to designation E-18 of the Earth

Physical Properties Tests

(1) Compressive strength(2) Elastic modulus(3) Poisson’s ratio(4) Bulk specific gravity(5) Porosity(6) Absorption

Shear Tests

(1) Direct shear 1 Perform on intactspecimens and

(2) Triaxial shear I those with healedjoints

(3) Sliding friction Perform on openjoints

Other Tests

(1) Solubility(2) Petrographic analysis

2 - 2 6. Consistency of Presentation ofData. It is important that the design engineers,laboratory personnel, and geologists be able tod r a w t h e s a m e conclusions from theinformation presented in the investigations.T h e s t a n d a r d i z a t i o n o f t h e g e o l o g i cinformation and laboratory test results istherefore essential and is becoming increasinglyso with the newer methods of analysis.


J. CONSTRUCTION ASPECTS

17

2-27. General.-The construction problemsthat may be encountered by the contractor inconstructing the dam and related featuresshould be considered early in the design stage.One of the major problems, particularly innarrow canyons, is adequate area for thecontractor’s construction plant and equipmentand for storage of materials in the proximity ofthe dam. Locating the concrete plant tominimize handling of the concrete and theaggregates and cement can materially reducethe cost of the concrete.

Permanent access roads should be located tofacilitate the contractor’s activities as much aspracticable. This could minimize or eliminateunsightly abandoned construction roads.Structures should be planned to accommodatean orderly progression of the work. The lengtho f t h e c o n s t r u c t i o n s e a s o n s h o u l d b econsidered. In colder climates and at higherelevations it may be advantageous to suspendall or part of the work during the wintermonths. Adequate time should be allowed forconstruction so that additional costs forexpedited work are not encountered.

2 - 28. Construction Schedule. -Thecontractor’s possible methods and timing ofconstruction should be considered at all timesduring the design of the dam and itsappurtenant structures. Consideration of theproblems which may be encountered by thecontractor can result in significant savings inthe cost of construction. By developing ananticipated construction schedule, potentialproblems in the timing of construction of thevarious parts can be identified. If practicable,revisions in the design can be made to eliminateor minimize the effect of the potentialproblems. The schedule can be used to program

supply contracts and other constructioncontracts on related features of the project. Itis also useful as a management tool to thedesigner in planning his work so thatspecifications and construction drawings can beprovided when needed.

The construction schedule can be made byseveral methods such as Critical Path Method(CPM), Program Evaluation and ReviewTechnique (PERT), and Bar Diagram. Figure2-4 shows a network for a portion of ahypothetical project for a CPM schedule. Dataconcerning the time required for various partsof the work and the interdependencies of partsof the work can be programmed into acomputer which will calculate the critical path.It will also show slack time or areas which arenot critical. In this example, there are twopaths of activities. The path which is critical isthe preparation of specifications, awarding ofcontract, and the construction of “A,” “B,”and “ D ” . T h e s e c o n d p a t h t h r o u g hconstruction of “C” and “E” is not critical. Asthe work progresses, the current data on thestatus of all the phases of work completed andin progress can be fed back into the computer.The computer will then recompute the criticalpath, thus establishing a new path if anotherphase of the work has become critical, and willpoint out any portion of the work that isfalling behind the required schedule.

Figure 2-5 shows the construction schedulefor the hypothetical project on a bar diagram.This diagram is made by plotting bars to thelength of time required for each portion of thework and fitting them into a time schedule,checking visually to make sure interrelatedactivities are properly sequenced.

K. MISCELLANEOUS CONSIDERATIONS

2-29. Data to be Submitted.-Many items the adequacy and accuracy of the data shouldnot covered above affect the design and contemplate their possible subsequent utilityconstruction of a dam. Some of these are noted for expansion into specifications design data.below. In securing and preparing design data,


NOTESTL = Lotest allowable time for actlwty s+or+ or completionTE = Earllest expected time for octlwty start or completions = Slack or Float Time

[ = Estimated actfv~ty +!me

- C R I T I C A L P A T H (S=O)

Figure 2-4. Typical construction schedule using Critical Path Method (CPM).-288-D-2955

(1) Details of roadway on crest of dam (andapproaches) if required.

(2) Present o r f u t u r e r e q u i r e m e n t f o rhighway crossing on dam.

(3) Details on fishways and screens, withr ecommenda t ions o f a p p r o p r i a t e fishauthorities.

(4) Existing works to be replaced byincorporation into dam.

( 5 ) F u t u r e p o w e r p l a n t o r p o w e rdevelopment .

(6) Navigation facilities.(7) Possibility of raising crest of dam in

future.( 8 ) A n t i c i p a t e d f u t u r e r i v e r c h a n n e l

improvement or other construction whichmight change downstream river regimen.

(9) Recreational facilities anticipated to beauthorized, and required provisions for publicsafety.

( 10) Recommended period of construction.(11) Commitments for delivery of water or

power.( 1 2 ) D e s i g n a t i o n o f a r e a s w i t h i n

right-of-way boundaries for disposal of wastematerials.

2-30. Other Considerations. -Designc o n s i d e r a t i o n m u s t t a k e i n t o a c c o u n tconstruction procedures and costs. An earlyevaluation and understanding of these isn e c e s s a r y i f a rapid and economicalconstruction of the dam is to be attained.

Designs for mass concrete structures andtheir appurtenances should be such thatsophisticated and special constructionequipment will not be required. Thin, curvedwalls with close spacing of reinforcement maybe desirable for several reasons, and mayrepresent the minimum cost for materials suchas cement, flyash, admixtures, aggregates, andreinforcing steel. However, the cost of formingand labor for construction of this type and thedecreased rate of concrete placement mayresult in a much higher total cost than wouldresult from a simpler structure of greaterdimensions.

Design and construction requirementsshould permit and encourage the utilization ofmachine power in place of manpower whereverpracticable. Any reduction in the requirementfor high-cost labor will result in a significantcost savings in the completed structure. Work

TIME0 4 8 12 16 20 24 26 32 36 40 44 46 52 56 60 64 66 72 76 80 64 68 92 96 100 0

IllI I I I I

Prepare speclflcotton Drowlngs

IPrepare spe

oragrophsClI I

I L-LI Prepore'

T

crgs f

r

I

c

zo r

' PR(cc

Prepare const.Dwgs for "B" and "C"and portlon of"D"reaulred to finollze "B"

7

II

4Construct "A"

F

complete

lndlcotes slack time

D Prepore const Dwgs for"E"ond 11 portlonof"F"requlred toflnallze"E"/

t

1I

:It

i Flnlsh construction Dwgs"F"

I

ECTIPLETE- 1

1I1 Construct'F'

I I /

Figure 2-5. Typical construction schedule using a bar diagram.-2CG-D-2956

20

areas involved in a high labor use include theplacing, compaction, and cu r ing o f t heconcrete, t h e t r e a t m e n t a n d c l e a n u p o fconstruction joints, and the repair and finishingof the concrete surfaces.

Forming is a significant cost in concretestructures. Designs should permit the simplerforms to be used, thus facilitating fabrication,


installation, and r e m o v a l o f t h e f o r m s .Repetitive use of forms will materially reduceforming costs. Although wooden forms arelower in initial cost, they can only be used alimited number of times before they warp andfail to perform satisfactorily. The reuse of steelforms is limited only by the designs and thedemands of the construction schedule.

L. BIBLIOGRAPHY

ill

[21

131

141

2-3 1. Bibliography [51

U.S. Department of Agriculture, Agricultural ResearchService, “Determining Consumptive Use and Irrigation [61Water Requirements,” Technical Bullet in No. 1275,December 1962.U.S. Department of Agriculture, Soil ConservationService, “Irrigation Water Requirements,” TechnicalRelease No. 21, April 1967.Jensen, M. E. , “Water Consumption by AgriculturalPlants,” Water Defici ts and Plant Growth, vol . II ,

(71

[slAcademic Press, New York, N.Y., 1968, pp. l-22.“Field Permeability Tests in Boreholes,” Earth Manual,Designation E-18, Bureau of Reclamation, 1974.

“Morrow Point Dam Shear and Sliding Friction Tests,”Concrete Laboratory Report No. C-1161, Bureau ofReclamation, 1965.Wallace, G. B., Slebir, E. J., and Anderson, F. A., “RadialJacking Test for Arch Dams,” Tenth Rock MechanicsSymposium, University of Texas, Austin, Tex., 1968.Wallace, G. B., Slebir, E. J., and Anderson, F. A., “In SituMethods for Determining Deformation Modulus Used bythe Bureau of Reclamation,” Winter Meeting, AmericanSociety for Testing and Materials, Denver, Colo., 1969.W a l l a c e , G. B. , S lebi r , E . J . , and Anderson, F . A. ,“Foundation Testing for Auburn Dam,” EleventhSymposium on Rock Mechanics, University of California,Berkeley, Calif., 1969.

<<Chapter III

Design Data and Criteria

A. INTRODUCTION

3 - 1. Basic Assumptions. -Computationalmethods require some basic assumptions forthe analysis of a gravity dam. The assumptionswhich cover the continuity of the dam and itsfoundation, competency of the concrete in thedam, adequacy o f t he founda t i on , andvariation of stresses across the sections of thedam are as follows:

(1) Rock formations at the damsite are, orwill be after treatment, capable of carrying theloads transmitted by the dam with acceptablestresses.

(2) The dam is thoroughly bonded to thefoundation rock throughout its contact withthe canyon.

(3) The c o n c r e t e i n the dam ish o m o g e n e o u s , u n i f o r m l y e l a s t i c i n a l ldirections, and strong enough to carry theapplied loads with stresses below the elasticlimit.

(4) Contraction joints that are keyed andgrouted may be considered to create amonolithic structure, a n d l o a d s m a y b etransferred horizontally to adjacent blocks byboth bending and shear. If the joints are keyedbut not grouted, loads may be transferredhorizontally to adjacent blocks by shear acrossthe keys. Where joints are neither keyed norgrouted, the entire load on the dam will betransferred vertically to the foundation. Ifjoints are grouted, they will be grouted beforethe reservoir loads are applied so that thestructure acts monolithically.

(5) Horizontal and vertical stresses varyl i n e a r l y f r o m t h e u p s t r e a m f a c e t o t h edownstream face.

( 6 ) H o r i z o n t a l s h e a r s t r e s s e s h a v e aparabolic variation from the upstream face tothe downstream face.

B. CONCRETE

3-2. Concrete Properties. -A gravity dam Tests must be made on specimens using themust be constructed of concrete which will full mass mix and the specimens must be ofmeet the design criteria for strength, durability, sufficient age to adequately evaluate thepermeability, and other properties. Although strength and elastic properties which will existmix proportions are usually controlled by for the concrete in the dam [ 1 I 1 .strength and/or durability requirements, the (a) Strength.-The strength of concretecement content should be held to an should satisfy early load and constructionacceptable minimum in order to minimize the requirements, and at some specific age shouldheat of hydration. Properties of concrete varywith age and with proportions and types of ‘Numbers in brackets refer to items in the bibliography,ingredients. sec. 3-23.

21

22

have the specified compressive strength asdetermined by the designer. This specific age isoften 365 days but may vary from onestructure to another.

Tensile strength of the concrete mix shouldbe determined as a companion test series usingthe direct tensile test method.

Shear strength is a combination of internalfriction, which varies wi th the normalcompressive stress, and cohesive strength.Companion series of shear strength tests shouldbe conducted at several different normal stressvalues covering the range of normal stresses tobe expected in the dam. These values should beused to obtain a curve of shear strength versusnormal stress.

(b) Elastic Properties.-Concrete is not atruly elastic material. When concrete issubjected to a sustained load such as may beexpected in a dam, the deformation producedby that load may be divided into twoparts-the elastic deformation, which occursimmediately due to the instantaneous modulusof elasticity; and the inelastic deformation, orcreep, which develops gradually and continuesfor an indefinite time. To account for theeffects of creep, the sustained modulus ofelasticity is used in the design and analysis of aconcrete dam.

The stress-strain curve is, for all practicalpurposes, a straight line within the range ofusual working stresses. Although the modulusof elasticity is not directly proportional to thestrength, the high strength concretes usuallyhave higher moduli. The usual range of theinstantaneous modulus of elasticity forconcrete at 28-day age is between 2.0 x 10”and 6.0 x lo6 pounds per square inch.

(c) Thermal Properties.-The effects oftemperature change on a gravity dam aredependent on the thermal properties of theconcrete. Thermal properties necessary for theevaluation of temperature effects are thecoefficient of thermal expansion, thermalconductivity, and specific heat [7]. Thecoefficient of thermal expansion is the lengthchange per unit length per degree temperaturechange. Thermal conductivity is the rate ofheat conduction through a unit thickness overa unit area of the material subjected to a unit


temperature difference between faces. Thespecific heat is defined as the amount of heatrequired to raise the temperature of a unit massof the material 1 degree. Diffusivity ofconcrete is an index of the facility with whichconcrete will undergo temperature change.Diffusivity is a function of the values ofspecific heat, thermal conductivity, anddensity.

(d) Dynamic Properties.-Concrete, whensubjected to dynamic loadings, may exhibitcharacteristics unlike those occurring duringstatic loadings. Testing is presently underwayin the Bureau’s laboratory to determine theproperties of concrete when subjected todynamic loading. Until sufficient test data areavailable, static strengths and the instantaneousmodulus of elasticity should be used.

(e) Other Properties.-In addition to thes t r e n g t h , e l a s t i c m o d u l u s , a n d t h e r m a lproperties, several other properties of concreteshould be evaluated during the laboratorytesting program. These properties, which mustb e d e t e r m i n e d f o r c o m p u t a t i o n s o fdeformations and stresses in the concretesfrucfures, are Poisson’s ratio, unit weight, andany autogenous growth or drying shrinkage.

(f) Average Concrete Properties.-Forpreliminary studies until laboratory test dataare available, the necessary values may beestimated from published data [2] for similartests. Until long-term load tests are made todetermine the effects of creep, the sustainedmodulus of elasticity should be taken as 60 to70 percent of the laboratory value of theinstantaneous modulus of elasticity.

If no tests or published data are available,the following may be assumed for preliminarystudies:

Specified compressive strength = 3,000 to5,000 p.s.i.

Tensile strength = 4 to 6 percent of thecompressive strength

Shear strength:Cohesion = 10 percent of the compressive

strengthCoefficient of internal friction = 1 .O

Sustained modulus of elasticity = 3.0 x lo6p.s.i. (static load including effects ofcreep)

DESIGN DATA AND CRITERIA-Sec. 3-3

Instantaneous modulus of elasticity = 5.0 xlo6 p.s.i. (dynamic or short time load)

Coefficient of thermal expansion = 5.0 x1 Om6 per degree F.

23

Poisson’s ratio = 0.20Unit weight of concrete = 150 pounds per

cubic foot.

C. FOUNDATION

3-3. Introduction.-Certain informationconcerning the foundation is required fordesign of the gravity dam section. The designof the dam and any treatment to thefoundation (see sec. 6-3) to improve itsproperties are considered separate problems. Iftreatments are applied to the foundation, thedata used for the design of the dam should bebased on the properties of the foundation aftertreatment. A geologic investigation is requiredto determine the general suitability of the siteand to identify the types and structures of thematerials to be encountered. After theseidentifications have been made the followingthree parameters should be determined:

(1) For each material the shear strengths ofintact portions, the sliding friction strengths ofdiscontinuities, and the shear strength at eachinterface with a different material (includingthe strength at the interface of concrete andthe material exposed on the completedexcavated surface).

(2) The permeability of each material.( 3 ) T h e d e f o r m a t i o n m o d u l u s o f t h e

foundation.The discussion of foundation investigation in

chapter II (sets. 2-20 through 2-26) lists thephysical properties normally required and thesamples desired for various foundationmaterials.

3 -4. Foundation Deformation. -Accurateknowledge of the modulus of deformation ofthe foundation of a gravity dam is required to:

( 1) Determine the extent of relativedeformation between locations where physicalproperties vary along the foundation in thevertical or horizontal directions.

(2) Determine the stress concentrations inthe dam or foundation due to local lowmodulus regions adjacent to or below the dam.

(3) Determine the stress distribution to be

used in detailed stability studies.The foundation investigation should provide

information related to or giving deformationmoduli and elastic moduli. (Deformationmodulus is the ratio of stress to elastic plusinelastic strain. Elastic modulus is the ratio ofstress to elastic strain.) The informationi n c l u d e s e l a s t i c m o d u l u s o f d r i l l c o r especimens, elastic modulus and deformationmodulus from in situ jacking tests, deformationmodulus of fault or shear zone material, andlogs of the jointing occurring in recovered drillcores. Knowledge of the variation in materialsand their relative prevalence at variouslocations along the foundation is provided bythe logs of drill holes and by any tunnels in thefoundation.

When the composition of the foundation isnearly uniform over the extent of the damcontact, has a regular jointing pattern, and isf r e e o f l o w m o d u l u s s e a m s , the threeconditions listed above do not exist and thusan accurate deformation modulus is notrequired. An estimate based on reduction ofthe elastic modulus of drill core specimens willsuffice. However, when a variation of materials,an irregular jointing pattern, and fault andshear zones exist, the deformation moduli ofeach type of material in the foundation will berequired for design. The analysis of theinteraction of the dam and foundation may beaccomplished by using finite element analysis.

The moduli values are determined bylaboratory or in situ testing, and if necessaryare modified to account for factors notincluded in the initial testing. The modificationto the modulus value of rock may bedetermined according to the rock quality index[3] or joint shear index [4]. Modification ofthe moduli values for shear or fault zonematerial may be required if the geometry of


later for the condition of an existing joint.Also, it may be very difficult to differentiatebetween cohesive and friction resistance formaterials other than intact rock.

In the case of an existing joint in rock, theshear strength is derived basically from slidingfriction and usually does not vary linearly withthe normal load. Therefore, the shear resistanceshould be represented by a curve of shearresistance versus normal load, as shown by thecurve OA in figure 3-l. If a straight line? BC,had been used, it would have given values ofshear resistance too high where it is above thecurve OA, and values too low where it is below.A linear variation may be used to represent aportion of the curve. Thus, the line DE can beused to determine the shear resistance foractual normal loads between Nr and Nzwithout significant error. However, for normalloads below N1 or above Nz , its use would givea shear resistance which is too high and thedesign would therefore be unsafe.

Other potential sliding planes, such as shearzones and faults, should be checked todetermine if the shear resistance should belinear or curvilinear. As with the jointed rock, alinear variation can be assumed for a limitedrange of normal loads if tests on specimensverify this type of variation for that range ofnormal loads.

The specimens tested in the laboratory or insitu are usually small with respect to the planesanalyzed in design. Therefore, the scale effectshould be carefully considered in determiningthe shear resistance to be used in design.

the zone is quite variable. An example of sucha modification is given in reference [ 4 1 .

3-5. Foundation Strength. -Compressivestrength of the foundation rock can be animportant factor in determining thicknessrequirements for a dam at its contact with thefoundation. Where the foundation rock isnonhomogeneous, a sufficient number of tests,as determined by the designer, should be madeto obtain compressive strength values for eachtype of rock in the loaded part of thefoundation.

A determination of tensile strength of therock is seldom required because discontinuitiessuch as unhealed joints and shear seams cannottransmit tensile stress within the foundation.

Resistance to shear within the foundationand between the dam and its foundation resultsfrom the cohesion and internal frictioninhe ren t i n the materials and at theconcrete-rock contact. These properties arefound from laboratory and in situ testing asdiscussed in sections 2-24 and 2-25. However,when test data are not available, values of theproperties may be estimated (subject to thelimitations discussed below) from publisheddata [2, 5, 61 and from tests on similarmaterials.

The results of laboratory triaxial and directshear tests, as well as in situ shear tests, willtypically be reported in the form of theCoulomb equation,

R=CA+Ntan@ (1)

where:

R = shear resistance,C = unit cohesion,A = area of section,N = effective normal force, and

tan @ = tangent of angle of friction,

which defines a linear relationship betweenshear resistance and normal load. Experiencehas shown that such a representation of shearresistance is usually realistic for most intactrock. For other materials, the relationship maynot be linear and a curve of shear strengthversus normal load should be used as discussed

V I1 I0 NI ‘42

N O R M A L L O A D (Nl

Figure 3-I. Shear resistance on an existing joint inrock.-288-D-2957


Among the factors to be considered indetermining the scale effect at each site are thefollowing:

( 1) Comparisons of tests of various sizes.(2) Geological variations along the potential

sliding planes.(3) Current research on scale effect.When a foundation is nonhomogeneous, the

potential sliding surface may be made up ofdifferent materials. The total resistance can bedetermined by adding the shear resistancesoffered by the various materials, as shown inthe following equation:

R, =R1 +R, +R, +.*-..R, (2)

where :

R, = total resistance, andR, , R, , R3, etc. = resistance offered by

the various materials.

When determining the shear resistanceoffered by the various materials, the effect ofdeformation should be considered. The shearresistance given by the Coulomb equation orthe curves of shear resistance versus normalload are usually the maximum for the testspecimen without regard to deformation. Somematerials obtain their maximum resistance withless deformation than others. For example,intact rock will not deform as much as a jointin rock or a sheared zone when maximum shearresistance of the material is reached.

The following example illustrates theimportance o f i n c l u d i n g t h e e f f e c t o fdeflection in determining the resistance offeredb y e a c h m a t e r i a l i n nonhomogeneousfoundations. This example has only 5 percentintact rock to emphasize that a small quantityof high-strength intact rock can make asignificant contribution to the total resistance.Such a situation is not normally encounteredbut can and has occurred.

Example: Determine the shear resistance ona potential sliding plane which is 1,000 squarefeet in area for the following conditions:

(1) Normal load, N = 10,000 kips.(2) The plane is 5 percent intact rock (A, =

50 square feet), 20 percent sheared material

25

(A, = 200 square feet), and 75 percent joint(Ai = 750 square feet).

(3) The values of cohesion and tan @ foreach material are as follows:

(4) The normal load on each material is:

Intact rock N, = 2,000 kipsSheared material N, = 1,000 kipsJoint Ni = 7,000 kips

The shear resistance is determined as follows:

R r = 2oo,ooo(50) + 1 8(2 000)1,000 . ’

= 13,600 kips

R s = 3’ooo(200) + 0 3( 11.000 . ’

000)

= 900 kips

Ri =w+ 0.75(7,000)3

= 5,250 kips

R, = 13,600 + 900 + 5,250

= 19,750 kips

For this example, an analysis of the shearstrength versus deflection shows that themovement of the intact rock at failure is 0.02inch. At this deflection the sheared materialwill have developed only 50 percent of itss t r eng th and the j o in t on ly 5 percent.Therefore, the actual developed strength at thetime the rock would fail is:

13,600 + 900 x 0.50 + 5,250 x 0.05= 14,312 kips.

26

This is about 70 percent of the maximum shearstrength computed above without consideringdeformation.

In some situations, the potential slidingsurface comprised of several different materialsmay exhibit greater total shear resistance afterany intact materials are sheared. For example,if the cohesive strength of intact rock is lowbut the normal load acting on the total surfaceis large, the sliding friction strength of thecombined materials can exceed the shearresistance determined before the rock issheared. For this reason, a second analysisshould be performed which considers only thesliding friction strength of the surfaces.

3-6. Foundation Permeability. -The designof a gravity dam and its foundation requires aknowledge of the hydrostatic pressuredistribution throughout the foundation. Theexit gradient for shear zone materials that


surface near the downstream toe of the damshould also be determined to check against thepossibility of piping (see sec. 6-4).

The laboratory values for permeability ofsample specimens are applicable only to thatportion or portions of the foundation whichthey represent. The permeability is controlledby a network of geological features such asj o i n t s , f a u l t s , a n d s h e a r z o n e s . T h epermeability of the geologic features can bedetermined best by in situ testing. Pressuredistributions for design should include theappropriate influences of the permeability andextent of all the foundation materials andgeologic features. Such a determination may bemade by several methods including two- andthree-dimensional physical models, two- andthree-dimensional finite element models, andelectric analogs.

D. LOADS

3-7. Reservoir and Tailwater. -Reservoir andtailwater loads to be applied to the structureare obtained from reservoir operation studiesand tailwater curves. These studies are based onoperating and hydrologic data such as reservoircapaci ty, storage allocations, streamflowrecords, flood hydrographs, and reservoirreleases for all purposes. A design reservoir canbe derived from these operation studies whichwill reflect a normal high water surface.

The hydrostatic pressure at any point on thedam is equal to the hydraulic head at thatpoint times the unit weight of water (62.4 lb.per cu. ft.).

The normal design reservoir elevation is thehighest elevation that water is normally stored.It is the Top of Joint Use Capacity, if joint usecapacity is included. If not, it is the Top ofActive Conservation Capacity. For definitionsof reservoir capacities, see section 2-9.

Maximum design reservoir elevation is thehighest anticipated water surface elevation andusually occurs in conjunction with the routingof t he in f low des ign f lood th rough thereservoir.

T h e t a i l w a t e r e l e v a t i o n u s e d w i t h aparticular reservoir elevation should be theminimum that can be expected to occur withthat reservoir elevation.

3-8. Temperature. -Volumetric changes dueto temperature change [7] will transfer loadacross transverse contraction joints if the jointsare grouted. These horizontal thrusts will thenresult in twist effects and in additional loadingof the abutments. These effects may or maynot be beneficial from a stress and stabilitystandpoint and should be investigated using the“Trial-Load Twist Method of Analysis”discussed in chapter IV (sets. 4-25 through4-29).

When making studies to determine concretetemperature loads, varying weather conditionscan be applied. Similarly, a widely fluctuatingreservoir water surface will affect the concretetemperatures. In determining temperatureloads, t h e f o l l o w i n g conditions andtemperatures are used:

( 1) Usual weather conditions.-Thecombination of daily air temperatures, al-week cycle representative of the cold


(hot) periods associated with barometricpressure changes, and the mean monthlyair temperatures. This condition willaccount for temperatures which arehalfway between the mean monthly airtemperatures and the minimum(maximum) recorded air temperatures atthe site.

(2) Usual concrete temperatures.-Theaverage concrete temperatures betweenthe upstream and downstream faces whichwill result from usual air temperatures,reservoir water temperatures associatedwith the design reservoir operation, andsolar radiation.

Secondary strcsscs c a n o c c u r a r o u n dopenings and at the faces of the dam due totemperature differentials. These temperaturedifferentials are caused by differences in thetemperature of the concrete surfaces due toambient air and water temperature variations,solar radiation, temperature of air or water inopenings, and temperature of the concretemass. These secondary stresses are usuallylocalized near the faces of the dam and mayproduce cracks which give an unsightlyappearance. If stress concentrations occuraround openings, cracking could lead toprogressive deterioration. Openings filled withwater, such as outlets, are of particular concernsince cracks, once formed, would fill withwater which could increase the uplift or porepressure within the dam.

3 - 9 . I n t e r n a l H y d r o s t a t i c Pressures.-Hydrostatic pressures from reservoir water andtailwater act on the dam and occur within thedam and foundation as internal pressures in thep o r e s , c r a c k s , j o i n t s , a n d s e a m s . T h edistribution of pressure through a horizontalsection of the dam is assumed to vary linearlyfrom full hydrostatic head at the upstream faceto zero or tailwater pressure at the downstreamface, provided the dam has no drains or unlinedwater passages. When formed drains areconstructed, the internal pressure should bemodified in accordance with the size, location,and spacing of the drains. Large unlinedpenstock transitions or other large openings indams will require special modification ofinternal pressure patterns. Pressure distribution

27

in the foundation may be modified by theground water in the general area.

The internal pressure distribution throughthe foundation is dependent on drain size,depth, location, and spacing; on rock porosity,jointing, faulting; and to some extent on thegrout curtain. Determination of such pressuredistribution can be made from flow netscomputed by several methods including two-and three-dimensional physical models, two-and three-dimensional finite element models,and electric analogs. Such a flow net, modifiedby effects of drainage and grouting curtains,should be used to determine internal pressuredistribution. However, the jointing, faulting,variable permeability, and other geologicfeatures which may further modify the flownet should be given full consideration.

The component of internal hydrostaticpressure acting t o r e d u c e t h e v e r t i c a lcompressive stresses in the concrete on ahorizontal section through the dam or at itsbase is referred to as uplift or pore pressure.Records are kept of the pore pressuremeasurements in most Bureau of Reclamationdams. Figure 3-2 illustrates actual measureduplift pressures at the concrete-rock contact ascompared with design assumptions for ShastaDam.

Laboratory tests indicate that for practicalpurposes pore pressures act over 100 percent ofthe area of any section through the concrete.Because of possible penetration of water alongconstruction joints, cracks, and the foundationc o n t a c t , i n t e r n a l p r e s s u r e s s h o u l d b econsidered to act throughout the dam. It isassumed that the pressures are not affected byearthquake acceleration because of thetransitory nature of such accelerations.

Internal hydrostatic pressures should be usedfor analyses of the foundation, the dam, andoverall stability of the dam at its contact withthe foundation.

For preliminary design purposes, upliftpressure distribution in a gravity dam isassumed to have an intensity at the line ofdrains that exceeds the tailwater pressure byone-third the differential between headwaterand tailwater levels. The pressure gradient isthen extended to headwater and tailwater

28

8OC

7oc

600

500


W.S. 4-11-72 E l . 1 0 5 6 . 5 0

Uplift pressure measured an 4 -11-72.- -- Assumed uplift pressure based on a gradient varying

from full reservoir pressure at the upstream faceof the dam to one- third the differential pressurebetween the faces plus normal tailwater at theline of drains, and from there to normaltailwater at the downstream face.

Uplift measuring pipes E

a‘sr’

dra ins ZG

Avg. foundation El. 531.16 A

\

Figure 32. Comparison of assumed and uplift pressures on a gravity dam (Shasta Dam in California).-288-D-2959

levels, respectively, in straight lines. If there isno tailwater, the downstream end of a similarpressure diagram is zero at the downstreamface. The pressure is assumed to act over 100percent of the area.

In the final design for a dam and itsfoundation, the internal pressures within thefoundation rock and at the contact with thedam will depend on the location, depth, andspacing of drains as well as on the joints,shears, and other geologic structures in therock. Internal pressures within the dam dependon the location and spacing of the drains.These internal hydrostatic pressures should be

determined from flow nets computed byelectric analogy analysis, three-dimensionalfinite element analysis, or other comparablemeans.

3-10. Dead Load.-The magnitude of deadload is considered equal to the weight ofconcrete plus appurtenances such as gates andbridges. For preliminary design the unit weightof concrete is assumed to be 150 pounds percubic foot. For final design the unit weight ofconcrete should be determined by laboratorytests.

3-11. Ice. -Existing design information onice pressure is inadequate and somewhat


approximate. Good analytical procedures existfor computing ice pressures, but the accuracyof results is dependent upon certain physicalda t a wh ich mus t come f rom f i e ld andlaboratory tests [8].

Ice pressure is created by thermal expansionof the ice and by wind drag. Pressures causedby thermal expansion are dependent on thetemperature rise of the ice, the thickness of theice sheet, the coefficient of expansion, theelastic modulus, and the strength of the ice.Wind drag is dependent on the size and shapeof the exposed area, the roughness of thesurface, and the direction and velocity of thewind. Ice loads are usually transitory. Not alldams will be subjected to ice pressure, and thedesigner should decide after consideration ofthe above factors whether an allowance for icepressure i s a p p r o p r i a t e . T h e m e t h o d o fMonfore and Taylor [9] may be used todetermine the anticipated ice pressure. Anacceptable estimate of ice load to be expectedon the face of a structure may be taken as10,000 pounds per linear foot of contactbetween the ice and the dam, for an assumedice depth of 2 feet or more when basic data arenot available to compute pressures.

3-12. Sift.-Not all dams will be subjected tosilt pressure, and the designer should considerall available hydrologic data before decidingwhether an allowance for silt pressure isnecessary. Horizontal silt pressure is assumedto be equivalent to that of a fluid weighing 85pounds per cubic foot. Vertical silt pressure isdetermined as if silt were a soil having a wetdensity of 120 pounds per cubic foot, themagnitude of pressure varying directly withdepth. These values include the effects of waterwithin the silt.

3- 13. Earthquake. -Concrete dams areelastic structures which may be excited tor e s o n a n c e w h e n subjected to seismicdisturbances. Two steps are necessary to obtainloading on a concrete dam due to such adisturbance. First, an estimate of magnitudeand location must be made of the earthquaketo which the dam will be subjected and theresulting rock motions at the site determined.The second step is the analysis of the responseof the dam to the earthquake by either the

29

response spectrum or time-history method.Most earthquakes are caused by crustal

movements of the earth along faults. Geologicexaminations of the area should be made tolocate any faults, determine how recently theyhave been active, and estimate the probablelength of fault. Seismological records shouldalso be studied to determine the magnitude andlocation of any earthquakes recorded in thearea. Based on these geological and historicaldata, hypothetical earthquakes usually ofmagnitudes greater than the historical eventsare estimated for any active faults in the area.These earthquakes are considered to be themost severe earthquakes associated with thefaults and are assumed to occur at the point onthe fault closest to the site. This defines theMaximum Credible Earthquake and its locationin terms of Richter Magnitude M and distanced to the causative fault.

Methods of determining a design earthquakethat represents an operating-basis event areunder development . These methods shouldconsider historical records to obtain frequencyof occurrence versus magnitude, useful life ofthe structure, and a statistical approach todetermine probable occurrence of variousmagnitude earthquakes during the life of thestructure. When future developments producesuch methods, suitable safety factors will beincluded in the criteria.

The necessary parameters to be determinedat the site using attenuation methods [ 101 areacceleration, predominant period, duration ofshaking, and frequency content.

Attenuation from the fault to the site isgenerally included directly in the formulas usedto compute the basic data for response spectra.A response spectrum graphically represents themaximum response of a structure with onedegree of freedom having a specific dampingand subjected to a particular excitation. Aresponse spectrum should be determined foreach magnitude-distance relationship by eachof three methods as described in appendix D ofreference [ 101. The design response spectrumof a structure at a site is the composite of theabove spectra.

Time-history analyses of a dam are sometimesdesirable. The required accelerograms may be


produced by appropriate adjustment of existing recorded accelerograms.or artificially generated accelerograms. The The analytical methods used to computepreviously mentioned parameters are necessary material frequencies, mode shapes, andconsiderations in the development of synthetic structural response are discussed in chapter IV.accelerograms or in the adjustment of actual

E. LOADING COMBINATIONS

3-14. General.-Designs should be based onthe most adverse combination of probable loadconditions, but should include only those loadshaving reasonable probability of simultaneousoccurrence. Combinations of transitory loads,each of which has only remote probability ofoccurrence at any given time, have negligibleprobability of simultaneous occurrence andshould not be considered as a reasonable basisfor design. Temperature loadings should beincluded when applicable (see sec. 3-8).

Gravity dams should be designed for theappropriate loading combinations whichfollow, using the safety factors prescribed insections 3-19 through 3-22.

3- 15. Usual Loading Combination. -(1) Normal design reservoir elevation, with

appropriate dead loads, uplift, silt, ice, andtailwater. If temperature loads are applicable,use minimum usual temperatures.

3- 16. Unusual and Extreme LoadingCombinations. -

(1) Unusual Loading Combination.-Maxi-

m u m d e s i g n r e s e r v o i r e l e v a t i o n , w i t happropriate dead loads, uplift, silt, minimumt e m p e r a t u r e s o c c u r r i n g a t t h a t t i m e i fapplicable, and tailwater.

( 2 ) E x t r e m e L o a d i n g Combination.-Normal design reservoir elevation, withappropriate dead loads, uplift, silt, ice, usualminimum temperatures if applicable, andtailwater, plus the effects of the MaximumCredible Earthquake.

3-l 7. Other Studies and Investigations. -(1) Maximum design reservoir elevation,

with appropriate dead loads, silt, minimumt e m p e r a t u r e o c c u r r i n g a t t h a t t i m e i fapplicable, and tailwater, plus uplift withdrains inoperative.

(2) Dead load.(3) Any of the above loading combinations

for foundation stability.(4) Any other loading combination which,

in the designer’s opinion, should be analyzedfor a particular dam.

F. FACTORS OF SAFETY

3-18. General.-All design loads should bechosen to represent as nearly as can bedetermined the actual loads which will act onthe structure during operation. Methods ofdetermining load-resisting capacity of the damshould be the most accurate available. Alluncertainties regarding loads or load-carryingcapacity must be resolved as far as practicableb y f i e l d o r l a b o r a t o r y t e s t s , t h o r o u g hexploration and inspection of the foundation,

good concrete control, and good constructionpractices. On this basis, the factor of safety willbe as accurate an evaluation as possible of thecapacity of the structure to resist applied loads.All safety factors listed are minimum values.

Dams, like other important structures,should be frequently inspected. In particular,where uncertainties exist regarding such factorsas loads, resisting capacity, or characteristics ofthe foundation, it is expected that adequate


observations and measurements will be made ofthe structural behavior of the dam and itsfoundation to assure that the structure is at alltimes behaving as designed.

The factors of safety for the dam are basedon the “Gravity Method of Stress and StabilityAnalysis” (sets. 4-5 through 4-10). Althoughlower safety factors may be permitted forlimited local areas within the foundation,overall safety factors for the dam and itsfoundation (after beneficiation) should meetthe requirements for the loading combinationbeing analyzed. Somewhat higher safety factorsshould be used for foundation studies becauseof the greater amount of uncertainty involvedin assessing foundation load resisting capacity.For other loading combinations where safetyfactors are not specified, the designer isresponsible for selection of safety factorsconsistent with those for loading combinationcategories discussed in sections 3-14 through3-17.

3-19. Allowable .Stresses.-The maximumallowable compressive stress in the concrete forthe Usual Loading Combinations should be notgreater than the specified compressive strengthdivided by a safety factor of 3.0. Under noc i r c u m s t a n c e s s h o u l d t h e a l l o w a b l ecompressive stress exceed 1,500 pounds persquare inch for Usual Loading Combinations.In the case of Unusual Loading Combinations,the maximum allowable compressive stressshould be determined by dividing the specifiedcompressive strength by a safety factor of 2.0.The maximum allowable compressive stress forthe Unusual Loading Combinations should, inno case, exceed 2,250 pounds per square inch.The allowable compressive stress for theEx t r eme Load ing Combina t i on sha l l bedetermined in the same way using a factor ofsafety greater than 1 .O.

In order not to exceed the allowable tensilestress, the minimum allowable compressivestress computed without internal hydrostaticpressure should be determined from thefollowing expression, which takes into accountthe tensile strength of the concrete at liftsurfaces:

Uz n=pwh-$

31

(3)where :

%I = minimum allowable compressivestress at the upstream face,

p = a reduction factor to account fordrains,

w = unit weight of water,h = depth below reservoir surface,ft = tensile strength of concrete at

lift surfaces, ands = safety factor.

All parameters must be specified usingconsistent units.

The value of p should be 1 .O if drains are notpresent and 0.4 if drains are used. The value ofs should be 3.0 for Usual and 2.0 for UnusualLoading Combinations. The allowable value ofu for the usual loading combination shouldn%er be less than zero. Cracking should beassumed to occur if the stress at the upstreamface is less than uZu computed from the aboveequation with a value for s of 1.0 for theExtreme Loading Combination. The structuremay be deemed safe for this loading if, aftercracking has been included, stresses in thestructure do not exceed specified strengths andsliding stability is maintained.

The maximum allowable compressive stressin the foundation shall be less than thecompressive strength of the foundationmaterial divided by safety factors of 4.0, 2.7,and 1.3 for the Usual, Unusual, and ExtremeLoading Combinations, respectively.

3-20. Sliding Stability. -The shear-frictionfactor of safety, Q, as computed using equation(4), is a measure of the safety against sliding orshearing on any section. It applies to anysection of the structure or its contact with thefoundation. For gravity dams the shear-frictionfactor of safety should be greater than 3.0 forUsual Loading Combinations, 2.0 for UnusualLoading Combinations, and 1.0 for theExtreme Loading Combination.

The shear-friction factor of safety, Q, is theratio of resisting to driving forces as computedby the expression:


Q=CA+(XN+XU)tan@

ZV (4)

where :

C = unit cohesion,A = area of the section considered,

ZN = summation of normal forces,2 U = summation of uplift forces,

tan f$ = coefficient of internal friction,and

x I’ = summation of shear forces.

All parameters must be specified usingconsistent units a n d w i t h p r o p e r signsaccording to the convention shown in figure4-l.

Values of cohesion and internal frictionshould be determined by actual tests of thef o u n d a t i o n m a t e r i a l s a n d t h e c o n c r e t eproposed for use in the dam.

3-21. Cracking. -Cracking is assumed tooccur in a gravity dam if the vertical normalstress (computed without uplift) at theupstream face is less than the minimumrequired stress as computed by equation (3).Such cracking is not permitted in new designsexcept for the Extreme Loading Combination.However, for existing dams, cracking may bepermitted for the condition of maximum watersurface with drains inoperative in addition tothe Extreme Loading Combination.

When checking the stability of an existingdam for the loading condition of maximumwater surface with drains inoperative, the uplift(or internal hydrostatic) pressure is assumed tovary linearly from full reservoir level at theupstream face to tailwater level at thedownstream face. If cracking occurs thefoundation pressure diagram is assumed to beas shown in figure 3-3(D). The foundationp r e s s u r e d i a g r a m i s d e t e r m i n e d b y t h efollowing procedure:

(1) A horizontal crack is assumed to extendfrom the upstream face to a point where thevertical stress is equal to the uplift pressure atthe upstream face, point 4 on figure 3-3(D).

(2) From figures 3-3(A) and (D), takingmoments about the center of gravity of the

base, the following equations are obtained:

and

T1 =3 -$d( >

(6)

where :

e’ = eccentricity of the stress diagramafter cracking,

IZM = summation of moments of allforces,

Z W = summation of vertical forces,A 3 = internal hydrostatic pressure at the

upstream face,T = thickness of section, and

T, = remaining untracked portion of thethickness.

Therefore the stress at the downstream face,B, is:

B7=2(cW-A3T) +A3 (7)

Because of the rapidly cycling changes instress during earthquakes, it should be assumedthat the internal hydrostatic pressures are zeroin the cracks caused by the extreme loading.Equations (5) and (7) should be revised toaccount for the zero internal hydrostaticpressure in the crack. For these computations,T should be taken as the thickness of theuntracked portion shown as T1 in equations(6) and (7). The value of n should be theuplift pressure at the end of the crack in theuntracked portion and ZM should include themoment of the altered uplift pressures takenabout the center of gravity of the originalsection. The T in equation (6) is the fullthickness of the original section. The value ofT1 to be used as T in equation (5) must bee s t i m a t e d f o r t h e f i r s t c o m p u t a t i o n .Thereafter, for succeeding computations of e’,the value obtained for T1 in equation (6)should be used. Several cycles of computation

D E S I G N D A T A AND CRITERIA--Sec. 3-22 33

Reservoir w a t e r s u r f a c e - :

“l-l

c e n t e r o f grovlty o f8

(A) VERTICAL CROSS-SECTION

Al“-----\1,

(B) P R E S S U R E D I A G R A M W I T H O U T U P L I F T

:t.-ril-- 84

(C) UPLIFT PRESSURE DIAGRAM

T<-3

(D) COMBINED PRESSURE DIAGRAM

D I A G R A M S O F B A S E P R E S S U R E SA C T I N G O N A G R A V I T Y D A M

Figure 3-3. Foundation base pressures for a gravitydam.-288-D-25 10

using equations (5) and (6) may be required toobtain adequate agreement between the valueused for T in equation (5) and the value

computed for T1 in equation (6).The untracked area of the base is substituted

for A in equation (4). The section is consideredsatisfactory for any of these loading conditionsif the stress at the downstream face, fromequation (7), does not exceed the allowablestress, and the shear-friction factor of safety issufficient to ensure stability. A shear-frictionfactor of safety greater than 2.0 would becon sidered satisfactory for the UnusualLoading Combination and greater than 1.0 forthe Extreme Loading Combination.

A gravity dam should be considered safeagainst overturning if B5, the ordinate in figure3-3(D), is less than the allowable stresses in theconcrete and the foundation rock for theappropriate loading combinations.

3-22. Foundation Stability. Joints, shears,and faults which form identifiable blocks ofrock are often present in the foundation.Effects of such planes of weakness on thestability of the foundation should be carefullyevaluated. Methods of analysis for foundationstab il i tv under these circumstances arediscussed in section 4-50. The determination ofeffective shear resistance for such foundationconditions is given in detail in section 3-5.

The factor of safety against sliding failure ofthese foundation blocks, as determined by theshear-friction factor, Q, using equation (4),should be greater than 4.0 for the UsualLoading Combination, 2.7 for the UnusualLoading Combination, and 1.3 for the ExtremeLoading Combination. If the computed safetyfactor is less than required, foundationtreatment can be included to increase thesafety factor to the required value.

Treatment to accomplish specific stabilityobjectives such as prevention of differentialdisplacements (see sec. 4-51) or stressconcentrations due to bridging (see sec. 4-52)should be designed to produce the safety factorrequired for the loading combination beinganalyzed.

G. BIBLIOGRAPHY

3-23. Bibliography. -[ 1] “Concrete Manual,” Bureau of Reclamation, eighth

edition, 1975.

[2] “Properties of Mass Concrete in Bureau of ReclamationDams,” Concre te Labora to ry Repor t No . C-1009 ,Bureau of Reclamation, 1961.


[3] Stagg, K. G., and Zienkiewicz, 0. C., “Rock Mechanicsin Engineering Practice,” John Wiley & Sons, London,England, 1968.

[4] Von Thun, J . L. , and Tarbox, G. S. , “DeformationModuli Determined by Joint Shear Index and ShearCatalog,” Proceedings, International Symposium onRock Mechanics, Nancy, France, 197 1.

[S] “Physical Propert ies of Some Typical FoundationRocks,” Concrete Laboratory Report No. SP-39, Bureauof Reclamation, 1953.

[6] Link, Harald, “The Sliding Stability of Dams,” WaterPower-Part I, March 1969; Part II, April 1969; Part III,May 1969, London, England.

[7] Townsend, C. L., “Control of Cracking in Mass Concrete

Structures,” Engineering Monograph No. 34, Bureau ofReclamation, 1965.

[8] Monfore , G. E. , “Experimental Investigations by theBureau of Reclamation,” Trans. ASCE, vol. 119, 1954,p. 26.

[9] Monfore, G. E., and Taylor, F. W., “The Problem of anE x p a n d i n g I c e Sheet,” B u r e a u o f ReclamationMemorandum, March 18, 1948.

[lo] Boggs, H. L., Campbell, R. B., Klein, I. E., Kramer, R.W., McCafferty, R. M., and Roehm, L. H., “Methods forEstimating Design Earthquake Rock Motions,” Bureauof Reclamation, April 1972.

[ 111 “Design of Small Dams,” Bureau of Reclamation, secondedition, 1973.

<<Chapter IV

layout and Analysis

4-l. Introduction. -A brief discussion ofguidelines for making a gravity dam layout isgiven in sections 4-2 through 4-4. The layoutrepresents the initial step in the designprocedure for a new structure. After a layout iscompleted, a stress and stability analysis of thestructure must be made to determine the stressdistributions and magnitudes and the stabilityfactor. If the analytical results do not fallwithin the established allowable limits or thestress distributions are not satisfactory becauseof stress concentrations, modifications toimprove the design must be made by reshapingthe structure. The design of a gravity dam isaccomplished by making successive layouts,each one being progressively improved basedon the results of a stress analysis. It is difficultto discuss layouts without discussing analysisand vice versa, because each operation isessential to the other.

Stress analyses of gravity dams fall into twoclassifications-those analyses based on gravityaction and those based on the trial-loadmethod. (See also sec. 4-30.) The “GravityMethod of Analysis,” which is discussed inconsiderable detail in sections 4-5 through4-l 0, provides a two-dimensional solution forstraight gravity dams. The method is based onthe assumptions that a straight gravity dam iscomprised of a number of vertical elements,each of which carries its load to the foundationwithout any transfer of the load from or toadjacent vertical elements and that verticalstresses vary linearly. It is usually sufficient tocompute stresses and stability factors at thebase elevation and selected elevations above thebase for both a maximum overflow section anda maximum nonoverflow section. This method

of analysis is used for designing straight gravityc o n c r e t e d a m s i n w h i c h t h e t r a n s v e r s econtraction joints are neither keyed norgrouted.

The stress analysis of a straight gravity damin which the transverse contraction joints arekeyed, whether grouted or not, is athree-dimensional problem. One method usedby the Bureau is the “Trial-Load Method ofAnalysis” in which it is assumed that the damis comprised of three systems of elements eachoccupying the entire volume of the structureand independent of the others. These systemsare the vertical cantilevers, the horizontalbeams, and the twisted elements. The loads onthe dam are divided between these systems insuch a manner as to produce equal deflectionsand rotations at conjugate points.

The more recently developed “FiniteElement Method”, which can be used fortwo-dimensional studies to determine the stressdistributions and for the three-dimensionalstudies for grouted joints, is discussed insections 4-36 through 448. An example of itsuse is presented in appendix C.

Analytical methods of determining theresponse of gravity dams to earthquake groundaccelerations are presented in sections 4-3 1through 4-35. The response of a structure isdefined as its behavior as a result of anearthquake disturbance. The response is usuallyrepresented as a measure of the structure’sdisplacement acceleration or velocity. Eitherthe time variation of a particular response or itsmaximum value during the disturbance may beof interest. The determination of naturalfrequencies and mode shapes is a fundamentalpart of dynamic analysis. Dynamic analyses are

35

36

used in stress analysis methods to determineloadings for computing stresses due toearthquake.

A discussion of foundation analyses is givenin sections 4-49 through 4-52. A dam is nobetter than its foundation, and therefore anevaluation of the foundation behavior isnecessary to ensure a competent load-bearingsystem cons i s t i ng o f t he dam and thefoundation. Analytical methods are presentedto evaluate foundation stability and localoverstressing due to foundation deficiencies.

Certain special, rigorous methods of analysis,such as the “Slab Analogy Method” [ I] ’ and


“Lattice Analogy Method” [2], which may beused for the determination of nonlinear stressdistributions are included in lesser detail inappendix D along with photoelastic modelstudies.

(a) Level of Design, -The level of design fora gravity dam, whether appraisal, feasibility, orfinal, differs only by the level of investigationused to determine design data. Details of theselevels of investigation in the field are discussedin section 2-21. The levels of investigations inthe laboratory are usually dependent on thelevels of field investigations.

A. LAYOUT

4-2. Nonoverflow Section. -The shape ofthe max imum nonove r f low sec t ion i sd e t e r m i n e d b y t h e p r e s c r i b e d l o a d i n gconditions, the shear resistance of the rock,and the height of the maximum section. Theupstream face of a gravity dam is usually madevertical to concentrate the concrete weight atthe upstream face where it acts to overcomethe effects of the reservoir waterload. Exceptwhere additional thickness is required at thecrest, as discussed below, the downstream facewill usually have a uniform slope which isdetermined by both stress and stabili tyrequirements at the base. This slope will beadequate to meet the stress and stabil i tyrequirements at the higher elevations unless alarge opening is included in the dam. The crestthickness may be dictated by roadway or otheraccess requirements, but in any case it shouldbe adequate to withstand possible ice pressuresand the impact of floating objects. Whenadditional crest thickness is used, thedownstream face should be vertical from thedownstream edge of the crest to an intersectionwith the sloping downstream face.

A batter may be used on the lower part ofthe upstream face to increase the thickness atthe base to improve the sliding safety of thebase. However, unacceptable stresses maydevelop at the heel of the dam because of the


change in moment arm for the concrete weightabout the center of gravity of the base. If abatter is used, stresses and stability should bechecked where the batter intersects the verticalupstream face. The dam should be analyzed atany other changes in slope on either face.

4-3. Spillway Section. -The overflow orspillway section should be designed in a similarmanner to the nonoverflow section. The curvesdescribing the spillway crest and the junctionof the slope with the energy dissipator aredesigned to meet hydraulic requirementsdiscussed in chapter IX. The slope joining thesecurves should be tangent to each curve and, ifpracticable, parallel to the downstream slopeon the nonoverflow section. The spillwaysection should be checked for compliance withstress and stability requirements. An upstreambatter may be used on the spillway sectionunder the same conditions as for thenonoverflow section. Figure B-l in appendix Bis a typical layout drawing of a gravity damshowing a nonoverflow section, a typicalspillway section, a plan, and a profile.

4-4. Freeboard.-Current Bureau practice isto allow the maximum water surface elevationto be coincident with the top of thenonoverflow section of the dam, and toconsider that the standard 3.5-foot-high solidparapet acts as a freeboard. Exceptional casesmay point to a need for more freeboard,depending on the anticipated wave height.

LAYOUT AND ANALYSIS--Sec. 4-5

B. THE GRAVITY METHOD OF STRESS AND STABILITY ANALYSIS

37

4-5. Description and Use. -The “GravityMethod of Stress and Stability Analysis” isused a great deal for preliminary studies ofgravity dams, depending on the phase of designand the information required. The gravitymethod is also used for final designs of straightg r a v i t y d a m s i n w h i c h t h e t r a n s v e r s econtraction joints are neither keyed norgrouted. For dams in which the transversejoints are keyed and grouted, the “Trial-LoadTwist Analsysis” including the beam structureshould be used. If the joints are keyed but leftungrouted, the “Trial-Load Twist Analysis”should omit the beam structure.

The gravity method provides an approximatemeans for determination of stresses in a crosssection of a gravity dam. It is applicable to thegeneral case of a gravity section with a verticalupstream face and with a constant downstreamslope and to situations where there is a variableslope on either or both faces. Equations aregiven with standard forms and illustrationsshowing calculation of normal and shearstresses on horizontal planes, normal and shearstresses on vertical planes, and principals t resses , for both empty-reservoir andfull-reservoir conditions, including the effectsof tailwater and earthquake shock. Upliftpressures on a horizontal section are usuallynot included with the contact pressures in thecomputation of stresses, and are consideredseparately in the computation of stabilityfat tors.

The formulas shown for calculating stressesare based on the assumption of a trapezoidaldistribution of vertical stress and a parabolicdistribution of horizontal shear stress onhorizontal planes. These formulas provide adirect method of calculating stresses at anypoint within the boundaries of a transversesection of a gravity dam. The assumptions aresubstantially correct, except for horizontalplanes near the base of the dam where theeffects of foundation yielding are reflected inthe stress distributions. At these locations thestress changes which occur due to foundationyielding are usually small in dams of low ormedium height but they may be important in

high dams. Stresses near the base of a highmasonry dam should therefore be checked bythe “ F i n i t e E l e m e n t M e t h o d ” o r o t h e rcomparable methods of analysis.

The analysis of overflow sections presents noadded difficulties. Usually, the dynamic effectof overflowing water is negligible and anyadditional head above the top of the sectioncan be included as an additional vertical loadon the dam. In some cases some increase inhorizontal load may be justified for impact. Anexample of the gravity method of analysis isgiven in appendix A.

4-6. Assumptions. -Design criteria are givenin chapter III. However, those assumptionspeculiar to the gravity analysis are listed below:

( 1 ) The concrete in the dam is ahomogeneous, isotropic, and uniformly elasticmaterial.

(2) There are no differential movementswhich occur at the damsite due to waterloadson the reservoir walls and floors.

(3) All loads are carried by the gravityaction of vertical, parallel-side cantileverswhich receive no support from the adjacentelements on either side.

(4) Unit vertical pressures, or normalstresses on horizontal planes, vary uniformly asa straight line from the upstream face to thedownstream face.

(5) Horizontal shear stresses have aparabolic variation across horizontal planesfrom the upstream face to the downstream faceof the dam.

4-7. Notations for Normal ReservoirLoadirzg.-Symbols and definitions for normalreservoir loading are given below. This loadingincludes full-reservoir load and usual tailwaterloads on the dam, as shown on figure 4-l. The“section” referred to is one formed by ah o r i z o n t a l p l a n e t h r o u g h t h e c a n t i l e v e relement, except when otherwise specified.

Properties and Dimensions.

0 = origin of coordinates, at down-stream edge of section.


Pos i t i ve Shears

<+

tyz JOE z1;ZY Y

R e s e r v o i r W a t e r Surface---‘+_ _ _ _- I +l-

Posi t i ve Forces and Moments

Y+3 +

_ I \- \

k----L--&-dy --t--1- ,

a!

I - B a s e o f s e c t i o nZ

(CI) V E R T I C A L C R O S S S E C T I O N

Ib) H O R I Z O N T A L C R O S S S E C T I O N

Figure 4-1. Cross section of a parallel-side cantilever showing usual loadingcombination.-DS2-2(l)

LAYOUT AND ANALYSIS-Sec. 4-8 39

Q, = angle between face of elementand the vertical.

T = horizontal distance from up-stream edge to downstreamedge of section.

c = horizontal distance from centerof gravity of section toeither upstream or down-stream edge, equal to T/2.

A = area of section, equal to T.I= moment of inertia of section

about center of gravity,equal to T3 / 12.

gravity. It is equal toM, +M, +M; +MP +M;. Apositive moment producescompression on the section atthe upstream face. Allpositive normal stresses arecompressive.

U = total uplift force on horizontalsection.

P o s i t i v e h o r i z o n t a l f o r c e s a c t i n t h eupstream direction.

Stresses.% = unit weight of concrete or

masonry.o = unit weight of water.

h or h’ = vertical distance from reservoiror tailwater surface,respectively, to section.

p or p’ = reservoir water or tailwaterpressure, respectively, atsection. It is equal towh or wh’.

% = normal stress on horizontalplane.

uY = normal stress on vertical plane.

rzY = ryz = shear stress on vertical orhorizontal plane. A positiveshear stress is shown by thesketch in the upper left offigure 4- 1.

a,a,,a,,b,bl,b2,c,,c2,d2=constants.Forces and Moments.

WC = dead-load weight above base ofsection under consideration.

MC = moment of W, about center ofgravity of section.

W, or Wk = vertical component of reservoiror tailwater load, respectively,on face above section.

M, or Mk = moment of W, or Wh aboutcenter of gravity of section.

V or V” = horizontal component of reservoiror tailwater load, respectively,on face above section. This

OP 1 = first principal stress.

OP2 = second principal stress.

@P 1 = angle between up 1 and thevertical. It is positive in aclockwise direction.

Subscripts.

= upstream face.1 = downstream face.w = vertical water component.p = horizontal water component.

4 - 8 . N o t a t i o n s f o r H o r i z o n t a lEarthquake. -The hydrodynamic pressures dueto horizontal rock motions from earthquakesare computed using the method introduced insection 4-3 1. The notation is as follows:

oh2is equal to-2MP or ML: = moment of V or V’ about center

of gravity of section, equal tooh3 w (hy3-Or-z-.6

c W = resultant vertical force above sec-tion, equal to WC + W, + Wk.

C V = resultant horizontal force abovesection, equal to V + V’.

ZM = resultant moment of forces

ps = pressure normal to face.-(y = horizontal earthquake acceleration ,

acceleration of gravityvaries by elevation as computedin section 4-33.

z = depth of reservoir at sectionabove section about center of being studied.


to produce an acceleration of the mass of thedam and water in direct proportion to thevalue of (Y. This is equivalent to increasing ordecreasing the density of concrete and water,depending on direction of shock.

4-9. Forces and Moments Acting onCantilever Element. -Forces acting on thecantilever element, including uplift, are shownfor normal loading conditions on figure 4-l.Reservoir and tailwater pressure diagrams areshown for the portion of the element above thehorizontal cross section 0 Y. Positive forces,moments, and shears are indicated by thedirectional arrows.

Hydrodynamic and concrete inertia forcesa c t i n g o n t h e c a n t i l e v e r e l e m e n t f o r ahorizontal earthquake shock are in addition tothose forces shown on figure 4-l. The forcesare negative for a foundation accelerationacting in an upstream direction and positive fora f o u n d a t i o n a c c e l e r a t i o n a c t i n g i n adownstream direction.

Forces and moments for static loads areeasi ly c o m p u t e d f o r e a c h s e c t i o n b ydetermining areas and moment arms of thetriangular pressure diagrams and the area andeccentricity of vertical sections. However, toevaluate the quantities VpE, ViE, IV,, , andWhE for hydrodynamic effects of earthquakeshock, it is necessary to use the procedureoutlined in sections 4-3 1 through 4-35.

4-10. Stress and Stability Equations. -Asummary o f t h e e q u a t i o n s for stressescomputed by the gravity method is given onfigures 4-2 and 4-3. These equations includethose for normal stresses on horizontal planes,shear stresses on horizontal and vertical planes,normal stresses on vertical planes, and directionand magnitude of principal stresses, for anypoint within the boundaries of the cantileverelement. In the equations of figure 4-3, termsthat are due to earthquake are preceded by thealgebraic signs, plus or minus (2). The correctsign to use is indicated by accompanying notes.

Effects of earthquake shocks on stresses maybe excluded merely by omitting the termspreceded by the plus or minus (+) signs fromthe equations, which results in the correctequations for computing stresses for normalloading conditions.

h = vertical distance from thereservoir surface to theelevation in question.

C, = a dimensionless pressurecoefficient obtained fromfigure 4- 18.

wWE Or whE = change in vertical componentof reservoir water load ortailwater load on face abovesection due to horizontalearthquake loads.

MWE orMbE =momentof Ww, or WhEabout center of gravity ofsection.

V, = horizontal inertia force ofconcrete weight abovesection.

ME = moment of V, about centerof gravity of section.

vpE Or v;E = change in horizontal compo-nent of reservoir ortailwater load on face abovesection due to horizontalearthquake loads.

M pE OrM;E = moment Of vpE Or I$E aboutcenter of gravity ofsection.

Z W = resultant vertical force abovesection, equal tow,+w,+w;*WW E ’ wi’E.

2 V’= resultant horizontal forceabove section, equal toI/+ v’f v,f vpE f v;E.

CM = resultant moment of forcesabove horizontal sectionabout center of gravity.It is equal to M, + M,+Md+M,+Mi*ME*MWE +M iJE f”pE*MdE.

The algebraic signs of the terms with subscriptE in the earthquake equations for C W, C I’, andEM depend upon the direction assumed for thehorizontal earthquake acceleration of thefoundation.

No notation is given for vertical earthquakeshock. A vertical earthquake shock is assumed

LAYOUT AND ANALYSIS-Sec. 4-10

DERIVATION OF STRESS FORMULAE

(HORIZONTAL E A R T H Q U A K E U P S T R E A M )

From F i g u r e o

T o molntoin r o t a t i o n a l e q u i l i b r i u m a b o u t A .

(1ZYU dy)k = (r2 yzudz) +

Tzyu = 1 y z u

T o m o i n t o i n vertical e q u i l i b r i u m ,

(P+P)E)dy-ozudy -fyzudz = 0

2 = ton+”

lyzu = 1 zyu = - [uzU - p - PE] tonhJ

F r o m F i g u r e bT o m o i n t a i n r o t o t i o n o l e q u i l i b r i u m about B,

(-Tzyody)+ =(-ryzodz)+-

I[- ZYD = TyzD

T o m o i n t o i n v e r t i c a l e q u i l i b r i u m ,

(P’-p;)dy - 4ody -( -Tyzo)dz = 0

TyzDdZ = OZD dy - ( P ’ - P ; ) dy

TyzD = bZD- (P’- P;)] d yd z

--r yZO=~~y0=[~~0- p’+ PIE] ton@D

(a) - F O R C E S A C T I N G O NDIFFERENTIAL ELEMENT AT

UPSTREAM FACE

F r o m F i g u r e C

T o molntoin r o t o t i o n o l e q u i l i b r i u m o b o u t C ,

(rIudr)!$ =O

-rI”=o

T o m a i n t a i n v e r t i c a l equilibrium,

qudy-[(pfpE)ds]sln@u - (OIudr)cos~,f(Zrudr)sin~u=O

%u =uzudy -[(P + p,)ds]sin@u

d r cos+u

d s = d y sin&d r = d y cos@u

01, =Uzudy - ( P + PE )dY sin’%

d y cos*@u

Then :

u Ill= Uzu secz Qu- ( p + p,)ton* 0~

I n 0 s i m i l o r m a n n e r :

DID= ozD Set’ QD- (PI- &)ton*@D

(b)- F O R C E S A C T I N G O NDIFFERENTIAL ELEMENT AT

DOWNSTREAM FACE

(c) - D I F F E R E N T I A L E L E M E N TAT UPSTREAM FACE

41

Figure 4-2. Derivation of stress formulae for a concrete gravity dam.-DS2-2(4)

42

N O R M A L S T R E S SO N H O R I Z O N T A L P L A N E

O N “ERTlCAL P L A N E

N O R M A L S T R E S SO N YERTICAL P L A N E

DESIGN OF GRAVITY DAMSSTRESSES IN STRAIGHT GRAVITY DAMS, INCLUDING EFFECTS OF

TAILWATER AND HORIZONTAL EARTHQUAKE

IU*=a+byNORMAL STRESS ON HORIZONTAL PLANE, bz

al~az==w-fzET TZ

b= 12rMTJ

SHEAR STRESS ON HORIZONTALOR VERTICAL PLANE,& = TSruII Tzy = “tyz - (I, + b,y + c,y*

a,=TCZ D = (a,, - PI?* P:) t a n 00

b,=-$(+ 2~Zyu+4~zyo)

Ct=~(y+3Tzy" + 3fzyD iCheck at face for y = T, Zzy”=-(u~“-P~fPE)tonQ”Note.(‘“se I+1 slg” If horlzontol acceleration of foundation IS “Pstreom )

(t “se (-I stgn \f hori~ontoi acceleratmn of foundaimn is upstream.)NORMAL STRESS ON VERTICAL PLANE, Uy

III.~y==o,+blytc~y’+d~y’o,=cJyy,=a,ton~,+P’~f PIE ; bt = b,+an@o + 2 t’ ,.WG

(0 W to be omltted If tall&voter is absent1

t a n $J” - ian6l;az= A Z

j$= ~~(~)-~(~+6~YU+6T~Y~)l+~[3(~)+3(~)]

Check at face f o r y = T, uyu = ( P ’ PE -Tryu+anm”)MAGNITUDE OF PRINCIPAL STRESSES, Up,,(Tp2

Alternate s,gn gives Up* which

Check ot upstream face either Up, Or OP = 5 sec2@‘“-(P’*Pr)+~nz@uCheck at downstream foCe either UP, or d 8&sec24%-( p’?‘pdton%pe =

DIRECTION OF FIRST PRINCIPAL STRESS, 6p,

p *Pt”i OTC tan (-&I {,f +a" zap, = (+), 0.~ "p,< C t45") Measured from VerticalIf +onz@p, = (-j (-45=v@p,c 0, } ClockwIse positive.

I.

2.

3 .

4 .

5 .

6 .

7

8 .

9 .

/ I

Check at ups+ream:nd downstream face, 0p, =@, or(90’=0)

METHOD OF CONSTRUCTING LINES OF PRINCIPAL STRESSFrom the ,n+ersec+,on of o chose” ver+,cal plow and thebase of thecontllever cross-Section,mecsure $0, ot thoi Point and draw ianqent I-2 half way to the horizontal section d-8 next above.At tne two bolnts on section A-B between which +he line must pass, iay off the angles wh~chgivethe d#rec+lon of the pr~ncipol s1ress being considered and prolong thel~nestothelrpointof mtel-sectlo”Setween th,s pot”, of ,n+ersec+ion a.>d point 2 of the tangent /- 2, draw tongent 2-3 half way tothe horizontal section C-D nexi above A-D.Con+,n”e the,nterpolo+,o” unth thesuccess~on of tongenis has reached either Of the fOC’2sor thetop of the cantilever cross-section (I+ may be necessary to Interpolate betweenanqles ot the,n+ersect,one of successive horizontol sections and 0 vertito, plone)Through the po,n+s of ,“+erse‘:,on of these tangents and the hOrIzo”+oi seCtIons(or YertlCOI planes),draw the curves or lines of princlpai stress. Draw sufficient hnes to Include the whole section.From +he Intersectfonofo horlzontol sectton and the uostreom facetor from the ~ntersectionofovertical plow and the base), measure the angle of the stress complementary to the oneju~r drownand draw tinoent 5-6 from the wstreom face half way to the first hne of principal stress alreadydrawnFrom 6, drowtorgent 6-7 perpendlculor to the first lone of pr~nc~pol stress andextending halfwayto the next line of principal sfress.Continue the construction of the tangents perpendicular to the lines of principal stress alreadydrown until the too. bose.ordownstreom face of the cont~lever cross-section ~sreached.Connect the pofnts of int&sect!on of these tangents and the lines of principal s+ress first drownwith curves or lines of complementary principal stress. Draw sufflclent curves to include the wholeSectIon.

NOTEThe f,gures on +h,s sheetore for illustrative ~“rposes only. They donot represent results

for any speuflc condltlon of loodlng.:. The value of the quont,ty IS to be de;ernined ot o hor,zon+ul plane n Z distance abcve thehorlzontol sect>on under cons,dera+,on

Figure 4-3. Stresses in straight gravity dams.-288-D-3152

LAYOUT AND ANALYSIS-Sec. 4-l 1

The shear-friction factor, Q, for horizontalplanes, is the ratio of resisting to driving forcesas computed by the expression:

Q=CA+(ZN+XU)tanQCV (4)

where:

C = unit cohesion,A = area of horizontal section considered,

CN = summation of normal forces,C U = summation of uplift forces,

tan @ = coefficient of internal friction, andZ V = summation of shear forces.

All parameters must be specified usingconsistent units a n d w i t h p r o p e r signsaccording to the convention shown in figure4-l.

Shear-friction factors are computed for eachrespective elevation for which stresses arecalculated in the cantilever element for thesame condition of loading. All possibleconditions of loading should be investigated. Itshould be noted that high stability is indicated

43

by high shear-friction factors. The allowableminimum value for this factor for use in designis given in section 3-20.

The factor of safety for overturning is notusually tabulated with other stability factorsfor Bureau dams, but may be calculated ifdesired by dividing the total resisting momentsb y t h e t o t a l m o m e n t s t e n d i n g t o c a u s eoverturning about the downstream toe. Thus:

[Overturning safety = moments resisting

factor 1 moments overturning

Before bodily overturning of a gravity damcan take place, other failures may occur such ascrushing of the toe material, and cracking ofthe upstream material with accompanyingincreases in uplift pressure and reduction of theshear resistance. However, it is desirable toprovide an adequate factor of safety against theo v e r t u r n i n g t e n d e n c y . T h i s m a y b eaccomplished by specifying the maximumallowable stress at the downstream face of thedam. Because of their oscil latory nature,earthquake forces are not considered ascontributing to the overturning tendency.

C. TRIAL-LOAD METHODS OF ANALYSIS

1. Trial-Load Twist Method of

Analysis, Joints Ungrouted

4-11. Introduction. -A gravity dam may beconsidered to be made up of a series of verticalcanti lever elements from a b u t m e n t t oabutment. If the cross-canyon profile is narrowwith steep sloping walls, each cantilever fromthe center of the dam towards the abutmentswill be shorter than the preceding one.Consequently, each cantilever will be deflectedless by the waterload than the preceding oneand more than the succeeding one. If thetransverse contraction joints in the dam arekeyed, and regardless of whether grouted orungrouted, the movements of each cantileverwill be restrained by the adjacent ones. Thelonger cantilever will tend to pull the adjacentshorter cantilever forward and the shorter

cantilever will tend to hold it back. Thisinteraction between adjacent cantileverelements causes torsional moments, or twists,which materially affect the manner in whichthe waterload is distributed between thecantilever elements in the dam. This changesthe stress distribution from that found by theordinary gravity analysis in which the effects oftwist, as well as deformation of the foundationrock, are neglected. All straight gravity damshaving keyed transverse contraction jointss h o u l d t h e r e f o r e b e t r e a t e d a sthree-dimensional structures and designed onthat basis.

If the canyon is wide and flat, the cantileversin the central portion of the dam are of aboutthe same length and the effects of twist areusually negligible. However, twist effects maybe important in the abutment regions wherethe length of the cantilevers changes rapidly.


This twist action tends to twist the cantileversfrom their seats on the sloping canyon walls,thus tending to develop cracks in the dam inthese regions.

A sharp break in the cross-canyon profilewill result in an abrupt change in the length ofcantilevers in that region. This has the effect ofintroducing an irregular wedge of rock in thedam and causes a very marked change instresses and stability factors. Such conditionsshould be eliminated, if possible, by providingadditional rock excavation so that a smoothprofile is obtained.

4- 12. Theory.-The use of a twistedstructure for analyzing dams was suggested in areview of the trial-load method of analysismade for the Bureau of Reclamation in 1930.It was proposed that instead of replacing thearch dam by two systems of structuralelements, one of arches and the other ofcantilevers, one could replace it by threesystems each occupying the whole volume ofthe dam. These three systems would consist ofvertical cantilevers, horizontal arches, and atwisted structure. The new system, designatedthe twisted structure, would have the primarypurpose of resisting the twisting moments inhorizontal and vertical sections. Thus thevertical cantilevers would be considered ashaving no torsional resistance, since thetwisting moments would be assigned to thet w i s t e d s t r u c t u r e . S u b s e q u e n t l y , t h econception of the twisted structure was appliedto the analysis of a gravity dam.

A gravity dam is constructed as a series ofvertical blocks fixed at the base, as shown onfigure 4-4. These blocks may be assumed to becapable of resisting torsions and shears inhorizontal planes and bending in vertical planesfor the condition of joints ungrouted. Thisassumption is based upon the theory that thecontraction joints, through the action of thekeyways, can transfer load horizontally to theabutments by means of shear in the horizontalelements and torsion in the vertical element,b u t c a n n o t t r ans fe r tw i s t ing momenthorizontally to the abutment. For jointsungrouted, it is obvious that the contractionjoints cannot be assumed to provide resistanceto bending in either vertical or horizontalplanes.

ELEVATION

PLAN

Figure 4-4. Schematic view simulating partial constructionof a gravity dam in vertical blocks.-288-D-3 113

In the “Trial-Load Twist Method ofAnalysis,” the dam is assumed to be dividedinto a number of vertical and horizontalelements, the vertical elements of which areusually considered to be 1 foot in width andthe horizontal elements 1 foot in height.Further, in the manner described below, thesee l e m e n t s a r e a s s u m e d t o m a k e u p t w ostructural systems, called the canti leverstructure and the twisted structure, each ofwhich occupies the entire volume of the dam.

The cantilever structure consists of a seriesof vertical cantilever elements as describedabove, which abut on the foundation andtransfer thereto the dead load and a portion ofthe total external loads by gravity action only.These cantilevers carry external loadsdownward to the foundation by bending andshear along horizontal planes without beingrestrained by the twisted-structure elements.The cantilever is subjected to two types ofdeformation: bending caused by flexure, anddetrusion caused by shear in each cantileverelement.

The twisted structure consists of verticaltwisted elements with the same structuralproperties as the cantilevers in the cantilever


structure; and of horizontal elements which aresubjected to shear only. The vertical twistedelements resist no bending and shear, but resistonly twisting moments produced by the sheardue to loads on the horizontal elements of thet w i s t e d s t r u c t u r e . A m a j o r p a r t o f t h edeflection of the horizontal twisted-structureelements is caused by the angular rotations ofthe cantilevers. Also included in the totaltwisted-structure deflection are the movementof the abutment due to forces brought downby the cantilever which joins the foundation ata common point with the horizontal element,and the shear deflection in the horizontalelement due to loads on the twisted structure.The horizontal elements are segmental and areincapable of resisting bending moments if thejoints are not grouted. The cantilever structureand twisted structure are illustrated on figure4-5.

In order to make a twist analysis it isnecessary to load the cantilever structure andtwist structure by trial. For convenience, onlya limited number of selected elements areanalyzed which will provide satisfactory resultsfor representative points in the dam. Afterselection of the elements, the total waterloadon the dam is divided between the twostructures by trial. The deflections of thecantilevers and twisted structure are thendetermined at conjugate points. For the firsttrial there will be little agreement in deflectionat these points, but the process is repeateduntil the continuity of the structures isrestored. Stresses may then be computed fromknown forces and moments and are assumed torepresent the true stresses within the dam.

The following sections show the equationsand procedure for analyzing a dam for jointsungrouted. Detailed computations are notgiven for the complete procedure, sinceanother analysis, which is given later for jointsg r o u t e d , shows the calculations whichdemonstrate the principles involved in thepresent analysis.

4-l 3. Notations.-

x, y, z = coordinates along X axis, Y axis,and Z axis, respectively.

M, = bending moment in plane parallelto YZ plane, foot-pounds.

M, = bending moment in plane parallelto XY plane, foot-pounds.

MXY = twisting moment in horizontalXY plane, foot-pounds.

MZY = twisting moment in vertical ZYplane, foot-pounds.

V = horizontal thrust of waterload,pounds.

V, = shear in cantilever due to hori-zontal component of water-loadcarried by cantilever, pounds.

I’, = shear in horizontal element oftwisted structure due to hori-zontal component of waterloadcarried by the twisted structure,pounds.

Subscript A such as in *Mx y and A VCindicates abutment value fortwisting moment in XY planeand shear at base of cantilever,respectively.

T = thickness of dam at a givenelevation, feet.

E, = modulus of elasticity of concretein tension or compression,pounds per square foot.

E, = modulus of elasticity of abut-ment material in tension orcompression, pounds persquare foot.

G = modulus of elasticity of con-crete in shear, pounds persquare foot.

p = Poisson’s ratio.19~ = angular rotation in horizontal

plane, radians.LJY = deflection normal to axis of

dam, feet.Z = vertical distance from base of

cantilever, feet.I= moment of inertia for a vertical

cantilever of unit width or ahorizontal beam of unit heightof cross-section, feet4.

J = a factor used in computingangular rotations of canti-levers due to torsions-jointsungrouted.

T H E C A N T I L E V E R S T R U C T U R E S Y S T E M

DEFLECTION OF HORIZONTAL ELEMENT DUETO TWIST OF VERTICAL ELEMENTS DEFLECTION OF HORIZONTAL ELEMENT DUE

T O S H E A R DETRUSION

T H E T W I S T E D - S T R U C T U R E S Y S T E M

N o t e . Horizontal e l e m e n t rncapable o f resistingbending moment or torsional shear.

F&u-e 4-5. Cantilever and twisted-structure systems-joints ungrouted.-DS2-2(23)

0n


A = area of cross-section of a canti-lever or beam, square feet.For a unit width or height,A = T.

L = length of a horizontal beam,feet.

p = external pressure at depth h,pounds per square foot.

P = unit load ordinate, pounds persquare foot.

K = a constant which depends uponthe ratio of the actual sheardistribution to a shear distri-buted uniformly. In theseanalyses K/G = 3/E andK = 1.25.

$ = angle between canyon wall atcantilever base and thevertical, degrees.

(Y = angular movement of abutmentin vertical plane due to unitbending moment A I%!, , radians.

y = abutment movement normal toaxis of dam due to unit shear

=

I

force at the abutment, feet.angular movement of abutment

in vertical plane due to unithorizontal shear force at the

a2 abutment, radians.= abutment movement normal to

axis of dam due to unitbending moment AMx, feet.

6 = angular movement of abutmentin horizontal plane due tounit twisting momentA Mxv, radians.

The convention of signs to be used is shown onfigure 4-6.

4-14. Foundation Constants. -Rotation anddeformations of the foundation surface formoments and forces of unity, per unit length,are given by the following formulas, in which kis a function of p and b/a, and T is equal to a’(see figs. 4-7 to 4-10).

(1)

II - k,QI -q--F

k3

y’=F-r

k,6’ =-4 p

47

(2)

(3)

(4)

T h e a b o v e e q u a t i o n s c o n t a i n e l a s t i cc o n s t a n t s , E, and P, w h i c h a r e u s u a l l ydetermined by direct experimental methods.The curves shown on figures 4-7 to 4-10provide an easy means for determining valuesof k, to k,, inclusive, after the ratio b/a hasbeen determined by means described below. Itis impossible to obtain a definite value of b/afor an irregular foundation surface. Anapproximation of some kind is necessary, andat present the following method is used. Thesurface of contact between the dam andfoundation is developed and plotted as shownon figure 4-l 1. This surface is replaced by arectangle of the same area and approximatelythe same proportions, called the equivalentdeveloped area. The ratio of length to width ofthe rectangle is taken as the ratio b/a for thefoundation in question. The value of b/a istherefore a constant for a particular dam. Incomputing deformations for a particularelement, the width a’ is made equal to T, thethickness of the dam at the elementconsidered, making T/b’ = a/b, or b’ = (b/a) T.

The final equations for the foundationmovements of a unit horizontal element ateither abutment of the dam are shown below.The algebraic signs are as used for the leftabutment, and the asterisk (*) indicates thatsigns are to be reversed for movements at theright abutment.

*5 =M, CI + V/cr2 (5)

ny=V,y+MZcw2 (6)

for which:

a! = a’ cos3 J/ + 6 ’ sin’ $ cos $J (7)


N OTES:

Normal loads are applied tothe faces.

Twist loads ore applred att h e contllever $

Cantilever foundation

(a) V E R T I C A L C R O S S - S E C T I O N

1 Right

I, Left

(b) H O R I Z O N T A L C R O S S - S E C T I O N

M A X I M U M CANTlLEvER A N D CANTILEVERT O L E F T O F M A X I M U M V E R T I C A L CROSS-

S E C T I O N (L) ( L O O K I N G U P S T R E A M )

D’REGTloN DIRECTIOND’R;yloN OF POSITIVE oF

DIRECTION OF DIWZTION OFFORCES AND WEMENTS

POSITIVEtiOVEMENTS

Fy;;S POS,TIVE MOMENRDUE D U E T O

LOADSTO POSITIVE POSITIVE

MOMENTS LOADS LOADS

A L L D I R E C T I O N S R E F E R T O F I G U R E S

F I G U R E (al- -

F I G U R E (b)

8 +3 +3 TWlST+c ‘M-c 0 -c*

CANTI L E V E R T O R I G H T O F M A X I M U M V E R T I C A LC R O S S - S E C T I O N (R) ( L O O K I N G U P S T R E A M )

A L L D I R E C T I O N S R E F E R T O F I G U R E S

F I G U R E (a)

“I‘il,“g=

F I G U R E (b)

Figure 4-6. Direction of positive movements, forces, moments, and loads; and direction of forces, moments,and movements due to positive loads.-DS2-2(24)


0

5a

EXPLANATION

“0” and “b” ore dimensions of the loaded surfaceE, IS the modulus of elasticity of the foundotlon

materla I” d i rect s t ressT IS the thickness of the unit element as shown

FOUNDATION DEFORMATIONV A L U E S O F k , I N aC’- &

a;’ - ROTATION NORMAL TO FOUNDATION SURFACEDUE TO UNIT BENDING MOMENT PER UNIT ELEMENT

P O I S S O N ’ S R A T I O

-Figure 4-7. Foundation deformation-values of /cl in equation (1).




E X P L A N A T I O N

“a”and “b”are the dimensions of the lo&c surfaceEr IS the modulus of elasticity of the foundation

material ID direct s t r e s sT 1s the thickness of the untt element OS shown

DEPIRTMENT OF THE ,NTERlORBUREAU OF RECLAMATION

FOUNDATION DEFORMATIONV A L U E S O F k , I N 7’ = e

P’=DEFORMATION IN PLANE OF FOUNDATION SVRFACEDUE TO UNIT SHEAR FORCE PER UNIT ELEMENT.

Figure 4-8. Foundation deformation-values of k3 in equation (3).


POISSON’S RATIO

POISSON’S RATIO

EXPLANATION“a” o&b” ore dimensions of the loaded surfaceE, 1s the modulus of elostnty of the foundotlon

moterlal I” drect stressT 1s the thickness of the unit element as shown

FOUNDATION DEFORMATIONVALUES OF k. IN # = +r

6 ’ = ROTATION IN PLANE OF FOUNDATION SURFACEDUE TO UNIT TWSTING MOMENT PER UNIT ELEMENT

Figure 4.9. Foundation deformation-values of k4 in equation (4).


POISSON’S RATIO

POISSON’S RATIO

EXPLANATION“a”and “b” are d~menslons of the loaded surfaceEr 1s the modulus of elastlclty of the foundation

materlot in direct stressT IS the thickness of the unit element as shown

Figure 4-10. Foundation deformation-values of k5 in equation (2).


F L O W

1 : AXIS OF DAM--l 1 I , ,

(a) P L A N

b'b

-----L-- ---------- -_1II a'

AXIS OF DAM>

I / a

\ Unit differential area Developed area of loaded portion

of foundation surfaceEqulvolent developed rectangular area

(b) DEVELOPMENT

Figure 4-11. Loaded area of a foundation surface.-288-D-3153

ff2 = a” cos2 I// (8)

y = y’ cos $J (9)

It is customary to require that 6’ for a unitdifferential area on one side of the dam be anaverage value for the equivalent developed areaof that side of the dam. If the damsite isa p p r o x i m a t e l y s y m m e t r i c a l a b o u t t h emaximum section, d imens ions o f t heequivalent developed area for either or bothsides of the dam are a and b/2. For this reason,

ratios@ and &are substituted for the ratioa

b/a in some cases in obtaining values from thecurves on figures 4-7 through 4-10. Thesesubstitutions are indicated below:

For a’, a”,band y’ use ratio;.

For 6 ’ use ratio%.u

The final equations for movements of a unitvertical element at either abutment of the damare shown below. As before, the algebraic signsare as used for the left abutment and theasterisk (*> indicates that signs are to bereversed for movements at the right abutment.

ex =M, a+ vaa[2 (10)

*e z ‘Mxy 6 (11)

Ay= Vy+M, a2 (12)

for which:

a=a’sin3 $ +6’sinJ/ cos2 $J (13)

a2 = a” sin’ $ (14)

6 =6’ sin3 J/ +e’sin ti cos’ IL (15)

y = y’ sin ICI (16)


trial-load deflections, as explained later.4- 17. Initial and Unit Deflections of

Cantilevers. -Prior to starting an adjustment, itis necessary to determine the properties of thecantilevers and calculate initial and unitdeflections of cantilevers due to initial loadsand unit normal loads, respectively.

The calculation of unit forces and momentsdue to unit normal loads is illustrated on figure4-12. These loads are a system of triangularloads having a unit value of P, generally 1,000pounds per square foot, at each respectiveelevation and decreasing uniformly to zero atelevations above and below the point ofapplication.

Normal deflections of each cantilever due toinitial loads and those due to unit normal loadsare calculated by the equation,

4-15. Selection of Elements. -If the dam issymmetrical, only half of the dam need beanalyzed. If it is not symmetrical, the dam isdivided at a convenient plane near the centerwhere the canyon floor is relatively flat, orwhere it is expected that little twist action islikely to exist. Each part of a nonsymmetricaldam is analyzed separately and continuity isestablished by bringing deflections intoagreement at the dividing plane. For analyzingone-half of a symmetrical dam, usually five toseven horizontal elements and from four toseven vertical elements are selected to representthe structure. For a nonsymmetrical dam,usually nine to eleven vertical elements arerequired. Along a steeply sloping abutment andat points of irregularity, additional verticalelements may be required. Horizontal andvertical elements should be selected so thatt h e y h a v e c o m m o n a b u t m e n t s a n dfoundations. Occasionally, this may not bepossible for one or two vertical elements whichmust be placed at critical locations. The closestspacing of elements should be in the region ofgreatest twist.

4-16. Loads, Forces, and Moments. -Forcesand moments due to dead load, waterload,earthquake shock, and other loads, andnotations are determined as indicated insections 4-7, 4-8, and 4-9. The concrete weightis assigned to the cantilevers entirely, since it isassumed that deflections due to weight takeplace gradually during construction of the damprior to grouting of contraction joints. Theposition assumed by the cantilevers due toconcrete weight is the zero position fromwhich subsequent movements of the structureare measured. Stresses due to concrete weightare added to those determined from thetrial-load adjustment. The calculation ofdeflections due to concrete weight is notrequired in the analysis.

It is convenient to assign certain loadsinitially to the cantilevers. These includeh o r i z o n t a l a n d v e r t i c a l e a r t h q u a k econcrete-inertia loads, vertical si l t load,superstructure load, horizontal ice load, andstatic and hydrodynamic vertical waterloads.The deflections caused by these initial loadsmust be considered subsequently along with

K vc+AMx a2 +(z-----t GA

AZ+. v, r> (17)I

in which the symbols have the meanings givenin section 4-13. Unit abutment movements (Y,Q(~, and y, for use in the above equation, aredetermined for each cantilever by means ofequations and curves given in section 4-14. Theunderlined portion of equation ( 17) representsdeflection due to shear, while the remainderrepresents deflection due to bending. Nospecial attention need be given the underlinedportion of the equation when used for theanalysis with joints ungrouted, but it will bereferred to in the explanation for the analysiswith joints grouted.

4-18. Unit Rotations of Vertical Elementsof Twisted Structure Due to Unit TwistingCouple. -Unit rotations of vertical twistedelements due to unit triangular twisting-coupleloads are i l lustrated on figure 4-l 3. Aspreviously stated, the vertical elements havethe same structural characteristics as thecantilevers.

As shown on the figure, each twisting-coupleload has a unit value of P, usually 1,000foot-pounds per square foot, at the elevation at

LAYOUT AND ANALYSIS-Sec. 4-18 55U N I T C A N T I L E V E R E L E M E N T - P A R A L L E L S I D E S

i 00 3 t‘&-‘4T--21

.- P=lood per sq. unit I Unit -’

SHEARS AND MOMENTS DUE TO UNIT NORMAL LOADS

At E leva t i on 400Load 500 (No.1)

AV = $. lOO= 50 PLoad 400 (No.2)

AMx =~~100+100=3333PAV= :.lOO=5OP

AMx =;~100+100~1667P

At Elevation 300Load 500 (No. I) Load 400 (No.21

nv= 5OPfiMx = ~~IOO(~lOOtlOO)~8333P

nv = ~~2oo=looPAM x = 5 200~100=10,000 P

Load 300 (No.3)nv = +00=5o*P

AM,=;-100 +. 100 = 1667 P

Other Elevations Similar

AV q Horizontal force of portion of load above an elevation.

AM = Moment of AV about on elevation.

Note: In accordance with sign convention,AVand AM are negative.

Figure 4-12. Unit normal loads on a cantilever.-DS2-2(25)


UNIT C A N T I L E V E R ELEMENT - PARALLEL SIDES

“-P= load in ft Ibs.per sq. unit. I unit - -”

T W I S T I N G M O M E N T S D U E T O U N I T T W I S T L O A D S

A t E l e v a t i o n 4 0 0L o a d 5 0 0 ( N o . 1 1 L o a d 4 0 0 ( N o . 2 1

Aby, = + IO0 - 5OP aMxy, - +i 100 = 50 P

A t E l e v a t i o n 3 0 0Load 5 0 0 (No.11

A”XY, =+oo= 5OPL o a d 4 0 0 ( N o . 2 1

AMxy, - $200~ IOOPL o a d 3 0 0 ( N o . 3 1

A”XY3 = 3 roe= 5OP

A t E l e v a t i o n 2 0 0

A”XY, z 5OP A”XY3 = IOOP

A”xY * - 1OOP nMxyq= 5OP

O t h e r E l e v a t i o n s S i m i l a r

Note: In accordance wi th s ign convent ion, Mxy is negat ive.

Figure 4-I 3. Unit twist loads on a cantilever.-DS2-2(26)


which the load is applied, which decreasesuniformly to zero at elevations of horizontalelements above and below the point ofapplication. The value of the twisting momentat any elevation due to a given unit load isequal to the volume of the portion of thewedge representing that load, above the givenelevation, as may be seen by the calculationsgiven on figure 4-l 3. Unit rotations of avertical element on the left side of the dam arecalculated by substitution of the above twistingmoments in the equation which follows, wherethe symbols have the meanings given in section4-13.

elevation at which J’is to be computed, thevalue of P is determined from the curve. Thisvalue of P, together with the values of b and c,is then substituted in equation (19) and Jcomputed for that elevation. This procedure isrepeated for each elevation analyzed. Thevalues of J thus computed are for a blockhaving a width equal to the distance betweenthe ungrouted contraction joints. To determineJ for an element 1 foot wide, the computedvalues are divided by the distance between thecontraction joints.

The values of J determined by the abovemethod will hold for any unit element withinthis block or similar blocks having the samedistance between the contraction joints and thesame thickness at each elevation. However, ifthere are other blocks in the dam that havedifferent distances between the contractionjoints, thus changing the ratio of b/c atdifferent beam elevations, values of J for theseblocks must also be determined. Care should betaken to assign the proper values to b and c ineach computation, b being the longer side ofthe rectangular cross section of the block at theelevation under consideration and c the shorterside.

(18)

In the above, J is a factor for determiningtwist in a shaft of uniform cross section. Thev a l u e s o f J a r e c o m p u t e d [3] f rom theequation,

J=/3bc3 (19)

where:

b = longer side of horizontal cross sectionof element. (In this case the elementis the block between two ungroutedcontraction joints.)

c = shorter side of horizontal crosssection of element.

The following tabulation gives values of 0 forvarious ratios of b/c:

To facilitate determining the proper valuesof J for the different elevations of each verticalelement, the data in the above tabulation havebeen plotted and a curve drawn as shown onfigure 4-14. The ordinates of the curve are thevalues of /3 and the abscissas a re t hecorresponding ratios of b/c from the abovetable. Using the computed ratio of b/c for the

Equation (19) was developed for shafts orbeams of uniform cross section, and the valuesof J computed from this equation for thevertical elements in the dam are therefore onlyapproximately correct since the cross sectionsare not uniform.

4- 19. Unit Deflections of HorizontalElements of Twisted Structure.-Unitdeflections of horizontal elements due to shearare used in calculating deflections for eachadjustment. Unit loads are applied to thehorizontal elements by means of triangularloads which have a value of P pounds persquare foot at the abutment and vary as astraight line to zero at the intersections of eachrespective vertical element with the horizontalelement. The shear deflections due to auniform load and those due to a unitconcentrated load at the vertical dividing planeare also computed (see fig. 4-15). Theconcentrated load is used to provide deflectionagreement of the two portions of the dam. Thegeneral equation used to compute the abovedeflection is:


Dota f o r d e t e r m i n i n g f a c t o r “J” d u e t o twist o fo s h a f t o f r e c t o n g u l o r c r o s s sectjon.

“ S t r e n g t h o f Materiali;

O*0 2 4 6 6

R A T I O S O F ft

Figure 4-14. Graph for determining J factor due to twist of a shaft of rectangular cross section.-288-D-3154

ay =J

K ‘Tmdx +A VT Y cw

in which the symbols have the meanings givenin section 4-13.

Using K = 1.25 and G = E/2( 1 + P), thegeneral equation reduces to the following,where L is the length of the half-element, L’ isthe length of the loaded portion, measuredfrom the abutment, and x is the distance fromthe abutment to the point where deflection isdesired. For a unit triangular load,

Pny=-2EAL’ [3 (L’)2 x - 3 L’ x* +x31

+ v, Y (21)

For a uniform load,

AY=-~EA-x- [2Lx-x’] + VA y ( 2 2 )

For a unit concentrated load,

3 P xAY=- EA +f’--/j ‘Y (23)

Shear forces are equal to the area under theunit-load diagram from the dividing plane oft h e d a m t o t h e c a n t i l e v e r p o i n t s u n d e rconsideration, and are negative in sign.

Values for unit deflections due to shear inh o r i z o n t a l e l e m e n t s a r e t a b u l a t e d f o rconvenient use in the adjustments.

4 - 2 0 . T r i a l L o a d s . - F o l l o w i n g t h ecomputation of unit-load deflections and


/-P Ibs./sq. unitI

59

Ik--------X .___--

I II

(a) TRIANGULAR LOAD ON HORIZONTAL ELEMENT

*- --P Ibs./sq. unit

(b) UNIFORM LOAD ON HORIZONTAL ELEMENT

P Ibs.

Beam

(cl CONCENTRATED LOAD ON HORIZONTAL ELEMENT

Figure 4-15. Loads on a horizontal element.-DS2-2(28)


of the twisted-structure deflection. The otherpart is shear detrusion due to trial loads on thehorizontal elements, which is computed bysummating the respective products of the loadsand the unit deflections of horizontal elementsdue to shear (see sec. 4-19). The sum of thesetwo parts is the total twisted-structuredeflection due to trial loads. However, forcomparison with cantilever deflections as toagreement at conjugate points, there must beadded to the twisted-structure deflections theabutment movement of the particular verticalelement of the cantilever structure (hereintermed the conjugate vertical element) whichhas an abutment common with the horizontalelement of the twisted structure.

4 - 2 3 . D e f l e c t i o n s o f C a n t i l e v e rStructure. -Cantilever deflections due to trialloads are calculated by summating therespective products of these loads and thecantilever deflections due to unit normal loads(see sec. 4-17). To these deflections are addedalgebraically the deflections due to initialloads, and, for comparison with the totaltwisted-structure deflections, are also addedthe movement at the base of the cantilever dueto shear at the abutment of the conjugatehorizontal element of the twisted structure.For cantilevers in a relatively flat canyonbottom where the foundations do not coincidewith the ends of horizontal elements, this latterabutment movement is usually assumed equalto zero.

4-24. Stresses and Stability Factors. -Aftersatisfactory continuity of the structure, oragreement of deflections at conjugate points,has been obtained by trial, the total shears andmoments at various points in the cantileversmay be computed from the established trialloads. This is done by summating the productsof the trial loads and the unit moments andshears, respectively, due to l,OOO-pound unitloads. Stresses are then calculated for trialloads and added algebraically to stressescalculated for concrete weight at the faces ofthe dam. Stress equations are given in a latersection. Stability factors are calculated in theusual manner.

rotations of horizontal and vertical elements,the next step in the analysis is the trial divisionof horizontal waterload between the cantileverstructure and the twisted structure. Thisdepends a great deal on experience andjudgment. An examination of unit deflectionsis frequently of help in revealing the relativeelasticity of the elements. Generally thecantilevers carry the greater proportion of load,especially in the middle portion of the dam.Near the abutments, however, the twistedstructure usually carries the greater proportionof load, depending on the size of dam, shape ofcanyon, and elastic properties of the concreteand rock. One part of the total water-load isplaced on the cantilever structure and the otherpart on the horizontal elements of the twistedstructure. No external waterload is placeddirectly on the vertical twisted elements.

4-21. Angular Rotation of Vertical TwistedElements due to Trial Loads on HorizontalElements. -The shear force due to trial normalloads on a horizontal element, at the locationof any vertical element, is equal to the areaunder the load diagram from the dividing planeto the vertical element under consideration. Atwisting couple is produced in the verticalelement as a result of the shear force in thehorizontal element at that point. Since thewidth of the vertical element is unity, thetwisting couple in the cantilever is numericallyequal to the shear in the horizontal element.Since couple loads are in thousands offoot-pounds per square foot, shear forces mustbe expressed in thousands of pounds units. Thegeneral sign convention must be followed. Bysummating the respective products of thesecouple loads and the rotations of verticaltwisted elements due to unit twist loads, theangular rotations in the vertical elements dueto shear forces on the horizontal elements areobtained.

4 - 2 2 . D e f l e c t i o n s of T w i s t e dStructure. -The deflections of the twistedstructure due to angular rotations of verticalelements are obtained by integrating theangular rotations along the horizontal elementsfrom the abutment to the dividing plane of thedam. This, however, gives only one component


2. Trial-Load Twist Method of

Analysis, Joints Grouted

61

figure 4-16(b). It should be noted that one-halfof the twisted-structure load is carried to thefoundation by the vertical twisted elementsand one-half to the abutment by the horizontaltwisted elements. That such a distribution maybe assumed for the twisted-structure load wasshown by H. M. Westergaard in 1930 in hisreview of the trial-load analysis of arch dams.The principle will be explained by illustration.Figure 4-17(a) shows a triangular dam, 5 unitshigh and 10 units along the crest from thedividing plane o f s y m m e t r y t o t h e l e f tabutment. The vertical cross sections in planesnormal to the plane of the paper are assumedto be of unit uniform thickness from the top tothe base. Rigid foundations are assumed, henceabutment and foundation rotations are omittedfrom the analysis. A twisted-structure loadapplied at a point xs , zl,, produces angularrotations in the beams and cantilevers of thetwisted structure. The calculations on figure4-17 show that if these rotations are integratedalong their respective planes from beamabutment and cantilever foundation to thepoint of application of the load, the resultingdeflections at the latter point are equal [4],from which it can be concluded that equalamounts of load are transferred vertically andhorizontally by the twisted structure. It shouldbe noted that, while the assumption of anequal load distribution is correct for au n i f o r m - t h i c k n e s s section, it is onlyapproximately true for a variable-thicknesssection.

By hypothesis, the beam and cantileverstructures can resist only bending and shear,while the twisted structure can resist only twistand shear. Figure 4-l 7(b) illustrates an elementof the beam structure subjected to load. Anyportion of this element, AND, which may alsobe considered as part of a cantilever element, isseen to be in equilibrium due to moments andshears set up by load P. The total clockwisemoment acting on the element is P multipliedby the arm of 10 feet, plus a couple consistingof the shear P multiplied by an arm of 1 foot,which is balanced by a counterclockwiseresisting moment of P multiplied by 11 feet.Therefore, the load on the beam does notrequire a resisting twist in the cantilever

4-25. Description of Method. -The groutingof contraction joints welds the vertical blocksof the dam into a monolithic structure. In thiscase the dam has a different action under loadthan when joints are ungrouted. Groutingreduces the deflections of the structure for agiven loading, since both horizontal andvertical elements of the dam are subject tobending and twisting in both horizontal andvertical planes. For very small dams, say under50 feet in height, the effect of bending in thehorizontal elements is very small and may beneglected; for higher dams, however, it isusually included. The general procedure issimilar to that used for joints ungrouted, butan additional structure, designated the beamstructure, is introduced for resistance tobending in horizontal elements. For thisanalysis, then, we have the cantilever structure,the twisted structure, and the beam structure,or three structures instead of two, the twistedstructure being composed of both vertical andhorizontal elements as previously described.

If the dam acts as a monolith, as assumed,the deflections of the cantilevers, horizontalbeams, and twisted structure-due to trialdivisions of waterload between the threesystems-must be brought into agreement in allparts of the dam. Furthermore, for completecontinuity, the longitudinal slopes of thecantilever must equal the transverse slopes ofhorizontal elements, and the longitudinalslopes of the horizontal elements must equalthe transverse slopes of the cantilevers. Ageneral slope adjustment is not necessary,however, since the adjustment of deflections int h e h o r i z o n t a l e l e m e n t s o f t h e t w i s t e ds t r u c t u r e p r o d u c e s a g r e e m e n t o f t h elongitudinal slopes of the horizontal elementswith the transverse slopes of the cantilevers.

The adjustment is more complicated thanfor joints ungrouted, since three structures areused instead of two. As an initial step in theanalysis, the waterload is divided by trialbetween the three structures, as illustrateddiagrammatically for a cantilever element on


LOAD CARRIED BY TWISTED STRUCTURE~~--- T r a n s f e r r e d l a t e r a l l y t o a b u t m e n t------ Transferred vertically to foundation

LOAD CARRIED BY CANTILEVER STRUCTURE- - - - - -T rans fe r red v e r t i c a l l y t o f o u n d a t i o n

D C B A

(a) NEGLECTING EFFECTS OF HORIZONTALB E A M A C T I O N I N B E N D I N G

F

L O A D C A R R I E D B Y T W I S T E D S T R U C T U R E- - T rans fe r red laterally t o a b u t m e n t- - - T r a n s f e r r e d v e r t i c a l l y t o f o u n d a t i o n

___-

L O A D C A R R I E D B Y H O R I Z O N T A L B E A ME L E M E N T

--Tronsferred l a t e r a l l y t o a b u t m e n t

LOAD CARRIED BY CANTILEVER STRUCTURE

- - - T r a n s f e r r e d v e r t i c a l l y t o f o u n d a t i o n

I I IE D CB A

(b) INCLUDING EFFECTS OF HORIZONTALBEAM ACTION IN BENDING

Figure 4-16. Trial-load twist analysis for a straight gravity dam-joints grouted. Division of external horizontal loads isshown.-103-D-275


p---------Horizontal Twisted Structure (HTSI------------w*Axis

:of Symmetry of Dam

‘-x Fkc---- _____________ ____.___ 10 “ni+ spaces(l)------------------------~,

/-Y--Axis

(a) DISTRIBUTION OF TWISTED- STRUCTURE LtiD

BASIC ASSUMPTIONS

Dam is symmetrical in triangular site about axis L,,,. Vertical cross-sectmsin plones normal to plane of paper are of umt uniform thicknessfrom top to base of dam. ~GI : unity. Half length of dam,l,= twice height,h. Abutment and foundation deformations not included,shear detrusions omitted.

Let a unit twisted-structure load of P intensity be applied at a pomtxI, q. in the dam. Let the angular rotations in both the xy and yzplanes due to unit twisting moments - I per unit length. Assume one-halfthe twisted- structure load is carried horizontally to abutments andone-half carried vertically to foundation, by twist action.

In HTS Myz:g ,----- ByZ:f.x ,---- - AY=fB,, dz

I n V T S M,, =F, _____ 8xy=$z, _____ AY=/9,, dx

For HTS AY at point x5 zlo, Z = 5

’. . AY= dXz i?ifc 1 lo z 12,5pa 0For VTS AY at point x~z,~,X=~Z

:. AY&‘; -2z dz= [?]I = 12.5P

I

(c) TWISTED- STRUCTURE ELEMENT

Figure 4-I 7. Twisted-structure loads.-DS2-2(30)

64

element for equilibrium. Similarly, the loadcarried by a cantilever requires no resistingtwist in the beam element.

Figure 4-17(c) illustrates an element of thetwisted structure subjected to load. Anyportion of this element, ABCD, which may alsobe considered as part of a verticaltwisted-structure element, is subjected to aresultant shear couple of amount P with an armof 1 foot. Therefore, for equilibrium, a load onthe horizontal element of the twisted structurerequires a resisting twist in the vertical element,and similarly a load on the vertical elementrequires a resisting twist in the horizontalelement.

4-26. Assumptions. -From the foregoingconsiderations, the structural action of theelements of the dam may be assumed asfollows:

(1) The cantilever elements resist shears inhorizontal planes and bending in verticalplanes.

(2) The horizontal beam elements resistshears in vertical planes and bending inhorizontal planes.

(3) The twisted structure resists twistingmoments and shears in horizontal and verticalplanes.

4 - 2 7. Horizontal Beam Elements. -Thehorizontal beam elements are assumed to be 1foot in vertical thickness with horizontal topand bottom faces and vertical upstream anddownstream faces. Calculations of deflectionsare made by the ordinary theory of flexure forbeams, with contributions from abutmentyielding included. The same types of unit loadsas described in section 4-19 for horizontalelements of the twisted structure are used forcalculating unit deflections of each horizontal


beam. In addition, however, there is included aconcentrated moment load at the “free end” or“crown” of the beam, that is, at the dividingplane, and also a concentrated normal load atthe same free end. Unit slopes are calculatedfor the crown and the abutment. Unit slopes ofthe beams at the abutment are used to obtainthe effect of beam abutment forces on rotationof the base of the conjugate vertical twistedelement, and unit slopes at the crown are usedto establish slope agreement at the dividingplane between beams in the left half and beamsin the right half of the dam.

4 - 2 8 . N o t a t i o n s . - I n a d d i t i o n t onomenclature given in section 4-13, thefollowing terms are given for equations usedfor movement in horizontal beams. Figure4- 15, used for illustrating horizontal elementsof the twist structure, is also illustrative ofhorizontal beams.

x = distance from abutment to anypoint under load.

xP = distance from abutment to anypoint on beam wheredeflection is desired.

L’ = distance from abutment to endof load.

L = length of beam from abutmentto crown.

ML, V, = moment and shear, respectively,at any point due to externalload to right of point, forleft half of beam. For righthalf of beam use subscript R .

Subscript:

T = twisted structure.

4-29. Equations. -Equation (17) is used for computing cantilever deflections due to initial loadsand due to unit normal loads. The underlined portions of equation (17) and subsequent equationsgive cantilever deflections due to unit shear loads. The deflection of the cantilever due to theportion of load carried by vertical elements of the twisted structure may be dctcrmincd by use ofthese unit-shear deflection equations. The following equation is used in place of equation (18) forcalculating the angular rotations of cantilevers in horizontal planes:


The general equations for rotation and deflection at any point in a horizontal beam element,including effects of bending, shear, and abutment movement, are as follows:

(25)

-+MA crx+MAa,+V/, r+VA azx (26)

(a) Triangular Load.-Slopes and deflections due to a triangular normal load may be calculatedat any point along the centerline of a beam in the left half of the dam by means of the equationsgiven in this subsection. Equations for the right half of the dam are the same except for a reversalin the sign of slopes. Equations for moment and shear are:

./M=-p(L’-x)3=-pP6L’ 6L’

-3 (L’)2 x + 3 L’ x2

-x3 1

v=-P(L’-x)2- p2L’ --7j-p - 2 L’x +x2 1The equation for slope at any point is:

/

xP

e =0

F=-6hL, FL’)3 Lx’ dx-3(L’)2 I ” x d x

+3Lrlxp x2dx- i”x3dx]

P24EIL’ [

4 (L’)3 xp - 6 (L’)2 xp2 + 4 L’xp3 -xp4I

+M/, a+ VA cx2

For

xp = L’ tax, = L,

e=-$-g+MA a+vA a2

(27)

(28)

(29)

(30)


The equation for deflection at any point is:

xP xP

Ay =/

wxp -xl

EI dx + 3 V d xCl I0 EA

P=-120EIL’ [IO (L’)” xp2 - lO(L’)2 xp” -I- 5Lk,4 -xp51

P-2EAL’ 3 (L’)2 xp - 3 L’x,2 fXP3 + v, r+M/j a2

i[ 3

I

+ MA’y+VAcv2c 3

xp

When

xP= L’,

Ay =-x-w+ VA y+MA ct2 + PA a + VA a21 xp

For

(31)

(32)

xp >L’tox, =L,

ny=-$f$$-$&g(xp -L’) -I-V, y+M/, a2 + [M/, a+VI

A 2a 1 Xp (33)I I

(b) Uniform Load.-The equations for moment and shear due to a uniform normal load on ahorizontal beam are:

j,+,= -‘CL -x)22 (34)

v = -P(L - x )

The equation for slope at any point is:

s

xP

e= M dx0

(35)

(36)

P-‘=-6EI C

3L2xp -3Lxp2 +xp3 1 sMA a+V, (y2 (37)


When

xP =L,

PL3e=-6EI-+MA cw+ VA a2

The equation for deflection at any point is:

/

xP

Ay =M(xp -x)dx

E I +3 -0 /

xP

VdxE A

0

= -&- FLZxp? -4Lxp3 +x,4] --uf- FLX, -xpq2EA

i

+V, y+MA a,+I I 1 xp

When

xP =L,

PL4 3PL2Ay=-mEI-2EA +V, r+MA a2+ cv2 + V, 1y2 L1 1

(38)

(39)

(40)

(c) Concentrated Moment at Free End of Beam.-The equations for moment, shear, slope, anddeflection for this condition are:

M = - P v = o

‘xpe=-EI +MA” (41)

PxpZnY=-2EI +MA (~2 +MA cYxp (42)

For xp = L, the latter value is substituted in the above equations.

(d) Concentrated Normal Load at Free End of Beam.-The equations for moment, shear, andslope for this condition are:

M = - P ( L - x ) v = - P

8 =-&$2r.X, -Xp2)+MA cY+ VA a2 (43)


WhenxP = L,

PL2’ = - 2 E I-+MA cy+ VA cc2 (44)

The equation for deflection is:

Ay=-& (3Lx,2 -xl,+$+I , [

MA a + VA a21 x,+4, a2+I/A Y (45)I I

WhenxP = L,

PL3-~‘Y=-3EI a+ vA a21

L+MA 012 +VA 7t I

(46)

The underlined portions of the preceding equations are equivalent to expressions for unitcantilever deflections obtained by equations (21) to (23), inclusive. Therefore, by keeping separatethe underlined portions of equations (33), (40), and (46), shear deflections due to unit shear loadson horizontal elements are obtained at the same time as beam deflections due to unit normalloads. An example of a twist analysis of a gravity dam with joints grouted is shown in appendix B.

3. Analysis of Curved Gravity Dams

4-30. Method of Analysis.-If a gravity dam is curved in plan only for convenience in locatingthe structure on the existing topography and contraction joints are not grouted, the analysesshould be made as described for straight gravity dams. However, if the joints are grouted and thedam is curved, arch action is an important factor in the reliability of the structure. Under thesecircumstances, it is desirable to analyze such a structure by an arch dam analysis method ratherthan by the gravity method described earlier. The arch dam analysis, including computerizedapplication, is described in the Bureau of Reclamation publication “Design of Arch Dams” [ 171 .

D. DYNAMIC ANALYSIS

4-31. Introduction. -The following method for dynamic analysis of concrete gravity dams canbe described as a lumped mass, generalized coordinate method using the principle of modesuperposition [5]. Application of the method is done by computer, and matrix methods ofstructural analysis are used. The method is similar to that proposed by Chopra [6] .

4-32. Natural Frequencies and Mode Shapes.-The section analyzed is a two-dimensional crosssection of the dam. The section is represented by finite elements [7] with the concrete masslumped at the nodal points. The natural frequencies fr , f2, f3, etc., and the corresponding modeshapes (Qi), , (Gi), , (Gi), (where i indicates the assigned number of the mass point) are found bythe simultaneous solution of equations of dynamic equilibrium for free vibration. There is oneequation for each lumped mass. This problem is known as an eigenvalue problem. There arestandard computer solutions available for the eigenvalue problem.

The input that will be required for the solution of the eigenvalue problem will be the stiffnessmatrix [K] and the mass matrix [Ml. A typical element in the stiffness matrix, Kii, represents theforce at i due to a unit deflection of j with all other points remaining fixed. The mass matrix is a


diagonal matrix of the lumped masses. Each lumped mass includes the mass of the concreteassociated with that point. To represent the effect of the water against the dam on the frequenciesand mode shapes, a mass of water is divided appropriately between the mass points. The volume ofwater assumed to be vibrating with the dam is given by an equation developed by Westergaard [ 81.

The equation is:

b = 718 + (47)

where:

b = the dimension of the water measured horizontally from the upstream face,z = the depth of water at the section being studied, andh = the distance from the water surface to the point in question.

4-33. Response to an Earthquake.-Given the natural frequencies, mode shapes, and anacceleration record of an earthquake, the following equation expresses the acceleration of point iin mode ~1, ii,., , as a function of time:

. . ‘i Mi @in 2nXin = @in

2 I zn Jt

Z.M.@T Tn 0ig(7)e sin-$ (t - T) dr

n(48)

where:

T,=f,

h = viscous damping factor,;;,(T) = the acceleration of the ground as a function of time, digitized for the numerical

evaluation of the integral,# = nodal displacement,

M = mass,7 = time, andt = a particular time, T = t.

Little data are available on the damping in concrete gravity dams, expressed as h in equation(48). Chopra [9] indicates that a reasonable assumption for h in a concrete gravity structure is0.05.

Equation (48) is evaluated at chosen increments of time. An increment of 0.01 second has beenused. At the end of each of these time increments, the accelerations for all node points in all themodes being considered are summed as in the following equation:

,. = ~ j;i,‘ T O T A L n

(49)

The response history is scanned for the time of the maximum value of acceleration at the crest.The .xiT0 TA L at this time is the acceleration for the dam. These values can be divided by theacceleration of gravity to give Cyi.


After the acceleration ratios, ai, are determined for the necessary elevations in the dam, theresulting loads on the structure should be calculated as described in the following paragraphs.

4-34. Loads Due to Horizontal Earthquake Acceleration.-For dams with vertical or slopingupstream faces, the variation of hydrodynamic earthquake pressure with depth is given by theequations below [ 101 :

PE =c(Ywz (50)

(51)

where:

pE = pressure normal to the face,C = a dimensionless pressure coefficient,(y = horizontal earthquake acceleration

acceleration of gravity ’w = unit weight of water,z = depth of reservoir at section being studied,h = vertical distance from the reservoir surface to the elevation in question, and

C, = the maximum value of C for a given slope, as obtained from figure 4-18.

For dams with combination vertical and sloping face, if the height of the vertical portion of theupstream face of the dam is equal to or greater than one-half the total height of dam, analyze as ifvertical throughout.

If the height of the vertical portion of the upstream face of the dam is less than one-half thetotal height of the dam, use the pressure which would occur assuming that the upstream face has aconstant slope from the water surface elevation to the heel of the dam.

Values of vPE or VPi and MPE or MPL should be computed for each increment of elevationselected for the study and the totals obtained by summation because of the nonlinear response.The inertia forces for concrete in the dam should be computed for each increment of height, usingthe average acceleration factor for that increment. The inertia forces to be used in considering anelevation in the dam are the summation of all the incremental forces above that elevation and thetotal of their moments about the center of gravity at the elevation being considered.

The horizontal concrete inertia force (YE) and its moment (ME) can be calculated usingSimpson’s rule.

4-35. Effects of Vertical Earthquake Accelerations. -The effects of vertical accelerations maybe determined using the appropriate forces, moments, and the vertical acceleration factor. Theforces and moments due to water pressure normal to the faces of the dam and those due to thedead loads should be multiplied by the appropriate acceleration factors to determine the increase(or decrease) caused by the vertical accelerations.

E. THE FINITE ELEMENT METHOD

4-3 6. Introduction. -The finite element body may be considered an assemblage ofmethod utilizes the idea that a continuous distinct elements connected at their corners.

TYPICAL PRESDIAGRAM

SURE TYPICAL SECTION

D

eievot~o” under cons,dero+,on(ftl

Figure 4-18. Hydrodynamic pressures upon the sloping face of a dam due to horizontal earthquake effect.-288-D-3155


This computerized method has become awidely used and accepted means of stressanalysis in the last decade. The literature of thepast few years contains numerous examples ofspecialized uses of the finite element method.The reason for the ready acceptance andtremendous amount of use of this method isthat it made possible the approximate solutionof many problems which engineers had beenneg lec t ing , overdesigning, o r g r o s s l yapproximating. The inclusion of complexgeometrical and physical property variationsprior to adaption of the finite element methodand the modern high-speed digital computerwas simply beyond the realm of reality. Thefinite element method permits a very closeapproximation of the actual geometry andextensive variations of material propertiessimply and inexpensively. The formulation andtheory of the finite element method are givenin several publications including those byClough [ 111 and Zienkiewicz [ 121.

Because of the ability of the method toanalyze special situations, this is the area inwhich the most application has been made. Thetwo-dimensional finite element method iscapable of analyzing the majority of problemsassociated with variations in the geometry ofsections of the dam. Three-dimensional effectsc a n b e a p p r o x i m a t e d b y m a k i n g atwo-dimensional analysis in more than oneplane. The two-dimensional finite elementmethod is capable of solving for stresseseconomically even w h e n g r e a t d e t a i l i snecessary to attain sufficient accuracy.

When the structure or loading is such thatplane stress or strain conditions may not beassumed, the three-dimensional finite elementmethod may be used. The applicability of thismethod to problems with extensive detail islimited by computer storage capacity andeconomics. However, the method is often usedfor problems with near uniform cross sectionor where only the general state of stress isdesired. Additionally, the three-dimensionalmethod finds application when the effect of aneccentric load or member is to be found.

Many two- and three-dimensional finiteelement programs with varying accuracy andcapability have been written. The programs

used by the Bureau for analyses connectedwith gravity dams are discussed below.

1. Two-Dimensional

Finite Element Program

4 - 3 7 . P u r p o s e . - T h e p u r p o s e o f t h i sc o m p u t e r p r o g r a m i s t o d e t e r m i n ed e f o r m a t i o n s a n d s t r e s s e s w i t h i ntwo-dimensional plane stress structures ofarbitrary shape. The structure may be loadedbY c o n c e n t r a t e d f o r c e s , g r a v i t y , a n dtemperature, or by given displacements.Materials whose properties vary in compressionand tension may be included by successiveapproximations.

4-38. Method.-The structure is divided intoelements of arbitrary quadrilateral or triangularshape. The verticies of these shapes form nodalpoints. The deflections at the nodal points dueto various stresses applied to each element are afunction of the element geometry and materialproperties. The coefficient matrix relating thisdeflection of the element to the load applied isthe individual element stiffness matrix. Thesestiffnesses are combined with the stiffnesses ofall the other elements to form a global stiffnessmatrix. The loads existing at each node aredetermined. The deflections of each node intwo directions are unknown. The same numberof equations relating stiffness coefficients timesunknown deflections to existing loads (righthand members) have been generated. The very1 arge coefficient matrix i s b a n d e d a n dsymmetric. Advantage of this fact is taken intoaccount in the storage of this matrix. Theequations are solved by Gauss elimination.

I n t h i s m e t h o d e a c h u n k n o w n i sprogressively solved for in terms of the otherunknowns existing in the equation. This valueis then substituted into the next equation. Thelast equation then is expressible in only oneunknown. The value of this unknown isdetermined and used in the solution of theprevious equation w h i c h h a s o n l y t w ounknowns. This process of back substitutioncontinues until all unknowns are evaluated.The known deflections, the stiffness of theindividual elements, and the equations relatingstrain and stress for the element are then used


to calculate the stress condition for theelement.

4-39. Input.-The problem is defined by acard input that describes the geometry andboundary conditions of the structure, thematerial properties, the loads, the controlinformation for plotting, and the use ofoptions in the program. Mesh generation, loadgeneration, and material property generationare incorporated in the system.

4-40. Output.-The output of this programconsists primarily of a print of the input dataand the output of displacements at each nodeand stresses within each element. In addition, amicrofilm display of the mesh and of portionsof the mesh with stresses plotted on the displayis available. Some punched card output is alsoavailable for special purposes o f i n p u tpreparation or output analysis.

4-4 1. Capabilities. -(1) Loading. -External forces, temperature,

and known displacements are shown, andaccelerations given as a percentage of theacceleration due to gravity in the X and Ydirections.

( 2) Ph y sica I property variations. -Theprogram allows reading-in changes in modulus,d e n s i t y , r e f e r e n c e t e m p e r a t u r e , a n daccelerations after each analysis. Stresses anddisplacements may then be computed with then e w p r o p e r t i e s .and l o a d i n g w i t h o u tredefinition of the structure.

(3) Plotting. -A microfilm plot of the entiregrid or details of it may be obtained. Thedetailed plot may be blank or can be given withprincipal, horizontal, vertical, and shearstresses. Either plot may also be obtained withthe material number identification given withineach element.

(4) Bilinear material properties. -Theprogram allows for input of a modulus incompression and in tension. The tensionm o d u l u s i s i n c l u d e d i n successiveapproximations after the determination oftension in an element has been made.

( 5 ) O p e n i n g s . -An open ing may besimulated in the structure by assigning amaterial number of zero to any element or byactually defining the structure with theopening not included in the definition. Theformer method allows for optimum use of

73

mesh generation and allows for considerablymore flexibility.

(6) Checking and deck preparation. -Severaloptions exist that allow for checking andfacilitating input preparation.

(7) Shear stiffness.-The effect of shearstiffness in the third dimension may beincluded.

(8) Units. -The program output units matchthe input units. In general, these units are notshown on the output. The option exists,however, that allows units to be given on theoutput in feet and pounds per square inchprovided that the input was in feet and kips.

(9) Normal stress and shear stress on aplane.-The normal stress and the shear stresson any given plane can be computed. Inaddition, given the angle of internal frictionand the cohesion for the plane, the factor ofsafety against sliding can be computed.

(10) Reference temperature. -Temperatureloads are applied with respect to a givenreference temperature for the entire problem.If certain portions of the problem havedifferent reference temperatures, these may beinput on the material properties card andw o u l d o v e r r i d e t h e o v e r a l l r e f e r e n c etemperature for that material only.

(11) External forces may be applied usingboundary pressures. The program calculatesconcentrated loads at the nodes based on thesepressures.

(12) The input coordinates may be preparedby digitizing a scale drawing of the problem.The actual scale can be adjusted for within theprogram by inputting a scale factor on thecontrol card. The coordinates used by theprogram are the input coordinates times thescale factor. If no scale factor is involved, thecoordinates are used as they are given.

4-42. Limitations. -(1) Nodes, 999; elements, 949; materials,

100.(2) Bandwidth (maximum difference

between nodes of any element) = 42.(3) Maximum number of rows in a detailed

plot section = 25.4-43. Approximations. -(1) Linear deflection distribution between

nodes.(2) Curved surface has to be approximated


simplify the stiffness formulation for theelement. The displacements are also assumed tovary linearly between the nodes. Thus the sameinterpolation functions can be used fordisplacements. This common relationship ofgeometry and displacement is the reason forthe name isoparametric element.

Once the displacement functions have beenestablished, t h e e l e m e n t s t r a i n s c a n b eformulated. The nodal point displacements arer e l a t e d t o t h e e l e m e n t s t r a i n s i n thestrain-displacement relations. The elementstress is related to strain using the stress-strainr e l a t i o n s f o r a n e l a s t i c s o l i d . E n e r g yconsiderations (either minimum potentialenergy or virtual work) are used to establisht h e r e l a t i o n s h i p between nodal pointdisplacements and nodal point forces. Therelationship is a function of the stress-strainand the strain-displacement characteristics.This function, by definition, is the elementstiffness.

The element stiffness is the key feature inthe finite element solution. Each elementstiffness is combined into a global stiffnessmatrix. In this matrix the stiffness at each nodeis obtained by summing the contribution fromeach element which contains that node. A setof equations for the entire system is obtainedby equating the products of the unknowndisplacements times the stiffnesses to theknown forces at each nodal point.

Nodal displacements are determined bysolving this set of equations. Stresses arecomputed dt the nodes of each element, usingthe same strain-displacement and stress-strainrelations used in the formulation of theelement stiffness. The stresses at a node aretaken as the average of the contributions fromall the elements meeting at that node.

4-46. Capabilities and Limitations. -Thep r o g r a m i s a b l e t o a n a l y z e a n ythree-dimensional elastic structure. The lineardisplacement assumption, however, limits theefficient use of the program to problems wherebending is not the primary method of loadresistance. Accurate modeling of bendingrequires the use of several elements (three havebeen shown to work fairly well) across thebending section. When acceptance of load is by

by a series of straight lines.(3) Points of fixity must be established on

the boundaries.(4) Two-dimensional plane stress.4-44. A p p l i c a t i o n t o G r a v i t y

Dams. -Two-dimensional finite elementanalysis is adaptable to gravity dam analysiswhen the assumption of planarity is used. Thestress results for loading of typical transversesections (perpendicular to the axis) are directlyapplicable. Sections including auxiliary workscan be analyzed to determine their stressdistribution. Both transverse and longitudinalsections should be prepared and analyzed forlocal areas with extensive openings. The resultsof the stress distributions are combined toapproximate the three-dimensional state ofstress.

The two-dimensional finite element analysisallows the foundation with its possible widevariation in material properties to be includedwith the dam in the analysis. Zones of tensioncracks and weak seams of material can beincluded in the foundation. The internalhydrostatic pressure can be included as loadson the section to be analyzed.

Foundation treatment requirements forachieving suitable stresses and deformationscan be determined with acceptable accuracyusing this two-dimensional finite elementprogram.

An example is given in appendix C whichi l l u s t r a t e s t h e a p p l i c a t i o n o f t h etwo-dimensional finite element method toanalysis of a gravity dam and its foundation.

2. Three-Dimensional

Finite Element Program

4-45. Application. -This computer program,which was developed by the University ofC a l i f o r n i a a t B e r k e l e y , u s e s t h eZ i e n k i e w i c z - I r o n s i s o p a r a m e t r i ceight-nodal-point (hexahedron) element toanalyze three-dimensional elastic solids [ 121 .T h e e l e m e n t s u s e t h e l o c a l o r n a t u r a lcoordinate system which is related to theX-Y-Z system by a set of linear interpolationfunctions. These local coordinates greatly

LAYOUT AND ANALYSIS--Sec. 4-47 75

shear and/or normal displacement along withbending, the element is capable of modelingthe displacement efficiently. A comparison ofthe accuracy of elements by Clough [ 131demonstrates this point with several sampleproblems.

Nodal point number

T h e p r o g r a m c a p a c i t y f o r a65,000-word-storage computer is 900 elements,2,000 nodal points, and a maximum bandwidthof 264. The bandwidth is defined as threetimes the maximum difference between anytwo node numbers on an element plus 3. On aCDC 6400 electronic computer the time foranalysis in seconds is approximately:

coordinateme5

For a problem which uses the full programcapacity, this is equal to:

0.024(2,000) + 0.45(900)

+ 1oo(2’ooo) x 3 x775

or about 105 minutes.T h e c o s t o f o p e r a t i n g i n c r e a s e s

approximately as the square of the bandwidth.This economic consideration often restricts theuser to a relatively coarse mesh.

Capability for use of mesh generation,concentrated loads, automatic uniform orhydrostatic load application, and varyingmaterial properties exists in the program.

The elements (see fig. 4-19) are arbitrarysix-faced solids formed by connecting theappropriate nodal points by straight lines.Nonrectangular solid elements, however,require a d d i t i o n a l t i m e f o r s t i f f n e s sformulation because of the necessity ofincreased numerical integration.

4-47. Input.-The structure to be analyzedis approximated by an assemblage of elements.The finest mesh (smallest sized elements) arelocated in the region of greatest stress change

Figure 4-19. A finite element with nodal point numbersand coordinate axes.-288-D-2994

t o a l l o w f o r a c c u r a t e m o d e l i n g o fdeformations. The division is also made suchthat the minimum bandwidth is possible, andthe nodes and elements are numbered with thisconsideration in mind. The program requiresthe following basic information:

(1) Operational data such as t i t le,number of jobs, number of elements,m a x i m u m b a n d w i d t h , n u m b e r o fmaterials, etc.

(2) The conditions of restraint on theboundary.

(3) The material description of theelements.

( 4 ) T h e a c c u r a c y o f i n t e g r a t i o nrequired for each element.

(5) The X-Y-Z coordinates of eachnodal point and the eight nodal pointnumbers forming each element (meshgeneration can be used to accomplishthese functions).

(6) Applied forces (it is possible to useautomatic load generation).

4-48. Output.-The program output consistsof:

(1) A reprint of all input informationincluding the information automaticallygenerated.

(2) The displacements in the X, Y, and2 directions for each of the nodal points.

(3) The normal stress in the X, Y, and2 directions and the shear stress in the


XY, YZ, and XZ planes at each nodal formulation, input data, and output is given inpoint. appendix C.

A s a m p l e p r o b l e m s h o w i n g m e s h

F. FOUNDATION ANALYSIS

4-49. Purpose. -The foundation or portionsof it must be analyzed for stability wheneverthe rock against which the dam thrusts has aconfiguration such that direct shear failure ispossible or whenever sliding failure is possiblealong faults, shears, and joints. Associated withstability are problems of local overstressing inthe dam due to foundation deficiencies. Thepresence of such weak zones can causeproblems under either of two conditions: (1)when differential displacement of rock blocksoccurs on either side of weak zones, and (2)when the width of a weak zone represents anexcessive span for the dam to bridge over. Toprevent local overstressing, the zones ofweakness i n t h e f o u n d a t i o n m u s t b estrengthened so that the applied forces can bed i s t r i b u t e d w i t h o u t c a u s i n g e x c e s s i v edifferential displacements, and so that the damis not overstressed due to bridging over thezone. Analyses can be performed to determinethe geometric boundaries and extent of thenecessary replacement concrete to be placed inweak zones to limit overstressing in the dam.

1. Stability Analyses

4-50. Methods Available. -Methods availablefor stability analysis are:

(a) Two-Dimensional Methods.(1) Rigid section method.(2) Finite element method.

(b) Three-Dimensional Methods.(1) Rigid block method.(2) Partition method.(3) Finite element method.

Each of these analyses produces a shearingforce and a normal force. The normal force canbe used to determine the shearing resistance asdescribed in section 3-5. The factor of safetyagainst sliding is then computed by dividing theshear resistance by the shearing force.

4-5 1 . T w o - D i m e n s i o n a l M e t h o d s . - Aproblem may be considered two dimensional ift h e g e o l o g i c a l f e a t u r e s c r e a t i n g t h equestionable stability do not vary in crosssection over a considerable length so that theend boundaries have a negligible contributionto the total resistance, or when the endboundaries are free faces offering no resistance.The representation of such a problem is shownon figure 4-20.

(a) Rigid Section Method. -The rigid sectionmethod offers a simple method of analysis. Theassumption of no deformation of the sectionallows a solution according to statics andm a k e s t h e m e t h o d c o m p a r a b l e t o t h ethree-dimensional rigid block method. Asshown on figure 4-20, the resultant of all loadson the section of mass under investigation areresolved into a shearing force, V, parallel to thepotential sliding plane and a normal force, N.The normal force is used in determining theamount of resistance as discussed in section3-5. The factor of safety or shear frictionfactor is determined by dividing the resistingforce by the sliding force.

This method may also be used when two ormore features combine to form the potentialsliding surface. For this case each feature canbe assumed to form a section. Load whichcannot be carried by one section is thentransferred to the adjacent one as an externalload. This procedure is similar to the methodof slices in soil mechanics, except that thesurface may have abrupt changes in direction.

(b) Finite Element Method. -The finiteelement method, discussed in sections 4-36through 4-48, allows deformations to occurand permits more accurate placement of loads.The analysis gives the resulting stressdistribution in the section. This distributionallows the variation in normal load to beconsidered in determination of the resistingforce and shearing force along the potential


,/J=ltlO */t/ft3

77

ential slidmg p l ane

E = E x t e r n a l f o r c e s ( f r o m dam.etc)W = W e i g h t ( d e a d l o a d wght o f m a s s )S = S e e p o g e f o r c e s ( h y d r o s t a t i c )V = Sheor f o r c eN = N o r m a l f o r c e

Figure 4-20. Sketch illustrating the two-dimensionalstability problem.-288-D-2996

sliding plane. The shear friction factor can thenbe computed along the plane to determine thestability. When the stress distribution along theplane is known, a check can be made todetermine if stress concentrations may causefailure of the material in localized arcas.

It should be noted that this distribution canbe approximated without using the finiteelement method if the potential sliding massand underlying rock are homogeneous. Thefinite element method is very useful if there arematerials with significantly different propertiesin the section.

4-52. Three-Dimensional Methods.-Atypical three-dimensional stability problem is afour-sided wedge with two faces exposed andthe other two faces offering resistance tosliding. The wedge shown on figure 4-21 is usedin the discussion to illustrate the variousmethods.

( a ) R i g i d B l o c k M e t h o d 1141 . - T h efollowing assumptions are made for thismethod:

(1) All forces may be combined intoone resultant force.

(2) No deformation within the blockmass can take place.

(3) Sliding on a single plane can occuronly if the shear force on the plane isdirected toward an exposed (open or free)face.

(4) Sliding on two planes can occuronly in the direction of the intersection ofthe two planes and toward an exposedface.

(5) No transverse shear forces aredeveloped (that is, there is no shear on theplanes normal to the sliding direction).

The rigid block analysis proceeds in thefollowing manner:

(1) The planes forming the block aredefined.

(2) The intersections of the planesform the edges of the block.

(3) The areas of the faces of the blockand the volume of the block arecomputed.

( 4 ) T h e h y d r o s t a t i c f o r c e s , i fapplicable, are computed normal to thefaces.

(5) The resultant of all forces iscomputed.

(6) The possibility for sliding on oneor two planes is checked.

(7) The factor of safety against slidingis computed for all cases where sliding ispossible.

To determine whether the rock mass couldslide on one or two planes, a test is applied toeach possible resisting plane. If the resultantvector of all forces associated with the rockmass has a component normal to and directedinto a plane, it will offer resistance to sliding. Ifonly one plane satisfies the criterion, thepotential sliding surface will be one plane; andif two planes satisfy the criterion the potentialsliding surface will be the two planes.

Sliding on three planes is impossibleaccording to the assumptions of rigid block. Ifan analysis of a block with many resistant facesis desired according to rigid block procedure,several blocks will need to be analyzed withany excess shear load from each block appliedto the next.

The resultant force for the case of a singlesliding plane is resolved into one normal andone shear force. For the case of sliding on twoplanes, the resultant is divided into a shearforce along the intersection line and a resultantforce normal to the intersection line. Forcesnormal to the two planes are then computedsuch that they are in equilibrium with ther e s u l t a n t n o r m a l f o r c e . A s a r e s u l t o fassumption (5) at the beginning of thissubsection, t h e s e n o r m a l l o a d s a r e t h emaximum that can occur and the resultingshear resistance developed is a maximum.Figures 4-22(a) and 4-22(b) show a section


perpendicular to the sliding direction is thenp r o p o r t i o n a t e l y a s s i g n e d t o e a c h p l a n eaccording to the ratio of projected areas of theplanes with respect to the direction of loadingas shown on figures 4-23(c) and 4-23(d).(Note: If the external load is parallel to one ofthe planes, the load assignment may have to beassumed differently depending on the point ofload application.) All the forces on each planeare then combined to form a resultant on thatplane (fig. 4-23(e)). This resultant is assumedto be balanced by a normal force and a shearforce on that plane (fig. 4-23(f)). The normalforce is then used in determining the resistanceof the block to sliding.

F i g u r e 4 - 2 1 . F o u r - s i d e d f a i l u r e w e d g e f o rthreedimensional stability analysis.-288-D-2997

(b)

R, = The portlon of the resultant narmal to thedIrectIon of potent101 movement.

N = The normal load on the face lndlcoted by the subscrtpt.

Figure 4-22. Section through a sliding mass normal to theintersection line of two planes.-288-D-2998

through the potential sliding mass normal tothe intersection line of the two planes with theresultant normal load balanced by normals tothe two potential sliding planes.

The shearing resistance developed for eithera single plane or two planes is computed usingthe normal forces acting on the planes and themethods discussed in section 3-5.

(b) Partition Method.-The rigid blockmethod permits no deformation of the mass ofthe block. Because of this restriction no shearload is developed in the potential sliding planestransverse to the direction of sliding. Thedevelopment o f s h e a r i n t h e t r a n s v e r s edirection decreases the normal load andconsequently the developable shear resistance[ 151, An approximation to the minimumdevelopable shear resistance is made by thepartition method. In this method the planes(normal to the sliding direction) are partedaccording to the dead load associated with eachplane as shown on figures 4-23(a) and 4-23(b).T h e c o m p o n e n t o f t h e e x t e r n a l l o a d

A l t h o u g h i t i s r e c o g n i z e d t h a t t h edevelopable shear force is probably less thanthat required to balance the resultant, theassumption that this strength is developedallows c o m p u t a t i o n of the min imumdevelopable strength. The shear resistancedeveloped by using N, and Nz (fig. 4-23(f)) isconsidered the minimum possible.

The shearing force tending to drive the blockin the direction of sliding is determined asdescribed for the rigid block method. Thecomputation of the resistance according to thepartition method utilizes the informationobtained for the rigid block analysis, andtherefore requires very li t t le additionalcomputation. The shear resistance determinedby the rigid block method is an upper boundand that determined by the partition method isconsidered a lower bound. As the anglebetween the planes (see fig. 4-22(a)) increases,the results obtained from the two methodsconverge. The correct shear resistance liesbetween the upper and lower bounds and is afunction of the deformation properties of thesliding mass and host mass of rock, and evenmore impor t an t l y o f t he s l i d ing anddeformation characteristics of the joint orshear material forming the surface. The effectof these properties on the resistance developedc a n b e a p p r o x i m a t e d b y u s i n g athree-dimensional finite element program withplanar sliding zone elements. This method isdiscussed in the next subsection.

The partition method can be extended tomultifaced blocks very readily. Just as thesection normal to the direction of sliding is


W'

I tc7

01 @(a)

/ External

R'= E' + W'

--w; + w; =

E’=aE’’ o+b

E’=bE’2 o + b- -E', + E; =

(d) b’!‘I

W’

(e-1

Where W= DEAD LOADE= EXTERNAL LOADSR=RESULTANT LOAD ON MASS

SubscrIpts refer to the opproprlate portlons ofthe mass No subscrlpt implles that the entire mossIS being considered

Planes are normal to the dIrectton of potentlol shdlngLoods resolved Into the plone normal to dlrection of potentlal

sliding are Indicated wth o prime

Figure 4-23. Partition method of determining shearresistance of a block.-288-D-2999

partitioned, so can a section along the directionof sliding be divided as shown on figure 4-24.Excess shear load from one partition, A, mustbe applied to the adjacent one, R, as anexternal loading as shown on the figure.

(c) Finite Element Method.-A programdeve loped by Mah tab [ 161 a l l owsrepresentation of the rock masses bythree-dimensional solid elements andrepresentation of the potential sliding surfaceby two-dimensional planar elements. Theplanar elements are given properties ofdeformation in compression (normal stiffness)and in shear (shear stiffness) in two directions.

The ratio of the normal stiffness to the shearstiffness influences greatly the amount of loadwhich will be taken in the normal direction andin the transverse shear direction. If the normalstiffness is much greater than the shearstiffness, as is the case for a joint with a slickcoating, the solution approaches that given bythe rigid block method. However, as the shearstiffness increases with respect to the normalstiffness, more load is taken by transverse shear

and the solution given by the partition methodis approached.

The three-dimensional finite elementmethod allows another important refinementin the solution of stability problems. Sincedeformations are allowed, the stress state on allplanes of a multifaced block can be computedr a t h e r t h a n approximated and stressconcentrations located.

The refinements available in the analysis bythe three-dimensional finite element methodshould be used when the upper and lowerbounds determined by the other methods aresignificantly different. The method should alsobe used if there is considerable variation inmaterial properties either in the potentialsliding planes or in the rock masses.

A more detailed discussion of the finiteelement method is given in sections 4-36through 4-48.

2. Other Analyses

4-53. Differential Displacement Analysis. -The problem of relative deflection ordifferential displacement of masses or blockswithin the foundation arises due to variationsin the foundation material. Methods thatapproximate or compute the displacement ofmasses or zones within the foundation arerequired to analyze problems of this nature.Typical problems that may occur are asfollows:

(1) Displacement of a mass whosestability depends on sliding friction.

(2) Displacement of a mass sliding intoa low modulus zone.

(3) Displacement of a mass with partialintact rock continuity.

(4) Displacement of zones withvariable loading taken by competent rockin two directions but cut off fromadjacent rock by weak material incapableof transmitting shear load.

The displacements may be approximated by:(1) extension of shear-displacement dataobtained from specimen testing in situ or in thelaboratory; (2) model testing; (3) developmentof an analytical model which can be solved


distribution, and permits representation oftreatment necessary to obtain acceptabledisplacements.

4-54. Analysis of Stress Concentrations Dueto Bridging.-A stress concentration may occurin the dam due to the presence of alow-modulus zone within the foundation asshown on figure 4-25. To minimize the buildupof stress in the dam, a portion of the weakmaterial in the low-modulus zone may bereplaced w i t h c o n c r e t e . T h e d e p t h o freplacement required is determined as thedepth when stresses in the dam andfoundation are within allowable limits. Thetwo-dimensional finite element method,discussed in sections 4-37 through 4-44, is anexcellent method for solving this problem.

,,-MultIfaced block

SECTION B-B

SECTION C-C

NOTE: Circled numbers refer tc foCeSCircled letters refer to blocksR,,= The porttan afthe resultant osslgned to a face

Thesub-subscript mdlcotes the face numberF&=The portion of the resultant normal to the

dlrectlon of patentlol movement of a black.The sub-subscrlpt refers to the black.

Rn =Resultant external load acting on block A

Figure 4-24. Partition method extended to multifacedblocks.-288-D-3000

manually; or (4) two- or three-dimensionalfinite element methods.

Although the method used depends on theparticular problem, it should be noted that thefinite element method offers considerableadvantage over the other procedures. The finiteelement method allows accurate materialp r o p e r t y r e p r e s e n t a t i o n , gives stress

,,,.Applied l o a d

g h e r vertical s

region and possible

‘ t ress

ess

horizontal tension zone

Low-modulus zone

Figure 4-25. Stress distribution near a low-moduluszone.-288-D-3001

G. BIBLIOGRAPHY

4-5 5. Bibliography[l] Westergaard, H. M., “Computations of Stresses in Bridge

Slabs Due to Wheel Loads,” Public Roads, vol. II, March1930, pp. 1-23.

[2] McHenry, Douglas, “A Lattice Analogy for the Solutionof Stress Problems,” Institution of Civil Engineers, Paper5350, vol. 21, December 1943, pp. 59-82.

[3] Timoshenko, S., “Strength of Materials,” Part I, p. 270,1956.

[4] Timoshenko, S., “Theory of Elastic Stability,” Chapter6,196l.

[5] Clough, R. W., “Earthquake Response of Structures,”Chapter 12 of Earthquake Engineering (R. L. Wiegel,

coordinating editor), Prentice-Hall, Englewood Cliffs,N.J., 1970.

[6] Chopra , A. K. , and Chakrabar t i , P . , “A ComputerSolution for Earthquake Analysis of Dams,” Report No.EERC70-5, Earthquake Engineering Research Center,University of California, Berkeley, Calif., 1970.

[7] Morgan, E. D., and Anderson, H. W., “Stress AnalysisUsing Finite Elements,” Report No. SA-1, Bureau ofReclamation, 1969.

[8] Westergaard, H. M., “Water Pressures on Dams DuringEarthquakes,” Transactions, American Society of CivilEngineers, vol. 98, 1933.


[9] Chopra , A. K. , and Chakrabar t i , P . , “The KoynaEarthquake of December 11,1967, and the Performanceof Koyna Dam,” Report No. EERC-71-1, EarthquakeEngineering Research Center, University of California,Berkeley, Calif., p. 28, 1971.

[lo] Zanger, C. N., “Hydrodynamic Pressures on Dams Duet o H o r i z o n t a l E a r t h q u a k e E f f e c t s , ” B u r e a u o fReclamation, Special Assignments Section Report No.21, October is,-1950. -

I1 11 Cloueh. Rav W.. “The Finite Element Method in Plane. a

Stresi ‘Analysis;” ASCE Conference Papers (SecondConference on Electronic Computat ion, September1960).

[12] Zienkiewicz, 0. C., “The Finite Element in Structuraland Continuum Mechanics,” McGraw-Hill , London,1967.

[ 131 Clough, R. W., “Comparison of Three-DimensionalFinite Elements,” Proceedings of the Symposium on theApplication o f F i n i t e E l e m e n t M e t h o d s i n C i v i lEneineering, Vanderbilt University, Nashville, Tenn.,November 13-14,1969.

[14] Londe , P . , (1965), Une Methode d’Analyze o’troisdimensions de la stabilite d’une rive rocheme, AnnlsPonts Chaus. No. 1 37-60.

[ 151 Guzina, Bosko, and Tucovic, Ignjat, “Determining theMinimum Three-Dimensional Stability of a RockWedge,” Water Power, London, October 1969.

[16] M a h t a b , M . A . , a n d G o o d m a n , R . E . , “Three-Dimensional Finite Element Analysis of Jointed RockSlopes,” Final Report to Bureau of Reclamation,contract No. 14-06-D-6639, December 31,1969.

[17] “Design of Arch Dams,” Bureau of Reclamation, 1976.

<<Chapter V

River D ivers ion

A. DIVERSION REQUIREMENTS

5-1. General. -The design for a dam which isto be constructed across a stream channel mustconsider diversion of the streamflow around orthrough the damsite during the constructionperiod. The extent of the diversion problemwill vary with the size and flood potential ofthe stream; at some damsites diversion may becostly and time-consuming and may affect thescheduling of construction activities, while atother sites it may not offer any greatdifficulties. However, a diversion problem willexist to some extent at all sites except thoselocated offstream, and the selection of themost appropriate scheme for handling the flowof the stream during construction is importantto obtain economy in the cost of the dam. Thescheme selected ordinarily will represent acompromise between the cost of the diversionfacilities and the amount of risk involved. Theproper diversion plan will minimize seriouspotential flood damage to the work in progressat a minimum of expense. The followingfactors should be considered in a study todetermine the best diversion scheme:

(1) Characteristics of streamflow.(2) Size and frequency of diversion flood.(3) Regulation by existing upstream dam.(4) Methods of diversion.(5) Specifications requirements.(6) Turbidity and water pollution control.5 - 2 . C h a r a c t e r i s t i c s of Streamflow.-

Streamflow records provide the most reliableinformation regarding stream characteristics,and should be consulted whenever available.

Depending upon the geographical location ofthe drainage area, floods on a stream may be

the result of snowmelt, rain on snow, seasonalrains, or cloudbursts. Because these types ofrunoff have their peak flows and their periodsof low flow at different times of the year, thenature of runoff will influence the selection ofthe diversion scheme. A site subject mainly tosnowmelt or rain on snow floods will not haveto be provided with elaborate measures for uselater in the construction season. A site whereseasonal rains may occur will require only theminimum of diversion provisions for the rest ofthe year. A stream subject to cloudburstswhich may occur at any time is the mostunpredictable and probably will require themost elaborate diversion scheme, since thecontractor must be prepared to handle boththe low flows and floodflows at all timesduring the construction period.

5-3. Selection of Diversion Flood.-It is noteconomically feasible to plan on diverting thelargest flood that has ever occurred or may beexpected to occur at the site, and consequentlysome lesser requirement must be decided upon.This, therefore, brings up the question as tohow much risk to the partially completed workis involved in the diversion scheme underconsideration. Each site is different and theex t en t o f damage done by f l ood ing i sdependent upon the area of foundation andstructure excavation that would be involved,and the time and cost of cleanup andreconstruction that would be required.

In selecting the flood to be used in thediversion designs, consideration should be givento the following:

(1) How long the work will be under

83


construction, to determine the number offlood seasons which will be encountered.

(2) The cost of possible damage towork c o m p l e t e d o r s t i l l u n d e rconstruction if it is flooded.

(3) The cost of delay to completion ofthe work, including the cost of forcing thecontractor’s equipment to remain idlewhile the flood damage is being repaired.

( 4 ) T h e s a f e t y o f w o r k m e n a n dpossibly the safety of downstreaminhabitants in case the failure of diversionworks results in unnatural flooding.

After an analysis of these factors is made,the cost of increasing the protective works tohandle progressively larger floods can becompared to the cost of damages resulting ifsuch floods occurred without the increasedprotective work. Judgment can then be used inde t e rmin ing t he amoun t o f r i sk t ha t i swarranted. Figure 5-l shows a view from theright abutment of Monticello Dam with amajor flood flowing over the low blocks andflooding the construction site. This flood didnot damage the dam and caused only nominaldamage to the contractor’s plant.

The design diversion flood for each dam isdependent upon so many factors that rulescannot be established to cover every situation.Generally, however, for small dams which willbe constructed in a single season, only thefloods which may occur for that season needbe considered. For most small dams, involvingat the most two construction seasons, it shouldbe sufficiently conservative to provide for aflood with a probability of occurrence of 20percent. For larger dams involving more than a2-year construction season, a design diversionflood with a probability of occurrence ofanywhere between 20 and 4 percent may beestablished depending on the loss risk and thecompletion time for the individual dam.

Floods may be recurrent; therefore, if thediversion scheme involves temporary storage ofcloudburst-type runoff, facili t ies must beprovided to evacuate such storage within areasonable period of time, usually a few days.

5-4. Regulation by an Existing UpstreamDam.-If the dam is to be built on a streambelow an existing dam or other controlstructure, it is sometimes possible to modify

the characteristics of the streamflow byplanned operation of the existing structure.During the construction period, a modifiedprogram of operation of the existing structuremay be used to reduce the peak of the floodoutflow hydrograph and reduce the diversionr e q u i r e m e n t s a t the construction site.Upstream control can also be utilized to reduceflow during the construction of cofferdams,plugging of diversion systems and the removalof cofferdams.

S-5. T u r b i d i t y and Water PollutionControl. -One of the more important factors tobe considered in determining the diversionscheme is how the required construction workaffects the turbidity and pollution of thestream. A scheme that limits the turbidity,present in all diversion operations, to theshortest practicable period and creates lesstotal effect on the stream should be given

Figure 5-I. View from right abutment of partiallycompleted Monticello Dam in California, showingwater flowing over low blocks.-SO-1446-R2

RIVER DIVERSION-Sec. 5-6 85

much consideration. Factors which contributeto turbidity in the stream during diversion arethe construction and removal of cofferdams,required earthwork in or adjacent to thestream, pile driving, and the dumping of wastematerial. Therefore, all diversion schemesshould be reviewed for the effect of pollution

a n d t u r b i d i t y o n t h e s t r e a m d u r i n gconstruction and removal of the diversionworks, as well as the effect on the streamduring the time construction is carried onbetween the cofferdams. Sample specificationsfor the control of turbidity and pollution areshown in appendix I.

B. METHODS OF DIVERSION

5-6. Gene&.-The method or scheme ofdiverting floods during construction dependson the magnitude of the flood to be diverted;the physical characteristics of the site; the sizeand shape of dam to be constructed; the natureof the appurtenant works, such as the spillway,penstocks, and outlet works; and the probablesequence of construction operations. Theobjective is to select the optimum schemeconsidering practicability, cost, turbidity andpollution control, and the risks involved. Thediversion works should be such that they maybe incorporated into the overall constructionprogram with a minimum of loss, damage, ordelay.

Diverting streams during constructionutilizes one or a combination of the followingp rov i s ions : t unne l s d r i ven t h rough t heabutments, flumes or conduits through thedam area, or multiple-stage diversion over thetops of alternate construction blocks of thedam. On a small stream the flow may bebypassed around the site by the installation ofa temporary wood or metal flume or pipeline,or the flow may be impounded behind the damduring its construction, pumps being used ifnecessary to control the water surface. In anycase, barriers are constructed across or alongthe stream channel in order that the site, orportions thereof, may be unwatered andconstruction can proceed without interruption.

A common problem is the meeting ofdownstream requirements when the entire flowof the stream is stopped following closure ofthe diversion works. Downstream requirementsmay demand that a small flow be maintained atall times. In this case the contractor mustprovide the required flow by pumping or byother means (bypasses or siphons) until water

is stored in the reservoir to a sufficientelevation so that releases may be made throughthe outlet works.

Figure 5-2 shows how diversion of the riverwas accomplished during the construction ofFolsom Dam and Powerplant on the AmericanRiver in California. This photograph is includedbecause it illustrates many of the diversionprinciples discussed in this chapter. The river,flowing from top to bottom in the picture, isbeing diverted through a tunnel; “a” and “b”mark the inlet and outlet portals, respectively.Construction is proceeding in the original riverchannel between earthfill cofferdams “c” and“d.” Discharge from pipe “e” at the lower leftin the photograph is from unwatering of thefoundation. Since it was impracticable toprovide sufficient diversion tunnel capacity tohandle the large anticipated spring floods, thecontractor made provisions to minimizedamage that would result from overtopping ofthe cofferdam. These provisions included thefollowing:

(1) Placing concrete in alternate low blocksin the dam “f’ to permit overflowing with aminimum of damage.

(2) Construction of an auxiliary rockfill andcellular steel sheet-piling cofferdam “g” t oprotect the powerplant excavation “h” frombeing flooded by overtopping of the cofferdam.

(3) Early construction of the permanenttraining wall “i” to take advantage of theprotection it affords.

5-7. Tunnels.-It is usually not feasible todo a significant amount of foundation work ina narrow canyon until the stream is diverted. Ifthe lack of space or a planned power-plant orother feature eliminates diversion through theconstruction area by flume or conduit, a tunnel


Figure 5-2. Diversion of the river during construction of Folsom Dam and Powerplant in California.-AR-16270.

m a y p r o v e t h e m o s t f e a s i b l e m e a n s o fdiversion. The streamflow may be bypassedaround the construction area through tunnelsin one or both abutments. A diversion tunnelshould be of a length that it bypasses theconstruction area. Where suitable area requiredb y t h e contractor for shops, storage,fabrication, etc., is not readily available, it maybe advantageous to lengthen the tunnel toprovide additional work area in the streambed.However, the tunnel should be kept as short aspracticable for economic and hydraulicreasons. Figure 5-3 shows such a tunnel whichwas constructed at Flaming Gorge Dam site, arelatively narrow canyon, to permit diversionthrough the abutment.

The diversion system must be designed tobypass, possibly also contain part of, the designdiversion flood. The size of the diversiontunne l w i l l t hus be dependen t on t he

magnitude of the diversion flood, the height ofthe upstream cofferdam (the higher the head,the smaller the tunnel needs to be for a givendischarge), and the size of the reservoir formedby the cofferdam if this is appreciable. Aneconomic study of cofferdam height versustunnel size may be involved to establish themost economical relationship.

The advisability of lining the diversiontunnel will be influenced by the cost of a linedtunnel compared with that of a larger unlinedtunnel of equal carrying capacity; the nature ofthe rock in the tunnel, as to whether it canstand unsupported and unprotected during thepassage of the diversion flows; and thepermeability of the material through which thetunnel is carried, as it will affect the amount ofleakage through or around the abutment.

If tunnel spillways are provided in thedesign, it usually proves economical to utilize

\ ’

Figure 5-3. Diversion tunnel for Flaming Gorge Dam, a large concrete dam in Utah-plan, profile, and sections.


them in the diversion plan. When the proposedspillway tunnel consists of a high intake and asloping tunnel down to a near horizontalportion of tunnel close to streambed elevation,a diversion tunnel can be constructed betweenthe near horizontal portion of tunnel and thechannel elevation u p s t r e a m t o e f f e c t astreambed bypass. Figure 5-4 shows such atypical diversion tunnel which will permitdiversion through the lower, nearly horizontalportion of the spillway tunnel. Provisions forthe final plugging, such as excavation ofkeyways, grouting, etc., should be incorporatedinto the initial construction phase of thediversion tunnel.

Some means of shutting off diversion flowsmust be provided; in addition, some means ofregulating the flow through the diversiontunnel may be necessary. Closure devices mayconsist of a timber, concrete, or steel bulkheadgate; a slide gate; or stoplogs. Regulation offlow to satisfy downstream needs after storageof water in the reservoir has started can beaccomplished by the use of a slide gate on atemporary bypass until the water surface in thereservoir reaches the level of the outlet worksintake. Figure 5-5 shows the closure structureconstructed at Flaming Gorge Dam, which wasincorporated in the upstream SO-foot length ofthe diversion tunnel. A high-pressure slide gateon a small conduit was provided in the left sideof the closure structure to bypass requiredflows while filling the reservoir to the elevationof the river outlet.

Permanent closure of the diversion tunnel ismade by placing a concrete plug in the tunnel.If the tunnel passes close to and under thedam, the plug should be located near theupstream face in line with the grout curtaincutoff or it may extend entirely under thedam, depending on the stresses from the damand the condition of the foundation. If thediversion tunnel joins a permanent tunnel, theplug is usually located immediately upstreamfrom the intersection as indicated in figure 5-4.Keyways may be excavated into rock orformed into the lining to insure adequate shearresistance between the plug and the rock orlining. After the plug has been placed and theconcrete cooled, grout is forced through

previously installed grout connections into thecontact between the plug and the surroundingrock or concrete lining to insure a watertightjoint.

5 -8. Conduits Through Dam. -Diversionconduits at stream level are sometimesprovided through a dam. These conduits maybe constructed solely for the purpose ofdiversion or they may be conduits which laterwill form part of the outlet works or powerpenstock systems. As with tunnels, some meansof shutting off the flow at the end of thediversion period and a method of passingdownstream water requirements during thefilling of the reservoir must be incorporatedinto the design of the conduit. The mostcommon procedure for closing the diversionconduit before the placement of the permanentplug is by lowering bulkheads down theupstream face of the dam which will sealagainst the upstream face. Figure 5-6 showstypical details of a conduit through a dam.

After serving their purpose, all diversionconduits must be filled with concrete for theirentire length. This is accomplished with thebulkheads in place. The conduit should beprovided with keyways, metal seals, andgrouting systems within the initial constructionto assure a satisfactory permanent seal. Theshrinkage and temperature of the plug concreteshould be controlled by the installation of acooling system.

5 - 9 . F l u m e s . - I n a w i d e c a n y o n , a neconomical method of diversion may be the useof a flume to carry the streamflow around theconstruction area. A flume may also be used tocarry the streamflow over a low block andthrough the construction area. The flumeshould be designed to accommodate the designdiversion flood, or a portion thereof if theflume is used in conjunction with anothermethod of diversion. The most economicalscheme can be found by comparing costs ofvarious c o f f e r d a m h e i g h t s v e r s u s t h ecorresponding flume capacity. Large flumesmay be of steel or timber frame with a timberlining, and smaller flumes may be of timber ormetal construction, pipe, etc.

The flume is usually constructed around oneside or the other of the damsite or over a low

RIVER DIVERSION-Sec. 5-9 89


CLE L E V A T I O N A - A ELEVATION C-C

3’dl”

S E C T I O N A L P L A N 0-B

S E C T I O N E - E

Figure 5-5. Diversion tunnel closure structure for a large concrete darn (Flaming Gorge Dam in Utah).-288-D-3003

RIVER DIVERSION-Sec. 5-9

SECTION ALONG c OF CONDUIT

1i’Vent return.. .,;‘Vent header,

SECTION A-A SECTION B-8

No 20 qopr metal seal.Jomtr to be welded:

Figure 5-6. Diversion conduit through Morrow Point Dam, asections.-288-D-3004

OETAIL 2

thin arch structure in Colorado-plan and

92

block. The flume can then be moved to otherareas as the work progresses and stageconstruction can be utilized. During theconstruction o f C a n y o n F e r r y D a m , asteel-framed, t i m b e r - l i n e d f l u m e w a sconstructed along the right bank of the river tobe used as the first stage of diversion. Theflume was designed for a capacity ofapproximately 23,000 cubic feet per second.The completed flume can be seen in figure 5-7and a view of the flume in use can be seen infigure 5-8.

5-l 0. Multiple-Stage Diversion.-Themultiple-stage method of diversion over thetops of alternate low construction blocks orthrough diversion conduits in a concrete damrequires shifting of the cofferdam from oneside of the river to the other during


construction. During the first stage, the flow isrestricted to one portion of the stream channelwhile the dam is constructed to a safe elevationin the remainder of the channel. In the secondstage, the cofferdam is shifted and the stream iscarried over low blocks or through diversionconduits in the constructed section of the damwhile work proceeds on the unconstructedportion of the dam. The dam is then carried toits final height, with diversion ultimately beingmade through the spillway, penstock, orpermanent outlets. Figure 5-9 shows diversionthrough a conduit in a concrete dam, withexcess flow over the low blocks.

5-l 1. Cofferdams. -A cofferdam is atemporary dam or barrier used to divert thes t r e a m o r to enclose an area duringconstruction. The design of an adequate

Figure 5-7. Completed diversion flume at Canyon Ferry damsite in Montana. Note the large size of flume required topass the design flow, amounting to 23,000 cubic feet per second.-P-584-MRBP

RIVER DIVERSION-Sec. 5- l 1

Rgure S-8. Completed diversion flume at Canyon Ferry damsite in use for first-stage diversion.-P-591-MRBP

c o f f e r d a m i n v o l v e s t h e p r o b l e m o fc o n s t r u c t i o n e c o n o m i c s . W h e r e t h econstruction is timed so that the foundationwork can be executed during the low waterseason, use of cofferdams can be held to aminimum. Where the streamflow characteristicsare such that this is not practicable, thecofferdam must be so designed that it is notonly safe, but also of the optimum height. Theh e i g h t t o w h i c h a c o f f e r d a m s h o u l d b econstructed involves an economic study ofcofferdam height versus diversion workscapacity, including routing studies of thediversion design flood. This is particularly truewhen the outlet works requirements are small.It should be remembered that floodwater

accumulated behind the cofferdam must beevacuated in time to accommodate a recurrentstorm. The maximum height to which it isfeasible to construct the cofferdam withoutencroaching upon the area to be occupied bythe dam must also be considered. Furthermore,the design of the cofferdam must take intoconsideration the effect that excavation andunwatering of the foundation of the dam willhave on the cofferdam stability, and mustanticipate removal, salvage, and other factors.

When determining the type and location ofthe cofferdams, the effects on the stream asrelated to water pollution and turbidity shouldb e e x a m i n e d f o r e a c h s c h e m e u n d e rconsideration. Unwatering work for structural


Figwe 5-9. Flows passing through diversion opening and over low blocks of a concrete and earth dam (Olympus Damin Colorado).-EPA-PS-330CBT

foundations, constructing and removingcofferdams, and earthwork operations adjacentto or encroaching on streams or watercoursesshould be conducted in such a manner as toprevent muddy water and eroded materialsfrom entering the channel. Therefore, thecofferdams should be placed in such a locationthat earthwork near the stream will be kept toa minimum, by containing as much of theexcavation and work area within the confinesof the cofferdams as practicable. During theconstruction and removal of the cofferdams,mechanized equipment should not be operatedin flowing water except where necessary toperform the required work, and this should berestricted as much as possible.

Generally, cofferdams are constructed ofmaterials available at the site. The two typesnormally used in the construction of dams areearthfill cofferdams and rockfill cofferdams,

the design considerations of which closelyfollow those for permanent small dams of thesame type. Other types, although not ascommon, include timber or concrete cribsfilled with earth or rock, and cellular steelcofferdams filled with pervious material. Cribsand cellular steel cofferdams can be used whenspace for a cofferdam is limited or material isscarce. Cellular cofferdams are especiallyadaptable to confined areas where currents areswift and normal cofferdam constructionwould be difficult.

In many situations, a combination of severaltypes of cofferdams may be used to developthe diversion scheme in the most economicaland practical manner. The type of cofferdamwould be determined for each locationdepending upon such factors as the materialsavailable, required height, available space,swiftness of water, and ease of removal.

RIVER DIVERSION-Sec. 5-12

C. SPECIFICATIONS REQUIREMENTS

95

5-12. Contractor% Responsibilities. -It isgeneral practice to require the contractor toassume responsibility for the diversion of thestream during construction of the dam andappurtenant structures. The requirementshould be defined by appropriate paragraphs int h e s p e c i f i c a t i o n s w h i c h d e s c r i b e t h econtractor’s responsibilities and inform him ast o w h a t p r o v i s i o n s , i f a n y , h a v e b e e nincorporated in the design to facilitateconstruction. Usually the specifications shouldnot prescribe the capacity of the diversionworks, nor the details of the diversion methodto be used; but hydrographs prepared fromstreamflow records, if available, should beincluded. Also, the specifications usuallyrequire that the contractor’s diversion plan besubject to the owner’s approval.

In some cases the entire diversion schememight be left in the contractor’s hands, withthe expectation that the flexibility afforded tothe contractor’s operations by allowing him tochoose the scheme of diversion will bereflected in low bids. Since various contractorswill usually present different schemes, theschedule of bids in such instances shouldrequire diversion of the river to be included asa lump-sum bid. Sometimes a few pertinentparagraphs are appropriate in the specificationsgiving stipulations which affect the contractor’sc o n s t r u c t i o n procedures. For example,restriction from certain diversion schemes maybe specified because of safety requirements,geology, ecology, or time and space limitations.The contractor may also be required to havethe dam constructed to a certain elevation orh a v e t h e c h a n n e l o r o t h e r d o w n s t r e a mconstruction completed before closure of thediversion works is permitted.

These or similar restrictions tend to guidethe contractor toward a safe diversion plan.However, to further define the contractor’sresponsibility, other statements should be

made to the effect that the contractor shall beresponsible for and shall repair at his expenseany damage to the foundation, structures, orany other part of the work caused by flood,water, or failure of any part of the diversion orprotective works. The contractor should alsobe cautioned concerning the use of thehydrographs, by a statement to the effect thatthe contracting authority does not guaranteethe reliability or accuracy of any of thehydrographs and assumes no responsibility forany deductions, conclusions, or interpretationsthat may be made from them.

5-13. Designer’s Responsibilities. -Fordifficult and/or hazardous diversion situations,it may prove economical for the owner toassume the responsibility for the diversionplan. One reason for this is that contractorstend to increase bid prices for diversion of thestream if the specifications contain manyrestrictions and there is a large amount of riskinvolved. A definite scheme of cofferdams andtunnels might be specified where the loss of lifeand property damage might be heavy if acofferdam built at the contractor’s risk were tofail.

Another consideration is that many timesthe orderly sequence of constructing variousstages of the entire project depends on aparticular diversion scheme being used. If theresponsibility for diversion rests on thecontractor, he may pursue a different diversionscheme, with possible delay to completion ofthe entire project. This could result in a delayin delivery of irrigation water or in generationof power, or both, with a subsequent loss inrevenue.

If the owner assumes responsibility for thediversion scheme, it is important that thediversion scheme be realistic in all respects, andcompatible with the probable ability andcapacity of the contractor’s construction plant.

<<Chapter VI

Foundation Treatment

A. EXCAVATION

6-l . General. -The entire area to beoccupied by the base of the concrete damshould be excavated to firm material capable ofwithstanding the loads imposed by the dam,reservoir, and appu r t enan t structures.Considerable attention must be given toblasting operations to assure that excessiveblasting does not shatter, loosen, or otherwisea d v e r s e l y a f f e c t t h e s u i t a b i l i t y o f t h efoundation rock. All excavations shouldconform to the lines and dimensions shown onthe construction drawings where practicable;however, it may be necessary or even desirableto vary dimensions or excavation slopes due tolocal conditions.

F o u n d a t i o n s s u c h a s s h a l e s , c h a l k s ,mudstones, and sil tstones may requireprotection against air and water slaking, or insome environments, against freezing. Suchexcavations can be protected by leaving atemporary cover of several feet of unexcavatedmaterial, by immediately applying a minimumof 12 inches of pneumatically applied mortarto the exposed surfaces, or by any othermethod that will prevent damage to thefoundation.

6-2. Shaping.-If the canyon profile for adamsite is relatively narrow with steep slopingwalls, each vertical section of the dam from thecenter towards the abutments is shorter inheight than the preceding one. Consequentlysections closer to the abutments will bedeflected less by the reservoir load and sectionscloser toward the center of the canyon will bedeflected more. Since most gravity dams arekeyed at the contraction joints, the result is a

torsional effect in the dam that is transmittedto the foundation rock.

A sharp break in the excavated profile ofthe canyon will result in an abrupt change inthe height of the dam. The effect of theirregularity of the foundation rock causes amarked change in stresses in both the dam andfoundation, and in stability factors. For thisreason, the foundation should be shaped sothat a uniformly varying profile is obtainedfree of sharp offsets or breaks.

Generally, a foundation surface will appeara s h o r i z o n t a l i n t h e t r a n s v e r s e(upstream-downstream) direction. However,where an increased resistance to sliding isdesired, particularly for structures founded onsedimentary rock foundations, the surface canbe sloped upward from heel to toe of the dam.The foundation excavation for Pueblo Dam(fig. 6-l), a massive head buttress-type gravitydam, is an example of an excavation sloped inthe transverse direction. Figure 6-l alsorepresents a special type of situation whereinthe foundation excavation is shaped to theconfiguration of the massive head buttress.

6-3. Dental Treatment.-Very often theexploratory drilling or final excavationuncovers faults, seams, or shattered or inferiorrock extending to such depths that it isimpracticable to attempt to clear such areasout entirely. These conditions require specialtreatment in the form of removing the weakm a t e r i a l a n d b a c k f i l l i n g the resultingexcavations with concrete. This procedure ofreinforcing and stabilizing such weak zones isfrequently called “dental treatment.”

97

FOUNDATION TREATMENT-Sec. 6-3 99

‘\‘\


Theoretical studies have been made todevelop general rules for guidance as to howdeep transverse seams should be excavated.T h e s e s t u d i e s , b a s e d u p o n f o u n d a t i o nconditions and stresses at Shasta and FriantDams, have resulted in the development of thefo l lowing a p p r o x i m a t e f o r m u l a s f o rdetermining the depth of dental treatment:

d = 0.002 bH + 5 for H 1 150 feet

d = 0.3 b + 5 for H < 150 feet

where :

H = height of dam above generalfoundation level in feet,

b = width of weak zone in feet, andd = depth of excavation of weak zone

below surface of adjoiningsound rock in feet.

(In clay gouge seams, d should not be lessthan 0.1 H.)

These rules provide a means of approach tothe question o f h o w m u c h s h o u l d b eexcavated, b u t f i n a l j u d g m e n t m u s t b eexercised in the field during actual excavationoperations.

Although the preceding rules are suitable forapplication to foundations with a relativelyhomogeneous rock foundation with nominalfaulting, some damsites may have severaldistinct rock types interspersed with numerousfaults and shears. The effect of rock-typeanomalies complicated by large zones offaulting on the overall strength and stability ofthe foundation requires a definitive analysis.Such a study was performed for CouleeForebay Dam wherein the finite elementmethod of analysis was used in evaluating thefoundation. (See subchapter E of chapter IVand also appendix C.) This method provides away to combine the physical properties ofvarious rock types, and geologic discontinuitiessuch as faults, shears, and joint sets into a valuerepresentative of the stress and deformation ina given segment of the foundation. The methodalso permits substitution of backfill concrete in

faults, shears, and zones of weak rock, and thuse v a l u a t e s t h e d e g r e e o f b e n e f i c i a t i o ncontributed by the “dental concrete.”

Data required for the finite element methodof analysis are: dimensions and composition oft h e l i t h o l o g i c b o d i e s a n d g e o l o g i cdiscontinuities, deformation moduli for each ofthe elements incorporated into the study, andthe loading pattern imposed on the foundationby the dam and reservoir. Methods foro b t a i n i n g d a t a r e l a t e d t o t h e r o c k a n ddiscontinuities are discussed in the sections onfoundation investigations in chapter II.

“Dental treatment” may also be required toimprove the stabili ty of rock masses. Byinputting data related to the shearing strengthof faults, shear, joints, intact rock, pore waterpressures induced by the reservoir and/orground water, the weight of the rock mass, andthe driving forces induced by the dam andreservoir, a safety factor for a particular rockmass can be calculated.

Methods of rock stabili ty analysis arediscussed in chapter IV in the sections on finiteelement method and foundation analysis.

6 - 4 . P r o t e c t i o n A g a i n s t P i p i n g . - T h eapproximate and analytical methods discussedabove will satisfy the stress, deformation, andstability requirements for a foundation, butthey may not provide suitable protectionagainst piping. Faults and seams may containm a t e r i a l c o n d u c i v e t o p i p i n g a n d i t saccompanying dangers, so to mitigate thiscondition upstream and downstream cutoffshafts should be excavated in each fault orseam and backfilled with concrete. Thedimension of the shaft perpendicular to theseam should be equal to the width of the weakzone plus a minimum of 1 foot on each end tokey the concrete backfill into sound rock. Theshaft dimension parallel with the seam shouldbe at least one-half of the other dimension. Inany instance a minimum shaft dimension of 5feet each way should be used to provideworking space.

T h e d e p t h o f c u t o f f s h a f t s m a y b ecomputed by constructing flow nets andcomputing the cutoff depths required toeliminate piping effects, or by the methods

FOUNDATION TREATMENT-Sec. 6-5 101

outlined by Khosla in reference [ 11.’ Thesetwo methods are particularly applicable for

Other adverse foundation conditions may be

medium to high dams. For low head dams, thedue to horizontally bedded clay and shaleseams, caverns, or springs. Procedures for

weighted creep method for determining cutoffdepths as shown in chapter VIII of “Design of

treating these conditions will vary and willdepend upon field studies of the characteristics

Small Dams” [2] may be used. of the particular condition to be remedied.

B. GROUTING

6-5. General. -The principal objectives ofgrouting in a rock foundation are to establishan effective barrier to seepage under the damand to consolidate the foundation. Spacing,length, and orientation of grout holes and theprocedure to be followed in grouting afoundation are dependent on the height of thestructure and the geologic characteristics of thefoundation. Since the characteristics of afoundation will vary for each site, the groutingplan must be adapted to suit field conditions.

Grouting operations may be performedfrom the surface of the excavated foundation,from the upstream fillet of the dam, from thetop of concrete placements for the dam, fromgalleries within the dam, and from tunnelsdriven into the abutments, or any combinationof these locations.

T h e g e n e r a l p l a n f o r g r o u t i n g t h efoundation rock of a dam provides forpreliminary low-pressure, shallow consolidationgrouting to be followed by high-pressure, deepcurtain grouting. As used here, “high pressure”and “low pressure” are relative terms. Theactual pressures used are usually the maximumthat will result in filling the cracks and voids ascompletely as practicable without causing anyuplift or lateral displacement of foundationrock.

6-6. Consolidation Grouting. -Low-pressuregrouting to fill voids, fracture zones, and cracksat and below the surface of the excavatedfoundation is accomplished by drilling andgrouting relatively shallow holes, called “B”holes. The extent of the area grouted and thedepth of the holes will depend on localconditions.

‘Numbers in brackets refer to items in the bibliography,sec. 6-9.

Usually for structures 100 feet and more inheight, a preliminary program will call for linesof holes parallel to the axis of the damextending from the heel to the toe of the damand spaced approximately 10 to 20 feet apart.Holes are staggered on alternate lines toprovide better coverage of the area. The depthsof the holes vary from 20 to 50 feet dependingon local conditions and to some extent on theheight of the structure. For structures less than100 feet in height and depending on localconditions, “B” hole grouting has been appliedonly in the area of the heel of the dam. In thiscase the upstream line of holes should lie at ornear the heel of the dam to furnish a cutoff forleakage of grout from the high-pressure holesdrilled later in the same general location. “B”holes are drilled normal to the excavated surfaceunless it is desired to intersect known faults,shears, fractures, joints, and cracks. Drilling isusually accomplished from the excavatedsurface, although in some cases drilling andgrouting to consolidate steep abutments hasbeen accomplished from the tops of concreteplacements in the dam to prevent “slabbing” ofthe rock. In rarer cases, consolidation groutinghas been performed from foundation gallerieswithin the dam after the concrete placementhas reached a certain elevation. This method ofconsolidation grouting requires careful controlof grouting pressures and close inspection ofthe foundation to assure that the structure isnot being disbonded from the foundation.Figure 6-2 illustrates a typical spacing andlength pattern for “B” hole grouting.

In the execution of the consolidationgrouting program, holes with a minimumdiameter of 1% inches are drilled and grouted40 to 80 feet apart before spli t-spaced

-+---

-I-- -----v---

---i-- -

-I.-._4

0n

Figure 6-2. Foundation treatment for Grand Co&e Forebay Dam in Washington (sheet 1 of 2).-288-D-3005(1/2)

FOUNDATION TREATMENT-Sec. 6-6


the abutments especially for this purpose.However, when no galleries are provided, as isthe case for most low gravity dams,high-pressure grouting is done from curtainholes located in the upstream fillet of the dambefore reservoir storage is started. Suchgrouting holes are identified as “C” holes.

The alinement of holes should be such thatthe base of the grout curtain will be located onthe vertical projection of the heel of the dam.If drilled from a gallery that is some distancefrom the upstream face, the holes may beinclined as much as 15’ upstream from theplane of the axis. If the gallery is near theupstream face, the holes will be nearly vertical.Holes drilled from foundation tunnels may beinclined upstream or they may be verticaldepending on the orientation of the tunnelwith the axis of the dam. When the holes aredrilled from the upstream fillet, they areusually inclined downstream. Characteristics ofthe foundation seams may also influence theamount of inclination.

To facili tate drill ing, pipes of 2-footminimum length are embedded in the floor ofthe gallery or foundation tunnel, or in theupstream fillet. When the structure has reachedan elevation that is sufficient to preventmovement of concrete, the grout holes aredrilled through these pipes and into thefoundation. Although the tentative groutingplan may indicate holes to be drilled onlo-foot centers, the usual procedure will befirst to drill and grout holes approximately 40feet apart, or as far apart as necessary toprevent grout from one hole leaking intoanother drilled but ungrouted hole. Also,leakage into adjacent contraction joints mustbe prevented by prior grouting of the joints.Intermediate holes, located midway betweenthe first holes, will then be drilled and grouted.Drilling and grouting of additional intermediateholes, splitting the spaces between completedholes, will continue until the desired spacing isreached or until the amount of grout acceptedby the last group of intermediate holesindicates no further grouting is necessary.

The depth to which the holes are drilled willvary greatly with the characteristics of thefoundation and the hydrostatic head. In a hard,

intermediate holes are drilled. The amount ofgrout which the intermediate holes acceptdetermines whether additional intermediateholes should be drilled. This split-spacingprocess is continued until grout “take” for thefinal closure holes is negligible and it isreasonably assured that all groutable seams,fractures, cracks, and voids have been filled.

Water-cement ratios for grout mixes mayvary widely depending on the permeability ofthe foundation rock. Starting water-cementratios usually range from 8: 1 to 5: 1 by volume.Most foundations have an optimum mix thatcan be injected which should be determined bytrial in the field by gradually thickening thestarting mix. An admixture such as sand or claymay be added if large voids are encountered.

Consolidation grouting pressures varywidely and are dependent in part on thecharacteristics of the rock, i.e., its strength,tightness, joint continuity, stratification, etc.;and on the depth of rock above the stage beinggrouted. In general, grout pressures as high aspracticable but which, as determined by trial,are safe against rock displacement, are used ingrouting. These pressures may vary from a lowof 10 pounds per square inch to a high range of80 to 100 pounds per square inch. A commonrule of thumb is to increase the aboveminimum collar pressure by 1 pound persquare inch per foot of depth of hole above thepacker, as a trial. If the take is small thepressure may be increased.

6-7. Curtain Grouting. -Construction of adeep grout curtain near the heel of the dam tocontrol seepage is accomplished by drillingdeep holes and grouting them using higherpressure. These holes are identified as “A”holes when drilled from a gallery. Tentativedesigns will usually specify a single line of holesdrilled on IO-foot centers, although wider orcloser spacing may be required depending onthe rock condition. To permit application ofhigh pressures without causing displacement inthe rock or loss of grout through surfacecracks, this grouting procedure is carried outsubsequent to consolidation grouting and aftersome of the concrete has been placed. Usually,grouting will be accomplished from gallerieswithin the dam and from tunnels driven into

FOUNDATION TREATMENT-Sec. 6-8

dense foundation, the depth may vary from 30to 40 percent of the head. In a poorfoundation the holes will be deeper and mayreach as deep as 70 percent of the head. Duringthe progress of the grouting, local conditionsmay determine the actual or final depth ofgrouting. Supplementary grouting may also berequired after the waterload has come on thedam and observations have been made of therate of seepage and the accompanying uplift.

For high dams where foundation galleriesare located at a relatively long distance fromthe upstream face, as at Grand Coulee Dam,“A” hole grouting may be augmented by a lineof “C” holes, drilled from the upstream face ofthe dam and inclined downstream in order tosupplement the main grout curtain. The depthof these holes is usually about 75 feet and theirspacing is usually the same as for the “A”holes. The supplementary grout curtain formedby grouting this line of holes serves as anupstream barrier for subsequent “A” holegrouting, permitting higher “A” hole groutpressures with less chance of excessiveupstream grout travel.

Usually the foundation will increase indensity and tightness of seams as greater depthsare reached, and the pressure necessary to forcegrout into the tight joints of the deep planesmay be sufficient to cause displacements of theupper zones. Two general methods of groutingare used, each permitting the use of higherpressures in the lower zones.

(I) Descending stage grouting consistsof drilling a hole to a limited depth or toits intersection with an open seam,

105

grouting to that depth, cleaning out thehole after the grout has taken its initialset, and then drilling and grouting thenext stage. To prevent backflow of groutduring this latter operation, a packer isseated at the bottom of the previouslygrouted stage. This process is repeated,using h i g h e r p r e s s u r e s f o r e a c hsucceeding stage until the final depth isreached.

(2) Ascending stage grouting consistsof drilling a hole to its final depth andgrouting the deepest high-pressure stagefirst by use of a packer which is seated atthe top of this stage. The packer limitsgrout injection to the desired stage andprevents the grout from rising into thehole above the packer. After groutingthis stage, the grout pipe is raised so thatthe packer is at the top of the next stagewhich is subsequently grouted usingsomewhat lower pressure. This stageprocess is repeated, working upward untilthe hole is completely grouted.Ascending stage grouting is becomingmore generally used, as it reduces thec h a n c e s f o r d i s p l a c e m e n t o f t h efoundation rock, gives better control asto the zones of injection, and expeditesthe drilling.

The discussion in section 6-6 concerninggrout pressures applies in general to curtaingrouting. An exception is that higher initialcollar pressures are permitted, depending onthe height of concrete above the hole.

C. DRAINAGE

6-8. Foundation Drainage. -Although awell-executed grouting program may materiallyreduce the amount of seepage, some meansmust be provided to intercept the water whichwill percolate through and around the groutcurtain, and, if not removed, may buildprohibitive hydrostatic pressures on the base ofthe structure. Drainage is usually accomplishedby drilling one or more lines of holes

downstream from the high-pressure groutcurtain. The size, spacing, and depth of theseholes are assumed on the basis of judgment ofthe physical characteristics of the rock. Holesare usually 3 inches in diameter (NX size).Spacing, depth, a n d o r i e n t a t i o n a r e a l linfluenced by the foundation conditions.Usually the holes are spaced on lo-foot centerswith depths dependent on the grout curtain


and reservoir depths. As a general rule, holedepths vary from 20 to 40 percent of thereservoir depth and 35 to 75 percent of thedeep curtain grouting depth.

Drain holes should be dril led after allfoundation grouting has been completed in thearea. They can be drilled from foundation anddrainage galleries within the dam, or from thedownstream face of the dam if no gallery isprovided. Frequently drainage holes are drilled

from foundation grouting and drainage tunnelsexcavated into the abutments.

In some instances where the stability of arock foundation may be beneficiated byreducing the hydrostatic pressure along planesof potentially unstable rock masses, drainageholes have been introduced to alleviate thiscondition. A collection system for suchdrainages should be designed so that flows canbe gathered and removed from the area.

D. BIBLIOGRAPHY

6-9. Bibliography.[l] K h o s l a , A . N . , “ D e s i g n o f D a m s o n P e r m e a b l e

Foundations,” Central Board of Irr igat ion, India,September 1936.

[ 21 “Design of Small Dams,” Bureau of Reclamation, secondedition, 1973.

<<Chapter VII

T e m p e r a t u r e C o n t r o l o f C o n c r e t e

A. INTRODUCTION

7 - l . P u r p o s e s . - T e m p e r a t u r e c o n t r o lmeasures are employed in mass concrete damsto (1) facilitate construction of the structure,(2) minimize and/or control the size andspacing of cracks in the concrete, and (3)permit completion of the structure during theconstruction period. The measures and degreeof temperature control to be employed aredetermined by studies of the structure, itsmethod of construction, and its temperatureenvironment.

Cracking in mass concrete structures isu n d e s i r a b l e b e c a u s e i t a f f e c t s t h ewatertightness, internal stresses, durability, andappearance of the structures. Cracking willoccur when tensile stresses are developed whichexceed the tensile strength of the concrete.These tensile stresses may occur because ofimposed loads on the structure, but more oftenoccur because of restraint against volumetricchange. The largest volumetric change in massconcrete results from change in temperature.The cracking tendencies which occur as a resultof temperature changes and temperaturedifferentials can be reduced to acceptablelevels, in most instances, by the use ofa p p r o p r i a t e d e s i g n a n d c o n s t r u c t i o nprocedures.

T e m p e r a t u r e control measures whichminimize volumetric changes make possible theuse of larger construction blocks, therebyresulting in a more rapid and economicalconstruction. One of these measures, postcooling, is also necessary if contraction jointgrouting is to be accomplished. A gravity damwith longitudinal joints must have a monolithic

section in an upstream-downstream direction.Therefore, provision for the construction ofgravity dams with longitudinal contractionjoints must include measures by which theconcrete is cooled and contraction joints areclosed by grouting before the reservoir loadsare applied.

Complete temperature treatments, over andabove the use of precooling measures andembedded pipe cooling systems, have beenused in some structures. In these instances,reductions were made in the amount of cementused, low-heat cements were specified, andeffective use was made of pozzolan to replace apart of the cement. Glen Canyon Dam, becauseof the size of the construction blocks and therelatively low grouting temperature, wasconstructed with a 50’ F. maximum placingtemperature, embedded cooling coils, a type IIcement, and a mix containing 2 sacks ofcement and 1 sack of pozzolan per cubic yardof concrete.

7-2. Volumetric Changes. -Mass concretestructures undergo volumetric changes which,because of the dimensions involved, are ofconcern to the designer. The changes in volumedue to early-age temperature changes can becon trolled within reasonable limits andincorporated into the design of the structure.The final state of temperature equilibriumdepends upon site conditions, and little if anydegree of control over the subsequent periodicvolumetric changes can be effected.

The ideal condition would be simply toeliminate any temperature drop. This could beachieved by placing concrete at such a low

107


temperature that the temperature rise due toh y d r a t i o n o f t h e c e m e n t w o u l d b e j u s tsufficient to bring the concrete temperature upto its final stable state. Most measures for theprevention of temperature cracking, however,can only approach this ideal condition. Thedegree of success is related to site conditions,economics, and the stresses in the structure.

The volumetric changes of concern are thosecaused by the temperature drop from the peaktemperature, occurring shortly after placement,to the final stable temperature of the structure.A degree of control over the peak temperaturecan be attained by limiting the placingtemperature of the fresh concrete and byminimizing t h e t e m p e r a t u r e r i s e a f t e rplacement. The placing temperature can bevaried, within limits, by precooling measureswhich lower the temperatures of one or moreof the ingredients of the mix before batching.The temperature rise in newly placed concretecan be restrained by use of embedded pipecooling systems, placement in shallow lifts withdelays between lifts, and the use of a concretemix designed to limit the heat of hydration.T h e s e m e a s u r e s w i l l r e d u c e t h e p e a ktemperature which otherwise would have beenattained. Proportionately, this reduction inpeak temperature will reduce the subsequentvolumetric change and the accompanyingcrack-producing tendencies.

7-3. Factors to be Considered. -Themethods and degree of temperature controlshould be related to the site conditions and thestructure itself. Such factors as exposureconditions during and after construction, finalstable temperature of the concrete mass,seasonal temperature variations, the size andtype of structure, composition of the concrete,construction methods, and rate of constructionshould be studied and evaluated in order toselect effective, yet economical, temperaturecontrol measures. The construction scheduleand design requirements must also be studiedto determine those procedures necessary toproduce favorable temperature conditionsduring construction. Such factors as thicknessof lifts, time interval between lifts, heightdifferentials between blocks, and seasonallimitations on placing of concrete should be

evaluated. Study of the effect of these variableswill permit the determination of the mostfavorable construction schedules consistentw i t h t h e p r e v e n t i o n o f c r a c k i n g f r o mtemperature stresses.

Some structures favor the use of a particularmethod of temperature control. Since openlongitudinal contraction joints would prevent ablock from carrying its load as a monolith,gravity dams with longitudinal joints mustprovide for contraction joint grouting of thelongitudinal joints. This normally requirescooling by means of an embedded pipe coolingsystem and grouting of the joints before thereservoir load is applied. The gravity-type damwith no longitudinal contraction joints requiresonly that degree of temperature controlnecessary to prevent structural crackingcircumferentially across the block as the blockcools and approaches its f inal stabletemperature. Precooling of aggregates and theuse of low-heat cements, reduced cementcontent, and pozzolans are normally adoptedas temperature control measures for gravitydams containing no longitudinal joints.

While longitudinal contraction joints mustalways be grouted, any decision to grouttransverse contraction joints in straight gravitydams depends upon the magnitude of loadtransfer across the joint. Since this loadtransfer depends largely upon the height andaxis profile shape of the dam, no specificcriteria can be made for all straight gravitydams. If these transverse joints are to begrouted, an embedded pipe cooling system willnormally be required.

7-4. Design Data.-The collection of designdata should start at the inception of the projectand shou ld be con t inued t h rough theconstruction period. Data primarily associatedwith the determination of temperature controlmeasures include the ambient air temperaturesa t t h e s i t e , r i v e r w a t e r t e m p e r a t u r e s ,a n t i c i p a t e d reservoir and t a i l w a t e rtemperatures, and the diffusivity of theconcrete in the dam.

The estimate of air temperatures which willoccur in the future at a given site is based onair temperatures which have occurred in thepast, either at that location or one in the near

TEMPERATURE CONTROL OF CONCRETE-Sec. 7-5 109

vicinity. The U.S. Weather Service has collectedclimatological data at a great number oflocations, and long-time records from one ormore of these nearby locations may be selectedand adjusted to the site. For this adjustment,an increase of 250 feet in elevation can beassumed to decrease the air temperature lo F.Similarly, an increase of 1.4’ in latitude can beassumed to decrease the temperature lo F.River water temperatures and streamflow datac a n b e o b t a i n e d f r o m v a r i o u shydrometeorological and water supply reportsand papers. A program for obtaining actualmaximum and minimum daily air and riverwater temperatures at the site should beinstituted as soon as possible to verify or adjustt h e d a t a a s s u m e d f o r e a r l y s t u d i e s .Representative wet- and dry-bulb temperaturesshould also be obtained throughout the year.

The best estimate of the future reservoirwater temperatures would be one based onw a t e r t e m p e r a t u r e s r e c o r d e d a t n e a r b yreservoirs of similar depth and with similarinflow and outflow conditions. The Bureau ofReclamation has obtained reservoir watertemperatures over a period of several years in anumber of reservoirs. From these data,maximum ranges of temperature for theo p e r a t i n g con ditions encountered weredetermined. When no data are available onnearby reservoirs, the next best estimate of thereservoir temperatures can be obtained by theprinciple of heat continuity. This method takesin to c o n s i d e r a t i o n t h e q u a n t i t y a n dtemperature of the water entering and leavingthe reservoir, and the heat transfer across thereservoir surface. T h e s e h e a t b u d g e tcomputations, though accurate in themselves,are based on estimates of evaporation,conduction, absorption and reflection of solarradiation, and reradiation-which in turn arerelated to cloud cover, air temperatures, windvelocities, and relative humidity. Because ofthese variables, any forecast of temperatureconditions in a reservoir based on the principleof heat continuity can only be considered as anestimate.

The diffusivity of concrete, h2, is an indexof the facility with which concrete willundergo temperature change. Although

desirable from the heat standpoint, it is notpracticable to select aggregate, sand, andcement for a concrete on the basis of heatcharacteristics. The thermal properties of theconcrete must therefore be accepted for whatthey are. The value of the diffusivity ofconcrete is expressed in square feet per hour,and can be determined from the relationship,

where:

h2 =-$

K = conductivity in B.t.u. per foot perhour per ’ F.,

C = specific heat in B.t.u. per poundper ’ F., and

p = density in pounds per cubic foot.

Values of the diffusivity for a given concreteare determined from laboratory tests, althoughthey must normally be estimated for earlystudies. As the thermal characteristics of thecoarse aggregate largely govern the thermalcharacteristics of the concrete, the earliest ofthese estimates can be based upon the probabletype of coarse aggregate to be used in theconcrete. Table 7-l gives the thermal propertiesof concretes in Bureau of Reclamation damsand representative values for several rock types.

7-5. Cracking.-Temperature cracking inmass concrete occurs as tensile stresses aredeveloped when a temperature drop takes placein the concrete and some degree of restraintexists against this volumetric change. Thestresses developed are related to the amountand rate of the temperature drop, the age ofthe concrete when the temperature drop takesplace,,and the elastic and inelastic properties ofthe particular concrete. The restraint may beexternal, such as the restraint exerted by thefoundation of a structure; or it may beinternal, such as the restraint exerted by a massupon its surface. Tensile stresses also occurwhen a nonlinear temperature variation occursacross a section of the structure. Because of theinelastic properties of concrete, the stressesdeveloped are related to the temperaturehistory of the structure.


Dam

East Canyon . . . . . . . . . .(predominately quartzand quartzite)

Glen Canyon . . . . . . . . . .Seminoe . . . . . . . . . . . . .Norris . . . . . . . . . . . . . .Wheeler . . . . . . . . . . . . .Flaming Gorge . . . . . . . . .

(limestone and sandstone)Kortes mixes:

1 bbl. cement/cu. yd.and O.O-percent air . . . .

0.85 bbl. cement/cu. yd.and O.O-percent air . . . .

Hungry Horse . . . . . . . . .Hoover . . . . . . . . . . . . .Gibson . . . . . . . . . . . . .Canyon FerrySwift . . . . . : 1: 1: 1: 1:

(limestone)Alms . . . . . . . . . . . . . .Monticello . . . . . . . . . . .Yellowtail . . . . . . . . . . . .Angostura mixes:

0.9 bbl. cement/cu. yd.and 3.0-percent air . . . .

1.04 bbl. cement/cu. yd.and O.O-percent air . . . .

Hiwassee . . . . . . . . . . . .Parker . . . . . . . . . . . . . .Owyhee . . . . . . . . . . . . .O’Shaughnessy . . . . . . . . .Friant mixes:

Portland cement . . . . . .20-percent pumicite . _ . .

Shasta . . . . . . . . . . . . . .Bartlett . . . . . . . . . . . . .Morris . . . . . . . . . . . . . .Chickamauga . . . . . . . . . .Morrow Point . . . . . . . . .

(andesite-basalt)Grand Coulee . . . . . . . . . .Ariel . . . . . . . . . . . . . . .Bull Run . . . . . . . . . . . :

Quartzite . . . . . . . . . . . .Dolomite . . . . . . . . . . . .Limestone . . . . . . . . . . .Granite . . . . . . . . . . . . .Basalt . . . . . . . . . . . . . .Rhyolite . . . . . . . . . . . .

Table I-I.-Thermal properties of concrete for various dams.

Density(saturated)

Ib./cu. ft.

152.9 2.56 2.53 2.50 0.208 0.213 I3.217148.4 2.02 2.01 2.01 .211 .216 .222155.3 1.994 1.972 1.951 .204 .213 .222160.6 2.120 2.105 2.087 .234 .239 .241145.5 1.815 1.800 1.785 .223 .229 .236150.4 1.78 1.77 1.76 .221 .226 .232

157.6 1.736 .210 .215 .221

158.1 1.715150.1 1.72156.0 1.699155.2 1.676151.3 1.63158.2 1.82

1.724 1.711

1.710 1.7051.12 1.711.688 1.6711.667 1.6571.62 1.611.79 1.76

1.579 1.5801.56 1.551.56 1.55

.209 .215 .220

.217 .223 .229

.212 .216 .221

.218 .222 .229

.214 .218 .222

.237 .242 .246

149.7 1.578153.1 1.57152.8 1.57

.225 .229 ,234

.225 .230 .235

.219 .223 .221

151.2 1.491 .2211.484 1.478

1.554 1.5371.491 1.4781.402 1.3951.373 1.3691.338 1.354

1.312 1.3121.232 1.2341.309 1.3191.291 1.2891.291 1.2931.211 1.2660.97 0.94

1.077 1.0790.884 0.9150.847 0.860

Thermal Properties of Coarse Aggregate

.228 .234

152.6155.7155.1152.1152.8

1.5711.5051.4091.3761.316

.221

.218

.213

.208

.217

.234 .240

.225 .233

.216 .221

.214 .222,218 .223

153.6153.8157.0156.3156.9156.5145.5

1.3121.2291.2991.2931.2901.2870.99

.214

.216

.222

.216

.214

.225

.212

.214 .217

.221 ,227

.229 .235

.222 .230

.216 ,222.229 .233.211 .222

158.1146.2159.1

1.0750.8420.835

.219

.228

.215

.222 .227

.235 .244

.225 .234

T Conductivity KB.t.u./ft.-hr.-OF,

-I

500 900700 500

Specific heat CB.t.u./lb.-OF.L

7o"

I .211.231.224.220.226.226 I

.226

.238,230.224.230.232

0.081 0.078

.065 .063

.063 .060

.056 .055

.056 .054

.054 .052

.052 .05 1

.052 .050

.053 .051

.051 .050

.050 .048

.050 .049,049 .047

.047 .046

.046 .044

.047 .046

.045 .044

.044 .042

.043 ,042

.044 .042,040 .040

.040 .040

.037 ,036

.037 .037

.038 .037.039 .038.037 ,036.032 .031

.031 .031

.025 .026

.024 .024

.065

.055,055.046.034.037

.062

.053

.054

.045

.034

.036

Diffusivity hZft.2 /hr.

.061

.057

.053

.052

.050

.049

.050

.049

.047,048.04 1

.042

.042

.04 1

.04 1,041.040

.039,035.036,036.037.035,029

.030

.026

.023

,059.05 1.052.045.033.036

The most common cracking in mass concrete Under these conditions, foundation restraint isoccurs when large blocks of concrete are placed high, large drops in temperature are possibleon the foundation in the fall of the year, after because concrete placing temperatures andwhich concreting is stopped for the winter. peak temperatures are relatively high, and


concrete temperatures will be dropping quite that part of the block below the elevation ofrapidly due to exposure conditions. For blocks the adjacent blocks may remain at the samenot larger than 50 by 50 feet, cracking under t e m p e r a t u r e o r m a y p o s s i b l y r i s e i nthese conditions has no particular pattern. In temperature depending upon its age.larger blocks, and where the length-to-width Surface cracking which occurs because ofratio is over 2, cracking under the above internal restraint seldom follows any particularconditions often occurs at or near the third pattern. The most general cracking is along thepoints of the longer side. Generally, if the horizontal construction joints where the tensileblocks are not placed more than 10 or 15 feet strength is low. Such cracking normally occursoff the foundation, cracking will start at the when wood or insulated steel forms are usedexposed top edge of the block and progress and then removed when exposure temperaturesinto the block and down the side to within a are low. Upon removal of the forms, thefew feet of the foundation. Such cracks vary surface is subjected to a thermal drop whichfrom extremely small or hairline surface cracks sets up a severe temperature gradient betweenwhich penetrate only a few inches into the the surface and the interior. Practically all ofmass, to irregular structural cracks of varying these cracks are from hairline width to l/64width which completely cross the construction inch in thickness. Aside from the horizontalblock. The maximum crack width is at the top construction joints, most other surfaceedge and normally will be from l/32 to l/64 c r a c k i n g i s e v i d e n c e d b y v e r t i c a l o rinch in width. near-vertical cracks associated with surface

Similar cracking across the full width of a irregularities such as openings, reentrantblock can occur during the colder months of corners, or construction discontinuities whichthe year in a high block which has been occurred during placement. Most of theseconstructed well off the foundation and which cracks do not progress beyond the oneis 25 to 50 feet higher than the adjacent placement lift, but those that do often are theblocks. In this instance, the upper part of the beginning of the cracks described above.block will cool at a relatively fast rate while

B. METHODS OF TEMPERATURE CONTROL

7-6. tiecooling.-One of the most effectiveand positive temperature control measures isthat which reduces the placing temperature ofthe concrete. Methods of reducing the placingtemperature w h i c h w o u l d o t h e r w i s e b eobtained at a site can be varied from restrictingconcrete placement during the hotter part ofthe day or the hotter months of the year, to afull treatment of refrigerating the various partsof the concrete mix to obtain a predetermined,maximum concrete placing temperature.

The method or combination of methodsused to reduce concrete placing temperatureswill vary with the degree of cooling requiredand the contractor’s equipment and previousexperience. For some structures, sprinkling andshading of the coarse aggregate piles may bethe only precooling measures required. The

benefits of sprinkling depend largely on thetemperature of the applied water and on thecontractor’s operations at the stockpile. Asecondary benefit, evaporative cooling, can alsobe obtained but is restricted to areas with a lowrelative humidity. Insulating and/or paintingthe surfaces of the batching plant, water lines,etc., with reflective paint can also be beneficial.

Mixing water can be cooled to varyingdegrees, the more common temperatures beingfrom 32’ to 40’ F. Adding slush or crushed iceto the mix is an effective method of coolingbecause it takes advantage of the latent heat offusion of ice. The addition of large amounts ofice, however, may not be very practical in someinstances. For example, if the coarse aggregateand sand both contain appreciable amounts offree water, the amount of water to be added to


the mix may be so small that replacement ofpart of the added water with ice would not beappreciable.

Cooling of the coarse aggregates to about35’ F. can be accomplished in several ways.One method is to chill the aggregate in largetanks of refrigerated water for a given period oftime. Relatively effective cooling of coarseaggregate can also be attained by forcingrefrigerated air through the aggregate while theaggregate is draining in stockpiles, while it is ona conveyor belt and while it is passing throughthe bins of the batching plant. Spraying withcold water will also cool the aggregate. Sandmay be cooled by passing it through verticaltubular heat exchangers. Cold air jets directedon the sand as it is transported on conveyorbelts can also be used. Immersion of sand incold water is not practical because of thedifficulty in removing the free water from thesand after cooling.

Cooling of the cement is seldom practicable.Bulk cement in the quantities used for dams isalmost always obtained at relatively hightemperatures, generally from 140’ to 180’ F.Seldom will it cool naturally and lose a sizableportion of the excess heat before it is used.

Use of the above treatments has resulted inconcrete placing temperatures of 50’ F. in an u m b e r of instances. Concrete placingtemperatures as low as 45’ F. have beenattained, but these can usually be achievedonly at a considerable increase in cost. Thetemperature of the concrete at the mixingplant should be 3’ to 4’ F. lower than thed e s i r e d p l a c i n g t e m p e r a t u r e . T h i s w i l lcompensate for the heat developed andabsorbed by the concrete during mixing andtransporting.

7-7. Postcooling.-Postcooling of massconcrete in gravity dams is used primarily toprevent cracking during construction. It is alsorequired where longitudinal contraction jointsare used and where grouting of transversecontraction joints is required, in order toreduce the temperature of the concrete to thedesired value prior to grouting. The layout ofembedded cooling systems used in postcoolingmass concrete is described in section 7-20.

Postcooling is an effective means of crack

control. Artificially cooling mass concrete bycirculating cold water through embeddedcooling coils on the top of each constructionlift will materially reduce the peak temperatureof the concrete below that which wouldo t h e r w i s e b e a t t a i n e d . H o w e v e r , t h e s eembedded coils will not actually prevent atemperature rise in the concrete, because of thehigh rate of heat development during the firstfew days after placement and the relatively lowconductivity of the concrete. The use of anembedded pipe system affords flexibility incooling through operation of the system. Anydesired degree of cooling may be accomplishedat any place at any time. This can minimize theformation of large temperature gradients fromthe warm interior to the colder exterior. Theformation of such gradients in the fall andwinter is particularly conducive to cracking.

7-8. Amount and Type of Cement.--Massconcrete structures require lesser amounts ofcement than the ordinary size concretes t r u c t u r e s b e c a u s e o f a l o w e r s t r e n g t hrequirement. Because of their dimensions,however, less heat is lost to the surfaces and agreater maximum temperature is attained.Since the heat generated within the concrete isdirectly proportional to the amount of cementused per cubic yard, the mix selected should bethat one which will provide the requiredstrength and durability with the lowest cementcontent. The cement content in mass concretestructures has varied in the past from 4 to 6s a c k s o f c e m e n t p e r c u b i c y a r d , b u tpresent-day structures contain as low as 2 sacksof cement plus other cementing materials.

The heat-producing characteristics of cementplay an important role in the amount oftemperature rise. Although cements areclassified by type as type I, type II, etc., theheat generation within each type may varywidely because of the chemical compounds inthe cement. Types II and IV were developedfor use in mass concrete construction. Type IIcement is commonly referred to as modifiedcement, and is used where a relatively low heatgeneration is desirable. Type IV cement is alow-heat cement characterized by its low rateof heat generation during early age.

Specifications for portland cement generally


do not state within what limits the heat ofhydration shall be for each type of cement.They do, however, place maximum percentageson certain chemical compounds in the cement.T h e y f u r t h e r p e r m i t t h e p u r c h a s e r t ospecifically request maximum h e a t o fhydration requirements of 70 or 80 calories pergram at ages 7 and 28 days, respectively, fortype II cement; and 60 or 70 calories per gramat ages 7 and 28 days, respectively, for type IVcement.

In most instances, type II cement willproduce concrete temperatures which areacceptable. In the smaller structures, type Icement will often be entirely satisfactory.Other factors being equal, type II cementshould be selected because of i ts bet terresistance to sulfate attack, better workability,and lower permeability. Type IV cement isnow used only where an extreme degree oftemperature control is required. For example,it would be beneficial near the base of longblocks where a high degree of restraint exists.Concrete made with type IV cement requiresmore curing than concrete made with othertypes of cement, and extra care is required atearly ages to prevent damage to the concretefrom freezing during cold weather. Often, therun-of-the-mill cement from a plant will meetthe requirements of a type II cement, and thebenefits of using this type of cement can beobtained at little or no extra cost. Type IVcement, because of its special composition, isobtained at premium prices.

7-9. Use of Pozzolans.-Pozzolans are usedin concrete for several reasons, one of which isto reduce the peak temperature due to heat ofhydration from the cementing materials in themix. This is possible because pozzolans developheat of hydration at a much lower rate than doportland cements. Pozzolans can also be usedas a replacement for part of the portlandc e m e n t t o i m p r o v e w o r k a b i l i t y , e f f e c teconomy, and obtain a better quality concrete.The more common pozzolans used in massconcrete include calcined clays, diatomaceousearth, volcanic tuffs and pumicites, and fly ash.The actual type of pozzolan to be used isnormally determined by cost and availability.

7- 10. Miscellaneous Measures. -(a) Shallow

Construction Lifts. -Shallow construction orp l a c e m e n t l i f t s c a n r e s u l t i n a g r e a t e rpercentage of the total heat generated in thelift being lost to the surface. Such atemperature benefit exists only during periodsof time when the exposure temperatures arelower than the concrete temperature asdescribed in section 7-22. Unless the siteconditions are such that a sizable benefit canbe obtained, shallow placement lifts areg e n e r a l l y l i m i t e d t o p l a c e m e n t s o v e rconstruction joints which have experiencedp r o l o n g e d e x p o s u r e p e r i o d s , o r o v e rfoundation irregularities where they are helpfulin the prevention of settlement cracks.

(b) Water Curing.-Water curing on the topand sides of each construction lift will reducethe temperature rise in concrete near thesurfaces as described in section 7-29. Properapplication of water to the surfaces will causethe surface temperature to approximate thecuring water temperature instead of theprevailing air temperatures. In areas of lowhumidity, the effect of evaporative coolingmay result in a slightly lower surfacetemperature than the temperature of the curingwater.

(c) Retarding Age&S.-Retarding agentsadded to the concrete mix will provide atemperature benefit when used in conjunctionwith pipe cooling. The retarding agents reducethe early rate of heat generation of the cement,so that the total temperature rise during thefirst 2 or 3 days will be 2’ or perhaps 3’ F.lower than for a similar mix without retarder.The actual benefit varies with the type andamount of retarder used. The percentage ofretarder by weight of cement is generally abouto n e - f o u r t h t o o n e - t h i r d o f 1 p e r c e n t .Percentages higher than this may give addedt e m p e r a t u r e b e n e f i t b u t c a n c r e a t econstruction problems such as delay in formremoval, increased embedment of form tiesrequired, etc.

(d) Surface Treatments.-If the near-surfaceconcrete of a mass concrete structure can bemade to set at a relatively low temperature andcan be maintained at this temperature duringthe early age of the concrete, say, for the first2 weeks, cracking at the surface can be

114

minimized. Under this condition, tensions atthe surface are reduced or the surface may evenbe put into compression when the interior masso f t h e c o n c r e t e s u b s e q u e n t l y d r o p s i ntemperature. Such surface cooling can beaccomplished by circulating water in closelyspaced embedded cooling-pipe coils placedadjacent to and parallel with the exposedsurfaces, by use of cold water sprays onnoninsulated steel forms and on the exposedconcrete surfaces, or by use of specialrefrigerated forms.

( e ) R a t e o f T e m p e r a t u r e D r o p . -Temperature stresses and the resultanttendency to crack in mass concrete can bemin imized by con t ro l l i ng t he r a t e o ftemperature drop and the time when this dropoccurs, In thick sections with no artificialcooling, the temperature drop will normally beslow enough as to present no problem. In thin


sections with artificial cooling, however, thetemperature can drop quite rapidly and thedrop may have to be controlled. This can beaccomplished by reducing the amount ofcooling water circulated through the coils or byraising the cooling water temperature. Theoperation of the cooling systems, and thelayout of the header systems to supply coolingwater to the individual cooling coils, should besuch that each coil can be operatedindependently. No-cooling periods should alsobe utilized where necessary. In thin sectionswhere no artificial cooling is employed, thetemperature drop during periods of coldweather can be controlled by the use ofinsulated forms and insulation placed onexposed surfaces. Such measures not onlyreduce the rate of change, but also reduce thetemperature gradients near the surface resultingin a definite reduction in cracking.

C. TEMPERATURE STUDIES

7- 11. General Scope of Studies. -Themeasures required to obtain a monolithicstructure and the measures necessary to reducec rack ing t endenc i e s t o a m in imum a redetermined by temperature control studies. Inaddition to the climatic conditions at the site,the design requirements of the structure andthe probable construction procedures andschedules require study to determine themethods and degree of temperature control forthe structure.

Early design studies and specificationrequirements are based on existing data and ona possible construction schedule. The ambientt e m p e r a t u r e s a n d p r o b a b l e c o n c r e t et e m p e r a t u r e s a r e then related to thedimensions of the structure, the conditionsarising during construction, and the desireddesign stresses. As a result of these studies, amaximum concrete placing temperature maybe determined, measures taken to limit theinitial temperature rise within the concrete,and protective measures planned to alleviatecracking c on ditions arising during thec o n s t r u c t i o n period. Actual exposure

c o n d i t i o n s , w a t e r t e m p e r a t u r e s , a n dconstruction progress may vary widely fromthe assumed conditions, and adjustmentsshould be made during the construction periodto obtain the best structure possible consistentwith economy and good construction practices.

The following discussions cover the morec o m m o n temperature investigations andstudies. In all of these studies, certainconditions must be assumed. Since any heatflow computation is dependent on the validityof the assumed exposure conditions andconcrete properties, experience and goodjudgment are essential.

7-l 2. Range of Concrete Temperatures. -The ranges or amplitudes of the mean concretetemperature at various elevations of a gravitydam are used in several studies of stresseswithin the dam. This range of mean concretetemperature is determined from the air andwater temperatures at the site, as modified bythe effects of solar radiation. For preliminarystudies , t h e r a n g e o f m e a n c o n c r e t etemperature can be obtained in a shortcomputation by applying the air and water


exposure temperatures as sinusoidal waves withapplicable periods of 1 day, 1 week or 2 weeksdepending upon the severity of the weather tobe used for the design, and 1 year. Solarradiation is then added to obtain the finalrange of mean concrete temperature.

For average (mean) weather conditions, theambient air temperatures are obtained from aplotting of the mean monthly air temperatureson a year scale. For usual and extreme weatherconditions, the above ambient air temperaturesare adjusted for a 7-day period and a 14-dayperiod, respectively, at the high and low pointsof the annual curve. The amount of theadjustment for these weather conditions isdescribed in subsection (a) below.

The thickness of section for these studies ismeasured along lines normal to the exposedsurfaces, the intersection of the normals beingequidistant from the two faces.

(a) Ambient Air Temperatures. -Whencompu t ing t he r ange o f mean conc re t etemperature, mean daily, mean monthly, andmean annual air temperatures are used. Thetheory applies the daily and annual airt em peratures as sinusoidal variations oftemperature, even though the cycles are nottrue sine waves. T h e a n n u a l a n d d a i l yamplitudes are assumed to be the same for allweather conditions.

To account for the maximum and minimumrecorded air temperatures, a th i rd andsomewhat arbitrary temperature cycle isassumed. This temperature variation isassociated with the movements of barometricpressures and storms across the country. Plotsthroughout the western part of the UnitedStates show from one to two cycles per month.Arbitrarily, this third temperature variation isassumed as a sine wave with either a 7-day or14-day period for usual weather conditions andextreme weather conditions, respectively. Forextreme weather conditions, the amplitudes ofthe arbitrary cycle are assigned numericalvalues which, when added to the amplitudes ofthe daily and annual cycles, will account forthe actual maximum and minimum recordedair temperatures at the site. For usual weatherconditions, these amplitudes are assigned valueswhich account for temperatures halfway

b e t w e e n t h e m e a n m o n t h l y m a x i m u m(minimum) and the maximum (minimum)recorded. When computing the mean concretetemperature condition, no third cycle is used.

(b) Reservoir Water Temperatures. -Thereservoir w a t e r t e m p e r a t u r e s u s e d i ndetermining the range of mean concretetemperature for a proposed dam are thosetemperatures which will occur after thereservoir is in operation. These reservoir watertemperatures vary with depth, and for allpractical purposes can be considered to haveonly an annual cycle. For preliminary studies,the range of mean concrete temperature withfull reservoir is the normal condition. For finaldesigns, stage construction should be taken intoconsideration and t he de s ign reservoiroperation used. When the reservoir is to befil led or partially fi l led before concretetemperatures have reached their final stage oftemperature equilibrium, further studies areneeded for the particular condition.

( c ) S o l a r R a d i a t i o n E f f e c t . - T h edownstream face of a dam, and the upstreamface when not covered by water, receives anappreciable amount of radiant heat from thesun. This has the effect of warming theconcrete surface above the surrounding airtemperature. The amount of this temperaturerise above the air temperature was recorded onthe faces of several dams in the western portionof the United States. These data were thencorrelated with theoretical studies which tookinto consideration varying slopes, orientationof the exposed faces, and latitudes. The resultsof these studies are presented in reference [ 11 .lThese theoretical temperature rises due to solarradiation should be corrected by a terrainfactor obtained from an east-west profile of thesite terrain. This is required because thetheoretical computations assumed a horizontalplane at the base of the structure, and theeffect of the surrounding terrain is to block outsome hours of sunshine. This terrain factor willvary with elevation and from abutment toabutment.

‘Numbers in brackets refer to items in bibliography, sec.7-31.


7-13. Temperature Gradients. -Temperaturedistributions in a mass where boundaryconditions vary with time are easily determinedby the Schmidt method. (See references [ 11,[23, [3], [4] .) This method is generally usedfor temperature studies of mass concretestructures when the temperature gradient ordistribution across the section is desired. Thedepth of freezing, and temperature distributionafter placement are typical of the solutionswhich can be obtained by this step-by-stepmethod. Different exposure temperatures onthe two faces of the theoretical slab and theautogenous heat of hydration are easily takeninto consideration.

An early objection to the Schmidt methodof temperature computation was the timer e q u i r e d t o c o m p l e t e t h e s t e p - b y - s t e pcomputation. This has been overcome by theuse of electronic data processing machineswhich save many man-hours of work. Programshave been developed which will take intoconsideration any thickness of section, varyingexposures on the two faces of the slab, variableinitial temperatures, a varying heat ofhydration with respect to time, and increasingthe thickness of slab at regular intervals aswould occur when lifts of concrete are placedon previously placed lifts.

A s e c o n d m e t h o d o f t e m p e r a t u r ecomputation in mass concrete which isparticularly adaptable to thick walls andplacement lifts near the rock foundation wasdevised by R. W. Carlson. This method isdescribed in reference [ 51. It, like the Schmidtmethod, is essentially a step-by-step integrationwhich can be simplified by selection of certainvariables. C o n d i t i o n s s u c h a s i n i t i a ltemperature distributions, diffusivity, andadiabatic temperature rise must be known orassumed. Carlson’s method can also bemodified to take into account the flow of heatbetween different materials. This would be thecase where insulated or partially insulatedforms are used, or where concrete lifts areplaced on rock foundations.

T h e v a r i a t i o n i n t e m p e r a t u r e i n asemi-infinite solid at any particular point canalso be estimated from figure 7-4. Thisillustration gives the ratio of the temperature

(d) Amplitudes of Concrete Temperatures.-T h e r a n g e o r a m p l i t u d e o f c o n c r e t etemperatures is determined by applying theabove-described external sinusoidal air andwater t e m p e r a t u r e s t o t h e e d g e s o f atheoretical flat slab, the width of the slab beingequal to the thickness of the dam at theelevation under consideration. The problem isidealized by assuming that no heat flows in adirection normal to the slab. The law ofs u p e r p o s i t i o n i s u s e d i n t h a t t h e f i n a lamplitude in the concrete slab is the sum of theamplitudes obtained from the differentsinusoidal variations.

To apply the theoretical heat flow in apractical manner, unit values are assumed forthe several variables and a curve is drawn toshow the ratio of the variation of the meantemperature of the slab to the variation of theexternal temperature. Figure 7-1 shows therelationship thus derived for temperaturevariations in flat slabs exposed to sinusoidalvariations for h* = 1.00 square foot per day, aperiod of 1 day, and a thickness of slab of II . Acorrelation equation is given to take intoaccount the actual thickness of dam, diffusivityc o n s t a n t , a n d p e r i o d o f t i m e . Thecomputations are shown in figures 7-2 and7-3.* For the actual thickness of dam, I,, avalue of I, is obtained from the correlationequation for each of the air temperature cycles.For each value of I, , a ratio of the variation ofmean concrete temperature to the variation ofexternal temperature is obtained. The sums ofthe products of these ratios and their respectiveamplitudes are algebraically added to ands u b t r a c t e d f r o m t h e m e a n a n n u a l a i rt e m p e r a t u r e t o o b t a i n m e a n c o n c r e t etemperatures for the condition of air on bothfaces. Mean concrete temperatures are thenobtained in the same manner for a fictitiouscondition of water on both faces, and the twoconditions are simply averaged together toobtain the condition of air on one face andwater on the other. Solar radiation values arethen added to obtain the final range of meanconcrete temperatures.

2 These and sev~al other figures and tables in this chapterwere reprinted from Bureau of Reclamation EngineeringMonograph No. 34, listed as reference ] 11 in the bibliography,sec. 7-3 1.

TEMPERATURE CONTROL OF CONCRETE-Sec. 7-13

T e m p e r a t u r e V a r i a t i o n s o f F l a t S l a b sExposed to Sinusoidal TemperatureV a r i a t i o n o n B o t h F a c e s

C o n d i t i o n s :h2= 1.00 ft.2/ d a y

Period of temperature variation = I( = I dayThickness of slab as shown = 1,

For other condi t ions:

T H I C K N E S S O F S L A B - F E E T (1,)

Figure 7-I. Temperature variations of flat slabs exposed to sinusoidal temperature variations on bothfaces.-288-D-3008

range in the concrete at the particular point, tothe temperature range at the surface for daily,

be of concern not only during the construction

15day, and annual cycles of temperature.period but during the life of the structure.

Stresses due to temperature gradients mayStresses across a section due to temperaturegradients can be obtained from the expression


RANGE OF MEANCONCRETE TEMPERATURES

Hunsrv How DAM( E f f e c t o f s o l a r r o d i a t i o n n o t i n c l u d e d )

e,- e2For yearly change PI=- -dm = ~ L0 . 0 4 6 4 fJ

e,F o r 365-h,. change .!, = o.o53x M5 = &?LL&

For daily change L=, ez = 0.867 e,0.053124

Remarks: Aor temperatures taken from 34 war record ar ColumbiaFalls, Montana. h2 = 0.053 fro,,, laborator” data

Thick- Due to Due to Dus t o~,a”- n666 Yearly Rangexs-hcRon Daily Rorqe EX

I4501 811 3 . 7 6 1 .215[18.39 ,043 7184 .Olll 6 . 1 1 6.8]49.3[36.4 1 5 . 7 1 5 . 6 146.9137.4 4 7 . 5 3 9 . 5 43.01 4.51 1 . 2 144.2/41.8 146.7139.1 46.6 39.634001 1111 5.151 .156125.X+ .0321 1 - 14.41 4.9147.6138.3 14.1 14.1 147.3139.1 146.aj39.0142.a~ 3.01 0.5 j42.5]41.5145.0]39.7 144.9 40.3

3 3 5 0 1 ‘41 1 6.541 .122[32.011 .0251 1 1 13 .4 3.9 146.6 139.3 1 3 .2 1 3 .2 146.4 140.0 143.0 j 141.0;39.0 2.01 0.2 / 1 4 0 . 8 I43.9140.041.2 143.8 4 0 . 4

3300 ( ‘ 7 ’ 1 7.931 .‘wl38.82/ .0211 1 1 2 .8 1 3 .2 146.0 140.0 j 2 .6 1 2 .7 145.6 140.5 143.0 139.0 j j4 1 . 0 2.01 0.2 141.2 140.8 143.6140.4 143.5 140.637501 20’1 9.331 .065]45.631 .a’81 1 1 241 2.7 145.6 140.5 1 2 .2 1 2 .3 145.4 140.9 143.0139.0141.01 2.01 0.2 141.2 140.8 143.4140.6 143.3 140.8

NOT ES: e, = Thickness of dam, ft.Curve referred to is ‘Temperature

Variations of Flat Slabs Exposedto Sinusoidal Temperature Variationso n B o t h Faces:

Figure 7-2. Computation form, sheet 1 of 2-range of mean concrete temperatures.-288-D-3009

eEa’ = b3(1+)

+ 3(2x-b) b (2x-b)T(x)dx-b3 T(x)1where:

e = thermal coefficient of expansion,E = modulus of elasticity,p = Poisson’s ratio, andb = thickness of section with a tempera-

ture distribution T(x).

Where the temperature variation, T(x), cannotbe expressed analytically, the indicatedintegrations can be performed numerically bythe use of Simpson’s rule. For example, using b

= 30 feet, e = 6.0 x 10e6, E = 2,500,OOOpounds per square inch, p = 0.20, and anassumed T(x), the stresses would be computedas shown in table 7-2.

The above expression for stress is not validin all essentials for those temperature gradientswhich occur during the first few days afterp l a c e m e n t , because the extreme creepcharacteristics of the concrete during this ageresult in a highly indeterminate condition ofstress. The expression is also not valid whereexternal restraints occur such as near thefoundation of a block or structure.

7 - I 4. Temperature Rise. -Newly placedconcrete undergoes a rise in temperature due tothe exothermic reaction of the cementingmaterials in the concrete. Early temperaturerise studies may be based on past experiencerecords with the type of cement to be used.

TEMPERATURE CONTROL OF CONCRETE-Sec. 7-14

RANGE OF MEAN CONCRETE

T E M P E R A T U R E SHungry Horse D A M

( E f f e c t o f S o l a r R a d i a t i o n i n c l u d e d )

L a t i t u d e 48%

Remarks :

I

1 MEAN CONCRETE TEMPERATURES

Thick- E f fects 1 E x p o s e d t o air 1 A i r o n D . S F a c e

31001 70 1 I I I I I 0 1 6 3 1 4.4 1 6.7 1 4.7 I 4.4 4.7

I I I

Figure 7-3. Computation form, sheet 2 of 2-range of mean concrete temperatures.-288-D-3010

Figure 7-5 shows typical temperature rise characteristics of pozzolans vary widely. Whencurves for the various types of cement. The a pozzolan is to be used to replace a part of thetemperature rise curves are based on 1 barrel (4 cement, the heat of hydration of the pozzolan,sacks) of cement per cubic yard of concrete, a for early studies, can be assumed to be aboutdiffusivity of 0.050 square foot per hour, and 50 percent of that developed by an equalno embedded pipe cooling. These curves should amount of cement. For final temperaturebe used only for preliminary studies because control studies, the heat generation for athere are wide variations of heat generation particular concrete mix should be obtained bywithin each type of cement and of diffusivity laboratory tests using the actual cement,in concrete. (See reference [ 61.) Where less pozzolan, concrete mix proportions, andthan 4 sacks of cement per cubic yard is to be mass-cure temperature cycle for the concreteused, the temperature rise can be estimated by to be placed in the structure.direct proportion since the heat generation is The above heat of hydration relates to thedirectly proportional to the amount of cement. adiabatic temperature rise in the concrete.

As with cements, the heat-development Because the surfaces of a structure are exposed


T-

40SEMI- I N F I N I T E SOL10 4

/,

TEMPERATURE RANGE IN CONCRETERAT’o TEMPERATURE RANGE AT SURFACE

Figure 7-4. Temperature variations with depth insemi-infinite solid.-288-D-301 1

or in contact with inert or near-inert bodies, aflow of heat will take place through thesesurfaces and the actual temperature rise in theconcrete will be affected accordingly. The lossor gain of heat to the surface due to exposureconditions, and the loss or gain of heat from anunderlying lift or to the foundation areillustrated in reference [ 71. Schmidt’s methodor Carlson’s method can also be used todetermine the actual temperature rise.

Several difficulties are encountered in theconditions given in reference [ 71. For example,the theoretical equation for the adiabatictemperature rise is given as T = To (l-e- mt ),

of standard ceme

Cement content- I bbl per cu ydDlff”s,“Ity- 0 050 ft’/ hr

Figure 7-5. Temperature rise in mass concrete for varioustypes of cement.-288-D-3013

and To and m are selected to make thetheoretical curve fit the laboratory data. Anyvariance between the theoretical and actualcurves will result in some error in thetheoretical heat loss in the heat-generating lift.The loss from the inert lift does not take intoconsideration a varying surface temperature,which also introduces an error. A third errormay be introduced when a new lift is placed onan older lift which is still generating heat.Depending upon the age of the older lift, theheat generated may still be enough to beconsidered.

7-15. Artificial Cooling.-The design of anartificial cooling system requires a study ofeach structure, its environment, and themaximum temperatures which are acceptablefrom the standpoint of crack control. Thetemperature effects of various heights ofplacement lifts and such layout variables assize, spacing, and length of embedded coilsshould be investigated. Variables associatedwith the operation of the cooling systems, suchas r a t e o f w a t e r circulation a n d t h e


fi.

0369

1 21 51 82 12 42730

b

-

--

_-

-

0. 08. 3

15. 822. 729. 135. 140. 746. 050. 955. 660. 0

1003. 8

-

--

--

-

Table I-2.-Computation of temperature stress.

0- 199- 284- 272- 1 7 5

02445 5 2916

1 3 3 41 8 0 0

8862

-

-

For the given conditions:

eEbr(l=OJ

~,=0.1[(900)(1003.8)+ 3(22- 30) (8862)-(30)3T(41

Simplifying:a,=5317z-2700T(z)

+ 10,584

temperature differential between the coolingwater and the concrete being cooled, arestudied concurrently. All of these factorsshould be considered in arriving at aneconomical cooling system which can achievethe desired temperature control.

The theory for the removal of heat fromconcrete by embedded cooling pipes was firstdeveloped for use in Hoover Dam. (Seereference [7] .) From these studies, a numberof curves and nomographs were prepared for avertical spacing (height of placement lift) of 5feet. The concrete properties and a single rateof flow of water were also used as constants.Subsequent to the earlier studies, the theorywas developed using dimensionless parameters.Nomographs were then prepared on the basisof a ratio of b/a of 100, where b is the radiusof the cooled cylinder and a is the radius of thecooling pipe. Actual cooling pipe spacings arenominal spacings and will seldom result in a b/aratio of 100. In order to take the actualh o r i z o n t a l a n d v e r t i c a l s p a c i n g s i n t oconsideration, a fictitious diffusivity constantcan be used which is based on tests of concretemade with similar aggregates. Table 7-3 givesthe values of D, 02, and hzf for variousspacings of cooling pipe. The b/a ratios of thespacings shown vary from about 34 to 135.Within these limits, the values of h2f may beused with sufficient accuracy.

Figures 7-6 and 7-7 are used for pipe coolingcomputations. In these illustrations,

-

--

-

IbP/it.’

10,5844, 125- 1 7 4

- 2 , 8 5 3-4, 182- 4 , 4 3 1- 3,600- 1,959

7 6 24,0238.094

-

_-

-

lb.%.2

7 429

- 1- 2 0- 2 9- 3 1- 2 5- 1 4

52 85 6

Difference between mean temper-1ature of the concrete and temner-ature of the cooling water- I

itial temperature differencebetween the concrete and the 1

L cooling water Jr 1

y= Initial temperature difference

K = conductivity of the concrete,L = length of cooling coil,

CW = specific heat of water,

Pw = density of water,4w = volume of water flowing through

the coil,t = time from start of cooling,

0, = diameter of the cooling cylinder,and

h2 = diffusivity of the concrete.

Consistent units of time and distance must beused throughout.

The curves in figures 7-6 and 7-7 are used ina straight-forward manner as long as noappreciable heat of hydration is occurring inthe concrete during the period of time underconsideration. When the effect of artificialcooling is desired during the early age of the

T E M P E R A T U R E C O N T R O L O F C O N C R E T E - S W . 7-15 123


Table l-3.- Values of D, D2, and h”f for pipe cooling.

fJPWing

Vertkal Horl?.ontal(f@w (f-t)

2% 2%

5 2%5 35 45 55 6

D D: WI

2. 82 7. 95 1. 31h2

3. 99 15. 92 1. 19h’4. 35 18.92 1. 105. 02 25 .20 1. 125. 64 31 .81 1. 096. 18 38. 19 1. 07

- ~7%7%7%7%7%7%

2%456

7%9

4. 88 23 .81 1. 13hs6. 15 37 .82 1. 076. 86 47. 06 1. 047. 54 56 .85 1. 028. 46 71 .57 1. 009. 26 85.75 0. 98

10I

10 11.284 127. 33 0. 94hs

c o n c r e t e , a step-by-step computation isrequired which takes into consideration heatincrements added at uniform time intervalsduring the period.

Varying the temperature of the watercirculated through the coil, the length of theembedded coil, and the horizontal spacing ofthe pipe are effective means of varying thecooling operation to obtain the desired results.Figures 7-8, 7-9, and 7-lo3 show how thesevariables affect the concrete temperatures.These studies were made using 4 sacks of typeII cement per cubic yard, a diffusivity of 0.050square foot per hour, a flow of 4 gallons perminute through l-inch outside-diameter pipe,5-foot placement lifts, and a 3-day exposure ofeach lift. Figures 7-9 and 7- 10 were derivedusing the adiabatic temperature rise shown infigure 7-8. In general, cooling coil lengths of800 to 1,200 feet are satisfactory. Spacingsvarying from 2% feet on the rock foundationto 6 feet on tops of 7%foot lifts have beenused. The temperature of the cooling water hasvaried from a refrigerated brine at about 30’ F.to river water with temperatures as high as75’ F.3 These three illustrations are reprinted from an article

“Control of Temperature Cracking in Mass Concrete,” by C. L.Townsend, published in AC1 Publication SP-20, “Causes,Mechanism, and Control of Cracking in Concrete,” 1968.

A G E - D A Y S

Figure 7-8. Artificial cooling of concrete-effect ofcooling water temperature. (From AC1 PublicationSP-20.)-288-D-3017

” . ._ .- --

AGE- DAYS

Figure 7-9. Artificial cooling of concrete-effect of coillength. (From AC1 Publication SP-20.)-288-D-3018

I I I I I I4 8 12 16 20 24

A G E - D A Y S

Figure 7-10. Artificial cooling of concrete-effect ofhorizontal spacing of pipe. (From AC1 PublicationSP-20.)-288-D-3019


Varying the size of the embedded pipe will o f t h e t h e o r y in practical applications.affect the cooling results but is uneconomical Temperature distributions and gradients inas compared to the other methods of varying semi-infinite solids are given for both constantthe cooling. The use of l-inch outside-diameter exposure and variable exposure temperaturemetal pipe or tubing is common practice. conditions. Natural cooling of slabs, cylinders,Although black steel pipe is cheaper in material and spheres is discussed using initial uniformcost, aluminum tubing has been used in many temperature distributions, uniformly varyinginstances because it can be furnished in coils initial temperatures, constant exposureand will result in a lower installation cost. t e m p e r a t u r e s , and variable e x p osureIncreasing the rate of flow through l-inch pipe temperatures.will give a m a r k e d improvement of Studies for the insulation requirements onperformance up to a rate of 4 gallons per concrete structures as a protection againstminute. However, doubling the flow to 8 freezing and to minimize the formation ofgallons per minute decreases the time required extreme temperature gradients are discussed infor cooling by only 20 to 25 percent for reference [ 81.average conditions, whereas it doubles the Although specific methods of cooling arecapacity requirements, increases the friction n o r m a l l y l e f t t o t h e c o n t r a c t o r , t h elosses, and more than doubles the power costs. requirements for cooling the various parts of a

7-16. Miscellaneous Studies. -Solutions for concrete mix to obtain a predetermined placingidealized heat flow problems associated with temperature can require a detailed study. Thethe design and construction of mass concrete various considerations for such an operationdams are given in reference 171. Illustrative are discussed in an article by F. B. Kinley inexamples are given which demonstrate the use reference [ 91 .


7- 17. Placing Temperatures. -The maximumtemperature attained in mass concrete isdetermined to a large extent by thetemperature of the concrete as it is placed int h e s t r u c t u r e . T h i s m a k e s t h e p l a c i n gtemperature o f t h e c o n c r e t e o f c o n c e r nbecause (1) lower concrete temperatures willminimize temperature differentials near thesurface, and (2) a measure of control over thes u b s e q u e n t t e m p e r a t u r e d r o p f r o m t h emaximum c o n c r e t e t e m p e r a t u r e t o t h egrouting or final stable state temperature canbe achieved.

When no special provisions are employed,concrete placing temperatures will approximatethe mean monthly air temperature, rangingfrom 4’ to 6’ F. higher than the mean airtemperature in the wintertime and this sameamount lower than the mean air temperature inthe summertime. The actual temperature of theconcrete mix depends upon the temperatures,batch weights, and specific heats of theseparate materials going into the concrete mix.

The placing temperature of the concrete maybe lowered by reducing the temperatures ofone or more of the separate materials. Thecomputation for determining the temperatureof a mix, both with and without precoolingmeasures, is illustrated in references [ 11 and191.

Minimal tensile stresses at the base of aplacement lift will be developed if the placingtemperature of the concrete is at or slightlybelow the temperature of the foundation and ifthe temperature rise is minimized. These tensilestresses resulting after dlacement will be lowerif successive lift placements in a block are madeat regular, periodic intervals with the shortestpracticable time between lifts. Form removaland lifting of forms, installation of requiredmetalwork, and construction joint cleanup willnormally require a minimum of almost 3 daysbetween lifts.

7- 18. Closure Temperature. -One designconsideration related to temperature control isthe grouting or closure temperature of the


contraction joints in the dam. Normally, theclosure temperature in a gravity dam is theminimum mean concrete temperature duringoperation, but the actual temperature may bei n f l u e n c e d b y p r a c t i c a l o r e c o n o m i cconsiderations. The designer often has to makea design decision whether to use only the riverwater available to cool the concrete, therebylosing the benefit of 2’ to 5’ F. additionalcooling which could be obtained by artificialmethods, or to obtain the desired temperaturereduction by requiring mechanically refrigeratedwater to perform the cooling.

From the practical standpoint, it is possibleto cool the concrete by means of an embeddedpipe cooling system to within 4’ or 5’ F. ofthe mean temperature of the cooling water.Concrete temperatures as low as 35’ F. havebeen obtained with a refrigerating plant usingbrine as the coolant. Where cooling isaccomplished with river water, concretetemperatures attainable depend on the meanriver water temperature. At Hungry HorseDam, river water at 32’ to 34’ F. was availableduring the colder months of the year, and finalcooling was accomplished to 38’ F. with thisriver water. Where river water is limited inquantity and is relatively warm, refrigeration ofthe cooling water will be required.

7-19. Size of Construction Block.-Temperature cracking in mass concretestructures is related to the dimensions andshape of the construction blocks in thestructure and to the climatic conditionsoccurring during the construction period.Generally, a block with a length of 50 feet orless can be placed with only a minimum ofcontrol. Likewise, blocks up to 200 feet longcan be placed with normal temperature controlmeasures and have no more than nominalcracking. The location of appurtenancesgenerally controls the spacing betweentransverse contraction joints, but this spacingshould be guided to some extent by the shapeof the block as it progresses from thefoundation to the top of the dam.

(a) Length of Construction Block.-For agiven site and given loading conditions, thethickness of a dam is determined by gravity

analyses. Where this thickness is large, thesection can be broken into two or moreconstruction blocks separated by longitudinaljoints, or it can be constructed as a single blockb y a p p l y i n g r i g i d t e m p e r a t u r e c o n t r o lmeasures. Normally, a 25’ to 30’ F.temperature drop can be permitted in blocks ofthe size commonly used before tensile stressesare developed which will be great enough tocause cracking across the block. In lowtemperature climates, special precautions areneeded to avoid high differential temperaturescaused by sudden temperature drops.

The length of a construction block is notgoverned by the capacity of the concretemixing plant, since each block is firstconstructed to its full width and height at thed o w n s t r e a m e n d o f t h e b l o c k a n d t h e nprogressively placed to the upstream face. Moregenerally, the length of block is related to thetensile stresses which tend to develop withinthe block between the time the block is placedand the time it reaches its final temperature.The stresses are subject to some degree ofcontrol by operations affecting the overallt e m p e r a t u r e d r o p f r o m the m a x i m u mt e m p e r a t u r e t o t h e f i n a l o r c l o s u r etemperature, the rate of temperature drop, thethermal coefficient of expansion, and the ageof the concrete when it is subjected to thetemperature change. Factors in addition totemperature which affect the stresses in theblock are the effective modulus of elasticitybetween the block and its foundation, theelastic and inelastic properties of the concrete,and the degree of external restraint.

The actual stresses will further vary betweenrather wide limits because of conditionsoccurring during the construction period whichintroduce localized stress conditions. Tensilestresses and resulting cracks may occur becausethe larger blocks, by reason of their greaterarea, will have a greater number of stressconcentrations arising from the physicalirregularities and variable composition of thefoundation. Cracks may also occur because ofdelays in the construction schedule andconstruction operations. Longer blocks aremore likely to have cold joints created during


placement of the concrete, and these coldjoints are definite planes of weakness. A specialproblem exists with respect to the longerblocks at the base of the dam. These willnormally be exposed for longer periods of timebecause concrete placement is always slow atthe start of a job. Under this condition,extreme temperature gradients may form nearthe surfaces. The stresses caused by these steeptemperature gradients may then cause cracks toform along any planes of weakness which existas a result of construction operations.

U n l i k e o r d i n a r y structural membersundergoing temperature change, the stressesinduced in mass concrete structures bytemperature changes are not capable of beingdefined with any high degree of accuracy. Theindeterminate degree of restraint and thevarying elastic and inelastic properties of theconcrete, particularly during the early age ofthe concrete, make such an evaluation anestimate at best. Field experiences on otherjobs should guide the designer to a greatextent. Such experiences are reflected in table7-4 which can be used as a guide during theearly stages of design.

( b ) W i d t h of C o n s t r u c t i o n Block.-Contraction joints are normally spaced about50 feet apart, but may be controlled in someparts of the dam by the spacing and location ofpenstocks and river outlets, or by definitebreaks and irregularities of the foundation.Although a uniform spacing of joints is notnecessary, it is desirable so that the contractionjoint openings will be essentially uniform at thetime of contraction joint grouting. Spacingshave varied from 30 to 80 feet as measuredalong the axis of the dam. When the blocks are30 feet or less in width, a larger temperaturedrop than would otherwise be necessary maybe required to obtain a groutable opening ofthe contraction joint. This temperature dropshould be compatible with the permissible dropfor the long dimension of the block.

A further consideration is the maximumlength-to-width ratio of the blocks which willexist as construction of a block progresses fromits foundation to the top of the dam. If theratio of the longer dimension to the shorterdimension is much over 21/, cracking at

Table l-4.-Temperature treatment versus block length.

Block length

Over 200 feet

150 to 200 feet-120 to 150 feet-90 to 120 feet- -60to90feet--mUp to 60 feet. _

-

-.

-.

i-_

-

Treatment

use longitudinal joint. Stagger longitudinal jolIltsin adjoining blocks by minimum of 30 feet

Temperature drop from maximum concrete tern-per&ore to grouting tempersture-°F.

Foundation H=02L to 0.u 1a H=O.ZL 1-I

2 5 3 530 403 5 4 540 No restriction4 5 N o restriction

over Hs0.5L 1

404 5

No restrictionNo restrictionNo restriction

1 n=heigbt above foundation; G-block length.

approximate third points of the block can beexpected. Ratios of 2 to 1 or less are desirable,if practicable.

7-20. Concrete Cooling Systems.-Thelayout of the concrete cooling systems consistsof pipe or tubing placed in grid-like coils overthe top surface of each lift of concrete afterthe concrete has hardened. Coils are formed byjoining together lengths of thin-wall metal pipeor tubing. The number of coils in a blockdepends upon the size of the block and thehorizontal spacing. Supply and return headers,w i th m a n i f o l d s t o p e r m i t individualconnections to each coil, are normally placedon the downstream face of the dam. In someinstances, cooling shafts, galleries, andembedded header systems can be used toadvantage. Figures 7-l 1 and 7-l 2 show coolingdetails for Glen Canyon Dam.

The velocity of flow of the cooling waterthrough the embedded coils is normallyrequired to be not less than 2 feet per second,o r a b o u t 4 g a l l o n s p e r m i n u t e f o r t h ecommonly used l-inch pipe or tubing. Coolingwater is usually pumped through the coils,although a gravity system has at times beenused. When river water is used, the warmedwater is usually wasted after passing throughthe coils. River water having a high percentageof solids should be avoided as it can clog thecooling systems. When refrigerated water isused, the warmed water is returned to the

D E T A I L I


*--- Std p,pe thread

E X P L A N A T I O NThermocwple wfre.. _. ._.~. . .._ __.~. - .-l$‘Std pipe h e a d e r .._.__._.__ - ----_- - - - - - - - - - -, O”,h!” v/o,, tubing _._.._._____ - - - - - -

Detoll z-----

----Controctmn joints-,

--‘--‘-----~~.-Thermocouple ,unc+,ens placed at o&?ror,mots downst,’

I’ th,rd pm, of blacks, and at center of every fourthFor ,,ro,e~,,on ,,,DCB th.9,moco”plo W,,F r,e,t to coOh

IS trwnr luco ul bbck. Plots ad

EL. 3195 0 EL. 3375.0

L A Y O U T O F C O O L I N G C O I L S

Figure 7.11. Glen Canyon Dam-cooling pipe layout.-288-D-3021


E x t e n d beoder or tubmg b’mmthru high b l o c k T h e r m o c o u p l e w et o b e temporonl c o d e d a n d sus-p e n d e d o n h e od er or tubmg for pro-techon onttl e m b e d m e n t - - . -

- - - . .

TOP of7’6”/,ff -..

x.

I N I T I A L I N S T A L L A T I O N

T Y P I C A L S E C T I O N fHRlJ D A M

,,-Wrap e x p o s e d h e o d e r w t u b m g wth, ‘ paper to prevent b+ndmg to concrete

~-Co"troct,o" ,0/n t

F I N A L I N S T A L L A TION

’ thermocoupCdownsheom

rYPfCAL EXPANSfON COUPLfNGSHOWlN‘ CO”m4CIION JO!YT CROSSING

coohq t u b m g loid o v e r ranforcemen t.Cwllng cods may extend over top ofgallery a cods m o y b e terminated o n

: each s/de with /muted number of popes

icrossmg o v e r t o p , at optton of contractor

---V&olhg tduq to be embedded II) pkxement liftbelow qoftery Make complete coi ls on each stde ofgal lery ond aoss under gallery os fe* times osposSak

T Y P I C A L S E C T I O N THRU G A L L E R Y

grouhng lift5Extendlhermocoupfe wre t odownstream face-------------

A s s u m e d /me o fercovotion---’

ARRANyiEMENT OF INLETS AN0 OUTLETSAT THE DSWNSTREAM MCE

NOTES /Actual r e q u i r e d foundottons m o y d i f f e r wtdely f r o m assumed er-

covotion l i n e s s h o w nCoobnq COTS shall be placed ar top of wch 7’6*concrete /if tPlace tubing on o/l rock surfaces to with in 24’01 the top of the

lift b e i n g p l a c e dC o o b n q tubm

?t o b e placed t o clear openmgs 111 d o m o nun o f @‘or

m drrec c d-- - -- --.Expons~on couplmgs shall be used ot controctron faint crossingsWhere tubmg , s instollti for thernwmehr w/Is, the embedded end of the

tubing is to be flattened ondcrimped to SW/ ogoinst gmut leokoqeA n o n q e m e n t o f t u b m g may wry f r o m t h o t s h o r n The octuof

orron ement of the tubinq in the structure sb!be os directed.Where odock IS bounded by the downstream tote and requires two

or more cods. the contractor may e lect to termmote o/l coi lsof

dornstreom face ~1 heu o f u s i n g Ih’heoders Lprlrwmb ocks requiring two or more cods w/I reqmre headers

Tubmg placed on rock to be spaced ot 2!6’; tubing at top of each

Cods7:6’hft t o b e spaced occord!rlg t o zones O S s h o w n m table

p l a c e d !n Zare I shall b e opprorimotely eoo’a l e n g t h w i t h n oc o d longer t h a n SQO’ m fen@e/y 1 2 0 0 ’ m length w t B

t h . o/l other cods shall be oppror-n o co!/ lonqer t h o n I3W’m l e n g t h

Adfocen t tolls served by the some header shall be OS nearlyt h e s o m e /en

T h e r m o m e t e r It h OS possible

we/ 5 WI// b e u s e d t o determme c o n c r e t e teqmtotwes(I! locotlons dwected t o swkment o r r e p l a c e thermomuple

Cool,?&b,np pieced wrthn 2 5 t o 30 f&t of the foondotron nycs h a l l , w h e r e proctrc&le. b e piad os sepomte cods w wr))r

Eachsewrote bedse to facdilbk rpCcro/ codq , n thrs opw

b l o c k shall h o v e o n adepcndcnt cwhq s y s t e m o t eachcfmcrete I~ft

Figure 7-12. Glen Canyon Dam-concrete cooling details.-288-D-3022


water coolers in the refrigerating plant,retooled, and recirculated.

For control of - the cooling operations,electrical resistance-type thermometers can beembedded at midlift and the electrical cableextended to a terminal board where readingscan be taken whenever desired. Thermometertubes can also be embedded in the concrete.Insert-type thermometers are inserted intothese tubes when readings are desired. In manyinstallations thermocouples have been used andare n o t a s c o s t l y as the thermometerinstallations. The thermocouples are placed inthe fresh concrete at midlift and at least 10feet from an exposed face, with the lead wiresfrom the thermocouples carried to readilyaccessible points on the downstream face.

Varying the length of the embedded coil, thehorizontal spacing of the pipe, and thetemperature of the water circulated throughthe coil can be done during the constructionperiod to meet changed conditions. The effectof these variables is given in section 7-15.

S p e c i f i c a t i o n r e q u i r e m e n t s f o r t h einstallation and operation of the coolingsystems should provide for the cooling systemsto be water tested prior to embedment toassure the operation of each individual coil.The arrangement of the pipe headers andconnections to the individual cooling coilsshould be such as to insure dependable andcontinuous operation. Provisions should bemade in the pumping or header systems forreversing the flow of water in the individualcoils once each day. This is necessary to obtaina uniform cooling across the block. Because ofvarying construction schedules and progressa n d v a r y i n g climatic conditions, thespecifications should also provide that thetimes when cooling is to be performed in theindividual cooling coils be as directed by thecontracting officer. This will permit theoperation of the cooling systems to be such asto minimize adverse conditions of temperaturedrops and temperature gradients which couldlead to undesirable cracking.

7-21. Height Differentials.-A maximumheight differential between adjacent blocks isno rm a l l y s p e c i f i e d i n c o n s t r u c t i o nspecifications for concrete dams. From a

temperature standpoint, an even temperaturedistribution throughout the structure will beobtained when all blocks in the dam are placedin a uniform and continuous manner. This eventemperature distribution is desirable because ofthe subsequent uniform pattern of contractionjoint openings. Extreme temperature gradientson the exposed sides of blocks will also belessened when each lift is exposed for aminimum length of time.

Minimizing the overall height differentialbetween the highest and lowest blocks in thedam will cause construction of the dam toprogress uniformly up from the bottom of thecanyon. Contraction joints can then be groutedin advance of a rising reservoir, thus permittingstorage at earlier times than would be possibleif construction progress were concentrated inselected sections of the dam.

The height differential specified is acompromise between the uniform temperatureconditions and construction progress desired,and the contractor’s placement program. Inpractice, the maximum height differentialbetween adjacent blocks is usually 25 feetwhen 5-foot lifts are used or 30 feet when7X-foot l i f t s a r e u s e d . T h e m a x i m u mdifferential between the highest block in thedam and the lowest block is usually limited to40 feet when 5-foot lifts are used and 52.5 feetwhen 7X-foot lifts are used.

If cold weather is to be expected during anypart of the construction period, heightdifferentials between adjacent blocks should belimited to those needed for construction. Ifconcrete placement is to be discontinuedduring winter months, the height differentialsshould be reduced to practical minimumsbefore the shutdown period.

7 - 2 2 . L i f t T h i c k n e s s . -Economy o fc o n s t r u c t i o n s h o u l d b e c o n s i d e r e d i ndetermining the heights of placement lifts inmass concrete. Shallow lifts not only slow upc o n s t r u c t i o n b u t r e s u l t i n i n c r e a s e dconstruction joints which have to be cleanedand prepared for the next placement lift .Secondarily, the thickness of lift should beconsidered and related to the temperaturecontrol measures proposed for the structure.

When no precooling measures are used, the


placing temperature of the concrete willapproximate the ambient temperature at thesite. With this condition, a considerable portionof the total heat of hydration in a placementlift can be lost through the top exposed surfacebefore the next lift is placed. Shallow lifts andlonger delays between placement lifts willresult in the minimum temperature rise in theconcrete under these conditions. The oppositecondition may occur, and should be studied,when precooling measures are used. During thesummer months, the ambient temperatures willno rm a l l y be h ighe r t han t he conc re t etemperatures for the first few days afterplacement and a heat gain will result. Underthese conditions, higher placement lifts andminimum periods of time between placementswould be beneficial.

7 - 2 3 . D e l a y s B e t w e e n Placements-Construction of mass concrete blocks byplacement lifts incurs periodic time delaysbetween lifts. Depending upon ambienttemperatures, these delays can be beneficial orharmful. The minimum elapsed time betweenplacing of successive lifts in any one block isusually restricted to 72 hours, but temperaturestudies should be made to relate heat loss orheat gain to the placement lifts. These studiesshould take into account the anticipatedtemperature control measures and the seasonaleffects to be met during the construction

period. Delays between placements, and liftthicknesses should be studied simultaneouslyto take these variables into consideration asdiscussed in section 7-22.

The size and number of construction blocksin the dam will influence the time betweenp l a c e m e n t l i f t s . N o r m a l c o n s t r u c t i o noperations will require a minimum of 2 or 3days between lifts. On the larger dams,however, an average placement time of about 6or 7 days between successive lifts in a blockwill elapse because of the large number ofconstruction blocks and the concrete yardageinvolved.

7-24. Chure Slots.-Closure slots are 2- to4-foot-wide openings left in the dam betweenadjacent blocks during construction. Closure ismade by filling the slot with concrete at a timewhen temperature conditions are favorable,usually during the late winter months of theconstruction period when the adjacent blocksare at minimum temperature. The use ofclosure slots will often expedite constructionand will result in economy of labor andmaterials. Adverse stress conditions resultingfrom an unusual valley profile or undesirabletemperature effects may be noted during thedesign or construction phases of a dam, whichcan often be overcome or reduced to safeproportions by the use of open joints or slotsduring the construction period.

E. CONSTRUCTION OPERATIONS

7-25. Temperature Control Operations. -The typical temperature history of artificiallycooled concrete is shown on figure 7-13. Owingto hydration of the cement, a temperature risewill take place in the concrete after placement.After the peak temperature is reached, thetemperature will decline depending upon thethickness of section, the exposure conditions,the rate and amount of continued heat ofhydration, and whether or not artificial coolingis continued. The peak temperature is generallyreached between ages 7 and 20 days in massiveconcrete sections where no artificial cooling isemployed. These sections may maintain this

maximum temperature for several weeks, afterwhich the temperature will drop slowly over aperiod of several years. In thin structures orwhen artificial cooling is employed, the peaktemperature is generally reached at about age2% to 6 days, after which the temperature candrop at a fairly rapid rate. With artificialcooling, the rate of temperature drop is usuallylimited to So to lo F. per day, exposureconditions permitting. In thin structuresexposed to very low air temperatures, thee x p o s u r e conditions alone may causetemperatures to decline as much as 3’ to 4’ F.per day.


k ------- ----~------------------->k-----------~------------~ ----- ----->I Initial c o o l i n g I No pipe cooling. Period varies 1 intermediate and 1 Requires fram 2 or 3 i Final annual

from I or 2 months to about I final cooling I yeors to 20 yeors I temperotureI year, depending on grouting i cycle

0 PkICing iT?mperOture varies from 40°F. to SOoF.unless restricted to an intermediate temperature

0

because of length of block.Temperature history between cooling periods

dependent on exposure temperatures,thicknessof section,diffusivity of concrete,ond typeand amount of cement.

@ Range of mean concrete temperoture.

Figure 7.13. Temperature history of artificially cooled concrete.-288-D-3024

Initial cooling is normally accomplished withwater not warmer than that obtainable fromthe river. Intermediate and final cooling maybe accomplished with either river water orrefrigerated water, depending upon thetemperatures involved. River water will usuallybe sufficient if its temperature is 4’ to 5’ F.below the grouting temperature and if such atemperature persists for a minimum of about 2months. The main objection to refrigeratedwater is its high cost. Advantages, however,include its availability at any time of the yearand the wide range of temperatures possible.

Timely operation of the embedded coolingsystem will reduce the tendency of theconcrete to crack during the constructionperiod. The effects of unanticipated changessuch as a change in the type or amount ofcement used or the curing method employed,exposure temperatures varying from thoseassumed, or any other factor which influencesconcrete temperatures are normally taken intoaccount by varying the period of flow and thetemperature and rate of flow of the coolingwater. Intermittent cooling periods can be used

to lower interior temperatures prior toexposure of the concrete to cold weather.During cold weather placement, the normalperiod of initial cooling may be shortenedconsiderably to prevent forcing too rapid adrop in temperature. Depending upon thedimensions of the structure and the exposuresexpected, insulating the exposed surfaces whileartificially cooling the interior may benecessary to control temperature cracking. Thisis especially true for areas near corners of theconstruction blocks where temperatures candrop very rapidly.

(a) Initial Cooling. -Artificial cooling isemployed for a limited period of time initially.Upon completion of this initial cooling period,temperatures within the concrete may continueto drop but at a slower rate, they may holdsteady at about the same temperature, or theymay start rising again. This part of thetemperature history is primarily dependentupon the thickness of section and the exposureconditions existing at the time. Continued heatof hydration at this age may also affect theconcrete but would be of lesser importance.


The normal initial cooling period is from 10to 16 days. During this initial cooling period,the concrete temperatures are reduced fromthe maximum concrete temperature to such avalue that, upon stoppage of the flow of waterthrough the cooling system, the continued heatof hydration of the cement will not result int empera tu re s h ighe r t han the max imumpreviously obtained. The rate of cooling iscontrolled so that the tensions in the concretecaused by the drop in temperature will notexceed the tensile strength of the concrete forthat age of concrete.

In the early spring and late fall months whenexposure temperatures may be low, the lengthof the initial cooling period and the rate oftemperature drop can be critical in thinconcrete sections. In these sections, pipecooling, combined with the low exposuret e m p e r a t u r e s , can cause the concretetemperature to drop too fast. During theseseasons, artificial cooling should be stoppedshortly after the peak temperature is reachedand the concrete then allowed to cool in anatural manner. In structures with thickersections, the exposure temperatures have lesseffect on the immediate temperature drop, andthe initial cooling period can be continued witht h e p r i m a r y p u r p o s e o f c o n t r o l l i n g t h edifferential temperature between the exposedfaces and the interior.

(b) Intermediate and Final Cooling.-Subsequent to the initial cooling period,intermediate and final cooling periods areemployed to obtain desired temperaturedistributions or desired temperatures prior tocontraction joint grouting. Final cooling forcon t r ac t i on j o in t g rou t i ng i s no rma l lyaccomplished just prior to g rou t ing thecontraction joints, the program of coolingbeing dictated by construction progress,method of cooling, season of the year, and anyreservoir filling criteria.

As indicated in figure 7- 13, cooling prior togrouting the contraction joints is normallystarted after the concrete has attained an age of2 months to 1 year. Cooling is normallyperformed by grout lifts. In the smallerconstruction blocks, final cooling may beaccomplished in a single, continuous cooling

period. In the larger blocks, however, the finalcooling should be performed in two steps toreduce the vertical temperature gradientbetween grout lifts. The first of these steps iscommonly referred to as the intermediatecooling period and the second step as the finalcooling period.

In practice, the intermediate cooling periodfor a grout lift lowers the temperature of theconcrete in that lift to approximately halfwaybetween the temperature existing at the startof the cooling period and the desired finaltemperature. Each grout lift, in succession,undergoes this intermediate cooling periodbefore the final cooling of the next lower groutlift is undertaken.

Depending upon the temperature drop andfinal temperature to be obtained, the season ofthe year when this cooling is accomplished, andthe temperature of the cooling water, theintermediate and final cooling periods willrequire a total of from 30 to 60 days. The rateof temperature drop should be held to notmore than lo F. per day, and a rate of so to3/40 F. per day is preferable.

It is theoretically possible to compute therequired temperature drop to obtain a desiredjoint opening. The theoretical joint openingdoes not occur, however, because somecompression is built up in the block as thetemperature increases during the first few daysafter placement. A temperature drop of 4’ to8O F . f r om the max imum t empe ra tu r e ,depending on the creep properties of theconcrete, may be required to relieve thiscompression before any contraction jointopening will occur. Measured joint openings inHungry Horse Dam averaged 75 percent of thetheoretical. Other experiences with arch damshaving block widths of approximately 50 feethave indicated that a minimum temperatured r o p o f 25’ F . f r o m t h e m a x i m u mtemperature to the grouting temperature isdesirable, a n d w i l l r e s u l t i n g r o u t a b l econtraction joint openings of 0.06 to 0.10inch. For the wider blocks with 70 feet orm o r e b e t w e e n c o n t r a c t i o n j o i n t s , atemperature drop of 20’ F. will usually besufficient .

( c ) W a r m i n g O p e r a t i o n s . - P r o l o n g e d


exposure of horizontal construction joints willoften result in poor bond of the constructionlifts. Horizontal leafing cracks may occurbetween the older and newer concretes,extending from the face of the structure intothe interior. Cracks of this type quite oftenlead to freezing and thawing deterioration ofthe concrete. Preventive steps should bedirected toward obtaining a better than averagebond between the old concrete and the newconcrete. This includes minimizing thetemperature differential between the old andthe new concrete. Several shallow placementlifts placed over the cold construction jointmay be sufficient. For lifts exposed over awinter season, treatment may include warmingthe top 10 to 15 feet of the old concrete to theplacing temperature of the new concrete. Thiswill reduce the temperature gradient which willo c c u r . T h e w a r m i n g o p e r a t i o n c a n b eperformed by circulating warm water throught h e e m b e d d e d c o o l i n g c o i l s . W a r m i n goperations should immediately precede theplacement of the new concrete. If exposuretemperatures are extremely low at the timeplacement is to be resumed, insulation shouldbe placed over the tops of the lifts during thewarming operations.

7-26. Foundation Irregularities. -Althought h e d e s i g n s a s s u m e r e l a t i v e l y u n i f o r mfoundation and abutment excavations, the finalexcavation may vary wide ly f rom tha tassumed. Faults or crush zones are oftenu n c o v e r e d d u r i n g e x c a v a t i o n , a n d t h eexcavation o f t h e u n s o u n d r o c k l e a v e sdepressions or holes which must be filled withconcrete. Unless this backfill concrete hasundergone most of its volumetric shrinkage atthe time overlying concrete is placed, crackscan occur in the overlying concrete near theboundaries of the backfill concrete as loss ofsupport occurs due to continuing shrinkage ofthe backfill concrete. Where the area of suchdental work is extensive, the backfill concreteshould be placed and cooled before additionalconcrete is placed over the area.

Similar cond i t i ons ex i s t whe re t hefoundation has abrupt changes in slope. At thebreak of slope, cracks often occur because ofthe differential movement which takes place

between concrete held in place by rock, andconcrete held in place by previously placedconcrete which has not undergone its fullvolumetric shrinkage. A forced cooling of theconcrete adjacent to and below the break inslope, and a delay in placement of concreteover the break in slope, can be employed tominimize cracking at these locations. Ifeconomical, the elimination of these points ofhigh stress concentration is worthwhile. Suchcracks in lifts near the abutments very oftendevelop leakage and lead to spalling anddeterioration of the concrete.

7-27. Openings in Dam. -Because openingsconcentrate stresses at their corners, allpossible means should be used to minimizestresses at the surfaces of such openings. Propercuring methods should be used at all times. Theen trances t o s u c h o p e n i n g s s h o u l d b ebulkheaded and kept closed, with self-closingdoors where traffic demands, to prevent thecirculation of air currents th rough theopenings. Such air currents not only tend todry out the surfaces but can cause theformation of extreme temperature gradientsduring periods of cold weather.

7-28. Forms and Form Removal.-The timeof removal of forms from mass concretestructures is important in r educ ing thetendency to crack at the surface. This isespecially true when wooden fo rms o rinsulated steel forms are used. If exposuretemperatures are low and if the forms are leftin place for several days, the temperature ofthe concrete adjacent to the form will berelatively high when the forms are stripped,and the concrete will be subjected to a thermalshock which may cause cracking. From thetemperature standpoint, these forms shouldeither be removed as early as practicable orshould remain in place until the temperature ofthe mass has stabilized. In the latter case, au n i f o r m t e m p e r a t u r e g r a d i e n t w i l l b eestablished between the interior mass and thesurface of the concrete, and removal of theforms, except in adverse exposure conditions,will have no harmful results.

When the ordinary noninsulated steel form isused, the time of form removal may or maynot be important. The use of steel forms which


are kept cool by continuous water sprays willtend to cause the near-surface concrete to setat a lower temperature than the interior of themass. Form removal can then be accomplishedwith no detrimental effects. If, however, watersprays are not used to modify the temperatureof the steel forms, the early-age temperaturevariation of the fact concrete may be evengreater than the daily cycle of air temperaturebecause of absorbed heat from solar radiationand reradiation.

7-29. Curing.-Drying shrinkage can cause,as a skin effect, hairline cracks on the surfaceof a mass concrete structure. The primaryobjection to these random hairline cracks oflimited depth is that they are usually thebeginning of further and more extensivecracking and spalling under adverse exposureconditions. Following the removal of forms,proper curing is important if drying shrinkageand resulting surface cracking are to beavoided. Curing compounds which prevent theloss of moisture to the air are effective in thisrespect, but lack the cooling benefit which canbe obtained by water curing. In effect, watercuring obtains a surface exposure conditionmore beneficial than the fluctuating daily airtemperature. With water curing, the dailyexposure cycle is dampened because the dailyvariation of the water temperature is less thanthat of the air temperature.

A benefit also occurs from the evaporativecooling effect of the water on the surface. Theevaporative cooling effect is maximized byintermittent sprays which maintain the surfaceof the concrete in a wet to damp conditionwith some free water always available.

In general, water curing should be usedinstead of membrane curing on mass concretestructures. Where appearance is of primeimportance, other methods of curing may beconsidered because water curing will oftenresult in stains on the faces. Water curingduring periods of cold weather also can be a

safety problem because of icing hazards.7-30. Insulation.-During the fall of the year

when placing temperatures are still relativelyhigh, and during periods of cold weather, thetemperature of the surface concrete tends todrop rapidly to the exposure temperature. Thismay occur while the interior concrete is stillrising in temperature. Such conditions willcause high tensile stresses to form at thesurface. Surface treatments previouslyde scribed can reduce these temperatureg r a d i e n t s , p a r t i c u l a r l y w h e n u s e d i nconjunction with artificial cooling, but the useof insulation will give greater protection. Suchinsulation may be obtained by measuresvarying from simply leaving wooden orinsulated forms in place, to the use ofcommercial-type insulation applied to theforms or to the surfaces of the exposedconcrete. Tops of blocks can be protected withsand or sawdust when an extended exposureperiod is anticipated.

Unless required immediately after placementto prevent surface freezing, the insulations h o u l d b e p l a c e d a f t e r t he max imumtemperature is reached in the lift. This permitsloss of heat to the surface and will cause thenear-surface concrete to set at a relatively lowtemperature. Normally, during periods of coldweather, the insulation is removed at such timeas required for placement of the next lift.Otherwise, it may be removed when the coldw e a t h e r h a s a b a t e d o r w h e n i n t e r i o rtemperatures have been reduced substantiallybelow the peak temperatures.

Whatever the type of insulation, measuresshould be taken to exclude as much moisturefrom the insulation as practicable. Theinsulation should also be as airtight as possible.For a short period of exposure, small spaceheaters may be used, either by themselves or inconjunction with work enclosures. Care shouldbe taken when using space heaters in enclosedareas to avoid drying out the concrete surfaces.

F. BIBLIOGRAPHY

7-3 1. Bibliography. Engineering Monograph No. 34, Water Resources[l] “Control of Cracking in Mass Concrete Structures ,” Technical Publication, Bureau of Reclamation, 1965.

136

[2] Schack, Alfred, “Industrial Heat Transfer,” John Wiley &Sons, New York, N.Y., 1933.

[3] Jakob, Max, “Heat Transfer,” vol. I, pp. 373-375, JohnWiley & Sons, New York, N.Y., 1949.

[4] Grinter, L . E . , “Numerical Methods of Analysis inE’ngineering.” p. 86, Macmillan Co., New York, N.Y.,1949.

[5] “A Simple Method for the Computation of Temperaturesin Concrete Structures ,” AC1 Proceedings, vol. 34(November-December 1937 AC1 Journal).


[6] “Thermal Properties of Concrete,” Part VII, Bulletin No.1, Boulder Canyon Project Final Reports, Bureau ofReclamation, 1940.

[7] “Cooling of Concrete Dams,” Part VII, Bulletin No. 3,Boulder Canyon Project Final Repor ts , Bureau ofReclamation, 1949.

[8] “Insulation Facilitates Winter Concreting,” EngineeringMonograph No. 22, Bureau of Reclamation, 1955.

[9] Kinley, F. B., “Refrigeration for Cooling Concrete Mix,”Air Conditioning, Heating and Ventilating, March 1955.

<<Chapter VIII

Joints in Structures

8-l. Purpose.-Cracking in concrete dams isundesirable because cracking in randomlocations can destroy the monolithic nature oft h e s t r u c t u r e , t h e r e b y i m p a i r i n g i t ss e r v i c e a b i l i t y a n d l e a d i n g t o a n e a r l ydeterioration of the concrete. Joints placed inmass concrete dams are essentially designedcracks, located where they can be controlledand treated to minimize any undesirableeffects. The three principal types of joints usedin concrete dams are contraction, expansion,and construction joints.

C 0 ntrac tion and expansion joints arep r o v i d e d i n c o n c r e t e s t r u c t u r e s t oaccommodate volumetric changes which occurin the structure after placement. Contractionjoints are provided in a structure to prevent theformation of tensile cracks as the structureundergoes a volumetric shrinkage due to atemperature drop. Expansion joints areprovided in a unit-structure to allow for theexpansion (a volumetric increase due totemperature rise) of the unit in such a manneras not to change the stresses in, or the positionof, an adjacent unit or structure. Constructionjoints are placed in concrete structures tofacili tate construction, to reduce initialshrinkage stresses, to permit installation ofembedded metalwork, or to allow for thesubsequent placing of other concrete, includingbackfill and second-stage.

8-2. Contraction Joints.-In order to controlthe formation of cracks in mass concrete dams,current practice is to construct the dam inblocks separated by transverse contractionjoints. These contraction joints are vertical andnormally extend from the foundation to thetop of the dam. Transverse joints are normal to

the axis of the dam and are continuous fromthe upstream face to the downstream face.

Depending upon the size of the structure, itmay also be necessary to provide longitudinalcontraction joints in the blocks formed by thetransverse contraction joints. If longitudinalcontraction joints are provided, construction ofthe dam will consist of placing a series ofadjoining columnar blocks, each block free toundergo its own volume change withoutrestraint from the adjoining blocks. Thelongitudinal contraction joints are also verticaland parallel to the axis of the dam. The jointsare staggered a minimum of 25 feet at thetransverse joints. Generally, both transverseand longitudinal joints pass completely throughthe structure. As the longitudinal joint nearsthe sloping downstream face, and in theupstream sections of dams with slopingupstream faces, either the direction of the jointis changed from the vertical to effect aperpendicular intersection with the face, withan offset of 3 to 5 feet, or the joint isterminated at the top of a lift when it is within15 to 20 feet of the face. In the latter case,strict temperature control measures will berequired to prevent cracking of the concretedirectly above the termination of the joint.

Typical transverse contraction joints can beseen on figures 8-l and 8-2, and a typicallongitudinal contraction joint can be seen onfigure 8-3.

Contraction joints should be constructed sothat no bond exists between the concreteblocks separated by the joint. Reinforcementshould not extend across a contraction joint.The intersection of the joints with the faces ofthe dam should be chamfered to give a

137


concrete placing operations. Treatment andpreparation of construction joints are discussedin chapter XIV.

8-5. Spacing of Joints.-The location andspacing of transverse contraction joints shouldbe governed by the physical features of thedamsite, details of the structures associatedwith the dam, results of temperature studies,placement methods, and the probable concretemixing plant capacity.

Foundation defects and major irregularitiesin the rock are conducive to cracking and thiscan sometimes be prevented by judiciouslocation of the joints. Although cracks maydevelop normal to the canyon wall, it is notp r a c t i c a b l e t o f o r m i n c l i n e d j o i n t s .Consideration should be given to the canyonprofile in spacing the joints so that thetendency for such cracks to develop is kept toa minimum.

Outlets, penstocks, spillway gates, or bridgepiers may affect the location of joints andc o n s e q u e n t l y i n f l u e n c e t h e i r s p a c i n g .Consideration of other factors, however, mayl e a d t o a p o s s i b l e r e l o c a t i o n o f t h e s eappurtenances to provide a spacing of jointswhich is more satisfactory to the dam as awhole. Probably the most important of theseconsiderations is the permissible spacing of thejoints determined from the results of concretetemperature control studies. If the joints aretoo far apart, excessive shrinkage stresses willproduce cracks in the blocks. On the otherhand, if the joints are too close together,shrinkage may be so slight that the joints willnot open enough to permit effective grouting.Data on spacing of joints as related to thedegree of temperature control are discussed inchapter VII.

Contraction joints should be spaced closeenough so that, with the probable placementmethods, plant capacity, and the type ofconcrete being used, batches of concrete placedin a lift can always be covered while theconcrete is still plastic. For average conditions,a spacing of 50 feet has proved to besatisfactory. In dams where pozzolan andretarders are used, spacings up to 80 feet havebeen acceptable. An effort should be made tokeep the spacing uniform throughout the dam.

desirable appearance and to minimize spalling.In order to standardize block identilication onall future dams, a criterion has recently beenestablished which calls for the designation ofblocks in the longitudinal direction by number,starting with block 1 on the right abutment(looking downstream). The blocks in eachtransverse row are to be designated by letterstarting with the upstream block as the “A”block.

8-3. Expansion Joints. -Expansion joints areprovided in concrete structures primarily toaccommodate volumetric c h a n g e d u e t otemperature rise. In addition, these jointsfrequently are installed to prevent transferal ofstress from one structure to another. Notableexamples are: (1) powerplants constructedadjacent to the toe of a dam, wherein thepowerplant and the mass of the dam areseparated by a vertical expansion joint; and (2)outlet conduits encased in concrete andextending downstream from the dam, in whichcase an expansion joint is constructed near thetoe of the dam separating the encasementconcrete from the dam.

Like contraction joints, previously discussed,expansion joints are constructed so that nobond exists between the adjacent concretestructures. A corkboard, mastic, sponge rubber,or other compressible-type filler usuallyseparates the joint surfaces to prevent stress orl o a d t r a n s f e r a l . T h e t h i c k n e s s o f t h ecompressible material will depend on themagnitude of the anticipated deformationinduced by the load.

8-4. Construction Joints.-A constructionjoint in concrete is defined as the surface ofpreviously placed concrete upon or againstwhich new concrete is to be placed and towhich the new concrete is to adhere when thepreviously placed concrete has attained itsinitial set and hardened to such an extent thatthe new concrete cannot be incorporatedintegrally with the earlier placed concrete byvibration. Although most construction jointsare planned and made a part of the design ofthe structure, some construction joints areexpedients used by a contractor to facilitateconstruction. Construction joints may also berequired because of inadvertent delays in

JOINTS IN STRUCTURES-Sec. 8-5 139

TYPICAL E L E V A T I O N OF C O N T R A C T I O N JO/NT

S E C T I O N B-6

.-AXIS o f d a mS E C T / O N A - A

TOO o f 5’ iiffs

-Metal seoiing strrp

DETAIL ELEVATION OF CONTRACT/ON JO/N7I ill” ..,, I” “,Y”YLVLI.,

Figure 8-I. Typical keyed transverse contraction joint for a concrete gravity dam (Friant Dam inCalifornia).-288-D-3030

DESIGN OF GRAVITY DAMS140

6”Dto f o r m e d drorn

i f ” Vent ~-

P v c w01ers10p

\r.’-_

I1Metal cop -

Figure 8.2. Typical unkeyed transverse contraction joint (Grand Coulee Forebay Dam in Washington).(sheet 1 of 2).-288-D-3032(1/2)

JOINTS IN STRUCTURES-Sec. 8-6

Figure 8-2. Typical unkeyed transverse contraction joint (Grand Coulee Forebay Dam in Washington).(sheet 2 of 2).-288~D3032(2/2)

The practice of spacing longitudinal jointsfollows, in general, that for the transversejoints, except that the lengths of the blocks arenot limited by plant capacity. Depending onthe degree to which artificial temperaturecontrol is exercised, spacings of 50 to 200 feetmay be employed.

8-6. Keys. -Vertical keys in transverse jointsare used primarily to provide increased shearingresistance between blocks; thus, when thejoints and keys are grouted, a monolithicstructure is created which has greater rigidityand stability because of the transfer of loadfrom one block to another through the keys. Asecondary benefit of the use of keys is thatthey minimize water leakage through thejoints. The keys increase the percolation

distance through joints and, by forming a seriesof constrictions, are beneficial in hastening thesealing of the joints with mineral deposits.

Keys are not always needed in the transversecontraction joints of concrete gravity dams.Because the requirement for keys adds to formand labor costs, the need for keys and thebenefits which would be attained from theiruse should be investigated and determined foreach dam. Keys may be used to transferhorizontal loads to the abutments, therebyobtaining a thinner darn than would otherwisebe possible. Foundation irregularities may besuch that a bridging action over certainportions of the foundation would be desirable.Keys can be used to lock together adjacentblocks to help accomplish this bridging action.


,, From transverse qullery

Mefal sealmgshp - - - -

/3;

1 ’/‘Riser--

.T0

g-2.

SUPPYheaders.-.-:

+ ---__----_cVrrom transvrrse gallery

O’liff

ELEV A T I ON OF BLOCK FACESHOWING GROUT OUTLETS

E L E V A T I O N O F L O N G I T U D I N A L J O I N T i( K E Y D E T A I L S )

H O R I Z O N T A L S E C T I O N 8 - B

SECTION A-A

Figure 8-3. Typical longitudinal contraction joint for a concrete gravity dam (Grand Coulee Dam inWashington).-288-D-3034

In blocks where large openings are provided forpenstocks, gate chambers, or other largefeatures, keys can be used to improve thestability of the block.

The transverse joint key developed by theBureau has been standardized. The standardkey offers minimum obstruction to the flow ofgrout, provides a good theoretical shear value,eliminates sharp corners which commonlycrack upon removal of forms, improves the

reen t r an t angles c o n d u c i v e t o c r a c kdevelopment associated with volume changes,and is well adapted to the construction offorms. Figure 8-1 shows the shape anddimensions of the standard key on the face of atypical transverse contraction joint.

Shear keys are important accessories inlongitudinal contraction joints and areprovided to maintain stability of the dam byincreasing the resistance to vertical shear. The


key faces are inclined to make them conformapproximately with the lines of principal stressfor full waterload. Inasmuch as the direction ofprincipal stresses varies from the upstream faceto the downstream face of the dam and fromthe foundation to the crest, an unlimitednumber of key shapes with resulting highforming costs would be required if closeconformity were considered necessary. In orderto simplify keyway forms, a single key shape,determined largely by the general direction ofthe lines of principal stress in the lower,downstream portion of the dam where thevertical shear is at a maximum, has beenadopted for standard use. Details of the shapeand dimensions of longitudinal keys used onGrand Coulee Dam are shown on figure 8-3.These keys are proportioned to accommodatethe 5-foot concrete placement lifts used onthat dam.

8-7. Seals. -The opening of transversecontraction joints between construction blocksprovides passages through the dam which,unless sealed, would permit the leakage ofwater from the reservoir to the downstreamface. To prevent this leakage, seals are installedin the joints adjacent to the upstream face.Seals are also required on both transverse andlongitudinal joints during grouting operationsto confine the fluid grout in the joint. Figure8-4 illustrates typical seals used in contractionjoints.

For seals to be effective in the contractionjoints of concrete dams, installation is ofgreater importance than shape or material.Good workmanship in making connections,adequate protection t o k e e p t h e m f r o mbecoming tom prior to embedment, andcareful placement and consolidation of theconcrete around the seals are of primaryimportance.

(a) Metal Se&-The most common type ofseal used in concrete dams has been a metalseal embedded in the concrete across the joint.Metal seals are similar in design whether used aswater or grout seals. Bureau practice hasstandardized two shapes-the Z-type and theM-type. The Z-type seal is of simpler design, iseasi ly installed and spliced, b u t w i l laccommodate only small lateral movements.

Such a seal is well adapted to joints which aret o b e g r o u t e d , since grouting tends toconsolidate the two blocks and restrict anymovement. The M-type seal is more difficult tosplice, but its shape accommodates greatermovement of the joint. This shape is welladapted for use as a water seal in ungroutedjoints. Figure 8-4 shows the general dimensionsand connections for the Z- and M-type seals.

Metal seals are made from a 12- or 15-inchstrip of corrosion-resistant metal, usuallycopper or stainless steel. No. 20 gage UnitedStates Standard (0.0375~inch thick) stainlesssteel has proved satisfactory. The stainless steelis more rigid and will stay in position duringembedment better than the more ductilecopper. It is harder to weld, however, and isgenerally higher in initial cost. Copper strip canbe furnished in rolls and will minimize thenumber of connections which have to be made.

(b) Polyvinyl Chloride Seals.-Recentadvancements in the specifications for andmanufacture of materials have resulted in theacceptance of polyvinyl chloride (PVC) as asuitable material for joint seals. This materialcan be manufactured in a number of shapesand sizes. The 12-inch seal having a %-inchthickness, serrations, and a center bulb isacceptable for high dams. The 9-inch similarseal is satisfactory for low dams.

(c) Other Seals.-Rubber seals have beenused in special joints in concrete sections ofdams and appurtenant works where it is desiredto provide for greater movement at the jointthan can be accommodated by metal seals.Rubber seals have been used successfully incontraction joints between piers and thecantilevers of drum gate crests, to permitunrestrained deflection of the cantilevers andprevent leakage from the reservoir into thedrum gate chamber. They can also be used inexpansion and contraction joints of thincantilever walls in stilling basins to preventobjectionable leakage caused by unequaldeflection and settlement of the walls. Asimilar use would be in ungrouted contractionjoints of low diversion dams to prevente x c essive leakage caused by differentialsettlement.

Asphalt seals have not proved satisfactory


Figure 8-4. Metal seals and connections at contraction joints.-288-D-3200


for sealing contraction joints in concrete dams,and they are no longer used.

8-8. Joint Drains. -Drainage of contractionjoints is desirable to prevent development ofexcessive pressure in the joints during theconstruction period and seepage of reservoirwater through the joints during operation.Where contraction joints are to be ungrouted,5- or 6-inch-diameter formed joint drains areconstructed on the joints. These joint drainsdischarge the seepage water into the gallerydrainage system. Where joint grouting systemsare installed, the joints can be drainedeffectively during the construction period byutilizing the piping for the grouting system.Effective grouting when the joints are openedtheir widest will normally obviate any furtherneed for drainage of the joint. Since provisionfor open joint drains makes effective groutingdifficult, joint drains are usually omitted onBureau dams where contraction joint groutingis to be performed.

8-9. Grouting Systems.-The purpose ofcontraction joint grouting is to bind the blockstogether so that the structure will act as amonolithic mass. In some cases, the stability ofthe dam does not require the entire mass to actas a monolith and the transverse contractionjoints need not be grouted. Longitudinalcontraction joints must be grouted so thatblocks in a transverse row act monolithically.Also, grouting of transverse construction jointsmay be required only in the lower portion ofthe joint as shown on figure 8-2.

In order to make the individual blocks act asa mono l i t h , a g rou t mix tu re o f portlandcement and water is forced into each jointunder pressure. Upon setting, the mixture willform a cement mortar which fills the joint. Themeans of introducing grout into the joint isthrough an embedded pipe system. Typicalpipe systems are shown on figures 8-1, 8-2, and8-3.

In order to insure complete grouting of acontraction joint before the grout begins to set,and to prevent excessive pressure on the seals,the joint is normally grouted in lifts 50 to 60feet in height, although heights to about 75feet have been used. Such a grouting lift in atransverse joint consists of an area bounded on

the sides by seals adjacent to the upstream anddownstream faces of the dam, and on the topand bottom by seals normally 50 to 60 feetapart. Since the longitudinal joints arestaggered, the grouting area of a longitudinaljoint is bounded by vertical seals placed closeto the adjacent transverse joints and horizontalseals placed at 50- to 60-foot intervals inelevation. Each area of a transverse orlongitudinal joint is sealed off from adjacentareas and has its own piping systemindependent of all other systems.

The layout of a piping system for transversejoints is illustrated on figures 8-l and 8-2. Ah o r i z o n t a l l%-inch-diameter l o o p e dsupply-header-return is embedded in theconcrete adjacent to the lower boundary of thelift. One-half-inch-diameter embedded verticalrisers take off from the header atapproximately 6-foot intervals and terminatenear the top of the lift or near the downstreamface of the dam. Grout outlets are connectedto the risers at IO-foot staggered intervals togive better coverage of the joint. The loopedsupply-header-return permits the delivery ofgrout to the various ?&inch riser pipes fromeither or both ends of the header, as may bedesired, and provides reasonable assurance thatgrout will be admitted to all parts of the jointarea. The top of each grout lift is vented topermit the escape of air, water, and thin groutwhich rises in the joint as grouting proceeds. Atriangular grout groove can be formed in theface of the high block and covered with a metalplate which serves as a form for the concretewhen the adjacent low block is placed. Ventpipes are connected to each end of the groove,thereby providing venting in either directionwhich will allow venting to continue if anobstruction is formed at any one point in thesystem. In some cases, a row of vent outletsmay be used in lieu of a grout groove as shownon figure 8-1.

The piping arrangement for longitudinaljoints is illustrated on figure 8-3. A horizontall?&nch-diameter looped supply-header-returnline from either the downstream face or thegallery system is embedded in the concreteadjacent to the lower boundary of the lift. The1%inch supply line conveys the grout to the


opening equal to the joint opening is providedfor grout injection.

The grout grooves, formed in contractionjoints and used for venting air, water, and thingrout, are covered with metal cover plateswhich act as forms when the concrete is placedin the low block. Details of the installation ofthe metal cover plates and the grout groovesare shown on figure 8-5. Before the coverplates are placed, the grooves are cleanedthoroughly of all concrete, dirt, and otherforeign substances. At the upper edges of thecover plates, the joint between the cover plateand the concrete is covered with dry cementmortar or with asphalt emulsion to preventmortar from the concrete from plugging thegroove.

8-10. Grouting Operations. -Before any liftof a joint is grouted, the lift is washedthoroughly with air and water under pressure,the header and vent systems are tested todetermine that they are unobstructed, and thejoint is allowed to remain filled with water fora period of 24 hours. Immediately prior tobeing grouted, the water is drained from thejoint lifts to be grouted. During the groutingoperations, the lifts in two or more ungroutedadjacent joints at the same level are filled withwater to the level of the top of the lift beinggrouted. As the grouting of the lift of the jointnears completion, the grouting lift of the jointimmediately above the lift being grouted isfilled with water. Immediately after a groutingoperation is completed, the water is drainedfrom the joints in the lift above, but the wateris not drained from the adjacent ungroutedjoint lifts at the same level until 6 hours aftercompletion of the grouting operation.

The material used in grouting contractionjoints is a mixture of cement and water, theconsistency of which varies from thin to thickas the operation proceeds. Usually, a 2 to Imixture by volume of water and cement is usedat the start of the grouting operation to assuregrout travel and the filling of small cracks. Asthe grouting proceeds the mixture is thickenedto a 1 to 1 water-cement ratio to fill the groutsystem and joint. If the joint is wide andaccepts grout readily, grout of 0.7 to 0.8water-cement ratio by volume may be used to

piping at each longitudinal joint. At each sideof the grouting lift, a l-inch-diameter risertakes off from the header and extends nearlyto the top of the lift. The return line aids in therelease of entrapped air and water in thesystem, and may be used for grouting the jointin the event the supply line becomes plugged.One-half-inch-diameter horizontal distributionpipes are connected between these risers spacedat 5 feet or 7 feet 6 inches, conforming to theheight of the placement lifts. Grout outlets areattached to the horizontal distribution pipes atapproximately staggered IO-foot intervals. Asin the case of transverse joints, grout grooves orvent outlets are provided at the top of each liftand are connected to 1%inch-diameter ventpipes which lead to the downstream face or toa gallery.

The location of the inlets and outlets of thesupply-header-return and vents varies withconditions. Normally, these piping systemsterminate at the downstream face of the dam.Under some conditions, these systems can bearranged to terminate in galleries. In order thatthe exposed ends of these systems will not beexposed after grouting operations have beencompleted, the pipes are terminated with aprotruding pipe nipple which is wrapped withpaper to prevent bonding to the concrete. Thisnipple is removed when no longer needed andthe holes thus formed are dry-packed withmortar.

Typical grout outlets are shown on figure8-5. The metal fitting alternative consists oftwo conduit boxes connected to the riser by astandard pipe tee. The blockout alternative is ablockout with a galvanized sheet steel cover.The riser goes through the blockout and a2-inch section of the pipe is cut out. Inerection, the box or blockout is placed in thehigh or first placed block and secured to theform. After the concrete has hardened and theforms have been removed, the cover box orsheet steel cover is placed in position andfirmly held in place by wire or nails. A metalstrap fastened to the cover serves as an anchorto fasten the cover to the second or low blockso that the cover moves with it. When the twoblocks contract upon cooling, the covers andthe box or blockout are pulled apart and an


takes its set in the grouting system, but the liftis not grouted so rapidly that the grout will notsettle in the joint. In no case is the timeconsumed in filling any lift of a joint less than2 hours.

When thick grout flows from the ventoutlets, injection is stopped for awhile to allowthe grout to settle. After several repetitions ofa showing of thick grout, the valves on theoutlets are closed. The pressure on the supplyline is then increased to the allowable limit forthe particular joint to force grout into all smallopenings of the joint and to force the excesswater into the pores of the concrete, leaving agrout film of lower water-cement ratio andhigher density in the joint. The limitingpressure, usually from 30 to 50 pounds persquare inch as measured at the vent, must below enough to avoid deflecting the blockexcessively or causing opening of the groutedportion of the joint below. This maximumpressure is maintained until no more grout canbe forced into the joint, and the system is thensealed off.

finish the operation. Normally, the supply linefrom the grout pump is connected to thesupply so that grout first enters the jointthrough outlets in the most remote riser pipe,thereby setting up conditions most favorablefor the expulsion of air, water, and dilutedgrout as the grouting operations proceed. If thegrout introduced in the normal way makes aready appearance at the return, the indicationsare that the header system is unobstructed andthe return header can be capped. Grout fromthe header is forced up the risers and into thejoint through the grout outlets, while air andwater is forced up to the vent groove above.

Grouting of contraction joints in a dam isnormally done in groups and in separatesuccessive lifts, beginning at the foundationand finishing at the top of the dam. The groutis applied in rotation from joint to joint bybatches in such quantities and with such timedelays as necessary to allow the grout to settlein the joint. Each joint is filled atapproximately the same rate. The grouting ofeach joint lift is completed before the grout

<<Chapter IX

Spillways

A. GENERAL DESIGN CONSIDERATIONS

9-l. Function.-Spillways are provided at.storage and detention dams to release surplusor floodwater which cannot be contained inthe allotted storage space, and at diversiondams to bypass flows exceeding those whichare t u r n e d i n t o t h e d i v e r s i o n s y s t e m .Ordinarily, the excess is drawn from the top ofthe pool created by the dam and releasedthrough a spillway back to the river or to somenatural drainage channel. Figure 9-l shows thespillway at Grand Coulee Dam in operation.

The importance of a safe spillway cannot beoveremphasized; many failures of dams havebeen caused by improperly designed spillwaysor by spillways of insufficient capacity.However, concrete dams usually will be able towithstand moderate overtopping. Generally,the increase in cost of a larger spillway is notdirectly proportional to increase in capacity.Very often the cost of a spillway of amplecapacity will be only moderately higher thanthat of one which is obviously too small.

In addition to providing sufficient capacity,the spillway must be hydraulically andstructurally adequate and must be located sothat spillway discharges will not erode orundermine the downstream toe or abutmentsof the dam. The spillway’s flow surfaces mustbe erosion resistant to withstand the highscouring velocities created by the drop fromthe reservoir surface to tailwater, and usuallysome device will be required for dissipation ofenergy at the bottom of the drop.

The frequency of spillway use will bedetermined by the runoff characteristics of thedrainage area and by the nature of the

development. Ordinary riverflows are usuallystored in the reservoir, used for powergeneration, diverted through headworks, orreleased through outlets, and the spillway isnot required to function. Spillway flows willresult during floods or periods of sustainedhigh runoff when the capacities of otherfacilities are exceeded. Where large reservoirstorage is provided, or where large outlet ordiversion capacity is available, the spillway willbe utilized infrequently. Where storage space islimited and outlet releases or diversions arerelatively small compared to normal riverflows,the spillway will be used frequently.

9-2. Selection of Inflow Design Flood.-(a) Gen era1 Considerations. -When floodsoccur in an unobstructed stream channel, it isconsidered a natural event for which noindividual or group assumes responsibility.However, when obstructions are placed acrossthe channel, it becomes the responsibility ofthe sponsors either to make certain thathazards to downstream interests are notappreciably increased or to obligate themselvesfor damages resulting from operation or failureof such structures. Also, the loss of the facilityand the loss of project revenue occasioned by afailure should be considered.

If danger to the structures alone wereinvolved, the sponsors of many projects wouldprefer to rely on the improbability of anextreme flood occurrence rather than to incurthe expense necessary to assure completesafety. However, when the risks involvedownstream interests, including widespreaddamage and loss of life, a conservative attitude

149


Figure 9-I. Drumgate-controlled ogee-type overflow spillway in operation at Grand Coulee Dam in Washington. Note ThirdPowerplant construction in left background.-P1222-142-13418

is required in the development of the inflowdesign flood. Consideration of potentialdamage should not be confined to conditionsexisting at the time of construction. Probablefuture development in the downstream floodplain, encroachment by farms and resorts,construction of roads and bridges, etc., shouldbe evaluated in estimating damages and hazardsto human life that would result from failure ofa dam.

Dams impounding large reservoirs and builton principal rivers with high runoff potentialunquestionably can be considered to be in thehigh-hazard category. For such developments,conservative design criteria are selected on thebasis that failure cannot be tolerated because

of the possible loss of life and because of thepotential damages which could approachdisaster proportions. However, dams built onisolated streams in rural areas where failurewould neither jeopardize human life nor createdamages beyond the sponsor’s financialcapabilities can be considered to be in alow-hazard category. For such developmentsdesign criteria may be established on a muchless conservative basis. There are numerousinstances, however, where failure of dams oflow heights and small storage capacities haveresulted in loss of life and heavy propertydamage. Most dams will require a reasonableconservatism in design, primarily because ofthe criterion that a dam failure must not

SPI LLWAYS-Sec. 9-3 151

present a serious hazard to human life.(b) Inflow Design Flood Hydrograph. -

Concrete dams are usually built on rivers frommajor drainage systems and impound largereservoirs. Because of the magnitude of thedamage which would result from a failure ofthe dam, the probable maximum flood is usedas the inflow design flood. The hydrograph forthis flood is based on the hydrometeorologicalapproach, which requires estimates of stormpotential and the amount and distribution ofr u n o f f . T h e d e r i v a t i o n o f t h e p r o b a b l emaximum flood is discussed in appendix G.

The probable maximum flood is based on arational consideration of the chances ofsimultaneous occurrence of the maximum ofthe several elements or conditions whichcontribute to the flood. Such a flood is thelargest that reasonably can be expected and isordinarily accepted as the inflow design floodfor dams where failure of the structure wouldincrease the danger to human life. The inflowdesign flood is determined by evaluating thehydrographs of the following situations toascertain the most critical flood:

(1) A probable maximum rainstorm inconjunction with a severe, but not uncommon,antecedent condition.

(2) A probable maximum rainstorm inconjunction with a major snowmelt floodsomewhat smaller than the probable maximum.

(3) A probable maximum snowmelt flood inconjunction with a major rainstorm less severethan the probable maximum for that season.

9-3. Relation of Surcharge Storage toSpillway Capacity.-The inflow design flood isn o r m a l l y r e p r e s e n t e d i n t h e f o r m o f ahydrograph, which charts the rate of flow inr e l a t i o n t o t i m e . A t y p i c a l h y d r o g r a p hrepresenting a storm runoff is illustrated infigure 9-2, curve A. The flow into a reservoir atany time and the momentary peak can be readfrom this curve. The area under the curve is thevolume of the inflow, since it represents theproduct of rate of flow and time.

Where no surcharge storage is allowed in thereservoir, the spillway capacity must besufficiently large to pass the peak of the flood.The peak rate of inflow is then of primaryinterest and the total volume in the flood is of

lesser importance. However, where a relativelylarge storage capacity above normal reservoirlevel can be made available economically byconstructing a higher dam, a portion of theflood volume can be retained temporarily inreservoir surcharge space and the spillwaycapacity can be reduced considerably.

In many projects involving reservoirs,economic considerations will necessitate adesign u t i l i z ing s u r c h a r g e . T h e m o s teconomical combination of surcharge storageand spillway capacity requires flood routingstudies and economic studies of the costs ofspillway-dam combinations, subsequentlydescribed.

9 - 4 . F l o o d R o u t i n g . - T h e s t o r a g eaccumulated in a reservoir depends on thedifference between the rates of inflow andoutflow. For an interval of time At, thisrelationship can be expressed by the equation:

AS = Q,At - Q,At (1)

where:

AS = storage accumulated during At,Qi = average rate of inflow during

At, andQ, = average rate of outflow during

At.

Referring to figure 9-2, the rate of inflow atany time, t, is shown by the inflow designflood hydrograph; the rate of outflow may beobtained from the curve of spillway dischargeversus reservoir water surface elevation; andstorage is shown by the curve of reservoircapacity versus reservoir water surfaceelevation.

The quantity of water a spillway candischarge depends on the size and type ofspillway. For a simple overflow crest the flowwill vary with the head on the crest, and thesurcharge will increase with an increase inspillway discharge. For a gated spillway,however, outflow can be varied with respect toreservoir head by operation of the gates. Forexample, one assumption for an operation of agate-controlled spillway might be that the gateswill be regulated so that inflow and outflow are


60,000

rJ+L0:2 40,000

w(3lxaI(-$ 20,000

0II0

0273 4 5 6 7 8 9 10 II

T I M E I N H O U R S

Figure 9-2. Typical inflow and outflow hydrographs.-288-D-3035

equal until the gates are wide open; or anassumption can be made to open the gates at aslower rate so that surcharge storage willaccumulate before the gates are wide open.

Outflows need not necessarily be limited todischarges through the spillway but might besupplemented by other releases such as throughriver outlets, irrigation outlets, and powerplantturbines. In all such cases the size, type, andmethod of operation of the spillway and otherreleases with reference to the storage and/or tothe inflow must be predetermined in order toestablish an outflow-elevation relationship.

If simple equations could be established forthe inflow design flood hydrograph curve, theoutflow (as may be modified by operationalprocedures), and the reservoir capacity curve, asolution of flood routing could be made bymathematical integration. However, simpleequations usually cannot be written for thesevariables, and such a solution is not practical.Many techniques of flood routing have beendevised, each with its advantages anddisadvantages. These techniques vary from astrictly arithmetical method to an entirelygraphical solution.

Electronic computers are being used to makeflood routing computations. The computerprograms were developed using an iterationtechnique. For simplicity, an arithmetical trialand error tabular method is illustrated in thismanual. Data required for the routing, which isthe same regardless of the method used, are asfollows:

(1) Inflow hydrograph, figure 9-2.(2) Reservoir capacity, figure 9-3.(3) Outflow, figure 9-4. (Spillway discharge

only was assumed in this illustration.)The flood routing computations are shown

in table 9-l. The procedure for making thecomputations is as follows:

(1) Select a time interval, At, column(2).

(2) Obtain column (3) from the inflowhydrograph, figure 9-2.

(3) Column (4) represents averageinflow for At in c.f.s. (cubic feet persecond).

(4) Obtain column (5) by convertingcolumn (4) values of c.f.s. for At toacre-feet (1 c.f.s. for 12 hours = 1acre-foot).

SPI LLWAYS-Sec. 9-4

1 0 , 0 0 0 1 2 , 0 0 0 1 4 , 0 0 0 1 6 , 0 0 0 1 8 , 0 0 0 2 0 , 0 0 0 22,000 24,000 26,000R E S E R V O I R C A P A C I T Y - A C R E - F E E T

Figure 9-3. Typical reservoir capacity curve.-288-D-3036

W - - - I

v-w0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 l0,000 1 2 , 0 0 0 1 4 , 0 0 0 16,000 1 8 , 0 0 0

D I S C H A R G E I N C U B I C F E E T P E R S E C O N D

Figure 9-4. Typical spillway discharge curve.-288-D-3037

(5) Assume trial reservoir water surfacei n c o l u m n (6), d e t e r m i n e t h ecorresponding rate of outflow from figure9-4, and record in column (7).

(6) Average the rate o f o u t f l o wdetermined in step (5) and the rate ofoutflow for the reservoir water surfacewhich existed at the beginning of theperiod and enter in column (8).

(7) Obtain column (9) by converting

column (8) values of c.f.s. for At toacre-feet, similar to step (4).

(8) Column ( 10) = column (5) minuscolumn (9).

(9) The initial value in column (11)represents the reservoir storage at thebeginning of the inflow design flood.Determine subsequent values by addingAS values from column (10) to theprevious column (1 1) value.


Table 9-l .-Flood routing computations

(6) (7) (8) (9) (IO) ’ (I I) (12) (13)rriol reserwr Averoge rote Reservoir

storoge Outflow ot of outflow Outflow, lncremento I Toto Ielevotion ot

elevotion,t ime t , e n d o f Remark:

t i m e t , c. f. sQ 0:; et, acre-feet storoge As, storoge,

a c r e - f e e t a c r e - f e e t A t , f e e t

0 4 , 0 0 0I 6 , 0 0 0 5 0 0

I 8 , 0 0 0I 14 ,000 I,T

2 2 0 ,000I 3 0 , 0 0 0 2 , 5 0 0

3 4 0 , 0 0 0I

4 6 0 . 0 0 05 0 , 0 0 0 4, I6 7

2.I I 5 , 0 0 0

8,000 1,333

t

(10) Determine reservoir elevation incolumn (12) corresponding to storage incolumn ( 11) from figure 9-3.

( 11) Compare reservoir elevation incolumn (12) with trial reservoir elevationin column (6). If they do not agree within0.1 foot, make a second trial elevationand repeat procedure until agreement isreached.

The outflow-time curve resulting from theflood routing shown in table 9-l has beenplotted as curve B on figure 9-2. As the areaunder the inflow hydrograph (curve A)indicates the volume of inflow, so will the areaunder the outflow hydrograph (curve B)indicate the volume of outflow. It follows thenthat the volume indicated by the area betweenthe two curves will be the surcharge storage.The surcharge storage computed in table 9-lcan, therefore, be checked by comparing itwith the measured area on the graph.

A rough approximation of the relationshipof spillway size to surcharge volume can beobtained without making an actual floodrou t ing , b y a r b i t r a r i l y a s s u m i n g a napproximate outflow-time curve and thenmeasuring the area between it and the inflowhydrograph. For example, if the surcharge

volume for the problem shown on figure 9-2 issought where a 30,000-c.f.s. spillway would bep r o v i d e d , a n a s s u m e d o u t f l o w c u r v erepresented by curve C can be drawn and thearea between this curve and curve A can beplanimetered. Curve C will reach its apex of30,000 c.f.s. where it crosses curve A. Thevolume represented by the area between thetwo curves will indicate the approximatesurcharge volume necessary for this capacityspillway.

9-5. Selection of Spillway Size andT y p e . - ( a ) Gelzeral Corzsideratiom-Indetermining the best combination of storageand spillway capacity to accommodate theselected inflow design flood, all pertinentfactors of hydrology, hydraulics, geology,topography, design requirements, cost, andb e n e f i t s s h o u l d b e c o n s i d e r e d . T h e s econsiderations involve such factors as (1) thecharacteristics of the flood hydrograph; (2) thedamages which would result if such a floodoccurred without the dam; (3) the damageswhich would result if such a flood occurredwith the dam in place; (4) the damages whichwould occur if the dam or spillway should fail;(5) effects of various dam and spillwaycombinations on the probable increase or

SPI LLWAYS-Sec. 9-5

decrease of damages above or below the dam(as indicated by reservoir backwater curves andtailwater curves); (6) relative costs of increasingthe capacity of spillways; and (7) use ofcombined outlet facilities to serve more thanone function, such as control of releases andcontrol or passage of floods. Other outlets,such as river outlets, irrigation outlets, andpowerplant turbines, should be considered inpassing part of the inflow design flood whensuch facilities are expected to be available intime of flood.

The outflow characteristics of a spillwaydepend on the particular device selected tocontrol the discharge. These control facilitiesmay take the form of an overflow crest ororifice. Such devices can be unregulated orthey can be equipped with gates or valves toregulate the outflow.

After the overflow characteristics have beenselected, the maximum spillway discharge andthe maximum reservoir water level can bed e t e r m i n e d b y f l o o d r o u t i n g . O t h e rcomponents of the spillway can then beproportioned to conform to the requiredcapacity and to the specific site conditions, anda complete layout of the spillway can beestablished. Cost estimates of the spillway anddam can then be made. Estimates of variouscombinations of spillway capacity and damheight for an assumed spillway type, and ofalternative types of spillways, will provide abasis for selection of the economical spillwaytype and the optimum relation of spillwaycapacity to height of dam. Figures 9-5 and 9-6illustrate the results of such a study. Therelationships of spillway capacities tomaximum reservoir water surfaces obtainedfrom the flood routings is shown on figure 9-5for two spillways. Figure 9-6 illustrates thecomparative costs for different combinationsof spillway and dam, and indicates acombination which results in the least totalcost.

To make such a study as illustrated requiresmany flood routings, spillway layouts, andspillway and dam estimates. Even then, thestudy is not necessarily complete since manyo t h e r spillway arrangements c o u l d b econsidered. A c o m p r e h e n s i v e s t u d y t o

15 5

Figure 9-5. Spillway capacity-surchargerelationship.-288-D-3039

I I

fOptimum combmatmn gated

SPIIIWOY and darn III -“^*~-I comb,nat,on

I f

Cost Of dam. right

d overflow Of w9y. etc.

\ ‘\i \1 / I

Combined cost-Gatedsp!llwoy o n d dam

\-\\

-Cost of ungatedOverflow splllwoy

\I

I‘ I

Figure 9-6 . Comparat ive cost of spi l lway-damcombinations.-288-D-3040

determine alternative optimum combinationsand minimum costs may not be warranted forthe design of some dams. Judgment on the partof the designer would be required to select forstudy only the combinations which showd e f i n i t e advantages, e i t h e r i n c o s t o radaptability. For example, although a gatedspillway might be slightly cheaper overall thanan ungated spillway, it may be desirable toadopt the latter because of its less complicatedconstruction, its automatic and trouble-freeoperation, its ability to function without anattendant, and its less costly maintenance.

156

(b) Combined Service and AuxiliarySpillways. -Where site conditions are favorable,the possibility of gaining overall economy byutilizing an auxiliary spillway in conjunctionwith a smaller service-type structure should beconsidered. In such cases the service spillwayshould be designed to pass floods likely tooccur frequently and the auxiliary spillwaycontrol set to operate only after such smallfloods are exceeded. In certain instances theoutlet works may be made large enough toserve also as a service spillway. Conditionsfavorable for the adoption of an auxiliaryspillway are the existence of a saddle ordepression along the rim of the reservoir whichleads into a natural waterway, or a gentlysloping abutment where an excavated channelcan be carried sufficiently beyond the dam toavoid the possibility of damage to the dam orother structures.

Because of the infrequency of use, it is notnecessary to design the entire auxiliary spillwayfor the same degree of safety as required for


other structures; however, at least the controlportion must be designed to forestall failure,since its breaching would release large flowsfrom the reservoir. For example, concretelining may be omitted from an auxiliaryspillway channel excavated in rock which is noteasily eroded. Where the channel is excavatedthrough less competent material, it might belined but terminated above the river channelwith a cantilevered lip rather than extending toa stilling basin at river level. The design ofauxiliary spillways is often based on thepremise that some damage to portions of thestructure from passage of infrequent flows ispermissible. Minor damage by scour to anunlined channel, by erosion and underminingat the downstream end of the channel, and bycreation of an erosion pool downstream fromthe spillway might be tolerated.

An auxiliary spillway can be designed with afixed crest control, or it can be stoplogged orgated to increase the capacity withoutadditional surcharge head.

B. DESCRIPTION OF SPILLWAYS

9-6. Selection of Spillway Layout.-Thedesign of a spillway, including all of itscomponents, can be prepared by properlyconsidering the various factors influencing thespillway size and type, and correlatingalternatively selected components. Manycombinations of components can be used informing a complete spillway layout. After thehydraulic size and outflow characteristics of aspillway are determined by routing of thedesign flood, the general dimensions of thecontrol can be selected. Then, a specifics p i l l w a y l a y o u t c a n b e d e v e l o p e d b yconsidering the topography and foundationconditions, and by fitting the control structureand the various components to the prevailingconditions.

Site conditions greatly influence theselection of location, type, and components ofa spillway. Factors that must be considered int h e s e l e c t i o n a r e t h e p o s s i b i l i t y o fincorporating the spillway into the dam, the

steepness of the terrain that would be traversedby a chute-type spillway, the amount ofexcavation required and the difficulty of itsdisposal, the chances of scour of the flowsurfaces and the need for lining the spillwaychannel, the permeability and bearing capacityof the foundation, the stability of theexcavated slopes, and the possible use of atunnel-type spillway.

The adoption of a particular size ora r r a n g e m e n t f o r o n e o f t h e s p i l l w a ycomponents may influence the selection ofother components. For example, a widecontrol structure with the crest placed normalto the centerline of the spillway would requirea long converging transition to join it to anarrow discharge channel or to a tunnel; abetter alternative might be the selection of anarrower gated control structure or a sidechannel control arrangement. Similarly, a widestilling basin may not be feasible for use with acut-and-cover conduit or tunnel, because of the

SPI LLWAYS-Sec. 9-7

long, diverging transition needed.A spillway may be an integral part of a dam

such as an overflow section of a concrete dam,or it may be a separate structure. In someinstances, it may be integrated into the riverdiversion plan for economy. Thus, the location,type, and size of other appurtenances arefactors which may influence the selection of aspillway location or its arrangement. The finalplan will be governed by overall economy,hydraulic sufficiency, and structural adequacy.

The components of a spillway and commontypes of spillways are described and discussedhe re in . H y d r a u l i c d e s i g n c r i t e r i a a n dprocedures are discussed in sections 9-10through 9-29.

9-7. Spil lway Components. -(a) ControlStructure. -A major component of a spillway isthe control device, since it regulates andcontrols the outflows from the reservoir. Thiscontrol limits or prevents outflows below fixedreservoir levels, and it also regulates releaseswhen the reservoir rises above these levels. Thecontrol structure is usually located at theupstream end of the spillway and consists ofsome form of overflow crest or orifice.Sometimes the configuration of the spillwaydownstream from the control structure is suchthat with higher discharges the structure nolonger controls the flow. For example, with themorning glory spillway, shown on figure 9-44,the tunnel rather than the crest or orificeusually controls the flow at higher discharges(see sec. 9-25).

Control structures may take various forms inboth positioning and shape. In plan, overflowcrests can be straight, curved, semicircular,U-shaped, or circular. Figure 9-7 shows thecircular crest for the morning glory spillway atHungry Horse Dam. Orifice controls can beplaced in a horizontal, inclined, or verticalposition. The orifice can be circular, square,rectangular, triangular, or varied in shape.

An overflow can be sharp crested, ogeeshaped, broad crested, or of varied crosssection. Orifices can be sharp edged, roundedged, or bellmouth shaped, and can be placedso as to discharge with a fully contracted jet orwith a suppressed jet. They may dischargefreely or discharge partly or fully submerged.

figure 9-7. Circular crest for morning glory spillway atHungry Horse Dam in Montana.-P447-105-5587

(b) Discharge Channel . -Flow releasedthrough the control structure usually isconveyed to the streambed below the dam in adischarge channel or waterway. Exceptions arewhere the discharge falls free from an arch damcrest or where the flow is released directlyalong the abutment hillside to cascade downthe abutment face. The conveyance structuremay be the downstream face of a concretedam, an open channel excavated along theground surface on one abutment, or a tunnelexcavated through an abutment. The profilemay be variably flat or steep; the cross sectionmay be variably rectangular, trapezoidal,circular, or of other shape; and the dischargechannel may be wide or narrow, long or short.

Discharge channel dimensions are governedprimarily by hydraulic requirements, but theselection of profile, cross-sectional shape,width, length, etc., is influenced by thegeologic and topographic characteristics of thesite. Open channels excavated in the abutmentusually follow the ground surface profile; steep


the end of the spillway structure to prevent itfrom being undermined.

Where serious erosion to the streambed is tobe avoided, the high energy of the flow mustbe dissipated before the discharge is returnedto the stream channel. This can bea c c o m p l i s h e d b y t h e u s e o f a n e n e r g ydissipating device, such as a hydraulic jumpbasin, a roller bucket, an apron, a basinincorporating impact baffles and walls, or somesimilar energy absorber or dissipator.

(d) Entrance and Outlet Channels. -Entrance channels serve to draw water fromthe reservoir and convey it to the controlstructure. Where a spillway draws waterimmediately from the reservoir and delivers itdirectly back into the river, as in the case withan overflow spillway over a concrete dam,entrance and outlet channels are not required.However, in the case of spillways placedthrough abutments or through saddles orridges, channels leading to the spillway controland away from the spillway terminal structuremay be required.

Entrance velocities should be limited andchannel curvatures and transitions should bemade gradual, in order to minimize head lossthrough the channel (which has the effect ofreducing the spillway discharge) and to obtainuniformity of flow over the spillway crest.Effects of an uneven distribution of flow in theentrance channel might persist through thespillway s t r u c t u r e t o t h e e x t e n t t h a tundesirable erosion could result in thedownstream river channel. Nonuniformity ofhead on the crest may also result in a reductionin the discharge.

The approach velocity and depth below crestlevel each have important influences on thedischarge over an overflow crest. As discussedin section 9-1 l(b), a greater approach depthwith the accompanying reduction in approachvelocity will result in a larger dischargecoefficient. Thus, for a given head over thecrest, a deeper approach will permit a shortercrest length for a given discharge. Within thelimits required to secure satisfactory flowconditions and nonscouring velocities, thedetermination of the relationship of entrancechannel depth to channel width is a matter of

canyon walls usually make a tunnel desirable.In plan, open channels may be straight orcurved, with sides parallel , convergent,divergent, or a combination of these. Dischargechannels must be cut through or lined withmaterial which is resistant to the scouringaction of the high velocities, and which isstructurally adequate to withstand the forcesfrom backfill, uplift, waterloads, etc.

(c) Terminal Structure. -When water flowsin a spillway from reservoir pool level todownstream river level, the static head isconverted to kinetic energy. This energymanifests itself in the form of high velocitieswhich if impeded result in large pressures.Means of returning the flow to the riverwithout serious scour or erosion of the toe ofthe dam or damage to adjacent structures mustusually be provided.

In some cases the discharge may be deliveredat high velocities directly to the stream wherethe energy is absorbed along the streambed byimpact, turbulence, and friction. Such ana r r a n g e m e n t i s sat isfactory whereerosion-resistant bedrock exists at shallowdepths in the channel and along the abutmentsor where the spillway outlet is sufficientlyremoved from the dam or other appurtenancesto avoid damage by scour, undermining, orabutment sloughing. The discharge channelmay be terminated well above the streambedlevel or it may be continued to or belowstreambed.

U p t u r n e d d e f l e c t o r s , c a n t i l e v e r e dextensions, or flip buckets can be provided toproject the jet some distance downstream fromthe end of the structure. Often, erosion of thestreambed in the area of impact of the jet canbe minimized by fanning the jet into a thinsheet by the use of a flaring deflector.

Where severe scour at the point of jetimpingement is anticipated, a plunge pool canbe excavated in the river channel and the sidesand bottom lined with riprap or concrete. Itmay be expedient to perform a minimum ofexcavation and to permit the flow to erode anatural pool; protective riprapping or concretelining may be later provided to halt the scour ifnecessary. In such arrangements an adequatecutoff or other protection must be provided at

SPI LLWAYS-Sec. 9-8

economics. When the spillway entrance channelis excavated in material that will be eroded bythe approach velocity, a zone of riprap is oftenprovided immediately upstream from the inletlining to prevent scour of the channel floor andside slope adjacent to the spillway concrete.

Outlet channels convey the spillway flowfrom the terminal structure to the river channelbelow the dam. An outlet channel should beexcavated to an adequate size to pass theanticipated flow without forming a controlwhich will affect the tailwater stage in thestilling device.

The outlet channel dimensions and its needfor protection by lining or riprap will dependon the nature of the material through whichthe channel is excavated and its susceptibility toscouring. Although stilling devices areprovided, it may be impossible to reduceresultant velocities below the natural velocityin the original stream; and some scouring of theriverbed, therefore, may not be avoidable.Further, under natural conditions the beds ofmany streams are scoured during the risingstage of a flood and filled during the fallingstage by deposition of material carried by theflow. After creation of a reservoir the spillwaywill normally discharge clear water and thematerial scoured by the high velocities will notbe replaced by deposition. Consequently, therewill be a gradual retrogression o f t h edownstream riverbed, which will lower thet a i l w a t e r stage-discharge relationship.Conversely, scouring w h e r e o n l y a p i l o tchannel is provided may build up bars andislands downstream, thereby effecting anaggradation of the downstream river channelwhich will raise the tailwater elevation withrespect to discharges. The dimensions anderosion-protective measures at the outletchanne l m a y b e i n f l u e n c e d b y t h e s econsiderations.

9 - 8 . S p i l l w a y Types. -Spillways areordinarily classified according to their mostdistinguishing feature, either as it pertains tothe control, to the discharge channel, or tosome other component. Spillways often arereferred to as controlled or uncontrolled,depending on whether they are gated orungated. Common types are the free fall, ogee

159

(overflow), side channel, c h u t e o r o p e nchannel, tunnel, and morning glory spillways.

(a> Free Fall Spillways.-A free fall spillwayis one in which the flow drops freely, usuallyinto the streambed. Flows may be freedischarging, as with a sharp-crested weir ororifice control, or they may be supported partway down the face of the dam and thentrajected away from the dam by a flip bucket.

Where no artificial protection is provided atthe base, scour will occur in some streambedsand will form a deep plunge pool. The volumeand depth of the hole are related to the rangeof discharges, the height of the drop, and thedepth of tailwater. The erosion-resistantproperties of the streambed material includingbedrock have little influence on the size of thehole, the only effect being the time necessaryto scour the hole to its full depth. Probabledepths of scour are discussed in section 9-24.Where erosion cannot be tolerated, a plungepool can be created by constructing anauxiliary dam downstream from the mainstructure, or by excavating a basin which isthen provided with a concrete apron or bucket.

If tailwater depths are sufficient, a hydraulicjump will form when a free fall jet falls upon aflat apron. It has been demonstrated that themomentum equation for the hydraulic jumpmay be applied to the flow conditions at thebase of the fall to determine the elements ofthe jump.

(b) Ogee (Overflow) Spillways. -The ogeespillway has a control weir which is ogee- orS-shaped in profile. The upper curve of theogee ordinarily is made to conform closely tothe profile of the lower nappe of a ventilatedsheet of water falling from a sharp-crested weir.Flow over the crest is made to adhere to theface of the profile by preventing access of airto the underside of the sheet. For discharges atdesigned head, the flow glides over the crestwith minimum interference from the boundarysurface and attains near-maximum dischargeefficiency. The profile below or downstream ofthe upper curve of the ogee is continuedtangent along a slope to support the flowingsheet on the face of the weir. A reverse curve atthe bottom of the slope turns the flow ontothe apron of a stilling basin, into a flip bucket,


or into the spillway discharge channel. Figure9-1 shows this type of spillway in operation atGrand Coulee Dam.

The upper curve at the crest may be madeeither broader or sharper than the nappeprofile. A broader shape will support the sheetand positive hydrostatic pressure will occuralong the contact surface. The supported sheetthus creates a backwater effect and reduces theefficiency of discharge. For a sharper shape,the sheet tends to pull away from the crest andto produce subatmospheric pressure along thecontact surface. This negative pressure effectincreases the effective head, and therebyincreases the discharge.

An ogee crest and apron may comprise anentire spillway, such as the overflow portion ofa concrete gravity dam, or the ogee crest maybe only the control structure for some othertype of spillway. Because of its high dischargeefficiency, the nappe-shaped profile is used formost spillway control crests.

(c) Side Channel Spillways. -The sidechannel spillway is one in which the controlweir is placed along the side of andapproximately parallel to the upper portion ofthe spillway discharge channel. Flow over thecrest falls into a narrow trough behind theweir, turns an approximate right angle, andthen continues into the main dischargechannel. The side channel design is concernedonly with the hydraulic action in the upstreamreach of the discharge channel and is more orless independent of the details selected for theother spillway components. Flows from theside channel can be directed into an opendischarge channel or into a closed conduit orinclined tunnel. Flow into the side channelmight enter on only one side of the trough inthe case of a steep hillside location, or on bothsides and over the end of the trough if it islocated on a knoll or gently sloping abutment.Figure 9-8 shows the Arizona spillway atHoover Dam which consists of a side channeldischarging into a large tunnel.

Discharge characteristics of a side channelspillway are similar to those of an ordinaryoverflow and are dependent on the selectedprofile of the weir crest. However, formaximum discharges the side channel flow may

Figure 9-8. Drumgate-controlled side channel spillway inoperation at Hoover Dam on the Colorado River.-BCP5492

differ from that of the overflow spillway inthat the flow in the trough may be restrictedand may partly submerge the flow over thecrest. In this case the flow characteristics willbe controlled by the channel downstream fromthe trough.

Al though the side channel is nothydraulically efficient nor inexpensive, it hasadvantages which make it adaptable to certainspillway layouts. Where a long overflow crest isdesired in order to limit the surcharge head andthe abutments are steep and precipitous, orwhere the control must be connected to anarrow discharge channel or tunnel, the sidechannel is often the best choice.

(d) Chute Spil lways,-A spillway whosedischarge is conveyed from the reservoir to thedownstream river level through an openchannel, placed either along a dam abutment orthrough a saddle, is called a chute or openchannel spillway. These designations can apply


regardless of the control device used to regulatethe flow. Thus, a spillway having a chute-typedischarge channel, though controlled by anoverflow crest, a gated orifice, a side channelcrest, or some other control device, might stillbe called a chute spillway. However, the nameis most often applied when the spillway controlis placed normal or nearly normal to the axis ofan open channel, and where the streamlines offlow both above and below the control crestfollow in the direction of the axis.

Chute spillways ordinarily consist of anentrance channel, a control structure, adischarge channel, a terminal structure, and anoutlet channel. The simplest form of chutespillway has a straight centerline and is ofuniform width. Often, either the axis of theentrance channel or that of the dischargechannel must be curved to fit the alinement ofthe chute to the topography. In such cases, thecurvature is confined to the entrance channel ifpossible, because o f t h e l o w a p p r o a c hvelocities. Where the discharge channel must becurved, its floor is sometimes superelevated toguide the high-velocity flow around the bend,thus avoiding a piling up of flow toward theoutside of the chute.

C h u t e s p i l l w a y p r o f i l e s a r e u s u a l l yinfluenced by the site topography and bysubsurface foundation conditions. The controlstructure is generally placed in line with orupstream from the dam. Usually the upperportion of the discharge channel is carried atminimum grade until it “daylights” along thedownstream hillside to minimize excavation.The steep portion of the discharge channelthen follows the slope of the abutment.

Flows upstream from the crest are generallyat subcritical velocity, with critical velocityoccurring when the water passes over thecontrol. Flows in the chute are ordinarilymaintained at supercritical stage, either atconstant or accelerating rates, until theterminal structure is reached. For goodhydraulic performance, abrupt vertical changesor sharp convex or concave vertical curves inthe chute profile should be avoided. Similarly,the convergence or divergence in plan shouldbe gradual in order to avoid cross waves,“ride-up” on the walls, excessive turbulence, or

uneven distribution of flow at the terminalstructure.

Figure 9-9 shows the chute-type structure atElephant Butte Dam in New Mexico.

(e) Tunnel Spillways.-Where a tunnel isused to convey the discharge around a dam, thespillway is called a tunnel spillway. Thespillway tunnel usually has a vertical orinclined shaft, a large-radius elbow, and ahorizontal tunnel at the downstream end. Mostforms of control structures, including overflowcrests, vertical or inclined orifice entrances, andside channel crests can be used with tunnelspillways.

Wi th the excep t ion o f morn ing g lo ryspillways, discussed later, tunnel spillways aredesigned to flow partly full throughout theirlength. To guarantee free flow in the tunnel,the ratio of the flow area to the total tunnelarea is often limited to about 75 percent. Airvents may be provided at critical points alongthe tunnel to insure an adequate air supplywhich will avoid unsteady flow through thespillway.

Tunnel spillways may present advantages fordamsites i n n a r r o w c a n y o n s w i t h s t e e pabutments or at sites where there is danger toopen channels from snow or rock slides.

(f) Morning Glory Spillways.-A morningglory spillway (sometimes called a drop inletspillway) is one in which the water enters overa horizontally positioned lip, which is circularin plan, drops through a vertical or slopingshaft, and then flows to the downstream riverchannel through a horizontal or near horizontaltunnel. The structure may be considered asbeing made up of three elements; namely, anoverflow control weir, an orifice controlsection, and a closed discharge channel.

Discharge characteristics of the morningglory spillway usually vary with the range ofhead. The control will shift according to therelative discharge capacities of the weir, theorifice, and the tunnel. For example, as thehead increases, the control will shift from weirflow over the crest to orifice flow in the throatand then to full tunnel flow in the downstreamportion of the spillway. Full tunnel flow designfor spillways, except those with extremely lowdrops, is not recommended, as discussed in


Figure 9-9. Chute type spillway (left) at Elephant Butte Dam in New Mexico.-P24-500-1250

section 9-29.A morning glory spillway can be used

advantageously at damsites in narrow canyonswhere the abutments rise steeply or where adiversion tunnel is available for use as thedownstream leg. Another advantage of thistype of spillway is that near maximum capacityis attained at relatively low heads; thischaracteristic makes the spillway ideal for usewhere the maximum spillway outflow is to belimited. This characteristic also may beconsidered disadvantageous, in that there islittle increase in capacity beyond the designedheads, should a flood larger than the selectedinflow design flood occur. This would not be adisadvantage if this type of spillway were usedas a service spillway in conjunction with anauxiliary spillway.

9-9. Controls for Crests. -The simplest formof control for a spillway is the free oru n c on trolled o v e r f l o w cres t wh ich

automatically releases water whenever thereservoir water surface rises above crest level.The advantages of the uncontrolled crest arethe elimination of the need for constantattendance and regulation of the control deviceb y a n o p e r a t o r , a n d t h e f r e e d o m f r o mmaintenance and repairs of the device.

A regulating device or movable crest must beemployed if a sufficiently long uncontrolledcrest or a large enough surcharge head cannotbe obtained for the required spillway capacity.Such control devices will also be required if thespillway is to release storages below the normalreservoir water surface. The type and size ofthe selected control device may be influencedby such conditions as discharge characteristicsof a particular device, climate, frequency andnature of floods, winter storage requirements,flood control storage and outflow provisions,the need for handling ice and debris, andspecial operating requirements. Whether an


operator will be in attendance during periodsof flood, and the availability of electricity,operating mechanisms, operating bridges, etc.,are other factors which will influence the typeof control device employed.

Many types of crest control have beendevised. The type selected for a specificinstallation should be based on a considerationof the factors noted above as well as economy,adaptability, reliability, and efficiency. In theclassification of movable crests are such devicesas flashboards and stoplogs. Regulating devicesinclude vertical and inclined rectangular liftgates, radial gates, drum gates, and ring gates.T h e s e m a y b e c o n t r o l l e d m a n u a l l y o rautomatically. Automatic gates may be eithermechanical or hydraulic in operation. The gatesare often raised automatically to follow a risingwater surface, then lowered if necessary toprovide sufficient spillway capacity for largerfloods.

(a) Flashboards and Stoplogs. -Flashboardsand stoplogs provide a means of raising thereservoir storage level above a fixed spillwaycrest level, when the spillway is not needed forreleasing floods. Flashboards usually consist ofindividual boards or panels supported byvertical pins or stanchions anchored to thecrest; stoplogs are boards or panels spanninghorizontally between grooves recessed intosupporting piers. In order to provide adequatespillway capacity, the flashboards or stoplogsmust be removed before the floods occur, orthey must be designed or arranged so that theycan be removed while being overtopped.

Various arrangements of flashboards havebeen devised. Some must be placed andremoved manually, some are designed to failafter being overtopped, and others are arrangedto drop out of position either automatically orby being manually triggered after the reservoirexceeds a certain stage. Flashboards provide asimple economical type of movable crestdevice, and they have the advantage that anunobstructed crest is provided when theflashboards and their supports are removed.They have numerous disadvantages, however,which greatly limit their adaptability. Amongthese disadvantages are the following: (1) Theypresent a hazard if not removed in time to pass

floods, especially where the reservoir area issmall and the stream is subject to flash floods;(2) they require the attendance of an operatoror crew to remove them, unless they aredesigned to fail automatically; (3) if they aredesigned to fail when the water reaches certainstages their operation is uncertain, and whenthey fail they release sudden and undesirablylarge outflows; (4) ordinarily they cannot berestored to position while flow is passing overthe crest; and (5) if the spillway functionsf r e q u e n t l y t h e r e p e a t e d r e p l a c e m e n t o fflashboards may be costly.

Stoplogs are individual beams or girders setone upon the other to form a bulkheadsupported in grooves at each end of the span.The spacing of the supporting piers will dependon the material from which the stoplogs areconstructed, the head of water acting againstthe stoplogs, and the handling facilitiesprovided for installing and removing them.Stoplogs which are removed one by one as theneed for increased discharge occurs are thesimplest form of a crest gate.

Stoplogs may be an economical substitutefor more elaborate gates where relatively closespacing of piers is not objectionable and whereremoval is required only infrequently. Stoplogswhich must be removed or installed in flowingwater may require such elaborate hoistingmechanisms that this type of installation mayprove to be as costly as gates. A stoploggeds p i l l w a y r e q u i r e s t h e a t t e n d a n c e o f a noperating crew for removing and installing thestoplogs. Further, the arrangement may presenta hazard to the safety of the dam if thereservoir is small and the stream is subject toflash floods, since the stoplogs must beremoved in time to pass the flood.

(b) Rectangular Lift Gates.-Rectangular liftgates span horizontally between guide groovesin supporting piers. Although these gates maybe made of wood or concrete, they are oftenmade of metal (cast iron or steel). The supportguides may be placed either vertically orinclined slightly downstream. The gates areraised or lowered by an overhead hoist. Wateris released by undershot orifice flow for all gateopenings.

For sliding gates the vertical side members of

164

the gate frame bear directly on the guidemembers; sealing is effected by the contactpressure. The size of this type of installation islimited by the relatively large hoisting capacityrequired to operate the gate because of thesliding friction that must be overcome.

Where larger gates are needed, wheels can bemounted along each side of the rectangular liftgates to carry the load to a vertical track on thedownstream side of the pier groove. The use ofwheels greatly reduces the amount of frictionand thereby permits the use of a smaller hoist.

(c) Radial Gates.-Radial gates are usuallyconstructed of steel . They consist of acylindrical segment which is attached tosupporting bearings by radial arms. The facesegment is made concentric to the supportingpins so that the entire thrust of the waterloadpasses through the pins; thus, only a smallmoment need be overcome in raising andlowering the gate. Hoisting loads then consistof the weight of the gate, the friction betweenthe side seals and the piers, and the frictionalresistance at the pins. The gate is oftencounterweighted to partially counterbalancethe effect of its weight, which further reducesthe required capacity of the hoist.

The small hoisting effort needed to operateradial gates makes hand operation practical onsmall installations which otherwise mightrequire power. The small hoisting forcesinvolved also make the radial gate more


adaptable to operation by relatively simpleautomatic control apparatus. Where a numberof gates are used on a spillway, they might bearranged to open automatically at successivelyincreasing reservoir levels, or only one or twomight be equipped with automatic controls,while the remaining gates would be operatedby hand or power hoists.

( d ) D r u m G a t e s . - D r u m g a t e s areconstructed of steel plate and, since they arehollow, are buoyant. Each gate is triangular insection and is hinged to the upstream lip of ahydraulic chamber in the weir structure, inwhich the gate floats. Water introduced into ordrawn from the hydraulic chamber causes thegate to swing upwards or downwards. Controlsgoverning the flow of water into and out of thehydraulic chamber are located in the piersadjacent to the chambers. Figure 9-8 shows thedrum gates on the Arizona spillway at HooverDam, which are automatic in operation.

(e) Ring Gates.-A ring gate consists of afull-circle hollow steel ring with streamlinedtop surface which blends with the surface of amorning glory inlet structure. The bottomportion of the ring is contained within acircular hydraulic chamber. Water admitted toor drawn from the hydraulic chamber causesthe ring to move up or down in the verticaldirection. Figure 9-7 shows the morning gloryspillway for Hungry Horse Dam with the ringgate in the closed position.

C. CONTROL STRUCTURES

9 - 1 0 . S h a p e f o r Uncontrolled OgeeCrest. -Crest shapes which approximate theprofile of the under nappe of a jet flowing overa sharp-crested weir provide the ideal form forobtaining optimum discharges. The shape ofsuch a profile depends upon the head, theinclination of the upstream face of theoverflow section, and the he igh t o f theoverflow section above the floor of theentrance channel (which influences the velocityof approach to the crest).

A simple scheme suitable for most damswith a vertical upstream face is to shape the

upstream surface (in section) to an arc of acircle and the downstream surface to aparabola. The necessary information fordefining the shape is shown on figure 9-10.T h i s m e t h o d w i l l d e f i n e a c r e s t w h i c happroximates the more refined shape discussedbelow. It is suitable for preliminary estimatesand for final designs when a refined shape isnot required.

Crest shapes have been studied extensively int h e B u r e a u of Reclamation hydrauliclaboratories, and data from which profiles foroverflow crests can be obtained have been

SPI LLWAYS-Sec. 9-l 1 165

of coordinates

Figure 9-10. A simple ogee crest shape witha vertical upstream face.-288-D-3041

published [ 11 .l For most conditions the datacan be summarized according to the formshown on figure 9-11 (A), where the profile isdefined as it relates to axes at the apex of thecrest. That portion upstream from the origin isdefined as either a single curve and a tangent oras a compound circular curve. The portiondownstream is defined by the equation:

x=-K + n4 00

(2)

in which K and n are constants whose valuesdepend on the upstream inclination and on thevelocity of approach. Figure 9- 11 gives valuesof these constants for different conditions.

The approximate profile shape for a crestwith a vertical upstream face and negligiblevelocity of approach is shown on figure 9-l 2.The profile is constructed in the form of acompound circular curve with radii expressedin terms of the design head, Ho. This definitionis simpler than that shown on figure 9-l 1, sinceit avoids the need for solving an exponentialequation; further, it is presented in a formeasily used by a layman for constructing formsor templates. For ordinary conditions of designof spillways where the approach height, P (fig.9-l l(A)), is equal to or greater than one-halfthe maximum head on the crest, this profile issufficiently accurate to avoid seriously reduced

‘Numbers in brackets refer to items in the bibliography,sec. 9-31.

crest pressures and does not materially alter thehydraulic efficiency of the crest. When theapproach height is less than one-half themaximum head on the crest, the profile shouldbe determined from figure 9- 11.

In some cases, it is necessary to use a crestshape other than that indicated by the abovedesign. Information from model studiesperformed on many spil lways has beenaccumulated and a compilation of thec o e f f i c i e n t d a t a h a s b e e n m a d e . T h i si n f o r m a t i o n i s shown in EngineeringMonograph No. 9 [ 21. In this monograph, thecrests are plotted in a dimensionless form withthe design head, Ho, equal to 1. By plottingother crests to the same scale, comparisonswith model-tested crest shapes can be made.

9 - 11. Discharge Over an UncontrolledOverflow Ogee Crest. -The discharge over anogee crest is given by the formula:

Q = CLHe3’= (3)

where:

Q = discharge,C = a variable coefficient of

discharge,L = effective length of crest, and

H, = total head on the crest, includingvelocity of approach head, h,.

The total head on the crest, H,, does notinclude allowances for approach channelfkction losses or other losses due to curvatureof the upstream channel, entrance loss into theinlet section, and inlet or transition losses.Where the’ design of the approach channelresults in appreciable losses, they must beadded to H, to determine reservoir elevationscorresponding to the discharges given by theabove equation.

(a) Coefficient of Discharge. -The dischargecoefficient, C, is influenced by a number offactors, such as (1) the depth of approach, (2)relation of the actual crest shape to the idealnappe shape, (3) upstream face slope, (4)downstream apron interference, and (5)downstream submergence. The effect of thesevarious factors is discussed in subsections (b)

166 DESIGN OF

surface upstream from weir drawdawn

GRAVITY DAMS

(A) ELEMENTS OF NAPPE-SHAPED CREST PROFILES

! !40 00. 00s “0 0 I* 0 IS

0 ss

0s

Y

0.s

014

F i g u r e 9-11. Factors for definition of nappe-shaped crest profiles (sheet I of 2).-288-D-2406


I i

Figure 9-11. Factors for definition of nappe-shaped crest profiles (sheet 2 of 2).-288-D-2407


-~-- 0.147 Ho-.,--I--- -,- - -----,.640HF-------y, 0.264 Hk-*‘.:, I I

-_____--__ - 2.758 “6------------:1

1 *---I.230 H<---7 I.\ I

I I /

10I -r-------Q-,~

0I1---------i a//

,/' ----*, =12.000 Ho

// /’

//’/

/ / A’

,‘,-/’

/,6

L------- --__ 8.329 H& ____ ---_----

Figure 9-12. Ogee crest shape defined by compound curves.-288-D-2408

through (d). The effect of the discharge approximated by finding the design shapecoefficient for heads other than the design most nearly matches.head is discussed in subsection (e). The (b) Effect of Depth of Approach.-Fordischarge coefficient for various crest profiles high sharp-crested weir placed in a channel, thec a n b e d e t e r m i n e d f r o m E n g i n e e r i n g velocity of approach is small and the under sideMonograph No. 9 [21 or it may be of the nappe flowing over the weir attains


maximum v e rtical contraction. As theapproach depth is decreased, the velocity ofapproach increases and the vertical contractiondiminishes. When the weir height becomeszero, the contraction is entirely suppressed andthe overflow weir becomes in effect a channelor a broad-crested weir, for which thetheoretical coefficient of discharge is 3.087. Ifthe sharp-crested weir coefficients are relatedto the head measured from the point ofmaximum contraction instead of to the headabove the sharp crest, coefficients applicable toogee crests shaped to profiles of under nappesfor various approach velocit ies can beestablished. The relationship of the ogee crest

Pcoefficient, C, , to various values of-is shownHo

on figure 9- 13. These coefficients are valid onlywhen the ogee is formed to the ideal nappe

shape, that is when+ = 1.

downstream water surface: (1) Flow willcontinue at supercritical stage; (2) a partial ori n c o m p l e t e h y d r a u l i c j u m p w i l l o c c u rimmediately downstream from the crest; (3) atrue hydraulic jump will occur; (4) a drownedjump will occur in which the high-velocity jetwill follow the face of the overflow and thencontinue in an erratic and fluctuating path fora considerable distance under and through theslower water; and (5) no jump will occur-thejet will break away from the face of theoverflow and ride along the surface for a shortdistance and then erratically intermingle withthe slow-moving water underneath. Figure 9-l 5shows the relationship of the floor positionsand downstream submergences which producethese distinctive flows.

(c) Effect of Up;tream Face Slope. -Forsmall ratios of the approach depth to head onthe crest, sloping the upstream face of theoverflow results in an increase in thecoefficient of discharge. For large ratios theeffect is a decrease of the coefficient. Withinthe range considered in this text, thecoefficient of discharge is reduced for large

ratios of p only for relatively flat upstreamHo

slopes. Figure 9-14 shows the ratio of thecoefficient for an overflow ogee crest with asloping face to the coefficient for a crest with avertical upstream face as obtained from figure

9 13, as related to values of g.

W h e r e t h e d o w n s t r e a m f l o w i s a tsupercritical stage or where the hydraulic jumpoccurs, the decrease in the coefficient ofd i s c h a r g e i s d u e p r i n c i p a l l y t o t h eback-pressure effect of the downstream apronand is independent of any submergence effectdue to tailwater. Figure 9- 16 shows the effectof downstream apron conditions on thecoefficient of discharge. It will be noted thatthis curve plots the same data represented bythe vertical dashed lines on figure 9-l 5 in aslightly different form. As the downstreamapron l e v e l n e a r s the crest of the

overflowh, + d

4approaches 1.0

(d) Effect of Downstreai Apron Interfer-ence and Downstream Submergence.-Whenthe water level below an overflow weir is highenough to affect the discharge, the weir is saidto be submerged. The vertical distance fromthe crest of the overflow weir to thedownstream apron and the depth of flow in thedownstream channel, as it relates to the headpool level, are factors which alter thecoefficient of discharge.

coefficient of discharge is about 77 percent ofthat for unretarded flow. On the basis of acoefficient of 3.98 for unretarded flow over ahigh weir, the coefficient when the weir issubmerged will be about 3.08, which isvirtually’ the coefficient for a broad-crestedweir.

From figure 9-16 it can be seen that when

theh, + d~ values exceed about 1.7, the4

Five distinct characteristic flows can occurbelow an overflow crest, depending on therelative positions of the apron and the

downstream floor position has little effect onthe coefficient, but there is a decrease in thecoefficient caused by tailwater submergence.Figure 9-17 shows the ratio of the coefficientof discharge where affected by tailwaterconditions, to the coefficient for free flowconditions. This curve plots the data


3.2

3.00 I 2 3 4 3 6 7 8 9 IO I I 12

VALUES OF !?-HO

Figure 9-13. Coefficient of discharge for ogee-shaped crest with vertical upstream face.-288-D-3042

1.04

0.98

‘2:3

0 0.5 1.0 I.5

V A L U E S O F pHO

Figure 9-14. Coefficient of discharge for ogee-shaped crest with sloping upstream face.-288-D-2411

SPI LLWAYS-Sec. 9-l 1

/ 1 I,,

I I A I II ,,I ! I I

_I V I I I I l/l

deot

Downstream depths lnsufflctent to form

epths sufflclent f o r formm

Figure 9-15. Effects of downstream influences on flow over weir crests.-288-D-2412

represented by the horizontal dashed lines onfigure 9-l 5 in a slightly different form. Wherethe dashed lines on figure 9-l 5 are curved, thedecrease in the coefficient is the result of ac o m b i n a t i o n 0 f t ailwater effects anddownstream apron position.

(e) Effect of Heads Differing from DesignHead.-When the crest has been shaped for ahead larger or smaller than the one underconsideration, the coefficient of discharge, C,will differ from that shown on figure 9-13. Awidened shape will result in positive pressuresalong the crest contact surface, therebyreducing the discharge; with a narrower crest

shape negative pressures along the contactsurface will occur, resulting in an increaseddischarge. Figure 9-l 8 shows the variation of

Hethe coefficient as related to values of H,0

where H, is the actual head being considered.The adjusted coefficient can be used forpreparing a discharge-head relationship.

(f) Pier and Abutment Effects. -Where crestpiers and abutments are shaped to cause sidecontractions of the overflow, the effectivelength, L, will be less than the net length of thecrest. The effect of the end contractions may

0.76


I.0 IL1 1.2 I.3 I .4 1.5 1.6 I .7 I.8h,,td

POSITION OF DOWNSTREAM APRON -“e

Figure 9-I 6. Ratio of discharge coefficients due to apron effect.-288-D-2413

0 0. I 0 2 0.3 0.4 0.5 0.6

DEGREE O F SUBMERGENCE 5He

Figure 9-17. Ratio of discharge coefficients due to tailwater effect.-288-D-2414

0.7 0.6

o.S”““““““‘,““““““““’0 0.2 0 . 4 0 . 6 0 . 0 1 . 0 1 . 2 1 . 4 1 . 6

R A T I O O F H E A D O N C R E S T T O D E S I G N H E A D =

Figure 9-18. Coefficient of discharge for other than the design head.-288-D-2410

be taken into account by reducing the net crestlength as follows:

L = L’ -2 (NKp + Ku) He (4)

where :

L =L’ =N =

Kp =K, =

He =

effective length of crest,net length of crest,number of piers,pier contraction coefficient,abutment contraction coefficient,

andtotal head on crest.

The pier contraction coefficient, Kp , .isaffected by the shape and location of the piernose, the thickness of the pier, the head inrelation to the design head, and the approachvelocity. For conditions of design head, H,,average pier contraction coefficients may beassumed as follows:

For square-nosed piers withcorners rounded on a radiusequal to about 0.1 of thepier thickness

JL

0.02

KpFor round-nosed piers 0.01For pointed-nose piers 0

The abutment contraction coefficient isaffected by the shape of the abutment, theangle between the upstream approach wall andthe axis of flow, the head in relation to thedesign head, and the approach velocity. Forconditions o f d e s i g n h e a d , Ho, a v e r a g ecoefficients may be assumed as follows:

For square abutments withheadwall at 90’ to directionof flow

For rounded abutments withheadwall at 90’ todirection of flow, whenOSH, 5 Y$. O.l5H,

For rounded abutments whereY > 0.5H, and headwall isplaced not more than 45’ todirection of flow

where Y = radius of abutment rounding.

Ka

0.20

0.10

0


9-12. Uncontrolled Ogee Crests Designedfor Less Than Maximum Head.-Economy inthe design of an ogee crest may sometimes beeffected by using a design head less than themaximum expected for determining the ogee

profile. Use of a smaller head for design resultsin increased discharges for the full range ofheads. The increase in capacity makes i tpossible to achieve economy by reducing eitherthe crest length or the maximum surchargehead.

Tests have shown that the subatmosphericpressures on a nappe-shaped crest do notexceed about one-half the design head whenthe design head is not less than about 75percent of the maximum head. As long as thesesubatmospheric pressures do not approachpressures which might induce cavitation, theycan be tolerated. Care must be taken, however,in forming the surface of the crest where thesenegative pressures will occur, since unevennesscaused by abrupt offsets, depressions, orprojections will amplify the negative pressuresto a magnitude where cavitation conditions candevelop.

The negative pressure on the crest may beresolved into a system of forces acting bothupward and downstream. These forces shouldbe considered in analyzing the structuralstability of the crest structure.

An approximate force diagram of thesubatmospheric pressures when the design headused to determine the crest shape is 75 percentof the maximum head, is shown on figure 9-19.These data are based on average results of testsmade on ideal shaped weirs with negligiblevelocit ies o f a p p r o a c h . Pressures forintermediate head ratios can be assumed tov a r y l i n e a r l y , c o n s i d e r i n g t h a t n o

H,subatmospheric pressure prevails when H isequal to 1. e

9-13. Gate-Controlled Ogee Crests.-Releases for partial gate openings for gatedcrests will occur as orifice flow. With full headon the gate and with the gate opened a smallamount, a free discharging trajectory willfollow the path of a jet issuing from an orifice.For a vertical orifice the path of the jet can beexpressed by the parabolic equation:

X2- Y =q.j- (5)

where H is the head on the center of theopening. For an orifice inclined an angle of 0from the vertical, the equation will be:

X2-Y = x kin 0 + 4H cos2 e (6)

If subatmospheric pressures are to be avoidedalong the crest contact, the shape of the ogeedownstream from the gate sill must conform tothe trajectory profile.

Gates operated with small openings underhigh heads produce negative pressures along thecrest in the region immediately below the gateif the ogee profile drops below the trajectoryprofile. Tests have shown that subatmosphericpressures would be equal to about one-tenth ofthe head when the gate is operated at smallopening and the ogee is shaped to the nappep r o f i l e a s d e f i n e d b y e q u a t i o n ( 2 ) f o rmaximum head H,. The force diagram for thiscondition is shown on figure 9-20.

The adoption of a trajectory profile ratherthan a nappe profile downstream from the gatesill will result in a wider ogee, and reduceddischarge efficiency for full gate opening.Where the discharge efficiency is unimportantand where a wider ogee shape is needed forstructural stability, the trajectory profile maybe adopted to avoid subatmospheric pressurezones along the crest. Where the ogee is shapedto the ideal nappe profile for maximum head,the subatmospheric pressure area can beminimized by placing the gate sill downstreamfrom the crest of the ogee. This will provide anorifice which is inclined downstream for smallgate openings, and thus will result in a steepertrajectory more nearly conforming to thenappe-shaped profile.

9-14. Discharge Over Gate-Controlled OgeeCrests.-The discharge for a gated ogee crest atpartial gate openings will be similar to flowthrough an orifice and may be computed bythe equation:

Q = +CL H1312 -Hz312) (7)

SPI LLWAYS-Sec. 9-14 17.5

Figure 9-19. Subatmospheric crest pressures for a 0.75ratio of II, to He.-288-D-3043

Figure 9-20. Subatmospheric crest pressures forundershot gate flow.-288-D-3044

where H, and H2 are the total heads (includingthe velocity head of approach) to the bottomand top of the orifice, respectively. Thecoefficient, C, will differ with different gateand crest arrangements; it is influenced by theapproach and downstream conditions as theyaffect the jet contractions. Thus, the topcontraction for a vertical leaf gate will differfrom that for a curved, inclined radial gate; theupstream floor profile will affect the bottomcon t r ac t i on o f t he i s su ing j e t ; and t hedownstream profile will affect the backpressure and consequently the effective head.

Figure 9-21 shows coefficients of discharge fororifice flows for various ratios of gate openingto total head. The curve represents averagesdetermined for the various approach anddownstream conditions described and issufficiently reliable for determining dischargesfor most spillway structures. The curve is for agate at the apex of the ogee crest, and so longas the bottom of the gate when closed is lessthan 0.03 H, vertically from the apex thecoefficient should not change significantly.

9-l 5. Orifice Control Structures. -Orificecontrol structures are often incorporated into aconcrete gravity dam, one or more orificesbeing formed through the dam. If the invert ofthe orifice is below normal water surface theorifice must be gated. If the invert is at orabove normal water surface the orifice may beeither gated or ungated. Figure 9-22 showstypical orifice control structures.

(a) Shape.-The entrance to the orifice mustbe streamlined to eliminate negative pressures.Portions of ellipses are used to streamline theentrances. The major axis of the ellipse is equalto the height or width of the oritice H or W infigure 9-22, and the minor axis is one-third ofthis amount. Orifices may be horizontal orthey may be inclined downward to change thelocation of the impingement area in the case ofa free fall spillway, or to provide improvedalinement into a discharge channel. If inclineddownward, the bottom of the orifice should beshaped similar to an ogee crest to eliminatenegative pressures. The top should be madeparallel to or slightly converging with thebottom.

(b) Hydraulics-The discharge characteris-tics of an orifice flowing partially full with theupper nappe not in contact with the orifice aresimilar to those of an ogee crest, and thedischarge can be computed by use of equation(3). The discharge coefficient, C, can bedetermined as described in section 9-10 for anoverflow crest. Where practicable, a modelstudy should be made to confirm the value ofthe coefficient. An orifice flowing full willfunction similar to a river outlet, and thedischarge can be determined using the sameprocedures as for river outlets discussed inchapter X.


kK 0 . 6 820

WK00-L

t

:v 0 . 6 6

0.6 40 0.1 0.2 0 . 3 0 . 4 0 . 8 0 . 6 0.7

R A T I O -$I

Figure 9-21. Coefficient of discharge for flow under a gate (orifice flow).-288-D-3045

9-16. Side Channel Control Structures. -Theside channel control structure consists of anogee crest to control releases from thereservoir, and a channel immediatelydownstream of and parallel to the crest tocarry the water to the discharge channel.

(a) Layout.-The ogee crest is designed bythe methods in section 9-10 if the crest isuncontrolled or section 9-13 if it is controlled.

The cross-sectional shape of the side channeltrough will be influenced by the overflow creston the one side and by the bank conditions onthe opposite side. Because of turbulences andvibrations inherent in side channel flow, a sidechannel design is ordinarily not consideredexcept where a competent foundation such asrock exists. The channel sides will, therefore,usually be a concrete lining placed on a slopeand a n c h o r e d d i r e c t l y t o t h e r o c k . Atrapezoidal cross section is the one most oftenemployed for the side channel trough. The

width of such a channel in relation to thedepth should be considered. If the width todepth ratio is large, the depth of flow in thechannel will be shallow, similar to thatdepicted by the cross section abfg on figure9-23. It is evident that for this condition a poordiffusion of the incoming flow with thechannel flow will result. A cross section with aminimum width-depth ratio will provide thebest hydraulic performance, indicating that across section approaching that depicted as adjon the figure would be the ideal choice bothf r o m t h e s t a n d p o i n t o f h y d r a u l i c s a n deconomy. Min imum bo t tom wid ths a r erequired, however, to avoid constructiondifficulties due to confined working space.Furthermore, the stability of the structure andthe hillside which might be jeopardized by anextremely deep cut in the abutment must alsobe considered. Therefore, a minimum bottomwidth must be selected which is commensurate

SPI LLWAYS-Sec. 9-16

TYPICAL HORIZONTAL ORIFICE SEC. A-A

TYPICAL INCLINED ORIFICE I

F i g u r e 9 - 2 2 . T y p i c a l o r i f i c e c o n t r o lstructures.-288-D-3046

with both the practical and structural aspectsof the problem.

The slope of the channel profile is arbitrary;however, a relatively flat slope will providegreater depths and slower velocities andconsequently will ensure better intermingling offlows at the upstream end of the channel andavoid the possibili ty of accelerating orsupercritical flows occurring in the channel forsmaller discharges.

A control section is usually constructeddownstream from the side channel trough. It isachieved by constricting the channel sides orelevating the channel bottom to produce apoint of critical flow. Flows upstream from thecontrol will be at the subcritical stage and willprovide a maximum of depth in the sidechannel trough. The side channel bottom andcontrol dimensions are then selected so thatflow in the trough immediately downstreamfrom the crest will be at the greatest depthpossible without excessively submerging the

177

flow over the crest. Flow in the dischargechannel downstream from the control will bethe same as that in an ordinary channel orchute type spillway. If a control section is notprovided, the depth of water and its velocity inthe side channel will depend upon either theslope of the side channel trough floor or thebackwater effect of the discharge channel.

Figure 9-24(A) illustrates the effect of acontrol section and the slope of the sidechannel trough floor on the water surfaceprofile. When the bottom of the side channeltrough is selected so that its depth below thehydraulic gradient is greater than the minimumspecific energy depth, flow will be either at thesubcritical or supercritical stage, depending onthe relation of the bottom profile to criticalslope or on the influences of a downstreamcontrol section. If the slope of the bottom isgreater than critical and a control section is notestablished below the side channel trough,supercritical flow will prevail throughout thelength of the channel. For this stage, velocitieswill be high and water depths will be shallow,resulting in a relatively high fall from thereservoir water level to the water surface in thetrough. This flow condition is illustrated byprofile B’ on figure 9-24(A). Conversely, if acontrol section is established downstream fromthe side channel trough to increase theupstream depths, the channel can be made toflow at the subcritical stage. Velocities at thisstage will be less than critical and the greaterdepths will result in a smaller drop from thereservoir water surface to the side channelwater surface profile. The condition of flow forsubcritical depths is i l lustrated on figure9-24(A) by water surface profile A’.

The effect of the fall distance from thereservoir to the channel water surface for eachtype of flow is depicted on figure 9-24(B). Itcan be seen that for the subcritical stage, theincoming flow will not develop high transversevelocities because of the low drop before itmeets the channel flow, thus effecting a gooddiffusion with the water bulk in the trough.Since both the incoming velocities and thechannel velocities will be relatively slow, afairly complete intermingling of the flows willtake place, thereby producing a comparatively


Figure 9-23. Comparison of side channel cross sections.-288-D-2419

smooth flow in the side channel. Where thechannel flow is at the supercritical stage, thechannel velocities will be high, and theintermixing of the high-energy transverse flowwith the channel stream will be rough andturbulent. The transverse flows will tend tosweep the channel flow to the far side of thechannel, producing violent wave action withattendant vibrations. It is thus evident thatflows should be maintained at subcritical stagefor good hydraulic performance. This can beachieved by establishing a control sectiondownstream from the side channel trough.

Variations in the design can be made byassuming different bottom widths, differentchannel slopes, and varying control sections. Aproper and economical design can usually beachieved after comparing several alternatives.

(b) Hydraulics.-The theory of flow in aside channel [3] is based principally on the lawof conservation of linear momentum, assumingthat the only forces producing motion in thechannel result from the fall in the water surfacein the direction of the axis. This premiseassumes that the entire energy of the flow overthe crest is dissipated through its interminglingwith the channel flow and is therefore of no

assistance in moving the water along thechannel. Axial velocity is produced only afterthe incoming water particles join the channelstream.

For any short reach of channel Ax, thechange in water surface, Ay, can be determinedby either of the following equations:

@ =$;;‘y; )) Iv2 -vl ) + lJz (Q2iQl)] C8)1 2 1

ay = e, (Vl +vz 1 VI (Q,-Q,)g (Q,+Q,> (v2-v1) + Q, 1 (9)

where Q, and v1 are values at the beginning ofthe reach and Q, and v2 are the values at theend of the reach. The derivation of theseformulas can be found in reference [ 31.

By use of equation (8) or (9), the watersurface profile can be determined for anyparticular side channel by assuming successiveshort reaches of channel once a starting point isfound. The solution of equation (8) or (9) isobtained by a trial-and-error procedure. For areach of length Ax in a specific location, Q,and Q, will be known.


.,-Reservoir water surfoce

‘Side channel trough floor profile

( A ) SIDE CHANNEL PROFILE

( B ) S I D E C H A N N E L C R O S S S E C T I O N

Figure 9-24. Side channel flow characteristics.-288-D-2418


section, the water surface at the downstreamend of the side channel can be determined byrouting the water between the two points. Withthe depth of water at the downstream pointknown, depths for successive short reaches canbe computed as previously described. It isa s s u m e d t h a t a m a x i m u m o f t w o - t h i r d ssubmergence of the crest can be toleratedwithout affecting the water surface profile.

A s i n o t h e r w a t e r s u r f a c e p r o f i l edeterminations, the depth of flow and thehydraulic characteristics of the flow will beaffected by backwater influences from somecontrol point, or by critical conditions alongthe reach of the channel under consideration.A control section is usually constructed at thedownstream end of the side channel. Afterdetermining the depth of water at the control

D. HYDRAULICS OF DISCHARGE CHANNELS

9-l 7. General. -Discharge generally passesthrough the critical stage in the spillwaycontrol structure and enters the dischargechannel as supercritical or shooting flow. Toavoid a hydraulic jump below the control, theflow must remain at the supercritical stagethroughout the length of the channel. The flowin the channel may be uniform or it may beaccelerated or decelerated, depending on theslopes and dimensions of the channel and onthe total drop. Where it is desired to minimizethe grade to reduce excavation at the upstreamend of a channel, the flow might be uniform ordecelerating, followed by accelerating flow inthe steep drop leading to the downstream riverlevel. Flow at any point along the channel willdepend upon the specific energy, (d + k,),available at that point. This energy will equalthe total drop from the reservoir water level tothe floor of the channel at the point underconsideration, less the head losses accumulatedto that point. The velocities and depths of flowalong the channel can be fixed by selecting thegrade and the cross-sectional dimensions of thechannel.

The velocities and depths of free surfaceflow in a channel, whether an open channel ora tunnel, conform to the principle of theconservation of energy as expressed by theBernoulli’s theorem, which states: “Theabsolute energy of flow at any cross section isequal to the absolute energy at a downstreamsection plus intervening losses of energy.” Asapplied to figure 9-25 this relationship can beexpressed as follows:

AZ+d, +k,l =d2 +kv2 +Ak, (10)

When the channel grades are not too steep, forpractical purposes the normal depth d, can beconsidered equal to the vertical depth d, andAL can be considered to be the horizontaldistance. The term Ah, includes all losseswhich occur in the reach of channel, such asfriction, turbulence, impact, and transitionlosses. Since in most channels changes are madegradually, ordinarily all losses except those dueto friction can be neglected. The friction losscan then be expressed as:

AAL = S A L (11)

where s is the average friction slope expressedby either the Chezy or the Manning formula.For the reach AL, the head loss can beexpressed as Ah,

= Y’ : “?>AL. From the

Manning formula, as given in section F-2(c) ofappendix F,

i 1

2

s =1. 4iY3-2’3

The coefficient of roughness, ~1, will dependon the nature of the channel surface. Forconservative design the frictional loss should bemaximized when evaluating depths of flow andminimized when evaluating the energy contentof the flow. For a concrete-lined channel, aconservative value of y1, varying from 0.0 14 fora channel with good alinement and a smoothfinish to 0.018 for a channel with poor


L-Reservoir Water Sur face, F-Datum L i n e

A

+,

AII

i(Ah,_ --_---- - - - - - - __---- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -I nI

I ‘---.SloW O f Gradient: sEnergy Gradient----\

4- ;AhL 1

h’v2

Figure 9-25. Sketch illustrating flow in open channels.-288-D-2421

alinement and some unevenness in the finish,should be used in estimating the depth of flow.For determining specific energies of flowneeded for designing the dissipating device, avalue of n of about 0.008 should be assumed.

Where only rough approximations of depthsand velocities of flow in a discharge channel aredesired, the total head loss E(Ah, ) to anypoint along the channel might be expressed interms of the velocity head. Thus, at any sectionthe relationship can be stated: Reservoir watersurface elevation minus floor grade elevation =d + h, + Kh, . For preliminary spillway layouts,K can be assumed as approximately 0.2 fordetermining depths of flow and 0.1 or less foreva lua t i ng t he ene rgy o f f l ow . Rough

approximations of losses can also be obtainedfrom figure 9-26. The assumptions used indetermining the losses in figure 9-26 arediscussed in section F-2(f) of appendix F.

9- 18. Open Channels. -(a) Profile-Theprofile of an open channel is usually selected toconform to topographic and geologic siteconditions. It is generally defined as straightreaches joined by vertical curves. Sharp convexand concave vertical curves should be avoidedto prevent unsatisfactory flows in the channel.Convex curves should be flat enough tomaintain positive pressures and thus avoid thetendency for separation of the flow from thefloor. Concave curves should have a sufficientlylong radius of curvature to minimize the

182

K E Y


\\\\\\\

\\i\

Figure 9-26. Approximate losses in chutes for various values of water surface drop andchannel length.-288-D-3047


dynamic forces on the floor brought about bythe centrifugal force which results from achange in the direction of flow.

To avoid the tendency for the water tospring away from the floor and thereby reducethe surface contact pressure, the floor shapef o r c o n v e x c u r v a t u r e s h o u l d b e m a d esubstantially flatter than the trajectory of afree-discharging jet issuing under a head equalto the specific energy of flow as it enters thecurve. The curvature should approximate ashape defined by the equation:

183

radii of not less than 5d have been foundacceptable.

(b) Convergence and Divergence. -The besthydraulic performance in a discharge channel isobtained when the confining sidewalls areparallel and the distribution of flow across thechannel is maintained uniform. However,economy may dictate a channel sectionnarrower or wider than either the crest or theterminal structure, thus requiring converging ordiverging transitions to fit the variouscomponents together. Sidewall convergencemust be made gradual to avoid cross waves,“ r i d e u p s ” o n the walls, and unevendistribution of flow across the channel.Similarly, the rate of divergence of thesidewalls must be limited or else the flow willnot spread to occupy the entire width of thechannel uniformly, w h i c h m a y r e s u l t i nundesirable flow conditions at the terminalstructure.

The inertial and gravitational forces ofstreamlined kinetic flow in a channel can beexpressed by the Froude number parameter,

2. Variations from streamlined flow due todaoutside interferences which cause an expansionor a contraction of the flow also can be relatedto this parameter. Experiments have shownt h a t a n a n g u l a r v a r i a t i o n o f t h e f l o wboundaries not exceeding that produced by theequation,

X2

-’ = x tane +K[4(d+h,)cos2 e] (12)

where 0 is the slope angle of the floor upstreamfrom the curve. Except for the factor K, theequation is that of a free-discharging trajectoryissuing from an inclined orifice. To assurepositive pressure along the entire contactsurface of the curve, K should be equal to orgreater than 1 S.

For the concave curvature, the pressuree x e r t e d u p o n t h e f l o o r s u r f a c e b y t h ecentrifugal force of the flow will vary directlywith the energy of the flow and inversely withthe radius of curvature. An approximaterelationship of these criteria can be expressedin the equations:

R = % or R - 2dv2

P P

where :

R = the minimum radius of curvaturemeasured in feet,

4 = the discharge in c.f.s. per foot ofwidth,

v = the velocity in feet per second,d = the depth of flow in feet, andp = the normal dynamic pressure exerted

on the floor, in pounds per squarefoot.

An assumed value of p = 100 will normallyproduce an acceptable radius; however, aminimum radius of 1 Od is usually used. For thereverse curve at the lower end of the ogee crest,

will provide an acceptable transition for eithera contracting or an expanding channel. In this

equation, F = -&

and (Y is the angular

variation of the sidewall with respect to thechannel centerline; v and d are the averages ofthe velocities and depths at the beginning andat the end of the transition. Figure 9-27 is anomograph from which the tangent of the flareangle or the flare angle in degrees may beobtained for known values of depth andvelocity of flow.

(c) Channel Freeboard.-In addition tousing a conservative value for y1 in determining

184

IO98

7

6

l - -w :

i f -- 2

2 -- _

3 1

s-LL -

B-

I+ Y-1.0

5 .90 .a

.7

.6

.5

.4

r.3

-.2

- .I

dF L O W

<

T A N F L A R E = &

F=J+


‘:L -45

.6,--o

. 7 - - 3 5

.6 -- - 3 0

I- .07--4 a$ . 0 6 -is . 0 5 - 3 a kz

:! -I.04LL

2.03

6

- 0I5 -

- zi

- t:- u-l

2 0 -

1 2- a

251- k

30: :IL

z4 0

z

5 0z

6 0 W>

7 0

8 0

9 0

100

2 0 0 -

Af te r C . F reeman

Figure 9-27. Flare angle for divergent or convergent channels.-288-D-2422

the depth of water, a freeboard of 3 to 6 feet isusually provided to allow for air bulking, wave

a minimal freeboard can be permitted. Wheredamage can occur, such as when the channel is

action, etc. When the channel is constructed onthe downstream face of the dam and some

located on an abutment, the higher freeboard isneeded for safety. Engineering judgment

overtopping of the wall will not cause damage, should be used in setting the height of


freeboard by comparing the cost of additionalwall height against the possible damage due toovertopping of the channel walls. Whereverpracticable, a hydraulic model should be usedin determining the wall height.

In some cases, a minimum wall height ofabout 10 feet is used since there is very littleincrease in cost of a IO-foot wall over a lowerwall. Also, the fill behind the wall provides aberm for catching material sloughing off theexcavation slope, thus preventing it fromgetting into the channel.

9-l 9. Tunnel Channels. -(a) Profile. -Figure9-28 shows a typical tunnel spillway channel.The profile at the upper end is curved tocoincide with the profile of the controlstructure. The inclined portion is usuallysloped at 55’ from the horizontal. Steeperslopes increase the total length of the tunnel.On flatter slopes the blasted rock tends to stayon the slope during excavation rather thanfalling to the bottom where it can be easilyremoved from the tunnel.

The radius of the elbow at the invert may bedetermined by using equation (13); however, a

radius of about 10 tunnel diameters is usuallysatisfactory. From the elbow, the tunnel isusually excavated on a slight downslope to thedownstream portal.

(b) Tunnel Cross Section. -In the transition,the cross section changes from that required atthe control structure to that required for thetunnel downstream from the elbow. Thistransition may be accomplished in one or morestages and is usually completed upstream of theelbow. Because a circular shape better resiststhe external loadings, it is usually desirable toattain a circular shape as soon as practicable.

The transition should be designed so that auniform flow pattern is maintained and nonegative pressures are developed which couldlead to cavitation damage. No criteria havebeen established for determining the shape ofthe transition. Preliminary layouts are madeusing experience gained from previous tunnels.The layout should be checked using equation(10) so that no portion of the transition willflow more than 75 percent full (in area). Thiswill allow for air bulking of the water andavoid complete filling of the tunnel. If the

E l 3 7 3 0 0 0Mox.WS. El.3711Nor. WS. El.37

SpIllway controlstructure

Crest-El 3648 00

sto. 20 i 45 0

Axis of crest-SW. 20+00

‘ x 5 2 . 5 ’ Radial g a t e

~~ El 3638.122

PT.-~1.3543.470

sta 21 f 4 6 . 3 6 5El 3 5 0 6 . 6 7 7sto. 21t 72.14&

%a. 2 6 t 1 2 . 9 4 3 -

El 3 4 8 7 363--\,d

PC.-El. 3286 611

Sto. 23t26.240

Downstream portal

,?I.- El. 3136.000

Sta 24+30.298-

(1,26+,,,7,s

StO. 36+96.00- 1

PROFILEDeflector bucket

Figure 9-28. Profile of typical tunnel spillway channel.-288-D-3048


high-velocity flow must be protected fromcavitation erosion. Cavitation will occur when,due to some irregularities in the geometry ofthe flow surface, the pressure in the flowingwater is reduced to the vapor pressure, about0.363 pound per square inch absolute at 70° F.As the vapor cavities move with the flowingwater into a region of higher pressure, thecavities collapse causing instantaneous positivewater pressures of many thousands of poundsper square inch. These extremely high localizedpressures will cause damage to any flow surfaceadjacent to the collapsing cavities (reference[41)-

Protection against cavitation damage mayinclude (1) use of surface finishes andalinements devoid of irregularities which mightproduce cavitation, (2) use of constructionmaterials which are resistant to cavitationdamage, or (3) admission of air into theflowing water to cushion the damaging highpressures of collapsing cavities. (See reference[51 .I

tunnel were to flow full, the control couldmove from the control structure and causesurging in the tunnel.

Downstream of the elbow, generally theslope of the energy gradient (equivalent to thefriction slope, S) is greater than the slope of thetunnel invert (see fig. 9-25). This conditioncauses the velocity of the water to decrease andthe depth of the water to increase. Usually it isnot economically feasible to change the tunnelsize downstream of the elbow, and thereforethe conditions at the downstream end of thetunnel determine the size of the tunnel. Thisportion of the tunnel is frequently used as apart of the diversion scheme. If diversion flowsare large, it may be economical to make thetunnel larger than required for the spillwayflows. Because proper function of the spillwayis essential, consideration should be given inthese instances to checking of the final layoutin a hydraulic model.

9-20. Cavitation Erosion of ConcreteSurfaces. -Concrete surfaces adjacent to

E. HYDRAULICS OF TERMINAL STRUCTURES

9-2 1. Hydraulic Jump Stilling Basins. -Where the energy of flow in a spillway must bedissipated before the discharge is returned tothe downstream river channel, the hydraulicjump basin is an effective device for reducingthe exit velocity to a tranquil state. Figure 9-29shows a hydraulic-jump stilling basin inoperation at Canyon Ferry Dam in Montana.

The jump which will occur in a stilling basinhas distinctive characteristics and assumes adefinite form, depending on the energy of flowwhich must be dissipated in relation to thedepth of the flow. Comprehensive tests havebeen performed by the Bureau of Reclamation161 in connection with the hydraulic jump.The jump form and the flow characteristics canbe related to the Froude number parameter,2. In this context v and d are the velocitymand depth, respectively, before the hydraulicjump occurs, and g is the acceleration due togravity. Fo rms o f t he hyd rau l i c j ump

phenomena for various ranges of the Froudenumber are illustrated on figure 9-30. Thedepth d, , shown on the figure, is thedownstream conjugate depth, or the minimumtailwater depth required for the formation of ahydraulic jump. The actual tailwater depthm a y b e s o m e w h a t g r e a t e r t h a n t h i s , a sdiscussed in subsection (d).

When the Froude number of the incomingflow is equal to 1.0, the flow is at critical depthand a hydraulic jump cannot form. For Froudenumbers from 1.0 up to about 1.7, theincoming flow is only slightly below criticaldepth, and the change from this low stage tothe high stage flow is gradual and manifestsitself only by a slightly ruffled water surface.As the Froude number approaches 1.7, a seriesof small rollers begin to develop on the surface,which become more intense with increasinglyhigher values of the number. Other than thesurface roller phenomena, relatively smoothflows prevail throughout the Froude number


Figure 9-29. Overflow gate-controlled spillway on Canyon Ferry Dam in Moatana.-P296-600-883

range up to about 2.5. Stilling action for therange of Froude numbers from 1.7 to 2.5 isdesignated as form A on figure 9-30.

For Froude numbers between 2.5 and 4.5 anoscillating form of jump occurs, the enteringjet intermittently flowing near the bottom andthen along the surface of the downstreamchannel. T h i s o s c i l l a t i n g f l o w c a u s e sobjectionable surface waves which carryconsiderably beyond the end of the basin. Theaction represented through this range of flowsis designated as form B on figure 9-30.

For the range of Froude numbers for theincoming flow between 4.5 and 9, a stable andwell-balanced jump occurs. Turbulence isconfined to the main body of the jump, andthe water surface downstream is comparativelysmooth. As the Froude number increases above

9, the turbulence within the jump and thesurface roller becomes increasingly active,resulting in a rough water surface with strongsurface waves downstream from the jump.Stilling action for the range of Froude numbersbetween 4.5 and 9 is designated as form C onfigure 9-30 and that above 9 is designated asform D.

Figure 9-3 1 plots relationships of conjugatedepths and velocities for the hydraulic jump ina rectangular channel or basin. Also indicatedon the figure are the ranges for the variousforms of hydraulic jump described above.

( a ) H y d r a u l i c Design of S t i l l i n gBasins. -Stilling basins are designed to providesuitable stilling action for the various forms ofhydraulic jump previously discussed. Type Ibasin, shown on figure 9-32, is a rectangular

F , B E T W E E N 1 . 7 A N D 2 . 5F O R M A - P R E - J U M P S T A G E

F , B E T W E E N 2 . 5 A N D 4 . 5FORM B- TRANSIT ION STAGE

F, B E T W E E N 4 . 5 A N D 9 . 0FORM C-RANGE OF WELL BALANCED JUMPS

F, H I G H E R TtiAN 9 . 0F O R M D - E F F E C T I V E J U M P B U T

ROUGH SURFACE DOWNSTREAM

Figure 9-B). Characteristic forms of hydraulic jumprelated to the Froude number.-288-D-2423

channel without any accessories such as bafflesor sills and is designed to confine the entirelength of the hydraulic jump. Seldom arestilling basins of this type designed since it ispossible to reduce the length and consequentlythe cost of the basin by the installation ofbaffles and sills, as discussed later for types II,III, and IV basins. The type of basin best suitedfor a particular situation will depend upon theFroude number.

(1) Basins for Froude numbers less thanI . 7 . - F o r a F r o u d e n u m b e r o f 1 . 7 t h econjugate depth dz is about twice the incomingdepth, or about 40 percent greater than thecritical depth. The exit velocity v2 is aboutone-half the incoming velocity, or 30 percentless than the critical velocity. No special stillingbasin is needed to still flows where theincoming flow Froude factor is less than 1.7,except that the channel lengths beyond the


point where the depth starts to change shouldbe not less than about 4d,. No baffles or otherdissipating devices are needed.

(2) Basins for Froude numbers between 1.7and 2.5. -Flow phenomena for basins wherethe incoming flow factors are in the Froudenumber range between 1.7 and 2.5 will be inthe form designated as the prejump stage, asillustrated on figure 9-30. Since such flows arenot attended by active turbulence, baffles orsills are not required. The basin should be atype I basin as shown on figure 9-32 and itshould be sufficiently long and deep to containt h e f l o w p r i s m while it is undergoingretardation. Depths and lengths shown onfigure 9-3 2 will provide acceptable basins.

(3) Basins for Froude numbers between 2.5a n d 4 .5 . - Jump phenomena whe re t heincoming flow factors are in the Froudenumber range between 2.5 and 4.5 aredesignated as transition flow stage, since a truehydraulic jump does not fully develop. Stillingbasins to accommodate these flows are theleast effective in providing satisfactorydissipation, since the attendant wave actionordinarily cannot be controlled by the usualbasin devices. Waves generated by the flowphenomena will persist beyond the end of thebasin and must often be dampened by meansof wave suppressors.

Where a stilling device must be provided todissipate flows for this range of Froudenumber, the basin shown on figure 9-33 whichis designated as type IV basin, has proved to berelatively effective for dissipating the bulk ofthe energy of flow. However, the wave actionpropagated by the oscillating flow cannot beentirely dampened. Auxiliary wave dampenersor wave suppressors must sometimes beemployed to provide smooth surface flowdownstream. Because of the tendency of thejump to sweep out and as an aid in suppressingwave action, the water depths in the basinshould be about 10 percent greater than thecomputed conjugate depth.

Often the need for utilizing the type IVbasin in design can be avoided ‘by selectingstilling basin dimensions which will provideflow conditions which fall outside the range oftransition flow. For example, with an 800-c.f.s.


Figure 9-31. Relations between variables in hydraulic jumps for rectangularchannels.-288-D-2424


- - - I I-.-

(A) T Y P E I B A S I N DIMENSIDN~

FROUDE N U M B E R

26

2 4

6

7

6

6

F ROIJDE NUMBER


7 ,---Chute blocks

[A) TYPE JS! BASIN DIMENSIONS

F A O U D E N U M B E R

1

F R O U O E N U M B E R

Figure 9-33. Stilling basin characteristics for Froude numbers between 2.5and 4.5.-288-D-3050


A = the area of the up-stream face of theblock, and

(~‘1 + h, 1 > = the specific energyof the flow enteringthe basin.

capacity spillway where the specific energy atthe upstream end of the basin is about 1.5 feetand the velocity into the basin is about 30 feetper second, the Froude number will be 3.2 fora basin width of 10 feet. The Froude numbercan be raised to 4.6 by widening the basin to20 feet. The selection of basin width thenbecomes a matter of economics as well ashydraulic performance.

(4) Busins for Froude numbers higher than4..5.-For basins where the Froude numbervalue of the incoming flow is higher than 4.5, atrue hydraulic jump will form. The installationof accessory devices such as blocks, baffles, andsills along the floor of the basin produces astabilizing effect on the jump, which permitsshortening the basin and provides a factor ofsafety against sweep-out due to inadequatetailwater depth.

The basin shown on figure 9-34, which isdesignated as a type III basin, can be adoptedwhere incoming velocities do not exceed 50feet per second. This basin utilizes chuteblocks, impact baffle blocks, and an end sill toshorten the jump length and to dissipate thehigh-velocity flow within the shortened basinlength. This basin relies on dissipation ofenergy by the impact blocks and also on theturbulence of the jump phenomena for itseffectiveness. Because of the large impactforces to which the baffles are subjected by theimpingement of high incoming velocities andbecause of the possibility of cavitation alongthe surfaces of the blocks and floor, the use ofthis basin must be limited to heads where thevelocity does not exceed 50 feet per second.

Cognizance must be taken of the addedloads placed upon the structure floor by thedynamic force brought against the upstreamface of the baffle blocks. This dynamic forcewill approximate that of a jet impinging upon aplane normal to the direction of flow. Theforce, in pounds, may be expressed by theformula:

Force = 2wA(d, + h, 1 1 (15)

where:

w = the unit weight ofwater,

Negative pressure on the back face of theblocks will further increase the total load.However, since the baffle blocks are placed adistance equal to 0.8d2 beyond the start of thejump, there will be some cushioning effect bythe time the incoming jet reaches the blocksand the force will be less than that indicated bythe above equation. If the full force computedby equation (15) is used, the negative pressureforce may be neglected.

Where incoming velocities exceed 50 feet persecond, or where impact baffle blocks are notemployed, the basin designated as type II onfigure 9-35 can be adopted. Because thedissipation is accomplished primarily byhydraulic jump action, the basin length will begreater than that indicated for the type IIIbasin. However, the chute blocks and dentatedend sill will still be effective in reducing thelength from that which would be necessary ifthey were not used. Because of the reducedmargin of safety against sweep-out, the waterdepth in the basin should be about 5 percentgreater than the computed conjugate depth.

(b) Rectangular Versus Trapezoidal StillingBasin. -The utilization of a trapezoidal stillingbasin in lieu of a rectangular basin may oftenbe proposed where economy favors sloped sidelining over vertical wall construction. Modeltests have shown, however, that the hydraulicjump action in a trapezoidal basin is much lesscomplete and less stable than it is in therectangular basin. In the trapezoidal basin thewater in the triangular areas along the sides ofthe basin adjacent to the jump is not opposedby the incoming high-velocity jet. The jump,which tends to occur vertically, cannot spreads u f f i c i e n t l y t o o c c u p y t h e s i d e a r e a s .Consequently, the jump will form only in thecentral portion of the basin, while areas alongt h e o u t s i d e w i l l b e o c c u p i e d b yupstream-moving flows which ravel off thejump or come from the lower end of the basin.


F R O U D E N U M B E R.^ 12

2 4 2 4

(Al TYPE IUI B A S I N D I M E N S I O N S

4 !~llil~lllllll~lll~l~ 4Ill IIll III

F R O U D E N U M B E R

Figure 9-34. Stilling basin characteristics for Froude numbers above 4.5 whereincoming velocity does not exceed 50 feet per second.-288-D-3051


(A ) TYPE II B A S I N D I M E N S I O N S


2 4

3 34 6 8 IO 12 14 16 18


Figure 9-35. Stilling basin characteristics for Froude numbersabove 4.5.-288-D-3052


The eddy or horizontal roller action resultingfrom this phenomenon tends to interfere andinterrupt the jump action to the extent thatthere is incomplete dissipation of the energyand severe scouring can occur beyond thebasin. For good hydraulic performance, thesidewalls of a stilling basin should be vertical oras near vertical as is practicable.

( c ) B a s i n D e p t h s b y A p p r o x i m a t eMethods.-The nomograph shown on figure9-36 will aid in determining approximate basindepths for various basin widths and for variousdifferences between reservoir and tailwaterlevels. Plottings are shown for the condition ofno loss of head to the upstream end of thestilling basin, and for 10, 20, and 30 percentloss. (These plottings are shown on thenomographs as scales A, B, C, and D,respectively.) The required conjugate depths,d, , will depend on the specific energy availableat the entrance of the basin, as determined bythe procedure discussed in section 9-17. Whereonly a rough determination of basin depths isneeded, the choice of the loss to be applied forvarious spillway designs may be generalized asfollows:

(1) For a design of an overflowspillway where the basin is directlydownstream from the crest, or where thechute is not longer than the hydraulichead, consider no loss of head.

(2) For a design of a channel spillwaywhere the channel length is between oneand five times the hydraulic head,consider 10 percent loss of head.

(3) For a design of a spillway wherethe channel length exceeds five times thehydraulic head, consider 20 percent lossof head.

The nomograph on figure 9-36 gives valuesof 4 > the conjugate depth for the hydraulicjump. Tailwater depths for the various types ofbasin described in subsection (a) above shouldbe increased as noted in that subsection.

(d) Tailwater Considerations. -The tailwaterrating curve, which gives the stage-dischargerelationship of the natural stream below thedam, is dependent on the natural conditionsalong the stream and ordinarily cannot bealtered by the spillway design or by the release

characteristics. As discussed in section 9-7(d),retrogression or aggradation of the river belowthe dam, which will affect the ultimatestage-discharge conditions, must be recognizedin selecting the tailwater rating curve to beused for stilling basin design. Usually riverflowswhich approach the max imum des igndischarges have never occurred, and an estimateof the tailwater rating curve must either bee x t r a p o l a t e d f r o m k n o w n c o n d i t i o n s o rcomputed on the basis of assumed or empiricalcriteria. Thus, the tailwater rating curve at bestis only approximate, and factors of safety tocompensate for variations in tailwater must beincluded in the design.

For a given stilling basin design, the tailwaterdepth for each discharge seldom corresponds tothe conjugate depth needed to form a perfectjump. The basin floor level must therefore beselected to provide tailwater depths whichmost nearly agree with the conjugate depths.Thus, the relative shapes and relationships ofthe tailwater curve to the conjugate depthcurve will determine the required minimumdepth to the basin floor. This is illustrated onfigure 9-37. The tailwater rating curve is shownin (A) as curve 1, and a conjugate depth versusdischarge curve for a basin of a certain width,W, is represented by curve 3. Since the basinmust be made deep enough to provide forconjugate depth (or some greater depth toinclude a factor of safety) at the maximumspillway design discharge, the curves willintersect at point D. For lesser discharges thetailwater depth will be greater than theconjugate depth, thus providing an excess oftailwater which is conducive to the formationof a so-called drowned jump. (With thedrowned jump condition, instead of achievingg o o d j u m p - t y p e d i s s i p a t i o n b y t h eintermingling of the upstream and downstreamflows, the incoming jet plunges to the bottomand carries along the entire length of the basinfloor at high velocity.) If the basin floor ismade higher than indicated by the position ofcurve 3 on the figure, the depth curve andtailwater rating curve will intersect to the leftof point D, thus indicating an excess oftailw ater for smaller discharges and adeficiency of tailwater for higher discharges.

196 DESIGN OF GRAVI

Note: The values of d2 are-

approximate with maximumerror not exceeding 2%

TY DAMS

Figure 9-36. Stilling basin depths vcmus hydraulic heads for various channellosses.-288-D-3053


DISCHARGElb)I I

4-tiotlwater r(

D i s c h a r g e - d e p t h r e l a t i o nw h i c h will g o v e r n s e l e c t t o no f bas in f l oo r e l eva t i onf o r bastn wtdth w - , /

f l oo r elevotton forbostn width

con juga te dep ths fo rb a s i n wtdth 2~ ~

I I

DISCHARGE03)

Itit

Figure 9-37. Relationships of conjugate depth curves to tailwater ratingcurves.-288-D-2439


As an alternative to the selected basin whichis represented by curve 3, a wider basin mightbe considered for which the conjugate depthcurve 2 will apply. This design will provide ashallower basin, in which the conjugate depthswill more nearly match the tailwater depths forall discharges. The choice of basin widths, ofcourse, involves consideration of economics, aswell as hydraulic performance.

Where a tailwater rating curve shaped similarto that represented by curve 4 on figure9-37(B) is encountered, the level of the stillingbasin floor must be determined for somedischarge other than the maximum designcapacity. If the tailwater rating curve weremade to intersect the required water surfaceelevation at the maximum design capacity, asin figure 9-37(A), there would be insufficienttailwater depth for most smaller discharges. Inthis case the basin floor elevation is selected sothat there will be sufficient tailwater depth forall discharges. For the basin of width W whoserequired tailwater depth is represented bycurve 5, the position of the floor would beselected so that the two curves would coincideat the discharge represented by point E on thefigure. For all other discharges the tailwaterdepth will be in excess of that needed forforming a satisfactory jump. Similarly, if abasin width of 2W were considered, the basinfloor level would be selected so that curve 6would intersect the tailwater rating curve atpoint F. Here also, the selection of basinwidths should be based on economic aspects aswell as hydraulic performance.

Where exact conjugate depth conditions forforming the jump cannot be attained, thequestion of the relative desirability of havinginsufficient tailwater depth as compared tohaving excessive tailwater depth should beconsidered. With insufficient tailwater the backpressure will be deficient and sweep-out of thebasin will occur. With an excess of tailwater thejump will be formed and energy dissipationwithin the basin will be quite complete untilthe drowned jump phenomenon becomescritical. Chute blocks, baffles, and end sills willfurther assist in energy dissipation, even with adrowned jump.

(e) Stilling Basin Freeboard. -A freeboard

of 5 to 10 feet is usually provided to allow forsurging and wave action in the stilling basin.For smaller, low-head basins, the requiredfreeboard will be nearer the lower value,whereas the higher value will normally be usedfor larger, high-head spillways. A minimumfreeboard may be used if overtopping by thewaves will not cause significant damage.Engineering judgment should be used in settingthe height of freeboard by comparing the costof additional wall height against possibledamage caused by overflow of the stilling basinwalls. Wherever practical, a hydraulic modelshould be used in determining the amount offreeboard.

9-22. Deflector Buckets.-Where thespillway discharge may be safely delivereddirectly to the river without providing anenergy dissipating or stilling device, the jet isoften projected beyond the structure by adeflector bucket or l ip. Flow from thesed e f l e c t o r s l e a v e s t h e s t r u c t u r e a s afree-discharging upturned jet and falls into thestream channel some distance from the end ofthe spillway. The path the jet assumes dependson the energy of flow available at the lip andthe angle at which the jet leaves the bucket.

With the origin of the coordinates taken atthe end of the lip, the path of the trajectory isgiven by the equation:

y = x tan /3 - __X2

K[4(d + h,) cos2 81(16)

where:

0 = the angle between the curve of thebucket at the lip and thehorizontal (or lip angle), and

K = a factor, equal to 1 for thetheoretical jet.

To compensate for loss of energy and velocityreduction due to the effect of air resistance,internal turbulences, and disintegration of thejet, a value for K of about 0.85 should beassumed.

The horizontal range of the jet at the level ofthe lip is obtained by making y in equation(16) equal to zero. Then:


f i g u r e 9 - 3 9 . T h e g e n e r a l n a t u r e o f t h edissipating action for each type is representedon figure 9-40. Hydraulic action of the twobuckets has the same characterist ics, butdistinctive features of the flow differ to theextent that each has certain limitations. Thehigh-velocity flow leaving the deflector lip ofthe solid bucket is directed upward. Thiscreates a high boil on the water surface and av io l en t g round roller moving clockwisedownstream from the bucket. This groundroller continuously pulls loose material backtowards the lip of the bucket and keeps someof the intermingling material in a constant stateo f a g i t a t i o n . I n t h e s l o t t e d b u c k e t t h ehigh-velocity jet leaves the lip at a flatter angle,and only a part of the high-velocity flow findsits way to the surface. Thus, a less violentsurface boil occurs and there is a betterdispersion of flow in the region above theg r o u n d r o l l e r w h i c h r e s u l t s i n l e s sconcentration of high-energy flow throughoutthe bucket and a smoother downstream flow.

Use of a solid bucket dissipator may beobjectionable because of the abrasion on theconcrete surfaces caused by material which isswept back along the lip of the deflector by theground roller. In addition, the more turbulentsurface roughness induced by the severe surface;oil carries farther down the river, causingobjectionable eddy currents which contributeto riverbank sloughing. Although the slottedbucket provides better energy dissipation withless severe surface and streambed disturbances,it is more sensitive to sweep-out at lowertailwaters and is conducive to a diving andscouring action at excessive tailwaters. This isnot the case with the solid bucket. Thus, thetailwater range which will provide goodperformance with the slotted bucket is muchnarrower than that of the solid bucket. A solidbucket dissipator should not be used whereverthe tailwater limitations of the slotted bucketcan be met. Therefore, only the design of theslotted bucket will be discussed.

Flow characteristics of the slotted bucketare illustrated on figure 9-41. For deficienttailwater depths the incoming jet will sweepthe surface roller out of the bucket and willproduce a high-velocity flow downstream, both

X=4K(d+h,) tan0 co? 8= 2K(d+h,) sin 28 (17)

The maximum value of x will be equal to2K (d + h,) when 0 is 45’. The lip angle isinfluenced by the bucket radius and the heightof the lip above the bucket invert. It usuallyvaries from 20’ to 4.5’, with 30’ being thepreferred angle.

The bucket radius should be made longenough to maintain concentric flow as thewater moves around the curve. The rate ofcurvature must be limited similar to that of avertical curve in a discharge channel (sec. 9-18),so that the floor pressures will not alter thestreamline distribution of the flow. Themin imum radius of curvature can bedetermined from equation (13), except thatvalues of p not exceeding 500 pounds persquare foot will produce values of the radiuswhich have proved satisfactory in practice.However, the radius should not be less thanfive times the depth of water. Structurally, thecantilever bucket must be of sufficient strengthto withstand this normal dynamic force inaddition to the other applied forces.

Figure 9-38 shows the deflector at the endof the spillway tunnel at Hungry Horse Dam inoperation.

9 - 2 3 . Su b merged Bucket EnergyDissipators.-When the tailwater depth is toogreat for the formation of a hydraulic jump,dissipation of the high energy of flow can beeffected by the use of a submerged bucketdeflector. The hydraulic behavior in this typeof dissipator is manifested primarily by theformation of two rollers; one is on the surfacemoving counterclockwise (if flow is to theright) and is contained within the region abovethe curved bucket, and the other is a groundroller moving in a clockwise direction and issituated downstream from the bucket. Themovements of the rollers, along with theintermingling of the incoming flows, effectivelydissipate the high energy of the water andprevent excessive scouring downstream fromthe bucket.

Two types of roller bucket have beendeveloped and model tested [6] . Their shapeand dimensional arrangements are shown on


,,-Boi I

Bucket rol ler.

(A) S O L I D T Y P E B U C K E T

/---Standrag wave

Bucket rol ler.:

_- -Ground m l ler

Figure 9-38. Deflector bucket in operation for thes p i l l w a y a t H u n g r y H o r s e D a m i nMontana.-P447-105-5924

(B) S L O T T E D T Y P E B U C K E T

Figure 9-40. Hydraulic action in solid and slottedbuckets.-288-D-2431

(A) SOLID BUCKET

along the water surface and along the riverbed.This action is depicted as stage (A) on figure9-41. As the tailwater depth is increased, therewill be a depth at which instability of flow willoccur, where sweep-out and submergence willalternately prevail. To obtain continuousoperation a t t h e s u b m e r g e d stage, theminimum tailwater depth must be above thisins table state. F low ac t ion wi th in theacceptable operating stage is depicted as stage(B) on figure 9-4 1.

When the tailwater becomes excessivelydeep, the phenomenon designated as divingflow will occur. At this stage the jet issuingfrom the lip of the bucket will no longer riseand c o n t i n u e a l o n g t h e s u r f a c e b u tintermittently will become depressed and diveto the riverbed. The position of thedownstream roller will change with the changein position of the jet. It will occur at thesurface when the jet dives and will form along

(6) SLOTTED BUCKET the river bottom as a ground roller when the jetrides the surface. Scour will occur in the

F i g u r e 9 - 3 9 . S u b m e r g e d bucke t energy streambed at the point of impingement whendissipators.-288-D-2430 the jet dives but will be filled in by the ground


Tallwater--_-.

Tai lwater below mlnimum. F law sweeps out

STAGE (A)

Tai lwater below average but above minimum,Within nom-101 operat ing range.

STAGE (6) ---0riainol channel bed

Tai lwater above mox~mum. Flow diving fromapron scours channel

STAGE (C) Origmol channel bed--. ,

Ta i lwater same as in C. Diving jet is l i f ted by groundrol ler . Scour hale backf i l ls similar to 6. Cycle repeats.

STAGE (D)

F i g u r e 9-41. Flow character i s t i cs in a s lo t tedbucket.-288-D-2432

roller when the jet rides. The characteristicflow pattern for the diving stage is depicted in(C) and (D) of figure 9-41. Maximum tailwaterdepths must be limited to forestall the divingflow phenomenon.

The design of the slotted bucket involvesdetermination of the radius of curvature of thebucket and the allowable range of tailwaterdepths. These criteria, as determined fromexperimental results, are plotted on figure 9-42in relation to the Froude number parameter.

The Froude number values are for flows at thepoint where the incoming jet enters the bucket.Symbols are defined on figure 9-43.

9-24. Plunge Pools. -When a free-fallingoverflow nappe drops almost vertically into apool in a riverbed, a plunge pool will bescoured to a depth which is related to theheight of the fall, the depth of tailwater, andthe concentration of the flow [7]. Depths ofscour are influenced initially by the erodibilityof the stream material or the bedrock and bythe size or the gradation of sizes of anyarmoring material in the pool. However, thearmoring or protective surfaces of the pool willbe progressively reduced by the abrading actionof the churning material to a size which will bescoured out, and the ultimate scour depth will,for all practical considerations, stabilize at alimiting depth irrespective of the material size.A n e m p i r i c a l a p p r o x i m a t i o n b a s e d o nexperimental data has been developed byVeronese [8] for limiting scour depths, asfollows:

where :

d, = 1.32 @.225 qo.s4 (18)

d, = the maximum depth of scourbelow tailwater levelin feet,

H, = the head from reservoir level totailwater level in feet,and

4 = the discharge in c.f.s. perfoot of width.

Three Bureau of Reclamation dams whichhave plunge pools for energy dissipators havebeen tested in hydraulic models. Reports of theresults of these tests are given in references[91, [lOl,and [ill.

F. HYDRAULICS OF MORNING GLORY (DROP INLET) SPILLWAYS

9 - 25. General Characteristics. -The flow respect that, in normal operation, the controlconditions and discharge characteristics of a changes as the head changes. As brought out inmorning glory spillway are unique in the the following discussion, at low heads the crest


MAX’IMljti TAl;WA;ER

I ! ! !’

! 1’M I N I M U M TAlLWATiR L’lMlT \ \

“1 I I

II-- I . 1 '

c m-l--~ ~- ---k-------zMINIMUM ALLOWABLE BUCKET RADIUS- Rmln

O,I I

2 l 6 (I 10

FROUOE NUMBER ‘Ft’

Figure 9-42. Limiting criteria for slotted bucket design.-288-D-2433

203

. :

* ... . ..- .

. .

.* .- . . . . . . . ..‘o..

Figure 9-43. Definition of symbols-submerged bucket.-288-D-2434


R e s e r v o i r E l e v a t i o n- - - - - _ _ - - - _ - - - - - -

is the control and the orifice and tunnel serveonly as the discharge channel; whereas atprogressively higher heads the orifice and thenthe tunnel serves as the control. Because of thisuniqueness the hydraulics of morning gloryspillways are discussed separately from otherspillway components.

Typical flow conditions and dischargecharacteristics of a morning glory spillway arerepresented on figure 9-44. As illustrated onthe discharge curve, crest control (condition 1)will prevail for heads between the ordinates ofa and g; orifice control (condition 2) willgovern for heads between the ordinates of gand h; and the spillway tunnel will flow full forheads above the ordinate of h (represented ascondition 3).

Flow characteristics of a morning gloryspillway will vary according to the proportionalsizes of the different elements. Changing thediameter of the crest will change the curve abon figure 9-44 so that the ordinate of g oncurve cd will be either higher or lower. For alarger diameter crest, greater flows can bedischarged over the crest at low heads andorifice control will occur with a lesser head onthe crest, tending to fill up the transition abovethe orifice. Similarly, by altering the size of theorifice, the position of curve cd will shift,changing the head above which orifice control

will prevail. If the orifice is made of sufficientsize that curve cd is moved to coincide with orlie to the right of point j, the control will shiftdirectly from the crest to the downstream endof the tunnel. The details of the hydraulic flowcharacteristics are discussed in followingsections.

9-26. Crest Discharge. -For small heads,flow over the morning glory spillway isgoverned by the characteristics of crestdischarge. The throat, or orifice, will flowpartly full and the flow will cling to the sidesof the shaft. As the discharge over the crestincreases, the overflowing annular nappe willbecome thicker, and eventually the nappe flowwill converge into a solid vertical jet. The pointwhere the annular nappe joins the solid jet iscalled the crotch. After the solid jet forms, a“boil” will occupy the region above the crotch:both the crotch and the top of the boil becomeprogressively higher with larger discharges. Forhigh heads the crotch and boil may almostflood out, showing only a slight depression andeddy at the surface.

Until such time as the nappe converges toform a solid jet, free-discharging weir flowprevails. After the crotch and boil form,submergence begins to affect the weir flow andultimately the crest will drown out. Flow isthen governed either by the nature of the

D E S I G N O F G R A V I T Y D A M S204H

r-0utlet leg of tunnel-

C O N D I T I O N 1. C R E S T C O N T R O L

ce contro l in throat

- d

C O N D I T I O N 2 . O R I F I C E C O N T R O L

- -b--7>ydroulic grodiant---5__ _

CONDITION 3. TUNNEL CONTROL

Tunnel control, Q-@( H,-

P o i n t o f c h a n g e f r o m o r i f i c et o t u n n e l f l o w

Ori f ice control , Q=F(Ha i), condit ionHead at which tunnel f lows 0.75

f u l l a t d o w n s t r e a m e n d

Point of change f rom crestt o o r i f i c e c o n t r o l

Crest control , Q= f(He

DISCHARGE - C. F. S.F i g u r e 9 - 4 4 . F l o w a n d d i s c h a r g e characterist ics of a morning glory

spillway.-288-D-3054


contracted jet which is formed by the overflowentrance, or by the shape and size of the throatas determined by the crest profile if it does notconform to the jet shape. Vortex action mustbe minimized to maintain converging flow intothe inlet. Guide piers are often employed alongthe crest for this purpose [ 12, 13, 141.

If the crest profile conforms to the shape ofthe lower nappe of a jet flowing over asharp-crested circular weir, the dischargecharacteristics for flow over the crest andthrough the throat can be expressed as:

Q = CLH3” (3)

where H is the head measured either to theapex of the under nappe of the overflow, tothe spring point of the circular sharp-crestedweir, or to some other established point on theoverflow. Similarly, the choice of the length Lis r e l a t e d t o s o m e specific point ofmeasurement such as the length of the circle atthe apex, along the periphery at the upstreamface of the crest, or along some other chosenreference line. The value of C will change withdifferent definitions of L and H. If L is takenat the outside periphery of the overflow crest(the origin of the coordinates in figure 9-45)and if the head is measured to the apex of theoverflow shape, equation (3) can be written:

Q = Co(2nR,)Ho3~2 (19)

It will be apparent that the coefficient ofdischarge for a circular crest differs from that

f low

Figure 9-45. Elements of nappe-shaped profile for acircular crest.-288-D-2440

for a straight crest because of the effects ofsubmergence and back pressure incident to thejoining of the converging flows. Thus, C, mustbe related to both Ho and R,, and can be

Hoexpressed in terms ofF. The relationship of

C, , as determined from ‘model tests [ 151 , toHovalues ofx for three conditions of approach

d e p t h i s klotted o n figure 9-46. Thesecoefficients are valid only if the crest profileconforms to that of the jet flowing over asharp-crested circular weir at Ho head and ifaeration is provided so that subatmosphericpressures do not exist along the lower nappesurface contact.

When the crest profile conforms to theprofile of the under nappe shape for an Ho

head over the crest, free flow prevails for?s

ratios up to approximately 0.45, and crestHocontrol governs. As the -Rs

ratio increases

above 0.45 the crest partly submerges and flowshowing characteristics of a submerged crest is

Hothe controlling condition. When the R ratios

approaches 1.0 the water surface above thecrest is completely submerged. For this and

higher stages of? the flow phenomena is that

of orifice flow. T/e weir formula Q = CLH3’*is used as the measure of flow over the cres;regardless of the submergence, by using acoefficient which reflects the flow conditions

through the various g ranges. Thus, from

figure 9-46 it will bes seen that the crestcoefficient is only slightly changed from that

Honormally indicated for values of- less thanRS Ho0.45, but reduces rapidly for the higher R

S

ratios.It will be noted that for most conditions of

flow over a circular crest the coefficient ofdischarge increases with a reduction of the

206 DESIGN OF GRAVITY DAMS42

I6

34

I30

26

22

18

14

IO0.0 04 06 12 I6 20

!!L

Rs

Figure 9-46. Relationship of circular crest coefficient CO to$-’ for different approach depths (aeratednappe).-288-D-2441 s

approach depth, whereas the opposite is truefor a straight crest. For both crests a shallowerapproach lessens the upward vertical velocitycomponent and consequently suppresses thecontraction of the nappe. However, for thecircular crest the submergence effect is reducedbecause of a depressed upper nappe surface,giving the jet a quicker downward impetus,which lowers the position of the crotch andincreases the discharge.

Coefficients for partial heads of He on thecrest can be determined from figure 9-47 toprepare a discharge-head relationship. Thedesigner must be cautious in applying theabove criteria, since subatmospheric pressure orsubmergence effects may alter the flow

conditions differently for variously shapedprofiles. These criteria, therefore, should not

be applied for flow conditions where -$s

exceeds 0.4.9-27. Crest fiofiles. -In this discussion, the

crest profile is considered to extend from thecrest to the orifice control, and forms thetransition to the orifice. Values of coordinatesto define the shape of the lower surface of anappe flowing over an aerated sharp-crested

Pcircular weir for various conditions of -and

RsHsR are shown in tables 9-2, 9-3, and 9-4. These

s


maximum. If subatmospheric pressures are tobe avoided along the crest profile, the crestshape should be selected so that it will givesupport to the overflow nappe for the smallerHe-ratios. Figure 9-51 shows the approximate4increase in radius required to minimizesubatmospheric pressures on the crest. Thecrest shape for the enlarged crest radius is then

based on agratio of 0.3.

9-28. Ori& Control.-The diameter of a jetissuing from a horizontal orifice can bedetermined for any point below the watersurface if it is assumed that the continuityequation, Q = av, is valid and if friction andother losses are neglected.

For a circular jet the area is equal to nR*.The discharge is equal to av = nR2 4%

Q, ’Solving for R, R = 5H, ‘/4 where H, is equal to

the difference between the water surface andthe elevation under consideration. Thediameter of the jet thus decreases indefinitelywith the distance of the vertical fall for normaldesign applications.

If an assumed total loss (to allow for jetcontraction losses, friction losses, velocitylosses due to direction change, etc.) is taken as0. lH,, the equation for determining theapproximate radius of the circular jet can bewritten:

c--

Figure 9-47. Circular crest coefficient of discharge forother than design head.-288-D-2446

data are based on experimental tests [ 151conducted by the Bureau of Reclamation. Therelationships of H, to Ho are shown on figure9-48. Typical upper and lower nappe profiles

4for various values ofRare plotted on figures

9-49 in terms ofgand&for the condition ofs s

P

R, = 2.0*Illustrated on figure 9-50 are typical lower

nappe profiles, plotted for various values of H,for a given value of R,. In contrast to thestraight crest where the nappe springs fartherfrom the crest as the head increases, it will beseen from figure 9-50 that the lower nappeprofile for the circular crest springs fartheronly in the region of the high point of the

Hsprofile, and then only for R values up tos

about 0.5. The profiles become increasingly

suppressed for larger gvalues. Below the high

point of the profile, tShe paths cross and theshapes for the higher heads fall inside those forthe lower heads. Thus, if the crest profile is

designed for heads where $ exceeds about

0.25 to 0.3, it appears that3 subatmosphericpressure will occur along some portion of theprofile when heads are less than the designed

Q”

R = o.204 47%(20)

Since this equation is for the shape of thejet, its use for determining the theoretical sizeand shape of a shaft in the area of the orificewould result in the minimum size shaft whichwould not restrict the flow and would notdevelop pressures along the sides of the shaft.

A theoretical jet profile or shaft asdetermined by equation (20) is shown by thed o t - d a s h l i n e s a b c o n f i g u r e 9 - 5 2 .Superimposed on the jet of that figure is anoverflow crest with a radius R,, which serves asan entrance to the shaft. If both the crest andthe shaft are designed for the same water


Hs PTable 9-2. -Coordinates of lower nappe surface for different values of F when ;= 2

[Negligible approach velocity and aerated nappel

10. “al

,010,020,030,040

,050 .0575.ow .0650,070 .0710.0&t .0765,090 .0820

100,120,140,160.180

.086”0940

lmll.1045.1080

2ccl,250,300,350,400

,450ml

:550,600,650

.I105

.lln,

.1105

.1060

.0970

.0845OiCKl.052u.0320.cao

IL.HS

0 ” “ ” 0.668- 020 io5-. 040 ,742-.OW .777-.08” .808

-. 100-. 150-. 290--.250-3w

-.400-.5””-.6w--.am-l.ooO

,338,913,978

1.0401. 1w

- 1 XXI- 1 400-1.600-1.800-2.m

-2. 500-3. ow-3. 500-4. ooo-4. 5lx

-5.wm-5.503-6.ooO

1 2071.3081.3971.5631.713

1.8461 9iO2 0852. lY62 302

2.5572. ii8

3R

0. 0”

2. alI I I I I I I I

For portion of the pro6le above the weir crest

0. “am.0116.0213

0289.0351

D. cm0

.0112.om2.0270.0324

.0402 .036a

.0448 .0404

.0487 .0432

.0521 .04550549 04il

05io .0482.0596 .0483.0599 .04fxl.0585 .04180559 .0361

.0521

.0380.0174

.0292

.0068

1. OaKJ 0. OOCQ 0. woo.0104 .0095 co86.0180 .0159 .0140.0231 .0198 .016a.OZlM .0220 Oli6

.02920305

.0308

.0301

.0287

.0264OlY5.OlOl

022% .016a.022Q .01470201 .0114.0172 o o i o.0135 .0018

““89

-

I. CKJOQ 0. woo

.0145 .0133.0265 oml.0365 .“35”.0460 .0435

3. ooo0

.0130

.0243.0337.0417

T

,

L

( 0. al""

0125.OWl.0317.0389

3. cm”

.0122

.0225

.0303

.0377

t. am”.0119.022U.0299.0363

I. OCMXI

On77.0115.0126.0117

.0535 .OYX

.0605 .0570

.0665 .0627

.0710 .0677

.0765 .0722

.0487

.0550

.Ow506.55

.0696

.0454

.0510.0560.0603.“+40

.0436

.0489

.0537

.0578

.0613

.04m,047”.0514.05xl.0581

.0092

.0”53

.a301

,081” .0762,088” .0826.0935 .0872.o?wJ .OQfJ51010 .OY27

Oi34

07Yo-0829OR55.0872

.0672-0720Oi50,076:OX6

.0642

.“683

.o 05

.0710oio5

0. o”oc

On70.oo9”.0085.wso

1025 .09381035 .“926

loo0 .0850(0936 .07xJ.0830 .“6al

.0877,085oOi64.0650.05&l

.0756 .0888

.0633 .0596.0559 .0446,041” 02800220 :KhXt

0611.0495.0327.0125

0450.0250.oQm

,031”.OlOQ

1. ooo"

.0128.0236.0327.0403

.0471

.0531

.0584,063”.0670

.0705

.07xOi92

.0812.082n

.0819

.07i3

.0668,054”.0365

.0170 .ooo

For portion of the profile below the weir crest- -0.615 0 554 0. 526 0 487 0 450 0 413 0 3i6 0 334 0 262 0 158 0.116 0 093 0 OiO 0 04R

,652 ,592 .sMl ,526 488 4 5 2 ,414 36Y .293 185 1 4 5 ,120 096 o i 4,688 ,627 ,596 ,563 524 4 8 7 ,448 ,400 320 212 1 6 5 140 ,115 ,088iZtl ,660 ,630 ,596 557 5 1 9 .4;8 ,428 342 2 3 2 182 155 129 loo752 ,692 ,662 ,628 ,589 .549 ,54x? .454 3 6 3 250 tsi ,169 1 4 0 ,110

.784 7 2 2 6 9 2 6 5 7 .618 5i7 ,532 478 381 ,266 2 1 0 l%l 150 118,857 i Y 3 i62 ,725 .686 ,641 5PY 531 4 2 3 299 2 3 8 204 1TO .132,925 ,860 ,826 Xl i 4 5 .698 6 4 0 5i5 ,459 ,326 264l 224 181 .144,985 919 ,883 .a47 ,801 ,750 ,683 6 1 3 490 ,348 280 ,239 ,196 153

1.043 Yi6 ,941 ,900 ,852 iY7 i 2 2 648 5 1 8 .36R 296 251 .206 .16il

1 150 l.Oi9 1.041 l.Mx) ,944 880 ,791 iO6 .5fx21. 246 1.172 1.131 1.08; 1.027 951 8 4 91 335 1.260 1. 215 1 167 1.102 1.012 : 898

7 5 3 59833 627

1sM) 1.422 1.369 1.312 1.231 1.112 ,974 ,854 6i31 646 1. 564 1 508 1.440 1 33i I. 189 1 n30 ,899 710

,400 ,322 2il ,226 16R.42i 342 28i 232 li3,449 ,359 ,300 ,240 179

4 8 2 384 ,320 ,253 184.m ,402 ,332 2fA 188

1.780 1.691 1 635 1 653 1.422 I. 248 1.074 9 3 3 i3Y ,5281.903 1.808 1. i48 1. 653 1 492 1.293 1.108 ,963 7ffl 5 4 22. 020 1.918 1.855 1.742 1. 548 1.330 1.133 ,988 .78” 5532.130 2 024 1.957 1. 821 1. 591 1.358 1 158 1.008 i97 5fI32. 234 2 126 2.053 1. x91 1. 630 1.381 1 180 1 025 810 5;2

4174 2 34 3 0

,433

3 4 0344

26fi

2.4i5 2.354 2 2662. 700 2.559 2.4282 Yl6 2. 749 2.5413.114 2.914 2.6203.306 3.053 2. 682

3.488 3.178 2. 7343. 653 3.794 2.7793.820 3.405 2.812

2.027 1.701 1.4302.11Y 1. i48 1.4fl32.171 1.7i7 1.4892.201 1.796 l..XNl2. 220 1.806 1. 509

1.2211.2521. 26iI.280

1.0591.0861.102

,8388.53

588

0. 10 020 0. 25 I2. 2272. 2292. 232

1.811

0. 30

Hs‘The t,ahulation for2 =O.lO was obtained by interpolation hetween--0 and 0.20.R

SPI LLWAYS-Sec. 9-28 2 0 9

Hs pTable 9-3.-Coordinates of lower nappe surface for different values ofF when z= 0.30.

!!2 0.20 0.25 0.30 II.35 0.40 0.45 Il.slL ,,.I;0 0 "I,R

.100 Oi40 .0690 .06w .062u .0575 0540 .05(K) 03YS O~W

1 2 0 .oMKl .0750 .0705 .0659 .06w ,,5Fu lJ.511J 1,3X" 1,12l,

.I40 .0840 Oi90 Oi35 OfiiO .0615 0569 1,515 .03% I"120

,160 08iO .0810 .0750 .06i5 .9610 05,sO 0.500 0310

I80 .0,8X5 .08x, Oi55 Mii5 ocdYI (153.5 0475 ,SZY,

,203 .0xX5 .0X20 (Ii45 ,"i,XJ .05;5 0505 .0435 OIXO

,250 on55 OX.5 0685 0511) 04x0 03yO lJ2iO

,300 Oiw) .06iO .05X0 .0460 ,034O .0220 IX154l,350 .wiE* .0540 .0425 .02Y5 I,lM

.4w .I,495 .03io lJ24CJ IJIIYJ

.4x, .03w .,J17,J ~"JZS

.xJo .ww -.OOW

.550

-0. WI 0 51Y 0 4M 0. 455 0 422 I,. 3x4 0. 34Y 0. 310 0 238 0 144

--.02U .560 ,528 4'95 4 6 2 ,423 .38i ,345 .2i2 Ii4

--.040 .5Y&l ,566 5 3 2 488 ,458 .42u .3iR .3W IYX

-.0+X, 632 .(*)I 56i 532 ,491 ,451 ,406 ,324 ,220

-.080 ,664 .M4 rw 5&i .?I22 ,480 ,432 348 ,238

-. 1*, .6Y3 ,664 .I!!1 SY4 ,552 ,508 4.56 .36&l 2 5 4

-.I50 .x3 .i34 .iOl ,661 .fil8 ,569 510 ,412 ,290

-.a0 .a1 .iYY .763 .i23 ,677 ,622 558 451 317

-.250 893 ,864 ,821; i81 .i29 .64X .5Y9 ,483 ,341- 300 ,953 ,918 .M ,832 7iY .X8 ti34 .510 ,362

-.4w I.060 I. 024 .9X, .Y32 ,867 Xl ti!u 5.x 3Mi

-.%B 1. 1% I. 119 1.072 l.OZll ,938 ,841 .i4S ,595 I'24

--.6oiJ 1.2C~ I. 203 1.153 I.098 1 Ooo .8Yl ix0 62i 441;

--.&lo 1.403 I 359 1 301 1 2% I. 101 Y70 .M45 6 7 2 .4i”-I.cim I. M Y 1.4Y8 I. 4m 1.333 1. I&w I.028 .!W .7Oi 504

-1.m 1.w 1.622 1 543 ,.41Y I.240 I.070 .93U .X3 524

-1.400 IMNI 1. i39 1. 647 1.4n9 I. 267 1,106 .Y59 iSi 540

-1. twu 1.912 l.84Y I. i40 1.546 I.323 I I31 ,983 .iiX .551- 1 en0 2.018 I. 951 I. 821 I. 590 1. 353 I. 155 1.005 .7Yi 560

-2.cKm 2. I20 2.049 l.Xy’L 1.62i 1.380 I. IiS 1. w!! 810 5 6 9

-2. ml 2.351 2. 261 2.02i I. 69i 1.42n I 21n 1.05Y .X3;

-3.wJ 2. 55i 2.423 2 113 1. i47 I. 464 I. 247 I 081 "52

-3. mu 2. 748 2. 536 2 16i 1. 7i8 I. 489 I. 263 1 099-4.fxx 2.911 2. 617 2. m I. 796 1.499 I. 2i4-4. xii 3.052 2.677 2. 217 1.805 I. 5u7

-5.ooo 3.173 2.731 2. 223 I. 810-5. MO 3. ml 2. 773 2. 228

-6.OMl 3. 400 2. 808

EsR ) o2o 0.25 , U.30 , 0.35 0.40 , 0.41, O.MJ , 0.W 0.w)

Aftw \v:I~ller


4 pTable 9-4-Coordinates of lower nappe surface for different values ofF when2 = 0.15.

HS 0.20 0.25 0.307i- 0.35 0.40 0.45 0.50 O.GO 080

XG

y For portion of the profik nhow the wair crestffs

0 ooo 0. OWJ 0 OO(M 0. oooo 0. owl 0. OWJ 0 owe 0. MXXI 0. woo 0. ,wuu

0 1 0 0120 .OIZO .Ull5 0115 .UllO .0110 .OlO.5 ."I00 .wJY,,

.020 .0210 .ozwJ .OlY5 .OlYO 0185 .OlM .OliO .UI60 .Ol40

,030 .0285 .0270 .ozG5 O!!M,040 ,034s .0335 .w25 :0310

.02,50 .0235 .0225 .lMJo .Olli5

.0300 ,028s .OZA5 .0230 .OliO

,050 .0405 .W85 .Wi5 .03GO .0345 .OJ20 .WJIJ o!!su OliO,060 .045u .0430 .04m .04M .0380 .0355 .0X30 : OX,5 "lti5

,070 .04Y5 .0470 .0455 .0430 .0410 .0380 .0350 ,027" YISO

.ofm .0525 .05lnJ ,048s .04M .0435 .04im .0365 .0270 0130

.oYo .05M .0530 .05lO .0480 .0455 .042U UJ70 .OZti5 : "100

100 .05YO .05M .0535 .0500 .0465 .0425 .tJJi5 .0255 wl5

I20 .0630 .lnwo .0570 0520 .0480 .0435 .03ti5 .0220

I40 .oiwJ .o+m .0585 0525 0475 0425 0345 .0175

IMl .0670 .oG35 .05YO .0520 .04+X .04W .0305 .OllO

I80 .0675 .OG35 oat40 0.500 0435 03&5 0260 cm40

,200 .OGiO .0X325 .05M U4&5 .OJY5 .032U .0200

,250 .ct615 .0560 .0470 .0360 .0265 .OIW .OOl5

.3(M .0520 (0440 .0330 .OZlO .YlOO

.3,54l .03Ro .0%5 .Ol65 .0030

.4Ou .OZlO .w90

,450 ml5

,500

,550

4

SPI L LWAY S-Sec. 9- 28 211

I I I I I I I I, m

1.06

I” I I I I I

NOTE: Dot ted lines arebased on extropolotion

- of data.

0 0.4 0.0 I. 2 1.6 2.0

“0

Figure 9-48. Relationship of-;;- to ‘;;- for circulat sharp-crested weirs.-244-D-2443

surface elevation, the crest profile shape will bethe same as the undernappe of the weirdischarge, the shaft will flow full at sectionA-A, and there will be no pressure on the crestor in the shaft for the design head. For higherheads, section A-A will act as an orificecontrol. The shaft above section A-A will flowfull and under pressure. Below section A-A, itwill flow full but will not be under pressure.For lower heads, the crest will control and theshaft will flow partially full. Assuming thesame losses, equation (20) can be rewritten, asfollows, to determine the orifice discharge:

Q = 23.90 R2H,” (21)

If the profile is modified to enlarge the shaftas shown by the solid lines be and aeration isprovided, the shaft will not flow full.Neglecting losses, the jet below section A-Awill then occupy an equivalent area indicatedby the lines bc.

Aeration is usually provided at the orifice

control, either through introduction of air at asudden enlargement of the shaft or at theinstallation of a deflector to ensure free flowbelow the control section A-A. Waterway sizesand slopes must be such that free flow ismaintained below the section of control.Failure to provide adequate aeration at thesection of control may induce cavitation.

For submerged flow at the crest, thecorresponding nappe shape as determined fromsection 9-27 for a design head Ho will be suchthat along its lower levels it will closely followthe profile determined from equation (20) ifH, approximates Ho. It must be rememberedthat on the basis of the losses assumed inequation (20) profile ubc will be the minimumshaft size which will accommodate the requiredflow and that no part of the crest shape shouldbe permitted to project inside this profile. Ashas been noted in section 9-l 2, smallsubatmospheric crest pressures can be toleratedif proper precautions are taken to obtain asmooth surface and if the negative pressure


X0.2 0.3 0.4 0.

0.1 ny+-mnlI ! ! ! ! ! ! ! ! ! 1

5 0.6 0.7I I I I

0

-2.5

-3.0

-3.5

-4.0

IHigh pointof boil-...

1

Qs----/ I

- 0 . 5Y

- 0 . 6

- 0 . 8

I

Figure 9-49. Upper and lower nappe profiles for acircular weir (aerated nappe and negligible approachvelocity).-288-D-2444

-1 .2forces are recognized in the structural design.The choice of the minimum crest and orificecontrol shapes in preference to some widershape then becomes a matter of economics,s t r u c t u r a l a r r angemen t , a n d l a y o u tadaptability.

Where the orifice control profile correspondsto the continuation of the crest shape asdetermined by tables 9-2, 9-3, and 9-4, thedischarge can be computed from equation (19)using a coefficient from figure 9-46. Where theorifice control profile differs from the crestshape profile so that a constricted controlsection is established, the discharge must bedetermined from equation (20). On figure 9-44the discharge head relationship curve ag willthen be computed from the coefficientsde t e rmined f rom f igu re 9 -47 wh i l e t hedischarge head relationship curve gh will bebased on equation (20).

-I .3

Figure 9-50. Comparison of lower nappe shapes for acircular weir for different heads.-288-D-2445

*.O1l-; (r”I

01.0

HoRS

Figure 9-51. Increased circular crest radius needed tom i n i m i z e subatmospheric pressure alongcrest.-288-D-2446


rWater surface--

Crest profileshape 1

A -

-Ha 4

v Jet profile 1

C

-4

b

CI e

I/

7,L

fspillwaycrest7

-Crest profileshape

- A

Figure 9-52. Comparison of crest profile shape with theoretical jet profile.-288-D-3058

9-29. Tunnel Design.-If, for a designated losses is flatter than the slope of the tunnel, thedischarge, the tunnel of a morning glory flow will accelerate and the tunnel couldspillway were to flow full without being under decrease in size. When the tunnel slopepressure, the required size would vary along its becomes flatter than the slope of the hydrauliclength. So long as the slope of the hydraulic gradient, flow will decelerate and a largergradient which is dictated by the hydraulic tunnel may be required. All points along the

214

tunnel will act simultaneously to control therate of flow. For heads in excess of that usedto proportion the tunnel, it will flow underpressure with the control at the downstreamend; for heads less than that used to determinethe size, the tunnel will flow partly full for itsentire length and the control will remainupstream. On figure 9-44 the head at which thetunnel just flows full is represented by point h.At heads above point h the tunnel flows fullunder pressure; at heads less than h the tunnelflows partly full with controlling conditionsdictated by the crest or orifice control design.

Because it is impractical to build a tunnelwith a varying diameter, it is ordinarily madeof a constant diameter. Thus the tunnel fromthe control point to the downstream end willhave an excess of area. If atmospheric pressurecan be maintained along the portion of thetunnel flowing partly full, the tunnel willcontinue to flow at that stage even though thedownstream end fills. Progressively greaterdischarges will not alter the part full flowcondition in the upper part of the tunnel, butfull flow conditions under pressure will occupyincreasing lengths of the downstream end ofthe tunnel. At the discharge represented bypoint h on figure 9-44, the full flow conditionhas moved back to the throat control sectionand the tunnel will flow full for its entirelength.

If the tunnel flows at such a stage that thedownstream end flows full, both the inlet andoutlet will be sealed. To forestall siphon action


by the withdrawal of air from the tunnel wouldrequire an adequate venting system. Unlessventing is effected over the entire length oftunnel, it may prove inadequate to preventsubatmospheric pressures along some portionof the length because of the possibility ofsealing at any point by surging, wave action, oreddy turbulences. Thus, if no venting isprovided or if the venting is inadequate, amake-and-break siphon action will attend theflow in the range of discharges approaching fullflow conditions. This action is accompanied byerratic discharges, by thumping and vibrations,and by surges at the entrance and outlet of thespillway. This is an undesirable condition andshould be avoided.

To avoid the possibility of siphonic flow, thedownstream tunnel size for ordinary designs(and especially for those for higher heads) ischosen so that the tunnel will never flow fullbeyond the throat. To allow for air bulking,surging, etc., the tunnel is selected of such asize that its area will not flow more than 75p e r c e n t f u l l a t t h e d o w n s t r e a m e n d a tmaximum discharges. Under this limitation, airordinarily will be able to pass up the tunnelfrom the downstream portal and thus preventthe formation of subatmospheric pressurealong the tunnel length. Precautions must betaken, however, in selecting vertical orhorizontal curvature of the tunnel profile andalinement to prevent sealing along someportion by surging or wave action.

G. STRUCTURAL DESIGN9-30. Gerteral.-The structural design of a

spillway and the selection of specific structuraldetails follow the determination of the spillwaytype and arrangement of components and thecompletion of the hydraulic design. The designcriteria for each component part should beestablished for any condition which may existat any time during the life of the structure.Design loads are different for each type ofspillway. Each component should be carefullyanalyzed for loads that can be applied to it.

Structures in or on the dam should be

designed for the stresses in the dam due toexternal loadings and temperatures, as well asthe hydraulic load and other loads applieddirectly to the structure. Slabs, walls, and ogeecrests should be designed for dead load andhydraulic pressures plus any other loads such asfill, surcharge, and control or operatingequipment. Appurtenant structures not builton the dam which are subject to uplift due tothe reservoir water and tailwater should bedesigned accordingly.

Because of the velocities involved, dynamic


water pressures should be considered in Normal methods of design should be usedaddition to the static water pressures in all for walls, slabs, etc. Where special designcases. Wherever practicable, laboratory model problems are encountered, the finite elementtests should be used to determine hydraulic method of analysis (appendix F) can be used toloads, particularly dynamic loads. determine the stresses.

H. BIBLIOGRAPHY

9-3 1. Bibliography.[l] Bureau of Reclamation, “Studies of Crests of Overfall

Dams,” Bulletin 3, Part VI, Hydraulic Investigations,Boulder Canyon Project Final Reports, 1948.

[2] Bureau of Reclamation, “Discharge Coefficients ForIrregular Overfall Spillways,” Engineering MonographNo. 9,1952.

[3] Hinds, Julian, “Side Channel Spillways,” Trans. ASCE,vol. 89, 1926, p. 881.

[4] Ball, J. W., “Construction Finishes and High-VelocityFlow ))’ Journal of the Construction Division, ASCEProceedings, September 1963.

[5] Colgate, D. M., “Hydraulic Model Studies of AerationDevices For Yellowtail Dam Spillway Tunnel,”Pick-Sloan Missouri River Basin Program, Montana,REC-ERC-7147,197l.

[6] Bureau of Reclamation, “Hydraulic Design of StillingBasin and Bucket Energy Dissipators,” EngineeringMonograph No. 25,1964. -

[7] Doddiah, D., Albertson, M. L., and Thomas, R. A.,“Scour From Je ts ,” Proceedings , MinnesotaInternational Association for Hydraulic Research andHydraulics Division, ASCE, Minneapolis, Minn., August1953,~. 161.

[B] Scimemi, Ettore, “Discussion of Paper ‘Model Study of

Brown Canyon Debris Barrier’ by Bermeal and Sanks,”Trans. ASCE, vol. 112,1947,p. 1016.

191 Bureau of Reclamation, “Hydraulic Model Studies ofMorrow Point Dam Spillway, Outlet Works andPowerplant Tailrace,” Report No. HYD-557. 1966.

[lo] Bureau of Reclamation, “Hydraulic Model Studies of thePueblo Dam Spi l lway and Plunge Basin ,”REC-ERC-71-18, 1971.

[ll] Bureau of Reclamation, “Hydraulic Model Studies ofCrysta l Dam Spi l lway and Out le t Works ,”REC-ERC-72-01, 1972.

[12] Peterka, A. J., “Morning-Glory Shaft Spillways,” Trans.ASCE, vol. 121,1956, p. 385.

[13] Brad ley , J . N., “Morning-Glory Shaft Spillways:Prototype Behavior,” Trans. ASCE, vol. 121, 1956, p.312.

[14] Blaisdell. F. W., “Hydraulics of Closed ConduitSpillways-Parts II through VII-Results of Tests onSeveral Forms of the SuiIlwav.” University ofMinnesota, Saint Anthony Falls Hydraulic Laboratory,Technical Paper No. 18, series B, March 1958.

[15] Wagner, W. E., “Morning Glory Shaft Spillways:Determination of Pressure-Controlled Profiles,” Trans.ASCE, vol. 121,1956,p. 345.

<<Chapter X

O u t l e t W o r k s a n d P o w e r O u t l e t s

A. INTRODUCTION

10-l. Types and Purposes. -An outlet worksis a combination of structures and equipmentrequired for the safe operation and control ofwater released from a reservoir to serve variouspurposes. Outlet works are usually classifiedaccording to their purpose such as river outlets,which serve to regulate flows to the river andcontrol the reservoir elevation; irrigation ormunicipal water supply outlets, which controlthe flow of water into a canal, pipeline, or riverto satisfy specified needs; or power outletswhich provide passage of water to the turbinesfor power generation. Each damsite has its ownrequirements as to the type and size of outletworks needed. The outlet works may bedesigned to satisfy a single requirement or acombination of multipurpose requirements.Typical outlet works installations are shown onfigures lo- 1 and 1 O-2.

C A N Y O N F E R R Y DAMM O N T A N A

S E C T I O N T H R U R I V E R O U T L E T S

T y p i c a l rave? o u t l e t w o r k s which discharges Intospillway stlllmg basin This o u t l e t conslstsofo condwt t h r o u g h t h e d a m o n d o regulating gatec o n t r o l l e d f r o m o c h a m b e r in t h e d a m . T h elntoke a n d t r a s h r a c k o r e o n t h e u p s t r e a m f a c eo f d a m

Figure 10-l. Typical river outlet works with stilling basin.-288-D-3060

S E C T I O N T H R U P E N S T O C K S(0)

(01 Typ~col p o w e r o u t l e t withpenstock t h r o u g h d o m

2-91’ DIO outlet p,pes78’ ha needle valves

S E C T I O N T H R U C A N A L O U T L E T(bl

(b) Typical conal o u t l e t w o r k s cons,st,ngOf conduits through the do”, w,thneedle valves A trashrack IS M theupstream face and o hydroullc humpSttllmg basm 15 utlllred t o disslpotethe energy downstream.

Figure 10-2. Spical power outlet and canal outletworks. -288-D-3062

D o w n s t r e a m w a t e r r e q u i r e m e n t s ,preservation of aquatic life, abatement ofstream pollution, and emergency evacuation ofthe reservoir are some of the factors thatinfluence the design of a river outlet. In certaininstances, the river outlet works may be usedto increase the flow past the dam inc o n j u n c t i o n wi th the normal spillwaydischarge. It may also act as a flood controlregulator to release waters temporarily stored

217

218

in flood control storage space or to evacuatestorage in anticipation of flood inflows.Further, the river outlet works may serve toempty the reservoir to permit inspection, tomake needed repairs, or to maintain theupstream face of the dam or other structuresnormally inundated.

The general details of operation and designof irrigation or municipal and industrial outletsare similar to those for river outlets. Thequantity of irrigation water is determined fromproject or agricultural needs and is related tothe anticipated use and to any special waterrequirements of the irrigation system. Thequality and quantity of water for domestic useis determined from the commercial, industrial,and residential water needs of the area served.The number and s i ze o f i r r i ga t i on and


municipal and industrial outlet works willdepend on the capacity requirements with thereservoir at a predetermined elevation, and onthe amount of control required as the elevationof the reservoir fluctuates.

Power outlets provide for the passage ofwater to the powerplant; therefore, theyshould be designed to minimize hydrauliclosses and to obtain the maximum economy inconstruction and operation. If the powerplantcan be located at the toe of the dam, a layoutwith the penstocks embedded through the damusually is most economical. Where thepowerplant must be located away from the toeof the dam, the penstocks can be located intunnels or embedded in the dam in the upperportion of their length and run exposed downthe abutment to the powerplant.

B. OUTLET WORKS OTHER THAN POWER OUTLETS

10-2. Gene&-An outlet works consists ofthe equipment and structures which togetherrelease the required water for a given purposeor combination of purposes. The flows throughriver outlets and canal or pipeline outlets varythroughout the year and may involve a widerange of discharges under varying heads. Theaccuracy and ease of control are majorconsiderations, and a great amount of planningmay be justified in determining the type ofcontrol devices that can be best utilized.

Ordinarily in a concrete dam, the mosteconomical outlet works consists of an intakestructure, a conduit or series of conduitsthrough the dam, discharge flow controldevices, and an energy dissipating device whererequired downstream of the dam. The intakestructure includes a trashrack, an entrancetransition, and stoplogs or an emergency gate.The control device can be placed (1) at theintake on the upstream face, (2) at some pointalong the conduit and be regulated fromgalleries inside the dam, or (3) at thedownstream end of the conduit with theoperating controls placed in a gatehouse on thedownstream face of the dam. When there is apowerplant or other structure near the face of

the dam, the outlet conduits can be extendedfurther downstream to discharge into the riverchannel beyond these features. In this case, acontrol valve may be placed in a gate structureat the end of the conduit.

10-3. Layout.-The layout of a particularoutlet works will be influenced by manycond i t i ons r e l a t i ng t o t h e h y d r a u l i crequirements, the height and shape of dam, thesite adaptability, and the relationship oft h e o u t l e t w o r k s t o t h e c o n s t r u c t i o nprocedures and to other appurtenances of thedevelopment. An outlet works leading to ahigh-level canal or into a closed pipeline willdiffer from one emptying into the river.Similaily, a scheme in which the outlet worksis used for diversion may vary from one wherediversion is effected by other methods. Incertain instances, the proximity of the spillwaymay permit combining some of the outletworks and spillway components into a singlestructure. As an example, the spillway andoutlet works layout might be arranged so thatdischarges from both structures will empty intoa common stilling basin.

The topography and geology of a site willhave a great influence on the layout. The

OUTLETS-Sec. 10-3 219

downstream location of the channel, thenearby location of any steep cliffs, and thewidth of the canyon are all factors affectingthe selection of the most suitable type andlocation of outlet works. The river outletsshould be located close to the river channel tominimize the downstream excavation. Geology,such as the location, type, and strength ofbedrock, is also an important factor to considerwhen making the layout of an outlet works. Anu n f a v o r a b l e f o u n d a t i o n s u c h a s d e e poverburden or inferior foundation rockrequires special consideration when selecting animpact area; with a weak foundation, a stillingbasin may be required to avoid erosion anddamage to the channel.

An outlet works may be used for divertingthe riverflow or portion thereof during a phaseof the construction period, thus avoiding thenecessity for supplementary installations forthat purpose. The outlet structure size dictatedby this use rather than the size indicated forordinary outlet requirements may determinethe final outlet works capacity.

The establishment of the intake level isinfluenced by several considerations such asmaintaining the required discharge at themin imum reservoir operating elevation,establishing a silt retention space, and allowingselective withdrawal to achieve suitable watertemperature and/or quality. Dams which willimpound waters for irrigation, domestic use, orother conservation purposes must have theoutlet works low enough to be able to draw thewater down to the bottom of the allocatedstorage space. Further, if the outlets are to beused to evacuate the reservoir for inspection orrepair of the dam, they should be placed as lowas practicable, However, it is usual practice tomake an allowance in a reservoir for inactivestorage for silt deposition, fish and wildlifeconservation, and recreation.

Reservoirs become thermally stratified andtaste and odor vary between elevations;therefore, t h e o u t l e t i n t a k e s h o u l d b eestablished at the best elevation to achievesatisfactory water quality for the purposein tended. Downstream fish and wildliferequirements may determine the temperatureat which the outlet releases should be made.

Municipal and industrial water use increases theemphasis on water quality and requires thewater to be drawn from the reservoir at theelevation which produces the most satisfactorycombination of odor, taste, and temperature.Mineral concentrations, algae growth, andtemperature are factors which influence thequality of the water and should be taken intoconsideration when establishing the intakeelevation. Water supply releases can be madethrough separate outlet works at differentelevations if the requirements for the individualwater uses are not the same and the reservoir isstratified in temperature and quality of water.

Downstream water requirements mayc h a n g e t h r o u g h o u t t h e y e a r a n d t h estratifications of water temperature and qualitymay fluctuate within the reservoir; therefore,the elevation at which the water should bedrawn from the reservoir may vary. Selectivew i t h d r a w a l c a n b e a c c o m p l i s h e d b y amultilevel outlet arrangement in which thestratum of water that is most desirable can bereleased through the outlet works. Twoschemes of multilevel outlet works arecommon. The first consists of a series of riveroutlet conduits through the dam at variouselevations, and the second consists of a singleo u t l e t t h r o u g h t h e d a m w i t h a s h u t t e rarrangement on the trashrack structure. Theshutters can be adjusted to allow selectivew i t h d r a w a l f r o m t h e d e s i r e d r e s e r v o i relevation. Figure 15-1 in chapter XV shows anexample of a multilevel outlet works consistingof four outlet conduit intakes at differentelevations, and figure 15-2 shows a typicalexample of a shutter arrangement on atrashrack structure.

Another factor to consider in determining alayout for an outlet works is the effect of aparticular scheme on construction progress. Ascheme which slows down or interferes withthe normal construction progress of theconcrete dam should be avoided if possible.Usually a horizontal conduit through the damhas the least effect on construction progress;however, sometimes other conditions restrictits use. Generally speaking, the fewer conduitor other outlet works components that must beinstalled within the mass concrete, the more

220

rapid the rate of construction.10-4. Intake Structures. -In addition to

forming the entrance into the outlet works, anintake structure may accommodate controldevices. It also supports necessary auxiliaryappurtenances (such as trashracks, fish screens,and bypass devices), and it may includetemporary diversion openings and provisionsfor installation of bulkhead or stoplog closuredevices.

An intake structure may take one of manyforms, depending on the functions it mustserve, the range in reservoir head under whichit must operate, the discharge it must handle,the frequency of reservoir drawdown, the trashconditions in the reservoir, the reservoir iceconditions, and other considerations.

An intake structure for a concrete damusually consists of a submerged structure onthe upstream face of the dam; however, intaketowers in the reservoir have been used in someinstances. The most common intake structureconsists of a bellmouth intake, a transitionbetween the bellmouth and conduit if required,a trashrack structure on the upstream face ofthe dam, and guides to be used with a bulkheadgate or stoplogs to seal off the conduit formaintenance and repair. The bulkhead gate orstoplogs are usually installed and removed byuse of either a gantry or a mobile craneoperating on top of the dam or from a barge inthe reservoir.

(a) Trashrack.-A trashrack is used to keeptrash and other debris from entering the outletconduit and causing damage or fouling of thecontrol device. Two basic types of trashracksare used for outlet works. One type is aconcrete or metal frame structure on whichmetal trashracks are placed, and the other is anall-concrete structure that consists of relativelylarge openings formed in the concrete and iswithout metal racks. The metal trashrack typeof structure provides for the screening of smalldebris when protection is needed to preventdamage to the conduit or control devices.Metal trashracks usually consist of relativelythin, flat steel bars which are placed on edgefrom 2 to 9 inches apart and assembled in racksections. The required area of the trashrack isfixed by a limiting velocity through the rack,which in turn depends on the nature of the


trash which must be excluded. Where thetrashracks are inaccessible for cleaning, thevelocity through the racks ordinarily shouldnot exceed 2 feet per second. A velocity up toapproximately 5 feet per second may betolerated for racks which are accessible forcleaning.

An example of a concrete trashrackstructure with metal racks is shown on figure10-3. The concrete frame structure consists ofa base cantilevered from the upstream face ofthe dam on which the trashrack structure issupported, a series of columns placed in asemicircle around the centerline of the intake,and a series of horizontal ribs spaced along thefull height of the structure. The spacingbetween columns is dependent upon thes t r u c t u r a l r e q u i r e m e n t s f o r t h e h e a ddifferential that may be applied to thetrashracks and the size of the metal racksection that can conveniently be fabricated andshipped. The vertical height of the trashrackstructure is divided into a series of bays byarch-shaped ribs that are attached to the faceof the dam and give lateral support to thecolumns. A solid concrete slab is usuallyconstructed as a top for the structure with aslot formed, where required, to allow forplacement and removal of the stoplogs orbulkhead gate. Grooves are formed into thevertical columns to hold the metal trashrackswhich are lowered into position from the top.When the intakes are deeply submerged, it maybe desirable to remove and install the metaltrashracks from the reservoir water surface.Guides can be supported on a curved concretewall or “silo” which will facilitate the removaland installation of the trashrack sections.

An all-metal trashrack structure containshorizontal steel arches spaced along the heightof the structure with vertical steel supportsbetween the arches. The structure can beconstructed so that the racks slide into themetal frame similar to the system used with theconcrete frame, or the frame and trashrackscan be fabricated into composite units andthese arch-trashrack sections assembled tocreate the final structure. The top of theall-metal structure usually consists of trashrackbars supported as required and containing theslot required for placement and removal of the

OUTLETS-Sec. 1 O-5

stoplogs or bulkhead gate.When small trash is of no consequence and

can be washed through the outlet workswithout damage to the conduit or controldevice, an all-concrete structure having onlyformed openings in the concrete can be used.The height and size of this trashrack structure,as well as the size of the formed openings, aredependent upon the desired discharge, thevelocity at the intake, and the size and amountof debris in the reservoir. The openings for thistype of trashrack usually range from 12 inchesto 3 feet. The shape of the trashrack structurein plan can be rectangular, circular, or built inchords for ease of construction as shown onfigure 1 O-4.

The frame used to support metal trashracksrequires considerable construction time whenformed of concrete; therefore, the use of ametal frame is often desirable because of thes h o r t e r construction t i m e r e q u i r e d f o rinstallation. This type also interferes least withthe rapid placement of concrete in a dam.

Where winter reservoir storage is maintainedin cold climates, the effect of possible icingconditions on the intake structure must beconsidered. Where reservoir surface ice canfreeze around an intake structure, there isdanger to the structure not only from the icepressure acting laterally, but also from theuplift forces if a filling reservoir lifts the icemass vert ically. These effects should beconsidered in the design of the trashrack andthe inlet structure, and may be a factor indetermining the height of the trashrackstructure. If practicable, the structure shouldbe submerged at all times. However, if thestructure will likely be above the reservoirwater surface at times and ice loadings willpresent a hazard, an air bubbling system can beinstalled around the structure to circulate thewarmer water from lower in the reservoirwhich will keep the surface area adjacent to thestructure free of ice. Such a system will requirea constant supply of compressed air and mustbe operated continuously during the wintermonths.

(b) Entmnce and Transition.-The entranceto a conduit should be streamlined and providesmooth, gradual changes in the direction of

221

flow to minimize head losses and to avoidzones where cavitation pressures can develop.Any abrupt change in the cross section of aconduit or any projection into the conduit,such as a gate frame, creates turbulence in theflow which increases in intensity as the velocityincreases. These effects can be minimized byshaping the entrance to conform to the shapeof a jet issuing from a standard orifice. Thesebellmouth entrances, as they are called, arediscussed in section 10-I 1. Any time that achange in cross section of the outlet works isrequired, such as where the outlet changesfrom the size and shape of the entrance to thatof the conduit, a smooth gradual transitionshould be utilized.

1 O-5. Conduits. -The outlet conduitsthrough a concrete dam are the passagewaysthat carry the water from the reservoirdownstream to the river, canal, or pipeline. Aconduit may consist of a formed openingthrough or a steel liner embedded in the massconcrete. The shape may be rectangular orround, or it may transition from one shape tothe other depending on the shape of the intakeentrance and on the type and location of thecontrol equipment. The outlet works maycontain one or more conduits depending on thedischarge requirements for a predeterminedreservoir water surface elevation. Two smallerconduits are preferable to one larger one, sothat one outlet can be operated while the otheris shut down for inspection and maintenance.

The design of the conduits required to passa given discharge through a concrete dam isbased upon the head, velocity of flow, type ofcontrol, length of conduit, and the associatedeconomic considerations. Generally, the mosteconomical conduit for an outlet is one that ishorizontal and passes through the narrowestportion of the dam; however, most outletworks require that the conduit inlet and outletbe at different elevations to meet controllingrequirements upstream and downstream. Thenumber of bends required in an outlet conduitshould be minimized and all the radii should bemade as long as practicable to reduce head loss.

10-6. Gates and Outlet ControkpThedischarges from a reservoir outlet works varyth roughou t t h e y e a r d e p e n d i n g u p o n


HALF SECTION5HOllNG CO”CRETE PLACED

‘ON B -B

S E C T I O N A - AS E C T I O N J - J

Figure 10-3. Iii!ver outlet trashrack structure-plans and sections (sheet 1 of 2). -288-r b-3063 (l/2)

downstream water needs and reservoir flood control, gates or valves must be installed atc o n t r o l r e q u i r e m e n t s . T h e r e f o r e , t h e some point along the conduit.impounded water must be released at specific Control devices for outlet works areregulated rates. To achieve this discharge categorized according to their function in the

OUTLETS-Sec. 10-6 223

Constructlo" ,,*,"ts . . . . .-r'..

;CO"StrUCtlO" JOl"t

Jomt,F3 h"!sh-----.

Jololnt, Pant toprevent bond

_I !--.?.+Morgi"oi beam support

.i- 7bracket may be Placedmonolithx wrth dam

Of co"troctort optron

S E C T I O N H - H

S E C T I O N L - L

S E C T I O N G - GCHLlMFERS NOT SHWN

Rib cmstructlonJ*l"t--------

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l"lnt-, ry ,y1

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H A L F S E C T / O N C - CR O O F P L A N

H A L F S E C T I O N D - D

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S E C . N - N

H A L F S E C T I O N E - E H A L F S E C T I O N F - FB A S E P L A N

CONCRETE REQUIREMENTSFlNiSHES

Ail surfaces except os noted-..--..-----~....Fz or UPSTRENGTH

Desi9n of concrete. other thon moss. is based on ocompressive strength of 3000 Ps, ot PB days

i"SPWe rubberJON f,,,er

N O T E SThe reference plane is i~~o’upstreom from the oxis ot S E C T I O N M - M

Sto 5+8zso ond at Ei 6049 17 w,th slope of 0 130 Ihorizonto, to verticoi

Chamfer a” or tool o/l exposed corners unless otherwespecified

Remforcement requrred out not shownice preventm air system cat shown

Figure 10-S. River outlet trashrack structure-plans and sections (sheet 2 of 2). -288-D-3063 (2/2)


LS E C T I O N A - A

S E C T I O N B - B

TYPICAL SECTION THdU CONOblT TYPICAL SECTION THRU C6NOUlT(RECTANGULAR TRASHRACK) (CIRCULAR TRASHRACK)

F&we 10-4. Typical trashrack installations. -288-D-3064

structure. Operating gates and regulating valvesare used to control and regulate the outletworks flow and are designed to operate in anyposition from closed to fully open. Guard oremergency gates are designed to effect closurein the event of failure of the operating gates, orwhere unwatering is desired either to inspectthe conduit below the guard gates or to inspectand repair the operating gates.

Guides may be provided at the conduite n t r a n c e t o a c c o m m o d a t e stoplogs o rbulkheads so that the conduit can be closedd u r i n g a n e m e r g e n c y p e r i o d o r f o rmaintenance. For such installations, guardgates may or may not be provided, dependingon whether the stoplogs can be readily installedif an emergency arises during normal reservoiroperating periods.

Standard commercial gates and valves areavailable and may be adequate for low-headinstallations involving relatively smalldischarges. High-head installations, however,

usually require specially designed equipment.The type of control device should be utilizedthat least affects flow in the conduit. Forexample, if possible, control and emergencygates or valves should be used that will notrequire transitions from one size and shape ofconduit to another because these transitionsare costly and can contribute greatly to thehead loss through the conduit.

(a) Location of Control Devices.-Thecontrol gate for an outlet works can bc placedat the upstream end of the conduit, at anintermediate point along its length, or at theoutlet end of the conduit. Where flow from acontrol gate is released directly into the openas free discharge, only that portion of theconduit upstream from the gate will be underpressure. Where a control gate or valvedischarges into a closed pressure pipe, thecontrol will serve only to regulate the releases:full pipe flow will occur in the conduit bothupstream and downstream from the controlgate. For the pressure-pipe type, the locationof the gate or valve will have little influence onthe design insofar as internal pressures arec o n c e r n e d . H o w e v e r , w h e r e a c o n t r o ldischarges into a free-flowing conduit, thelocation of the control gate becomes animportant consideration in the design of theoutlet.

Factors that should be considered inlocating the control devices to be used on anoutlet works include the size of the conduitsrequired, the type of dam, the downstreamstructures, and the topography. The use ofgates at the upstream or downstream face ofthe dam may be precluded if a satisfactorylocation for the gate and operating equipmentor access is not available due to the layout ofthe dam or to the surrounding topography. Theuse of gate chambers within the dam is possibleonly if the thickness of the dam is great enoughto safely contain the required chamber. Whenthe outlet works discharges onto a spillwayapron, the control device may, of necessity,have to be located either at a chamber withinthe dam or at the upstream face of the dam.

The most desirable location for the controldevice is usually at the downstream end of theconduit. This location permits most of the

OUTLETS-Sec. 1 O-7

energy to be dissipated outside of the conduit,removing a possible cause of cavitation andvibration from the conduit. By eliminating gateoperation at the entrance and within theconduit, b e t t e r f l o w c o n d i t i o n s c a n b emaintained throughout the entire conduitlength. Also, the size of the intake structurecan sometimes be reduced if the control gate isnot incorporated into the structure, and thism a y g i v e t h e d o w n s t r e a m l o c a t i o n a nadditional advantage of economy.

(b) Types of Gates and Valves. -Many typesof valves and gates are available for the controlof outlet works. Each outlet works planrequires gates or valves that are well suited forthe operating conditions and the characteristicsof that plan. The location of the control devicealong the conduit, the amount of head applied,and the size and shape of conduit are all factorsused in determining the type of control deviceconsidered likely to be most serviceable. Sometypes of gates and valves operate well at anyopening, thus can be used as control gates,while others operate satisfactorily only at fullopen and can be used only as emergency orguard gates.

Where the control device is located at theoutlet works intake and is to be operated underlow head, the most commonly used devicewould be a slide gate. If the control is at anintermediate point along the conduit, controldevices such as high-pressure slide gates,butterfly valves, or fixed-wheel gates can beused for the discharge control. Control at thedownstream end of the outlet conduit may beaccomplished by the use of a high-pressureslide gate, a jet-flow gate, or a hollow-jet valvedischarging into the channel or stiliing device.These are control devices that are commonlyused; other types of gates or valves can beutilized if found to be more suitable for aparticular situation.

Emergency or guard gates or valves areinstalled in the outlets upstream from thecontrol device, to provide an emergency meansof closing the conduit. These emergencydevices may consist of a fixed-wheel gate toclose the entrance to the conduit, a duplicateof the control gate or valve in tandem andoperated from a chamber or gallery in the dam

225

or in a control house on the downstream face,or a gate such as a ring-follower gate in tandemwith the control gate. A ring-follower gate iswell suited to serve as an emergency or guardgate (which operates either fully open or fullyclosed), since the ring-follower gate when fullyopen is the same size and shape as the conduitand causes little disturbance to the flow.

Stoplogs or a bulkhead gate on the face ofthe dam can be used to permit unwatering ofthe entire waterway and both are usuallydesigned to operate under balanced pressure.Either device is lowered into place over theentrance with the control gate or an emergencygate closed and the conduit is then unwatered.A means of bypassing water from the reservoirinto the conduit to balance the pressure onboth sides of the stoplogs or bulkhead gatebefore they are raised must be provided.Adequate air passageways should be providedimmediately downstream from the stoplogs orbulkhead gate, to prevent air from beingtrapped and compressed when the water isadmitted to the conduit through the fillingbypasses, and to reduce or eliminate negativepressure during unwatering.

IO- 7. Energy Dissipating Devices. -Thedischarge from an outlet, whether throughgates, valves, or free-flow conduits, will emergeat a high velocity, usually in a near horizontaldirection. The discharge may be releaseddirectly into the channel or riverbed ifdownstream structures are not endangered bythe high-velocity flow and if the geology andtopography are such that excessive erosion willnot occur. However, if scouring and erosion arelikely to be present, some means of dissipatingthe energy of the flow should be incorporatedin the design. This may be accomplished by theconstruction of a stilling basin or other energydissipating structure immediately downstreamof the outlet.

The two types of energy dissipating devicesmost commonly used in conjunction withoutlet works on concrete dams are hydraulicjump stilling basins and plunge pools. On somedams, it is possible to arrange the outlet worksin conjunction with the spillway to utilize thespillway stilling device for dissipating theenergy of the water discharging from the river


outlets. Energy dissipating devices for free-flowconduit outlet works are essentially the same asthose for spillways, discussed in chapter IX.The design of devices to dissipate jet flow isdiscussed in set tion lo- 12.

H, =h,th, +hs(8)

+hf(7)

+h,(7)

1. Hydraulic Design of Outlet Works

1 O-8. General Considerations. -Thehydraulics of outlet works involves either oneor both of two conditions of flow-openchannel (or free) flow and full conduit (orpressure) flow. Analysis of open channel flowin outlet works, either in an open waterway orin a partly full conduit, is based on theprinciple o f s t e a d y nonuniform flowconforming to the law of conservation ofenergy. Full pipe flow in closed conduits isbased on pressure flow, which involves a studyof hydraulic losses to determine the total headsneeded to produce the required discharges.

+hf(6)

+ hfu 1

+h, +hf(5) (4)

+ hC(4-3)

+h +hg(3) ex(3-2)

+hf(2)

+h, +h,(2) (2-I)

+h +hg(l) “(1)

(2)

where :

h, =he =h, =h, =

hg:

h”r =

trashrack losses,entrance losses,bend losses,contraction losses,expansion losses,gate or valve losses, andfriction losses.

Hydraulic jump basins, plunge pools, orother stilling devices can be employed todissipate the energy of flow at the end of theoutlet works if the conditions warrant theiruse.

In equation (2) the number subscripts refer tothe various components, transitions, andreaches to which head losses apply.

1 0 - 9 . P r e s s u r e F l o w i n O u t l e tConduits.-Most outlet works for concretedams have submerged entrance conditions andflow under pressure with a control device onthe downstream end.

For flow in a closed pipe system, as shownon figure 1 O-5, Bernoulli’s equation can bewritten as follows:

F o r a f r e e - d i s c h a r g i n g o u t l e t , H, i smeasured from the reservoir water surface tothe center of the outlet gate or the outletopening. If the outflowing jet is supported on adownstream floor, the head is measured to thetop of the emerging jet at the point of greatestcontraction; if the outlet portal is submergedthe head is measured to the tailwater level.

The various losses are related to the velocityhead in the individual components, andequation (2) can be written:

H,=h, +hvl (1)

where:

H, = the total head needed to overcomethe various head losses toproduce discharge,

h, = the cumulative losses of thesystem, and

hVl

= the velocity head exit loss atthe outlet.

Equation (1) can be expanded to list each loss,as follows: (Equation continued on next page.)

OUTLETS-Sec. 1 O-9

where :

D = diameter of conduit,g = acceleration due to force

of gravity,L = length of conduit,v = velocity,

Kt = trashrack loss coefficient,K, = entrance loss coefficient,Kb = bend loss coefficient,

(3)

227

f= friction factor in the Darcy-Weisbach equation for pipeflow,

K = expansion loss coefficient,EC = contraction loss coefficient,K = gate loss coefficient, andI(= exit velocity head coefficient

at the outlet.

Equation (3) can be simplified by expressingthe individual losses in terms of an arbitrarilychosen velocity head. This velocity head isusually selected as that in a significant sectionof the system. If the various velocity heads forthe system shown on figure 10-5 are related tothat in the downstream conduit, with an area(2), the conversion for any area (x) is found asshown below.

By the principle of continuity,

Q = av = a2 v2 = a, v,

ht-”

I

Ic‘I

0

‘Q

-L,--

c===-+-7If(n + hbm-) 7t

t-c<- L2-Horlzontolbend- Area (2)

Figure IO-5. Pictorial representation of typical head losses in outlet under pressure. -288-D-3065


1 0 - 1 0 . P r e s s u r e F l o w L o s s e s i nConduits. -Head losses in outlet worksconduits are caused primarily by the frictionalresistance to flow along the conduit sidewalls.Additional losses result from trashracki n t e r f e r e n c e s , e n t r a n c e c o n t r a c t i o n s ,c o n t r a c t i o n s and e x p a n s i o n s a t gateinstallations, b e n d s , g a t e a n d v a l v econstrictions, and other interferences in theconduit. For a conservative design, greater thanaverage loss coefficients should be assumed forcomputing required conduit and componentsizes, and smaller loss coefficients should beused for computing energies of flow at theoutlet. The major contributing losses of aconduit or pipe system are discussed in theremainder of this section.

(a) Friction Losses.-For flow in largepipes, the Darcy-Weisbach formula is mostoften employed to determine the energy lossesdue to frictional resistances of the conduit. Theloss of head is stated by the equation:

228

where :

Q = discharge,a = cross-sectional area of conduit, andv = velocity.

Then :

aZ2 vz2 = ax2 rlX2, and

az2 v,’ ax2 vx2-=-2g 2g

from which:

vx2 _ a, 2 v22

o-T$- a, 2g

Equation (3) then can be written

HT =$[(q (q +($)’ (Ke +EJ+(.)’ (%+Kb) +()‘($

+($.(% +K,J +(-$ (g -%.J+z 2i >( KC(4-3) tKg3 +Kex(3.2) 1

ex(3.2) tK - Kb2 -1C(Z-I)

(4)

If the bracketed part of the expression isrepresented by KL, the equation can bewritten:

Then :

Q=a, ‘$i

(5)

(6)

h =a v2f D 2g (7)

where f’is the friction loss coefficient and othersymbols are as previously defined. Thiscoefficient varies with the conduit surfaceroughness and with the Reynolds number. Thelatter is a function of the diameter of the pipeand the velocity, viscosity, and density of thefluid flowing through it. Data and proceduresfor evaluating the loss coefficient are presentedin Engineering Monograph No. 7 [ 11 .I Since fis not a fixed value, many engineers areunfamiliar with its variations and would ratheruse Manning’s coefficient of roughness, n,which has been more widely defined. If theinfluence of the Reynolds number is neglected,and if the roughness factor in relation to thepipe size is assumed constant, the relation ofJin the Darcy-Weisbach equation to y2 in theManning equation will be:

f= 1 16.5n2 = 185~2~r1/3 D”j (8)


OUTLETS-Sec. IO- I 0

where : In the above:

229

Y = hydraulic radius, andD = conduit diameter.

Relationships between the Darcy-Weisbach andManning’s coefficients can be determinedgraphically from figure 10-6.

W h e r e t h e c o n d u i t c r o s s s e c t i o n i srectangular in shape, the Darcy-Weisbachformula does not apply because i t is forcircular pipes, and the Manning equation maybe used to compute the friction losses.Manning’s equation (see sec. F-2(c) in appendixF) as applied to closed conduit flow is:

L*hf= 29.111~ 7 2g

Maximum and minimum values of y1 which maybe used to determine the conduit size and theenergy of flow are as follows:

Conduit materialMaximum Minimum

n n

Concrete pipe orcast-in-placeconduit

Steel pipe withwelded joints

0.014 0.008

.012 .008

Kt = the trashrack loss coefficient(empirical),

% = the net area through the rackbars,

57 = the gross area of the racks andsupports, and,

“n = the velocity through the nettrashrack area.

Where maximum loss values are desired,assume that 50 percent of the net rack area isclogged. This will result in twice the velocitythrough the trashrack. For minimum trashracklosses, assume no clogging of the openingswhen computing the loss coefficient, or neglectthe loss entirely.

(c) Entrance Losses.-The loss of head atthe entrance of a conduit is comparable to theloss in a short tube or in a sluice. If H is thehead producing the discharge, C is thecoefficient of discharge, and a is the area, thedischarge is

Q=Ca m

and the velocity is

v=cl/qg

(b) Trushruck Losses. -Trashrack structureswhich consist of widely spaced structuralmembers without rack bars will cause very

fJ’lv2c2 2g

(11)

little head loss, and trashrack losses in such acase might be neglected in computing conduitlosses. When the trash structure consists of

Since H is the sum of the velocity head k, and

racks of bars, the loss will depend on the barthe head loss at the entrance k,, equation (11)

thickness, depth, and spacing. As shown inmay be written:

reference [ 21, an average approximation can beobtained from the equation: --+h =ebtsV2

2&Y e C’2g

Loss = K 1::* 2

or

where: Then :

2

K, = 1.45 - 0.45Q: - 20 K,= b-1 (12)


0 . 0 2 5

Darcy ’s equa t ion fo rfriction loss in circular pipes

L v2hf= f- -D 2g

IO.09-o0 . 07 . 0

M a n n i n g ’ s e q u a t i o nfo r friction loss in pipes

6 . 0

hf- 1 8 5 t-b2 L2 2. 5 . 0

0% D 2g 4 . 015 ;L

v)3 . 0 2

IO0a

R e l a t i o n s h i p b e t w e e n aMannimgIs”n” a n d 2 . 0 0

Darcy ’s ‘If” if= 1 8 5 n2 = l16.5n2 5)

093 $3 5 aa

aw 0 . 6

Figure 10-6. Relationship between Darcy’sf and Manning’s n for flow in pipes. -288-D-3066

OUTLETS-Sec. IO-10

Coefficients of discharge and loss coefficientsfor typical entrances for conduits, as given invarious texts and technical papers, are listed intable 10-l.

(d) Bend Losses. -Bend losses in closedconduits in excess of those due to friction lossthrough the length of the bend are a functionof the bend radius, the pipe diameter, and theangle through which the bend turns.

Graphs taken in part from reference [3 Igiving Kb as a function of these parameters areshown on figure 10-7. Figure 10-7(b) shows thecoefficients for 900 bends for various ratios ofradius of bend to diameter of pipe. Figure10-7(c) indicates the coefficients for other than900 bends. The value of the loss coefficient,

RbKb , for various values of 7 can be applied

directly for circular conduits; for rectangularconduits D is taken as the height of the sectionin the plane of the bend.

(e) Transition Losses.-Head losses ingradual contractions or expansions in a conduitcan be considered in relation to the increase ordecrease in velocity head, and will varyaccording to the rate of change of the area andthe length of the transition. For contractionsthe loss of head, h,, will be approximately

, where Kc varies from

0.1 for gradual contractions to 0.5 for abruptcontractions. Where the flare angle does notexceed that indicated in section 10-l 1, the losscoefficient can be assumed as 0.1. For greaterflare angles, the loss coefficient can be assumedto vary in a straight-line relationship to a

231

maximum of 0.5 for a right angle contraction.For expansions, the loss of head, h,, , will

be approximately equal to &, z -VG( >

where K,, is as follows:

Flareangle (Y 25’ 30’ 40’ 50’ 60’

I I IKex [41 0.40 0.49 0.60 0.67 0.12

Kex [51 .55 .66 .90 1 .oo -

(f) Gate and Vulve Losses.-No gate lossneed be assumed where a gate is mounted atthe entrance to the conduit so that when wideopen it does not interfere with the entranceflow conditions. Also, emergency gates that areof the same size and shape as the conduit, suchas ring-follower gates in a circular conduit, donot affect the flow and their associated lossesare negligible. Emergency gates such aswhee l -moun ted o r roller-mounted gates,although only operated at full open, have a Kgof not exceeding 0.1 due to the effect of theslot.

For control gates, as with emergency gates,mounted in a conduit so that the floor, sides,and roof, both upstream and downstream, arecontinuous with the gate opening, only thelosses due to the slot will need to beconsidered, for which a value of Kg notexceeding 0.1 might be assumed. For partlyopen gates, the coefficient of loss will depend

Table 10-l .-Coefficients of discharge and loss coefficients for conduit entrances.

Coefficient C Loss coefficient K,Type of entrance Maxi- Mini- Aver- Maxi- Mini- Aver-

mum mum age mum mum age

(1) Square-cornered 0.85 0.77 0.82 0.70 0.40 0.50(2) Slightly rounded .92 .79 .90 .60 .18 .23(3) Fully rounded .96 .88 .95 .27 .08 .10

; 2 0.15

(4) Circular bellmouth .98 .95 .98 .lO .04 .05(5) Square bellmouth .97 .91 .93 .20 .07 .16(6) Inward projecting .80 .72 .75 .93 .56 .80


a) DEFINITION SKETCH

0.20I I I I

DEFLECTION ANGLE @, IN DEGREES RbRATIO D

(c)K, VS DEFLECTION ANGLE (b) K, VS 2 FOR 90° BENDS

Figure 10-7. Coefficient for bend losses in a closed conduit. -288-D-3067

on the top contraction.The loss and discharge coefficients for the

individual control gates and valves vary witheach type and design; therefore, the actualcoefficients used in design should be acquiredfrom the manufacturer or from tests performedin a laboratory. As stated above, the Kg alsovaries for partial openings of the gate or valve.

(g) Exit Losses.-No recovery of velocityhead will occur where the release from apressure conduit discharges freely, or issubmerged or supported on a downstreamfloor. The velocity head loss coefficient, K,, inthese instances is equal to 1.0. When adiverging tube is provided at the end of aconduit, recovery of a portion of the velocityhead will be obtained if the tube expandsgradually and if the end of the tube is

submerged. The velocity head loss coefficientwill then be reduced from the value of 1.0 bythe degree of velocity head recovery. If a, isthe area at the beginning of the diverging tubeand a, is the area at the end of the tube, K, is

2equal to z+ .I In

1 0 - 17. T r a n s i t i o n S h a p e s . - -(a) Entrances.-To minimize head losses and toavoid zones where cavitation pressures candevelop, the entrance to a pressure conduitshould be streamlined to provide smooth,gradual changes in the flow. To obtain the bestinlet efficiency, the shape of the entranceshould simulate that of a jet discharging intoair. As with the nappe-shaped weir, theentrance shape should guide and support thejet with minimum interference until it is

OUTLETS-Sec. lo-12

contracted to the dimensions of the conduit. Ifthe entrance curve is too sharp or too short,subatmospheric pressure areas may developwhich can induce cavitation. A bellmouthentrance which conforms to or slightlyencroaches upon the free-jet profile willprovide the best entrance shape. For a circularentrance, this shape can be approximated by anelliptical entrance curve represented by theequation:

2(OFiD) + 2co: 5Dy = lwhere x and y are coordinates whose x-x axis isparallel to and 0.650 from the conduitcenterline and whose y-y axis is normal to theconduit centerline and 0.5D downstream fromthe entrance face. The factor D is the diameterof the conduit at the end of the entrancetransition.

The jet issuing from a square or rectangularopening is not as easily defined as one issuingfrom a circular opening; the top and bottomcurves may differ from the side curves both inlength and curvature. Consequently, it is moredifficult to determine a transition for a squareor rectangular opening which will eliminatesubatmospheric pressures. An elliptical curvedentrance which will tend to minimize thenegative pressure effects is defined by theequation:

x2 + AL3 = ]D2 ( 0 . 3 3 0 ) (14)

where D is the vertical height of the conduitfor defining the top and bottom curves, and isthe horizontal width of the conduit fordefining the side curves. The major and minoraxes are positioned similarly to those indicatedfor the circular bellmouth.

( b) Con tractions and Expansions. -Tominimize head losses and to avoid cavitationt e n d e n c i e s a l o n g the conduit surfaces,contraction and expansion transitions to andfrom gate control sections in a pressure conduitshould be gradual. For contractions, themaximum convergent angle should not exceedthat indicated by the relationship:

tan Q! = t

233

(15)

where :

(Y = the angle of the conduit wallsurfaces with respect to itscenterline, and

U = an arbitrary parameter = -

The values of v and D are the averages of thevelocities and diameters at the beginning andend of the transition.

Expansions should be more gradual thanc o n t r a c t i o n s b e c a u s e o f t h e d a n g e r o fcavitation where sharp changes in the side wallsoccur. Furthermore, as has been indicated ins e c t i o n 10-10(e), loss coefficients forexpansions increase rapidly after the flare angleexceeds about loo. Expansions should bebased on the relationship:

1tan (Y = 2u (16)

The notations are the same as for equation(15). For usual installations, the flare angleshould not exceed about loo.

The criteria for establishing maximumcontraction and expansion angles for conduitsflowing partly full are the same as those foropen channel flow, as given in section 9-18(b)of chapter IX.

1 0 - 1 2 . E n e r g y D i s s i p a t i n gDevices. -Whenever practicable, the outletworks should be located so that the spillwayenergy dissipating structures can also be usedto still the flow of the outlet works. Deflectorbuckets and hydraulic jump basins arecommonly designed for stilling both outletworks and spillway flows when the outletworks flow can be directed into the spillwaystilling basin. The hydraulic design forfree-flow spillways a n d o u t l e t w o r k s i sdiscussed in chapter IX. Plunge pools andhydraulic jump stilling basins designed only foroutlet works are discussed below.

(a) Hydraulic Jump Basins.-Where theoutlet works discharge consists of jet flow, the


been developed by Veronese [8] for limitingscour depths, as follows:

open-channel flow hydraulic jump stillingbasins mentioned above are not applicable. Thejet flow either has to be directed onto thetransition floor approaching the basin so it willb e c o m e u n i f o r m l y d i s t r i b u t e d , t h u sestablishing open-channel flow conditions atthe basin, or a special basin has to be designed.

The design of such a basin that will workwell at all discharges is difficult usingtheoretical calculations, and model tests shouldb e c o n d u c t e d t o f i n a l i z e a l l d e s i g n s i fpracticable. The Bureau of Reclamationhydraulic laboratory has developed generalizeddesigns of several kinds of basins based uponpreviously run model tests. General design rulesare presented so that the necessary dimensionsfor a particular structure may be easily andquickly determined. One such example is thedesign of a hydraulic jump basin to still the jetflow from a hollow-jet valve. This basin isabout 50 percent shorter than a conventionalbasin. The stilling basin is designed to takeadvantage of the hollow-jet shape, so solid jetscannot be used. The general design procedurecan be found in Engineering Monograph No. 25161.

(b) Plunge Pools.-Where the flow of anoutlet conduit issues from a downstreamcontrol valve or freely discharging pipe, ariprap- or concrete-lined plunge pool might beutilized. Such a pool should be employed onlywhere the jet discharges into the air and thenplunges downward into the pool.

When a free-falling overflow nappe dropsvertically into a pool in a riverbed, a plungepool will be scoured to a depth which is relatedto the height of the fall, the depth of tailwater,and the concentration of the flow [ 71. Depthsof scour are influenced initially by theerodibility of the stream material or thebedrock and by the size or the gradation ofsizes of any armoring material in the pool.However, the armoring or protective surfacesof the pool will be progressively reduced by theabrading action of the churning material to asize which will be scoured out and the ultimates c o u r d e p t h w i l l , f o r a l l p r a c t i c a lconsiderations, stabilize at a limiting depthirrespective of the material size. An empiricalapproximation based on experimental data has

d, = 1.32 H;2== q”es (17)

where :

d,, = the maximum depth of scourbelow tailwater level in feet,

H, = the head from the reservoir totailwater levels in feet, and

q = the discharge in cubic feet persecond per foot of width. (Thewidth used for a circularvalve or discharge pipe shouldbe the diameter.)

Plunge pools used as energy dissipatorsshould be tested in hydraulic models or, ifpossible, compared with similar designs in useor previously tested in a hydraulic model.

10-13. Open Channel Flow in OutletWorks.-If the outlet control gate or valve is atthe upstream end or at some point along theconduit, open c h a n n e l f l o w m a y e x i s tdownstream of the control; however, upstreamof the control the flow is under pressure andthe analysis is similar to that discussed inprevious sections. The conduit downstream ofthe control may be enlarged or flared to assurenonpressure conditions, if desired. When openchannel flow conditions exist, the designprocedures are similar to those for openchannel spillway flow discussed in chapter IX.An example of an outlet works with openchannel flow downstream of the control gate isshown on figure 1 O-8.

2. Strucforal Design of Out let Works

10-14. General.-The structural design of anoutlet works is dependent upon the actualcharacteristics of that feature, the head, wherethe outlet works are incorporated in the damt h e s t r e s s e s i n t h e d a m d u e t o externa;loadings, and temperature. The design criteriafor each component of the outlet works shouldbe established for the conditions which exist or

OUTLETS-Sec. lo-15 235

M e t a l t r a s h r a c k

Figure 10-S. A river outlet works with open channelfhv. -288-D-3069

may be expected to exist at any time duringthe life of the structure.

10-15. Trashrack. -A trashrack structure,regardless of the type, should be designed for ahead differential due to the possible clogging ofthe rack with trash. This head differential willdepend upon the location of the trashrack andits susceptibility to possible clogging, butshould be a minimum of 5 feet. Temperatureloads during construction should also beinvestigated in the design. If the trashrack willsometimes be exposed or partially exposedabove the reservoir in areas subject to freezing,lateral loads from ice should be considered. Inthese instances, ice loads due to verticalexpansion and the vertical load applied to thestructure as ice forms on the members shouldalso be included in the final analysis.

10-16. Con&&-The outlet works conduitthrough a concrete dam may either be lined orunlined, but when the conduit is lined it maybe assumed that a portion of the stress is beingtaken by the liner and not all is beingtransferred to the surrounding concrete. Thetemperature differential between the relativelycool water passing through the conduit and therelatively warm concrete mass will produce

tensile stresses in the concrete in the immediatevicinity of the conduit. Also, the openingthrough the dam formed by the conduit willalter the distribution of stress in the dam in thevicinity of the conduit, tending to producetensile stresses in the concrete at the peripheryof the conduit. In addition, the bursting effectfrom hydrostatic pressures will cause tensilestresses at the periphery of the conduit. Theabove tensile stresses and possible propagationof concrete cracking usually extend only ashort distance from the opening of the conduit,so it is common practice to reinforce only theconcrete adjacent to the opening. The mostuseful method for determining the stresses inthe concrete surrounding the outlet conduit ist h e f i n i t e e l e m e n t m e t h o d o f a n a l y s i s ,discussed in appendix C and in subchapter E ofchapter IV.

10-17. Valve or Gate House. -The design ofa control house depends upon the location andsize of the structure, the operating and controlequipment required, and the conditions ofoperation. The loadings and temperatureconditions used in the design should beestablished to meet any situation which may beexpected to occur during construction orduring operation of the outlet works. The basicdesign approach should be the same as that forany commercial building.

1 O-l 8. Energy Dissipating Devices. -Thestructural design of an energy dissipating deviceis accomplished by usual methods of analysisfor walls, slabs, and other structural members.Because each type of outlet works usuallyrequires a different type of energy dissipator,the design loads depend upon the type of basinused, and have to be determined for thecharacteristics of the particular outlet works.Because of the dynamic pressures exerted onthe structure from the hydraulic stillingprocess, laboratory tests or other means areusually required to establish the actual designloadings.


C. POWER OUTLETS

10-19. General.-Power outlets are outletworks that serve as a passage for water fromt h e r e s e r v o i r t o t h e t u r b i n e s w i t h i n apowerplant. The power outlets consist of: (1)an intake structure which normally includesthe emergency gates, a bulkhead gate orstoplog slots and guides, a trashrack structureon the face of the dam, and a bellmouth intakeentrance; (2) a transition to the circular shapeat the upstream end of the penstock; and (3) apenstock. The penstock acts as a pressureconduit between the turbine scroll case and theintake structure. The power outlets should beas hydraulically efficient as practicable toconserve available head; moreover, the intakestructure should be designed to satisfactorilyperform all of the tasks for which it wasintended.

1 O - 2 0 . L a y o u t . - T h e l o c a t i o n a n darrangement of the power outlets will beinfluenced by the size and shape of theconcrete dam, the location of the river outletworks and the spillway, the relative location ofthe dam and powerplant, and the possibility ofi n c o r p o r a t i n g t h e p o w e r o u t l e t s w i t h adiversion tunnel or the river outlets. Forlow-head concrete dams, penstocks may beformed in the concrete of the dam; however, asteel lining is desirable to insure watertightness.The penstocks may be completely embeddedwithin the mass concrete of the concrete damas shown on figure 10-9(a), embedded throughthe dam while the downstream portionsbetween the dam and powerplant are aboveground as shown on figure 10-9(b), or in anabutment tunnel as shown on figure 10-10.

When a powerp l an t ha s two o r moreturbines, the question arises whether to use anindividual penstock for each turbine or a singlepenstock with a header system to serve allunits. Considering only the economics of thelayout, the single penstock with a headersystem will usually be less in initial cost;however, the cost of this item alone should notdictate the design. Flexibility of operationshould be given consideration, because with asingle penstock system the inspection or repairof the penstock will require shutting down the

entire plant. Further, a single penstock with aheader system requires complicated branchconnections and a valve to isolate each turbine.Also, the bulkhead gates will be larger,requiring heavier handling equipment. Inconcrete dams, it is desirable to have allopenings as small as possible. The decision as tothe penstock a r r a n g e m e n t m u s t b e m a d econsidering all factors of operation, design, andoverall cost of the entire installation.

Proper location of the penstock intake isimportant. The intake is usually located on theupstream face of the dam, which facilitatesoperation and maintenance of the intake gates.However, other structures or topographicconditions may influence the arrangement, andthe penstock intake may best be situated in anindependent structure located in the reservoir.Regardless of the arrangement, the intakeshould be placed at an elevation sufficientlybelow the low reservoir level and above theanticipated silt level to allow an uninterruptedflow of water under all conditions. Each intakeopening should be protected against floatingtrash and debris by means of a trashrackstructure.

Bends increase head loss and can cause thedevelopment of a partial vacuum during certainoperating conditions. Therefore, penstockprofiles from intake to turbine should,whenever practicable, be laid on a continuousslope. When vertical or horizontal bends arerequired in a penstock, their effect should bekept to a minimum by using as long a radiusand as small a central angle as practicable.

1 O-2 1. Intake Structures.-The intakestructure consists of several components, eachof which is designed to accomplish a specificpurpose. A trashrack is incorporated to keeptrash from entering the penstocks and causingdamage to the turbines: a bellmouth intake isused to establish flow lines at the entrancewhich minimize the amount of head loss; atransition, from the entrance size and shape tothe circular diameter of the penstock, isestablished to least affect the flow and tominimize head loss. Also, the emergency gatescan be incorporated into the intake structure

O U T L E T S - S e c . lo-21 237

to close off the flow through the penstock.Stoplogs a r e p r o v i d e d u p s t r e a m o f t h eemergency gates to unwater the entrance areaand the emergency gate seats and guides forinspection and maintenance.

The velocity of flow in power intakes isusually much less than that in high-velocityriver outlet works. For this reason, a smallerand less costly entrance structure can usuallybe designed for a power intake than for a riveroutlet works of equivalent physical size.

(a) Rushracks. -The trashrack structuresfor power intakes are similar to those requiredfor other outlet works. However, because ofthe possible damage to the turbine and otherh y d r a u l i c m a c h i n e r y , metal trashracksconsisting of closely spaced bars are almostalways required on power outlets to preventthe passage of even small trash and debris. Withthe lower velocity of flow through poweroutlets, large bellmouth openings at the intakesare not needed, and the length that thetrashrack structure is required to span may beless than that for a high-velocity outlet worksof equivalent physical size. The structure onwhich the trashracks are placed may consist ofstructlrral steel or of reinforced concrete asshown on figure 10-l 1. The determination ofthe type of trashrack structure depends notonly upon the comparison of costs between thevarious structures but also upon the influenceon the total time of construction for eachscheme. Construction time may be reduced insome instances by using an all-metal or precastconcrete structure instead of a cast-in-placestructure.

Submerged trashracks should be used, if atall possible, because fully submerged racksnormally require less maintenance than thosewhich are alternately wet and dry. Experiencehas shown that steel will last longer if fullysubmerged. However, by bolting the all-metaltrashrack structure to the concrete withstainless steel bolts, the racks can be replacedby divers if necessary.

When the reservoir surface fluctuates aboveand below the top of the trashrack structure,trash can accumulate on top of the structureand create a continuous maintenance problem.Normally, in large reservoirs submerged

L- AXIS o f d o m(ai Penstock encased I” m o s s

c o n c r e t e o f o d a m

unit trashrack

Mock o,r Inlet (b) A penstock e m b e d d e d m t h em a s s c o n c r e t e o f o d o m ot t h eupstream end and exposed aboveg r o u n d between dam and power

Figure 10-q. Typical penstock installations. -288-D-3071

.Bulkhead gate .’

Figure IO-IO. Embedded penstock in abutment tunnel.-,288-D-3073


S E C T I O N B - B S E C T I O N C - C

i-

SHOWING CONmErE PLlCED

_. Upstreom face o f damWIT” DAM

S E C T I O N A - A ”

Figure IO-II. Typical concrete trashrack structure for a penstock (sheet 1 of 2). -288-D-3074 (l/2)

trashracks do not have to be raked as a result prevented by the installation of an air bubblingof trash accumulations, except during the system around the structure. This systeminitial filling. Ice loads must be considered if circulates the warmer water from lower in thethe trashrack structure is above the reservoir at reservoir around the structure to keep thetimes during cold winters. Ice loadings may be members ice free.

OUTLETS-Sec. lo-21 239

E/594000-- ] , ,)& 1 -’ 1

o/one ._ 1,

H A L F S E C T I O N D - D H A L F S E C T I O N E - E

Symmetr~coi a b o u t @

‘fq(&-Tl

k---No chomfe!

S E C T I O N J - J

: - No chamfer

S E C T I O N H - H

CONCRETE FINISHESAil streomhned surface of ribs and columns ~40r UJA l l o t h e r rurfoces Q or~2

b a s e piotes

N O T E SThe reference plane is 8’.6”upstreom of ox~s at @ of trashrock

structure at El 604500 wrth o slope of 0 172.1 -horn? to vertChamfer f’or tool al/exposed corners unless otherwse specihed

H A L F S E C T I O N F - F H A L F S E C T I O N G - G

To reference

S E C T I O N L - L S E C T I O N P - P SECTION K-K

reference

Figure 10-11. Typical concrete trashrack structure for a penstock (sheet 2 of 2). -288-D-3074 (2/2)


The trash bars usually consist of relativelythin, flat steel bars which are placed on edgefrom 2 to 9 inches apart and assembled in racksections. The spacing between the bars isrelated to the size of trash in the reservoir andthe size of trash that can safely be passedthrough the turbines without damage. Therequired area of the trashrack is fixed by alimiting velocity through the rack, which inturn depends on the nature of the trash whichmust be excluded. Where the trashracks areinaccessible for cleaning, the velocity shouldnot exceed approximately 2 feet per second;however, a velocity up to approximately 5 feetper second may be tolerated for racksaccessible for cleaning.

(b) Bellmouth Entrance.-It was broughtout in section 10-l 1 that the entrance to a riveroutlet should be streamlined to providesmooth, gradual changes in the flow, thusmin imiz ing head l o s se s and avo id ingdisturbances of the flow in the conduit. This isalso true for power outlets; however, becausethe velocities in penstocks are considerablylower, the bellmouths do not have to be ass t r e a m l i n e d a s t h o s e d e s i g n e d f o r t h ehigh-velocity river outlets. Experience onhydraulic models has shown that relativelysimple rounding of corners eliminates most ofthe entrance losses when velocities are low.With the low velocities, pressure gradients inthe bellmouth area are less critical.

(c) Transition. -alike the bellmouthentrance, the transition for the power outletsdoes not need to be as gradual as does thetransition for the high-velocity river outletworks. The area throughout the transition canremain approximately the same, changing onlyfrom the shape of the gate to that of thepenstock, with the gate area nearly equal tothat of the penstock.

1 0 - 2 2 . Penstocks.-The penstock i s t h epressure conduit which carries the water fromthe reservoir to the powerplant. The penstockfor a low-head concrete dam may be formed inthe mass concrete; however, a steel shell orlining is normally used to assure watertightnessand prevent leakage into a gallery or chamberor to the downstream face. In large concretedams under a high-head condition, steel

penstock liners are always used to provide therequired watertightness in the concrete.Penstocks can be embedded in concrete dams,encased in concrete, or installed in tunnels andbackfilled with concrete. The penstocks shouldbe as short as practicable and should bedesigned hydraulically to keep head loss to aminimum. The size of the penstock isdetermined from economic and engineeringstudies that determine the most efficientdiameter for overall operation.

10-23. Gates or Valves. -Emergency gatesor valves are used only to completely shut offthe flow in the penstocks for repair, inspection,maintenance, or emergency closure. The wicketgates of the turbines act to throttle the flow innormal operation. The gates or valves, then,need to be designed only for full openoperation. Many types of gates or valves can beu t i l i z e d i n t h e p o w e r outlets. Commonemergency gates used in a concrete dam arefixed-wheel gates either at the face of the damand controlled from the top of dam (see fig.lo-12), or in a gate slot in the dam andcontrolled from a chamber beneath theroadway.

An in-line control device, such as a butterflyvalve, can be used anywhere along the length ofthe penstock and can be controlled from achamber or control house. Also, in-linecontrols should be used on each individualpenstock if more than one penstock branchesoff the main power outlet header, to permitt h e c l o s u r e o f e a c h penstock w i t h o u tinterfering with the flow of the others. Inaddition to butterfly valves, other types ofin-line control devices that can be used to closeoff the flow include gate valves, ring-followergates, and sphere valves. A determination ofthe type of valve or gate to be used isinfluenced by many factors such as the size ofpenstocks, the location best suited for controlsand operators, the operating head, and thegeneral layout of the power outlets. Anotherfactor to consider in determining the controldevice to be used is the amount of head lossthrough each alternative type of gate or valve.

10-24. Hydraulic Design of PowerOutlets. -The hydraulics of power outletsinvolves pressure flow through a closed

OUTLETS-Sec. 1 O-24

.‘. .. .

C Penstock

Figure 10-12. Typical fixed-wheel gate installation atupstream face of dam. -288-D-3075

241

conduit. The methods of hydraulic analysis aresimilar to those required for other outletworks. A power outlet is designed to carrywater to a turbine with the least loss of headconsistent with the overall economy ofinstallation. An economic study will size apenstock from a monetary standpoint, but thefinal diameter should be determined fromc o m b i n e d eng ineer ing and monetaryconsiderations.

(a) Size Determination of Penstock.-Amethod for determining the economic diametero f a penstock i s g i v e n i n E n g i n e e r i n gMonograph No. 3 [91. All the variables used inthis economic study must be obtained from themost reliable sources available, so as to predictas accurately as possible the average variablesfor the life of the project. The designer mustassure himself that all related costs ofconstruction are considered during theeconomic study.

The head losses used in the economic studyfor the power outlet are similar to the losses inother outlet works. Because of the lowervelocities, these losses are usually small. Butover a long period, even a small loss of headcan mean a sizable loss of power revenue. Thevarious head losses which occur betweenreservoir and turbine are as follows:

( 1) Trashrack losses.(2) Entrance losses.(3) Losses due to pipe friction.(4) Bend losses.(5) Contraction losses (if applicable).(6) Losses in gate or valve.Engineering Monograph No. 3 gives a

complete discussion of these losses and howthey should be used in the determination ofthe economic size of a penstock.

(b) Intake Structure.-As stated in earliersections, the lower velocity through a poweroutlet requires less streamlining of the intakestructure to achieve economically acceptablehydraulic head losses. The gate can be madesmaller, the bellmouths can be designed withsharper curvature, and the transition need notbe made as gradual as for a high-velocity riveroutlet works. The design of the trashrackstructure is similar to that for the river outletworks, discussed in section 10-4(a).

242

1 0 - 2 5 . S t r u c t u r a l D e s i g n of P o w e rOutlets.-The structural design of a powero u t l e t i s d e p e n d e n t u p o n t h e a c t u a lcharacteristics of the power outlet works: thehead; and where applicable, the stresses withinthe dam, due to temperature, gravity, andexternal loads. The design criteria for poweroutlet works should be established for theconditions which exist or may be expected toexist at any time during the operation or life ofthe structure.

(a) Trashrack.-The design of a trashrackstructure for a power outlet should be based ona head differential of 5 feet due to partialclogging of trash. This small head differentialminimizes power loss and is sufficient for thelow velocities at which the power outletsoperate. Ice loads should be applied in coldclimates if the trashrack is exposed or partiallyexposed above the reservoir. Temperature loadsduring construction should also be investigatedin the design procedures.

(b) Penstocks. -The penstocks through aconcrete dam are usually lined with a steel


shell; however, for low heads, penstocks may besimply a formed opening through the dam.Most penstock linings begin downstream fromthe transition. Therefore, when designingreinforcement around the penstocks, twoconditions, lined and unlined, are usuallypresent. In the a rea th rough which thepenstocks are lined, a reasonable portion of thestresses may be assumed to be taken by theliner and not transferred to the surroundingconcrete. Hydrostatic bursting pressures,concentration of the stresses within the dam,and temperature differentials between thewater in the penstock and the mass concrete allmay create tensile stresses in the concrete atthe periphery of the penstock. Reinforcementis therefore placed around the penstock withinthe areas of possible tensile stress. A commonmethod of analysis to determine the stresses inthe concrete is a finite element study using acomputer for the computations. Burstingpressures, dam loadings, and temperaturevariations can all be incorporated into thisanalysis to design the required reinforcement.

D. BIBLIOGRAPHY

[l

[2

] Bradley, J. N., and Thompson, L. R., “Friction Factorsf o r L a r g e C o n d u i t s F l o w i n g F u l l , ” E n g i n e e r i n gMonograph No, 7, Bureau of Reclamation, March 1951.

] Creager, W . P . , a n d J u s t i n , J . D . , “ H y d r o e l e c t r i cH,andbook.” second edition. John Wilev & Sons. Inc..

10-26. Bibliography.

New York:N. Y., 1954.[3] “Hydraul ic Design Cri ter ia , Sheet 228-1, Bend Loss

Coefficients,” Waterways Experiment Station, U.S. ArmyEngineers, Vicksburg, Miss.

[4] King, W. H., “Handbook of Hydraulics,” fourth edition,McGraw Hill Book Co., Inc., New York, N. Y., 1954.

[5] Rouse, Hunter, “Engineering Hydraulics,” John Wiley &Sons, Inc., New York, N. Y., 1950.

[6] “Hydraulic Design of Stilling Basins and EnergyDissipators,” Engineering Monograph No. 25, Bureau ofReclamation, 1964.

[7] Doddiah, D., Albertson, M. L., and Thomas, R. A., “ScourFrom Jets ,” Proceedings, Minnesota Internat ionalHydraulics Convention (Joint Meeting of InternationalAssociation for Hydraulic Research and HydraulicsDivision, ASCE), Minneapolis, Minn., August 1953, p.161.

[8] Scimemi, Ettore, “Discussion of Paper ‘Model Study ofBrown Canyon Debris Barrier’ by Bermeal and Sanks,”Trans. ASCE,vol. 112,1947, p. 1016.

[9] “Welded Steel Penstocks,” Engineering Monograph No. 3,Bureau of Reclamation, 1967.

<<Chapter XI

G a l l e r i e s a n d Adits

1 l-l. General.-A gallery is an openingwithin the dam that provides access into orthrough the dam. Galleries may run eithertransversely or longitudinally and may beeither horizontal or on a slope. Where used as aconnecting passageway between other galleriesor to other features such as powerplants,elevators, and pump chambers, the gallery isusually called an adit. Where a gallery ise n l a r g e d t o p e r m i t t h e i n s t a l l a t i o n o fequipment, it is called a chamber or vault.

1 l-2. Purpose. -The need for galleries variesfrom dam to dam. Some of the more commonuses or purposes of galleries are:

(1) To provide a drainageway for waterpercolating through the upstream face orseeping through the foundation.

(2) To provide space for drilling andgrouting the foundation.

(3) To provide space for headers andequipment used in artificially cooling theconcrete blocks and grouting contractionjoints.

(4) To provide access to the interior ofthe structure for observing its behaviorafter completion.

(5) To provide access to, and room for,mechanical and electrical equipment suchas that used for the operation of gates inthe spillways and outlet works.

(6) To provide access through the damfor control cables and/or power cables.

(7) To provide access routes forvisitors.

Other galleries may be required in a particulardam to fulfill a special requirement.

Galleries are named to be descriptive of their

location or use in the dam; for example, thefoundation gallery is the gallery that followsthe foundation of the dam, and the gate galleryis the gallery for servicing the gates. A typicalgallery layout is shown on figures 1 l-l and11-2.

1 l-3. Location and Size. -The location andsize of a gallery will depend upon its intendeduse or purpose. Some of the more commontypes of galleries are:

(a) Foundation Gallery. -The foundationgallery generally extends the length of the damnear the foundation rock surface, conformingin elevation to the transverse profile of thecanyon; in plan it is near the upstream face andapproximately parallel to the axis of the dam.It is from this gallery that the holes for themain grout curtain are drilled and grouted andfrom which the foundation drain holes aredrilled. Its size, normally 5 feet wide by 7%feet high, is sufficient to accommodate a drillrig. There should be a minimum of 5 feet ofconcrete between the floor of the gallery andthe foundation rock.

(b) Drainage Gallery.-In high dams asupplementary drainage gallery is sometimeslocated further downstream, about two-thirdsof the base width from the upstream face, forthe purpose of draining the downstreamportion of the foundation. This gallery usuallyextends only through the deepest portion ofthe dam. Drainage holes may be drilled fromthis gallery, so the .5- by 7%-foot size is usuallyadopted.

(c) Gate Galleries and Chambers.-Gategalleries and chambers are placed in dams toprovide access to, and room for, themechanical and electrical equipment required

243

GALLERIES AND ADITS-Sec. 1 l-3 245

PLAN OF FOUNDATION AN0 ORAINAOE CA”;;‘;

PLAN OFAOCESS OALLERY

+EtT)ON THR” GALLER,ES

Figure II-I. Galleries and shafts in Grand Coulee Forebay Dam-plans, elevations, section (sheet 2of 2). -288-D-3077 (2/2)

a, Do * r .;T Y P I C A L G A L L E R Y I N T E R S E C T I O N

:

.’h

.,t,:

.‘.’(I

9, SECTION TNRU OFFSET STAIRWELLSSW”.‘ ,,a,“* *or ,“01”

TYPICAL 3”VTllITY PfPING

S E C T I O N W&i STNRWE“AT GALLERY

,,,“.a1 IT.,“* IO7 IYO””

P L U M B - L I N E W E L LTYPICAL E X C E P T A S NO7EO SECTION A- A

TIPIC”‘ SECTIONALONG INCLINED 6ALLERY F L O O R OETAIL AT.DOORS

Figure 11-2. Galleries and shafts in Grand Co&e Forebay Dam-sections. -288-D-3079

GALLERIES AND SHAFTS-Sec. 1 l-4 247

for the operation of gates for outlets, powerpenstocks, or the spillway. Their size willdepend on the size of the gates to be served.

(d) Grouting Galleries. -If it is impracticableto grout contraction joints from the face of thedam, the grout-piping system should bearranged so as to locate the supply, return, andvent headers in galleries placed near the top ofeach grout lift. The piping system for artificialcooling of the blocks may also be arranged toterminate in these galleries.

Transverse galleries or adits may be requiredfor foundation consolidation grouting.

(e) Visitors’ Galleries. -Visitors’ galleries areprovided to allow visitors into points ofinterest or as part of a tour route betweenvisitors’ facilities and the powerplant. The sizewould depend upon the anticipated number ofvisitors.

(f) Cu ble Galleries.-Galleries may beutilized, in conjunction with tunnels, cut andcover sections or overhead lines, as a means tocarry control cables or power cables from thepowerplant to the switchyard or spreader yard.The size of the gallery will depend upon thenumber of cables, the space required for eachcable, and the space required for relatedequipment .

(g) Inspection Galleries. -Inspectiongalleries are located in a dam to provide accessto the interior of the mass in order to inspectthe structure and take measurements which areused to monitor the structural behavior of thedam after completion. All the galleriesdiscussed above, which are located primarilyfor other specific purposes, also serve asinspection galleries.

As mentioned previously, galleries areusually made rectangular and 5 feet wide by7% feet high with a 12-inch-wide gutter alongthe upstream face for drainage. The 4-footwidth is a comfortable width for walking andthe 7%-foot height corresponds with the7%-foot placement lift in mass concrete.Experience has shown that this size of gallerywill provide adequate work area and access forequipment for normal maintenance exceptwhere special equipment is required such as atgate chambers. Galleries as narrow as 2 feet

have been used; however, a minimum of 3 feetis recommended.

1 l-4. Drainage Gutter. -All galleries shouldhave gutters to carry away any seepage whichgets into the gallery. On horizontal runs, thedepth of gutter may vary from 9 to 15 inchesto provide a drainage slope. Pipes shouldcollect the water at low points in the gutterand take it to lower elevations where it willeventually go to the pump sump or draindirectly to the downstream face by gravity.

11-5. Formed Drains. -Five-inch-diameterdrains are formed in the mass concrete tointercept water which may be seeping into thedam along joints or through the concrete. Byintercepting the water, the drains minimize thehydrostatic pressure which could developwithin the dam. They also minimize theamount of water that could leak through thedam to the downstream face where it wouldcreate an unsightly appearance.

The drains are usually located about 10 feetfrom the upstream face and are parallel to it.They are spaced at approximately IO-footcenters along the axis of the dam. The lowerends of the drains extend to the gallery, or areconnected to the downstream face near thefillet through a horizontal drainpipe or headersystem if there are no galleries. The tops of thedrains are usually located in the crest of thedam to facilitate cleaning when required.Where the top of the dam is thin, the drainsmay be terminated at about the level of thenormal reservoir water surface. A 1%inch pipethen connects the top of the drain with thecrest of the dam and can be used to flush thedrains.

1 l-6. Reinforcement.-Reinforcement isusually required around galleries in a dam onlywhere high tensile stresses are produced, suchas around large openings, openings whoseconfiguration produces high tensile stressconcentrations, and openings which are locatedin areas where the surrounding concrete is intension due to loads on the dam ortemperature or shrinkage. Reinforcementshould also be utilized where conditions aresuch that a crack could begin at the gallery andpropagate through the dam to the reservoir.


Stresses around openings can be determinedusing the finite element method for variousloading assumptions such as dam stresses,t e m p e r a t u r e , a n d s h r i n k a g e l o a d s .Reinforcement is usually not required if thetensile stresses in the concrete around theopening are less than 5 percent of thecompressive strength of the concrete. If tensilestresses are higher than 5 percent of thecompressive strength, reinforcement should beplaced in these areas to limit cracking. Eachgallery should be studied individually using theappropriate dam section and loads.

In areas of high stress or where the stressesare such that a crack once started couldpropagate, reinforcement should be used. Ifunreinforced, such a crack could propagate tothe surface where it would be unsightly and/oradmit water to the gallery. It could alsothreaten the structure safety. The stressesdetermined by the finite element analysis canbe used to determine the amount ofreinforcement required around the opening tocontrol the cracking.

In some cases, reshaping or relocating thegallery can reduce or eliminate the tensilestresses.

1 l-7. Services and Utilities. -Service lines,such as air and water lines, can be installed int h e g a l l e r y t o f a c i l i t a t e o p e r a t i o n a n dma in t enance after the dam has beencompleted. To supply these lines, utility pipeshould be embedded vertically between thegalleries and from the top gallery to the top ofthe dam. This will enable the pipe at the top ofthe dam to be connected with an aircompressor, f o r e x a m p l e , a n d d e l i v e rcompressed air to any gallery. The number andsize of the utility piping would depend uponanticipated usage.

Galleries should have adequate lighting andventilation so as not to present a safety hazardto persons working in the galleries. Theventilation system should be designed to

prevent pockets of stale air from accumulating.T e l e p h o n e s s h o u l d b e i n s t a l l e d a t

appropriate locations in the gallery for use inan emergency and for use of operations andmaintenance personnel.

The temperature of the air in the galleryshould be about the same as that of thesurrounding mass concrete to minimizetemperature stresses. This may require heatingof incoming fresh air, particularly in colderclimates. Galleries used for high-voltage powercables may require cooling since the cables giveoff considerable heat.

1 l-8. Miscellaneous Details.-Horizontalruns of galleries, where practicable, should beset with the floor at the top of a placement liftin the dam for ease of construction. Gallerieson a slope should provide a comfortable slopefor walking on stairs. A 7% to 10 slope isreasonable for stairs, yet is steep enough tofollow most abutments. A slope of 7% to 9 hasbeen used on steeper abutments. Ramp slopesmay be used where small or gradual changes inelevation are required. Ramp slopes should beless than loo but can be up to 15O if specialnonslip surfaces and handrails are provided.

Spiral stairs in a vertical shaft are used wherethe abutments are steeper than can be followedby sloping galleries. These shafts are usuallymade 6 feet 3 inches in diameter toaccommodate commercially available metalstairs.

To minimize the possibility of a crackdeveloping between the upstream face of thedam and a gallery which would leak water,galleries are usually located a minimumdistance of 5 percent of the reservoir head ont h e g a l l e r y f r o m t h e u p s t r e a m f a c e . Aminimum of 5 feet clear distance should beused between galleries and the faces of the damand contraction joints, to allow room forplacement of mass concrete and to minimizestress concentrations.

<<Chapter XII

M i s c e l l a n e o u s A p p u r t e n a n c e s

12-1. Elevator Tower and Shaft. -Elevatorsare placed in concrete dams to provide accessbetween the top of the dam and the gallerysystem, equipment and control chambers, andpowerplant. The elevators can also be used bythe visiting public for tours through the dam.The elevator structure consists of an elevatorshaft that is formed within the mass concrete,and a tower at the crest of the dam. The shaftshould have connecting adits which provideaccess into the gallery system and intooperation and maintenance chambers. Theseadits should be located to provide access to thevarious galleries and to all locations at whichmonitoring and inspection of the dam ormaintenance and control of equipment may berequired. Stairways and/or emergency adits tothe gallery system should be incorporatedb e t w e e n e l e v a t o r s t o p s t o p r o v i d e a nemergency exit.

The tower provides a sheltered entrance atthe top of the dam and houses the elevatoroperating machinery and equipment. Moreover,the tower may be designed to provide space foruti l i t ies, storage, and offices. Touristconcession and information space may also beprovided in the tower at the top of the dam, ifthe project is expected to have a large touristvolume. The height of the tower above theroadway is dependent upon the number offloors needed to fulfill the space requirementsof the various functions for which the tower isintended. On large dams more than oneelevator may be incorporated into the design tomake access more available. Moreover, separateelevators may be constructed for visitors otherthan the elevators provided for operation andmaintenance. Since the towers provide the

entrance to the interior of the structure and areused by most visitors, they are a focal point ofinterest and their architectural considerationsshould be an important factor in their designand arrangement. The architectural objectiveshould be simplicity and effectiveness blendingwith the massiveness of the dam to present apleasing and finished appearance to thestructure.

The machinery and equipment areas shouldinclude sufficient space for the requiredequipment and adequate additional space forma in t enance and o p e r a t i o n activities.Electrical, telephone, water, air, and any otherservices which may be required should beprovided to the appropriate areas. Restroomsfor visitors as well as those for maintenancepersonnel may also be included in the layout ofthe tower. Stairways, either concrete or metal,are usually included for access to machineryand equipment floors to facilitate maintenanceand repair. Stairways can also be provided asemergency access between levels. An exampleof the layout of a typical elevator shaft andtower can be seen on figures 12- 1 and 12-2.

(a) Design o f S h a f t . - T h e d e s i g n o fr e i n f o r c e m e n t a r o u n d a s h a f t c a n b eaccomplished by the use of finite elementstudies, with the appropriate loads applied tothe structure. The stresses within the dam nearthe shaft and any appropriate temperatureloads should be analyzed to determine iftension can develop at the shaft and be of suchmagnitude that reinforcement would berequired. A nominal amount of reinforcementshould be placed around the shaft if it is nearany waterway or the upstream face of the damto minimize any chance of leakage through any

249

R O O F P L A N

UPSTREAM ELEVATION

A R C H I T E C T U R A L G R O O V ET Y P E G - 4

PLAN EL.IPSO.OO


SECTION A-A

DETAIL AY00lFlCATION O F AROHIZt?C+URAL

01100VE rYPE o - 4

ARGHITEOTURAL O R O O V ET Y P E O - f

NORTM E L E V A T I O N OOWNSTREAM E L E V A T I O N SOUTH E L E V A T I O N

Figure 12-I. Architectural layout of elevator tower in Grand Coulee Forebay Dam. -288-D-3082

MISCELLANEOUS APPURTENANCES-Sec. 12-2 2.51

cracks which may open. Reinforcement shouldalso be placed around the periphery of theshaft as it approaches the downstream face ofthe dam, where tensile stresses due totemperature loadings become more likely tooccur.

(b) Design of Tower. -The structural designof the elevator tower above mass concreteshould be accomplished by using standarddesign procedures and the appropriate loadsthat can be associated with the structure. Liveloads, dead loads, temperature loads, windloads, and earthquake loads should all beincluded in the design criteria. The magnitudeof earthquake load on the tower (see (2)bbelow) may be increased substantially by theresonance within the structure and must bedetermined by actual studies. Reinforcementto be placed in the structure at all the variouscomponents should be designed with respect tothe characteristics of the structure and therequirements of the reinforced concrete code.

Dead loads and live loads usually used in thedesign of an elevator tower are as follows:

( 1) Dead loads:Reinforced concrete- 150 pounds per

cubic footRoofing-varies with type of material

(2) Live loads:a. Uniformly distributed floor loads,

pounds per square foot.

Lobby . . . . . . . . . . . . . . . . . . . . . . . . . 150Office space . . . . . . . . . . . . . . . . . . . . . . 100Roof (includes snow) . . . . . . . . . . . . . . . . . 50Toilets . . . . . . . . . . . . . . . . . . . . . . . . . 100Stairways . . . . . . . . . . . . . . . . . . . . . . . 100Elevator-machinery floor . . . . . . . . . . . . . *250Storage space-heavy . . . . . . . . . . . . . . . . . 250Storage space-light . . . . . . . . . . . . . . . . . . 125

*Concentrated loads from the elevator machinery maycontrol the design instead of the uniform load given.

b. Other loads:

Wind loads . . . . . . . . . . . . 30 pounds per squarefoot on vertical

projectionEarthquake loads:

Horizontal . . . . . . . . . . . . . . . . . 0.1 gravityVertical . . . . . . . . . . . . . . . . . . 0.05 gravity

12-2. Bridges. -Bridges may be required on

the top of the dam to carry a highway over thespillway or to provide roadway access to thetop of the dam at some point other than at theend of the dam. A bridge may also be providedover a spillway when bulkhead gates for riveroutlets or spillway crest gates require the use ofa traveling crane for their operation ormaintenance. Where there is no highway acrossthe dam and no crane operations are required,a spillway bridge designed only to facilitateo p e r a t i o n and ma in t enance m a y b econstructed. When a bridge is to be used for ahighway or to act as a visitors’ access route,architectural treatment should be undertakento give the structure a pleasing appearance.This architectural treatment should be basedon the size of dam, the size and type of otherappurtenant structures, local topography, and at y p e o f b r i d g e structure which blendspleasingly with the entire feature.

Design criteria for highway bridges usuallyconform to the standard specifications adoptedby the American Association of State HighwayOfficials, modified to satisfy local conditionsand any particular requirement of the project.The width of roadway for two-way trafficshould be a minimum of 24 feet curb to curbplus sidewalk widths as required. However,with new highway regulations requiring greaterwidths, both Federal and local codes should beconsulted to establish a final width. Thestructural members can consist of reinforcedconcrete, structural steel, or a combination ofboth types of materials. The bridge structurecan be one of many types such as barrel-arch,slab and girder, or slab, depending on therequired architecture, loads, and span. Thestructure should be designed to carry the classof traffic which is to use the bridge; however,the traffic design load used should generallynot be less than the HS-20 classification.

Special heavy loads during the constructionperiod, such as powerplant equipment hauledon specially constructed trailers, may producestresses far in excess of those produced by thenormal highway traffic and these should beconsidered in the design criteria. If the bridgedeck is to be used for servicing gates or othermechanical equipment, the loading imposed bythe weight of the crane, the force necessary to


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Figure 12-2. Structural layout of elevator shaft and tower in Grand Coulee Forebay Dam (sheet 1 of 2).-288-D-3084 (l/2)

MISCELLANEOUS APPURTENANCES-Sec.

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Figure 12-2. Structural layout of elevator shaft and tower in Grand Coulee Forebay Dam (sheet 2 of 2).-288-D-3084 (2/2)


lift the gate or equipment, as well as thenormal traffic loads should all be included inthe design. Sidewalk and pedestrian bridgedesign loads should be a minimum live load of8 5 p o u n d s p e r s q u a r e f o o t . O t h e rconsiderations which should be covered in thedesign are camber, crown of roadway slab,storm drainage, and roadway lighting.

12-3. Top of Dam. -The top of the dammay contain a highway, maintenance road, orwalkway depending upon the requirements atthe site. If a roadway is to be built across thedam, the normal top of the dam can bewidened by the use of cantilevers from theupstream and downstream faces of the dam.Operation and maintenance areas, and whereconditions warrant visitors’ parking, may alsobe provided on the top of the dam by furtherenlarging the cantilevers to the required size.The width of the roadway on the top of thedam is dependent upon the type and size ofroadway, sidewalks, and maintenance andoperation spaces that are needed to accomplishthe tasks required. The minimum width for atwo-lane roadway is 24 feet between curbs;howeve r , t h e a c t u a l w i d t h s h o u l d b eestablished by the class of roadway crossing thedam. For highways, the roadway betweencurbs should be made the width required bythe American Association of State HighwayOfficials or stipulated by local considerations.The sidewalks should be a minimum of 18inches wide; however, the actual width shouldbe determined by the proposed usage and theoverall layout and space required for operationand maintenance. The top of Grand CouleeForebay D a m , which contains a two-laneroadway, can be seen in figure 12-3.

When a highway is not to be taken across thedam, the top width should be established tomeet the requirement for operation andmaintenance. A width can be established whichallows a truck to be taken out on the dam ifoperation requires it, or a walkway may be allthat is needed for normal operation andmaintenance. If only a walkway is required, theminimum width should be no less than theactual top width minus the width required forhandrails and/or parapets. Widened areas forservice decks can be constructed, where

required, to facili tate operation of outletworks, power outlets, and spillways.

Parapets or handrails are required bothupstream and downstream on the top of thedam and should be designed not only to meetthe safety requirements but also to blend intothe architectural scheme. On dams where alarge tourist traffic is expected, extreme careshould be taken to assure the safety of thepublic. Therefore, the parapets should be of aheight sufficient to keep anyone from fallingover the side. The minimum height of parapetabove the sidewalk should be 3 feet 6 inches;however, the minimum height may be more onsome dams because of local conditions. When ahandrail is used, chain-link fabric may be usedto prevent a child falling or crawling betweenthe rails. A solid upstream parapet may be usedto increase the freeboard above the top of damif additional height is needed.

Adequate drainage and lighting should beprovided along the top of the dam. Servicelines such as electricity, water, and air shouldalso be provided as required. Crane rails may beembedded in the top of the dam if a gantrycrane w i l l b e u s e d f o r o p e r a t i o n andmaintenance (see fig. 12-3).

The design of the reinforcement for the topof the dam involves determining the amount ofreinforcement required for the live and deadloadings on the roadway cantilevers and anytemperature stresses which may develop. If ahighway is to cross the dam, the cantileversshould be designed for a minimum AASHOloading of HS-20; however, special heavy loadswhich could occur during the constructionperiod should also be investigated. Crane loadsshould also be included in the design criteria ifa crane is to be used for operation andmaintenance. A sidewalk live load of 85pounds per square foot should be used in thedesign. Concrete parapets should be designedfor a transverse force of 10,000 pounds spreadover a longitudinal length of 5 feet; moreover,the parapets should be designed to withstandthe appropriate waterload if the parapet isexpected to create additional freeboard.

The temperature reinforcement requirementat the top of the dam is dependent upon theconfiguration and size of the area and the

MISCELLANEOUS APPURTENANCES-Sec. 12-4

temperature conditions which may occur at thesite. Many dams have a gallery or chamberbelow the roadway, which complicates theanalysis a n d i n c r e a s e s t h e a m o u n t o freinforcement needed to resist stresses causedb y v a r i a t i o n s b e t w e e n t h e o u t s i d e a i rtemperature and the temperature within theopening in the dam. All temperature studiesshould be based on historic temperature datafrom that area and the temperatures occurringin galleries or chambers within the dam. Afterthe temperature distributions are determinedby studies, the temperature stresses that occurcan be analyzed by the use of finite elementmethods.

1 2 - 4 . Fishways.-The magn i tude o f t hefishing industry in various localities hasresulted in Federal, State, and local regulationscontrolling construction activities whichinterfere with the upstream migration andnatural spawning of anadromous fish. All damsconstructed on rivers subject to fish runs mustbe equipped with facilities enabling the adultfish to pass the obstruction on their wayu p s t r e a m , o r o t h e r m e t h o d s o f f i s hconservation must be substituted. Since it isrequired that all facilities for fish protectiondesigned by Federal agencies be approved bythe U.S. Fish and Wildlife Service, this agencyand similar State or local agencies should beconsulted prior to the final design stage.

Low dams offer little difficulty in providingadequate means for handling fish. High dams,however, create difficulties not only inproviding passage for adult fish on their wayupstream, but also in providing safe passage forthe young fish on their journey downstream.Fish ladders for high dams may require suchlength and size as to become impracticable.Large reservoirs created by high dams maycause flooding of the spawning areas. Thevelocity and turbulence of the flow over thespillway or the sudden change in pressure inpassing through the outlet works may result inheavy mortality for the young fish. Thesedifficulties often necessitate the substitution ofartificial propagation of fish in lieu ofinstallation of fishways.

S e v e r a l t y p e s o f fishways h a v e b e e ndeveloped, the most common of which is the

fish ladder. In its simplest form, it consists ofan inclined flume in which vertical baffles areconstructed to form a series of weirs and pools.The slope of the flume is usually 10 horizontalto 1 vertical. The difference in elevation ofsuccessive pools and the depth of water flowingover the weirs are made such that the fish areinduced to swim rather than leap from pool topool, thereby insuring that the fish will stay inthe ladder for its entire length. The size of thestructure is influenced by the size of the river,height of dam, size of fish, and magnitude ofthe run.

Another type of fishway in common use isthe fish lock. This structure consists of avertical w a t e r chamber, gate-controlledentrance and exit, and a system of valves foralternately filling and draining the chamber.Fish locks are usually provided with ahorizontal screen which can be elevated,thereby forcing the fish to rise in the chamberto the exit elevation.

12-5. Restrooms. -Restrooms should beplaced throughout a dam and its appurtenantworks at convenient locations. The numberrequired depends on the size of dam, ease ofaccess from all locations, and the estimatedamount of usage. At least one restroom shouldbe provided at all dams for the use of operationand maintenance personnel. Separate restroomsshould be provided for tourists at dams whichmay attract visitors. In larger dams, restroomsshould be placed at convenient locationsthroughout the gallery system as well as inappurtenant structures such as elevator towersand gate houses.

12-6. Service Installations. -Variousutilities, equipment, and services are requiredf o r t h e o p e r a t i o n a n d m a i n t e n a n c e o fmechanical and electrical features of the dam,outlet works, spillway, and other appurtenantstructures. Other utilities and services arerequired for the convenience of operatingpersonnel and visitors. The amount and type ofservices to be provided will vary with therequirements imposed by the size, complexity,and function of the various appurtenantstructures. The elaborateness of installationsfor personal convenience will depend on thesize of the operating forces and the number of


Match he-4

Figure 12-3. Typical arrangement at top of a gravity dam (Grand Coulee Forebay Dam) (sheet 1 of 2).-285-D-3085 (l/2)

MISCELLANEOUS APPURTENANCES-Sec. 12-6 257

Figure 12-3. Typical arrangement at top of a gravity dam (Grand Coulee Forebay Dam) (sheet 2 of 2).-285-D-3085 (2/2)

tourists attracted to the project. lighting systems. Adequate lighting should be(a) Electrical Services. -Electrical services to installed along the top of the dam, at all service

be installed include such features as the power and maintenance yards, and internally in thesupply lines to gate operating equipment, galleries, tunnels, and appurtenant structures.drainage pumps, elevators, crane hoists, and all Power outlet receptacles should be provided at

258

t h e t o p o f t h e d a m , i n a l l a p p u r t e n a n tstructures, throughout the gallery system andat any location which may require a powersource.

(b) Mechanical Services. -Mechanicalinstallations and equipment that may berequired include such features as overheadtraveling cranes in gate or valve houses, gantrycranes on top of the dam for gate operationand trashrack servicing, hoisting equipment foraccessories located inside the dam, and theelevator equipment. Compressed air linesshould be run into the gallery system, intoservice and maintenance chambers, intoappurtenant structures, and anywhere elsewhere compressed air could be utilized.

(c) Other Service Installations. -Chambersor recesses in the dam may be provided for thestorage of bulkhead gates when these are not inuse. Adequate storage areas should be providedthroughout the dam such as in the gallerysystem, elevator towers, gate or valve house,and o t h e r a p p u r t e n a n t structures formaintenance and operation supplies andequipment. If gantry cranes are to be installedat a dam, recesses in the canyon walls may beprovided for housing them when they are notin use. The gallery system and all appurtenantstructures should be supplied with a heatingand ventilating system where required.

A telephone or other communication system


should be established at most concrete damsfor use in emergency and for normal operationand ma in t enance communication. Thecomplexity of the system will depend on thesize of the dam, the size of the operating force,a n d t h e a m o u n t of mechanical controlequipment. Telephones are usually placedthroughout the gallery system for ease ofaccess and safety in case of an emergency suchas flooding or power failure. Telephones arealso placed near mechanical equipment such asin gate or valve houses, elevator towers,machinery rooms, and other areas in whichmaintenance may be required. Telephonesshould also be placed at convenient locationsalong the top of the dam.

Water lines should be installed to provide awater source throughout the dam and theappurtenant structures. Water for operationand maintenance should be taken into thegallery system at the various levels of thegalleries and into the appurtenant structureswhere required. The water for operation andmaintenance can come from the river orreservoir but water for restrooms and drinkingfountains requires a potable water source.Drinking fountains should be placed atconvenient locations that are readily accessibleto both maintenance personnel and touristtraffic.

<<Chapter XIII

Structural Behavior Measurements

13-1. Scope and Purpose. -Knowledge ofthe behavior of a concrete gravity dam and itsfoundation may be gained by studying theservice action of the dam and the foundation,using measurements of an external and aninternal nature. Of primary importance is theinformation by which a continuing assuranceof the structural safety of the dam can begaged. Of secondary importance is informationon structural behavior and the properties ofconcrete that may be used to give addedcriteria for use in the design of future concretegravity dams.

In order to determine the manner in which adam and its foundation behave during theperiods of construction, reservoir filling, andservice operations, measurements are made onthe structure and on the foundation to obtainactual values of behavior criteria in terms ofstrain, temperature, stress, deflection, anddeformation of the foundation. Properties ofthe concrete from which the dam isconstructed, such as temperature coefficient,modulus of elasticity, Poisson’s ratio, andcreep, are determined in the laboratory.

( a ) D e v e l o p m e n t o f M e t h o d s . - T h einvestigations of the behavior of concrete damsbegan at least 50 years ago, and have includedscale model and prototype structures. Reportson the investigations are available in references[ 1 I, [2], and [31 .I Along with thedevelopment of instruments [4] to use formeasurements, and the instrumentationprograms, there was the development of asuitable method for converting strain, asdetermined in the concrete which creeps under

‘Numbers in brackets refer to items in the bibliography sec.13-l 1.

load [5], to stresses that are caused by themeasured deformation [6] . The basic method,which departs from simple Hooke’s lawrelationships obtained for elastic materials, hasbeen presented in reference [7] with laterrefinements presented in other publications[8, 91. As analyses of the behavioral data fromdams were completed, reports on the results ofthe investigations became available [ 10, 11 I .

S i m i l a r l y , r e p o r t s o n t h e r e s u l t s o finvestigations of foundation behavior havebecome available [ 12, 131.

(b) Two General Methods.-At a majorconcrete dam, two general methods -ofmeasurement are used to gain the essentialbehavioral information, each method having aseparate function in the overall program.

The first method of measurement involvesseveral types of instruments that are embeddedin the mass concrete of the structure and onfeatures of the dam and appurtenances to thedam. Certain types of instruments are installeda t the rock-concrete interfaces on theabutments and at the base of the dam formeasuring deformation of the foundation.Others are installed on the steel liners ofpenstocks for measuring deformation fromwhich stress is determined, and at the outersurface of the penstocks for measuringhydrostatic head near the conduit. This type ofinstrumentation may also be used with rockbolts in walls of underground openings such asa powerplant or tunnel and in reinforcementsteel around penstocks and spillway openingsto measure deformation from which stress isdetermined.

The second method involves several types ofprecise surveying measurements which are

259


made using targets on the downstream face of adam, through galleries and vertical wells in adam, in tunnels, on the abutments, and withtargets on the top of a dam.

13-2. Planning. -From the modest programsfor measurements provided at the earliestdams, there have evolved the extensiveprograms which are presently in operation inrecently constructed ‘Bureau of Reclamationdams. The formulation of programs for theinstallation of structural behavior instrumentsand measurement systems in dams has requiredcareful and logical planning and coordinationwith the various phases of design and ofconstruction.

Plans for a measurement program for a damshould be initiated at the time the feasibilityplans are prepared for the structure. The layoutshould include both the embedded instrumentsystem and systems for external measurements.Appropriate details must be included withthose layouts to provide sufficient informationfor preparing a cost estimate of items neededfor the program.

T h e i n f o r m a t i o n which a behavioralmeasurement system is to furnish is usuallysomewhat evident from the analytical designinvestigations which have been made for thedam and from a study of past experience withbehavioral measurements at other dams. Thisinformation includes temperature, strain,stress, hydrostatic pressure, contraction jointbehavior, deformation of foundation, anddeformation of the structure, all as influencedby the loading which is imposed on thestructure with respect to time.

The cost of a program is contingent on thesize of structure, the number of segmentswhich make up the program, the types ofinstruments to be used, and the number ofinstruments of the various types needed toobtain the desired information.

13-3. Measurement Systems. -Measurementsystems, their layouts, and the locations anduse of the various devices embedded in themass concrete of dams for determiningvolumetric changes are discussed in thefollowing sections. Measurement systems whichemploy surveying methods for determining

deformation changes in a dam are discussedseparately.

The locations of the instruments to beinstalled in a gravity dam are shown on theplan, elevation, and section of figures 13-l and13-2.

(a) Embedded Instrument Measurements-Embedded instruments in a concrete gravitydam usually consist of those which measurelength change (strain), stress, contraction jointopening, temperature, concrete pore pressure,and foundation deformation. Instruments tomeasure stress may be installed at locations inreinforcing steel such as around a spillwayopening or other opening in the dam and onthe steel liners of penstocks. All instrumentsare connected through electrical cables toterminal boards located at appropriate readingstations in the gallery system of the dam. Atthose stations readings from the instrumentsare obtained by portable readout units.Mechanical-type deformation gages whichutilize invar-type tapes, and a micrometer-typereading head may be installed vertically incased wells which extend from the foundationgallery into the foundation to any desireddepth. They may also be installed horizontallyin tunnels in the abutments.

In a gravity dam such as shown on figures13-1 and 13-2, the logical section forinstrumentation is the maximum section wherethe greater stresses and deformations may beexpected to occur. For investigation of thedam’s behavior, instrumentation to determinetemperature, stress, and deformation isrequired. Stress is investigated by clusters ofs t r a i n m e a s u r i n g i n s t r u m e n t s i nthree-dimensional configuration, located atseveral positions on a horizontal gagelinestreamwise on the centerline of the maximumblock near the base of the dam. For a structureof unusual size, similar installations are madealong horizontal gagelines streamwise atintermediate elevations between the base andthe top of the dam and at that same elevationin blocks near each abutment.

The instruments are installed at severallocations along each gageline in clusters of 12instruments each, designated as groups, for

STRUCTURAL BEHAVIOR MEASUREMENTS-Sec. 13-3 261

PLAN

UPSTREAM ELEVATION

Figure 13-I. Locations of instrumentation installed in agravity dam-plan and elevation.-288-D-3087

E l 3 8 0 8 5

E l 3 6 3 0 - d

E R S

MAXIMUM SECTION-t BLOCK 14

Figure 13-2. Locations of instrumentation installed in agravity dam-maximum section.-288-D-3089

determination of multidimensional stress at thecluster locations. From these configurations,stress distribution normal to vertical and tohorizontal planes at the gagelines may bedetermined as well as shear stresses andprincipal stresses. Duplicate instruments areinstalled on the three major orthogonal axes ineach cluster. Eleven instruments of each clusterare supported by a holding device or spider.The twelfth instrument is placed vertically

beside the cluster. Clusters are located alongeach gageline near each face and at midpointbetween. An additional cluster usually islocated between the interior cluster and theone near each face.

A pair of instruments, one vertical and onehorizontal, placed in the concrete under asupported surface, is usually installed near thecentrally located cluster of instruments. Thispair of instruments is needed to determinestress-free behavior of the mass concrete.Instruments in various arrays may be installednear the faces or near contraction joints todetermine conditions of special interest in theconcrete, or in structural elements. Data areobtained from all instruments at frequentintervals so that time lapse variations of stresswill be available for study during the entireperiod of observation, usually several years.

In s t rumen t s a r e installed across thec o n t r a c t i o n j o i n t s b o u n d i n g t h e b l o c k scontaining the instrument clusters. Theseinstruments provide a means of monitoring thebehavior of the joints to determine thebeginning and extent of joint opening due tocooling of the mass concrete. They serve asindicators of maximum joint opening toindicate when grouting should be performed.The instruments also give an indication of theeffectiveness of grouting and show whether anymovement in the joint occurs after grouting.

Several deformation measuring instrumentsare installed at selected locations in thef o u n d a t i o n b e l o w t h e c o n c r e t e o f t h emaximum section and other sections of agravity dam.

A pattern of temperature-sensing devices isincluded in the maximum section of the dam.In a s t r uc tu r e of unusual size, similarinstallations could be made in additionalsections when deemed desirable to determinethe manner in which heat of hydration fromthe mass concrete is generated and dissipated.These instruments should be located ongagelines at several elevations in a section. Theyare not located near the instrument clusters, ast h e s t r e s s in s t rumentation also sensestemperature.

A n i n s t a l l a t i o n o f i n s t r u m e n t s , w h e nrequired for investigation of stress in the steelliner of a penstock, consists of instruments

262

attached circumferentially to the penstock bysupporting brackets. Instruments to detectpore pressure are placed on the outer surface ofthe penstock when it is embedded in concreteo r when i t ex t ends t h rough rock . Theinstruments are connected by electrical cablesto terminal boards at appropriately locatedreading stations.

I n s t r u m e n t s f o r m e a s u r i n g s t r e s s a r esometimes installed in reinforcing steel whichsurrounds openings through a dam such aspenstocks, spillway openings, or galleries.Similarly, instruments may be installed in rockb o l t s u s e d t o s t a b i l i z e r o c k m a s s e s .Temperature-sensing devices installed on a gridpattern in the maximum section or in severalsections of a dam have been used to determinethe distribution of temperature. This is of greatimportance because the volume change causedby temperature fluctuation is one of thefactors which contributes significantly to stressand deflection. Temperature-sensing devices arealso used for control in the cooling operations.Another extensive use of these devices has beenthe development of concrete temperaturehistories to study the heat of hydration whichis generated and dissipated, and to evaluateconditions which contribute to or accompanythe formation of thermal cracking in massconcrete.

Concrete surface temperatures of dams areobtained by temperature-sensing devicesembedded at various random locations on thedownstream faces and embedded at uniformvertical intervals between the base and crest onthe upstream faces. The latter installationsfurnish information on temperature due to thethermal variations in the reservoir.

M e a s u r e m e n t s o f s t r a i n o b t a i n e d b yextensometers used with appropriate gagepoint anchors have been made on the faces ofdams and on gallery walls. These furnishrecords of change in strain due to change insurface stress. Similar measurements whichhave been made across contraction joints andacross cracks in concrete have furnishedrecords of the joint or crack opening or closingas variations occur with time.

( b ) D e f o r m a t i o n Measurements.-The


usually contain provisions for determininghorizontal structural deformation between itsbase and top elevation. An additional system isneeded to determine horizontal deformationswith respect to references located on theabutments. Both systems employ methods ofsurveying to obtain the required information.Their locations are shown on figure 13-l.

Plumblines are installed in gravity dams todetermine horizontal deformation of thestructure which occurs between its top and thebase. They are located in vertical wells usuallyformed in the maximum section and in sectionsabout midway between the abutments andthe maximum section. Each plumbline consistsof a wire with a weight hung on it at the lowestaccessible elevation, or the wire is anchored atthe bottom of the well and suspended by afloat in a tank of liquid at the top. Access tothe plumblines for measurements is fromstations at the several elevations where galleriesare located in the dam. Figure 13-3 shows thelayout of a typical plumbline well with readingstations at several elevations.

Horizontal deformation of the structurewhich occurs at its top elevation with respectto off-dam reference stations is determined bycollimation measurements normal to the axis atseveral locations. These measurements aremade between the stations at the top of thedam and sight lines between the off-damreference stations. The measurements are madeusing a movable reference on the dam, theon-line position being indicated by an operatorwith a sighting instrument at one off-damreference station. The horizontal deformationis obtained from differences between successivemeasurements.

To determine vertical deformations of thestructure, a line of leveling across the top ofthe dam is used. Stations for measurements arelocated on several blocks. The leveling shouldbegin and end at locations sufficiently distantfrom the dam to avoid locations which wouldbe materially affected by vertical displacementof the dam.

Similarly, leveling measurements are made inother locations such as in powerplants and ongate structures to detect settlement or tipping

deformation measuring systems for a dam of large machine units and appurtenant

STRUCTURAL BEHAVIOR MEASUREMENTS-Sec. 13-4

S E C T I O N A-A

S E C T I O N C-G I

E, 3181 YI(

S E C T I O N O - O

Figure 13-3. Typical plumbline well in a concrete dam with reading stations at severalelevations.-288-D-3090

263

features of a dam.13-4. Embedded Instrumentation.-The

Carlson elastic wire instrument [ 141 , is

instruments to be used for the embeddedavailable in patterns suited to most purposes.T h e y are dual-purpose instruments and

measurements in a concrete dam may be measure temperature as well as the function forselected from several types presently availableon the commercial market. One type, the

which designed. These instruments have provedreliable and stable for measurements which


cxtcnd OVC~ long periods of time. Installationshave been made in many Bureau ofReclamation dams and experience with theinstruments covers a period of many years. Thedescription of the instruments, their operation,and the manner in which they have beeninstalled appear in other publications [4, 15,161. Foreign made instruments have been usedoccasionally, as they were more applicable toparticular installations than the Carlson-typeinstruments. Satisfactory results have beenfurnished by those instruments.

For locations where only temperaturemeasurements which are a part of the behaviorprogram are desired, resistance thermometersare used. Temperature measurements of aspecial nature and of short duration such as forconcrete cooling operations are made withthermocouples.

T h e i n s t r u m e n t s w h i c h a r e u s e d f o rdetermining stress in a gravity or other typeconcrete dam are strain meters in groups of 12.Eleven strain meters are supported by aframework, or “spider,” and installed in acluster as shown on figure 13-4. The twelfthstrain meter is placed vertically adjacent to thecluster.

Stress meters as shown on figure 13-5 areused for some special applications such asdetermining vertical stress at the base of themaximum section for comparison and to check

Figure 13-4. A cluster of strain meters supported on a“ s p i d e r ” a n d r e a d y f o r e m b e d m e n t i nconcrete.-P557420-05870

F i g u r e 1 3 - 5 . A stress meter part ial ly embedded inConcrete.-PX-D-74011

results from strain meters. Contraction jointopenings are measured by joint meters asshown on figure 13-6. Temperatures aremeasured by resistance thermometers, andfoundation deformation is measured by aspecial joint meter which has a range ofmovement greater than that of the joint meterused on a contraction joint. Investigation ofhydrostatic pressure is made by means of porepressure meters.

The meters are terminated through electricalcables which connect the instruments toterminal boards as shown on figure 13-7,located at appropriate reading stations in thesystem of galleries throughout the dam. Ateach station, readings from the instruments areobtained with special type portable wheatstonebridge test sets shown on figure 13-8.

Mechanical deformation gages which utilizean invar tape and a micrometer reading headmay be installed vertically in each of severalcased wells which extend from the foundationgallery to distances of 30, 60, 90 feet, or morebelow the base of the dam, usually at locationsin the maximum section. The locations of theinstruments are shown on figures 13-1 and13-2.

Groups of strain meters in multidimensionalconfiguration as shown on figure 13-4 aree m b e d d e d i n t h e m a s s c o n c r e t e o n t h egagelines through the dam as shown on figure13-1 to measure volume changes from whichthe stresses can be computed. The strain metersalso measure temperature. The gagelines ofstrain meter groups usually are identical to the


Figure 13-6. A joint meter inp o s i t i o n a t a c o n t r a c t i o njoint.-P591-421-3321

Figure 13-7. An instrument terminal board and coverbox.-PX-D-74012

centerlines of the construction blocks. In themaximum section of a dam, gagelines of metergroups in addition to the gageline at the blockcenterline m a y b e i n s t a l l e d n e a r e a c hcontraction joint at the elevation of the metergroups on the block centerline. The threegagelines o f me te r g roups pe rmi t more

Figure 13-8. A special portable wheatstone bridge test setfor reading strain meters.-C-8343-2

extensive determination of stress distributionswithin the block than those resulting from asingle gageline.

Vertical and horizontal stresses aredetermined at the base of the maximumsection where maximum cantilever stresses maybe expected. Vertical and horizontal stressesare also determined at other locations in thedam.

Data regarding the volume changes in theconcrete that take place in the absence ofloading are required for analysis of stress.“No-stress” strain meters as shown on figure13-9(a) are installed to supply this information.A pair of “no-stress” strain meters are installednear each gageline of strain meter groups onthe block centerline. These strain meters areinstalled in a truncated cone of mass concreteas shown on figure 13-9(b) under a free surfaceat the interior of the dam so that theinstruments are not affected by vertical orhorizontal loads.

In some instrumentation layouts, stressmeters may be installed companion to eachstrain meter of a selected strain meter group asshown on figure 13-10. Strain meters in groupsindicate length changes which are used tocompute structural stresses. The stress metersindicate stress conditions from which stressesa re ob t a ined w i th on ly a min imum o fcomputation. These serve as a check on resultsfrom the strain meters.


In designs where stress in reinforcement steelis to be investigated, reinforcement meters asshown on figure 13-l 2 are installed in thereinforcement placed around a penstock,spillway, or other opening. The instruments areplaced on at least one bar of each row ofreinforcement at selected locations around theopen ing t o measu re de fo rma t ion i n t hereinforcement from which stress is determined.

Where stress in the steel liners of penstocksis to be investigated, strain meters are attachedto the outer surface of a penstock bysupporting brackets also shown on figure13-I 2. The instruments are installed at each ofthree equally spaced circumferential locationsand at two or more elevations on a steel liner.

At each location of a penstock strain meterinstallation, pore pressure meters shown onfigure 13-l 3 are installed at the outer surfaceo f t h e s t e e l l i n e r t o m e a s u r e p o s s i b l ehydrostatic pressure which may developbe tween t he l i ne r and t he su r round ingconcrete. The pore pressure meters areparticularly useful in cases where backfillconcrete is placed around a penstock in atunnel.

Pore pressure meters as shown on figure13-l 4 are sometimes placed at several locationsat the same elevation in the concrete on thecenterline of a block near the base of themaximum section to measure hydrostaticpressure in pores of the concrete if it develops.The meters usually are spaced 1, 3, 6, 10, 15,20, 30, and 40 to 50 feet from the upstreamface of the dam.

Resistance thermometers as shown on figure13-15, spaced at equal vertical intervalsbetween the base and top elevations of the damat the upstream face, are installed in themaximum section to record reservoir watertemperature at various depths. Resistancethermometers usually are installed at twoelevations at the downstream face of a dam inthe maximum section to record temperature ofthe concrete caused by solar heat.

At several general locations between thefoundation and the mass concrete at the baseof a dam, deformation meters as shown onfigure 13-l 6 are installed. These meters employa joint meter as the measuring device and are

3-d Dto steel cover plate Pxls of truncated cone

2’Plpe droln t og u t t e r In galleryo r t o n e a r e s tf o r m e d dra,n

\iStralnmeters

(a) STRAIN METER LAYOUT.-288-D-3091

TOP-

o f llfl

(b) TRUNCATED CONE OF MASS CONCRETECONTAINING STRAIN METERS.-P622427-3434NA

Figure 13-9. “No-stress” strain meter installation.

Trios of mutually perpendicular strainmeters are sometimes installed as shown onfigure 13-l 1 near the upstream and thedownstream face of a dam to determine straingradients near the surfaces. The trios of strainmeters are located on the gagelines of strainmeter groups, and are installed at distances of2, 4, and 6 feet from the upstream anddownstream faces of a dam.

Gagelines of strain meter groups may beinstalled near large openings which extendthrough a dam such as a spillway. Each gagelineusually contains two meter groups from whichthe stress distribution near those openings isdetermined .

In conjunction with the installations ofstrain meter groups and stress meter arrays atthe various locations throughout a dam, jointmeters as shown on figure 13-6 are placed onthe radial contraction joints at the sameelevations as the groups of strain meters andthe stress meters.

STRUCTURAL BEHAVIOR MEASUREMENTS-Sec. 13-4CP182

CPI83 CPIBJZ

P L A N

ITop of lift -.\

‘(

- Ctcn,nmotor cplderCPl82 and trace ofCP182YJ

u,, U,l,,,,L,C, .A

CPl85

T-

cbCP184

allow at least 6"clearancebetween cable and adjacentstressmeter.

4$-6"Mlll

261

“CPi85 and trace of CPl84

E L E V A T I O N

Figure 13-10. Meter group comprising strain meters and stress meters.-288-D-3092

installed in cased holes to detect deformation downstream boundaries of the blocks. In areasof the foundation rock, usuahy over depths of such as beside foundation and other galleries in30 to 90 feet below the rock-concrete contact the base of the dam, where access is available atsurface.2 a blockout on a gallery wall or floor location, a

Ordinarily, two deformation meters are mechanical-type deformation gage is installedi n s t a l l e d b e t w e e n t h e u p s t r e a m a n d in place of a deformation meter.

‘Depths of 200 feet are planned for the deformation metersto be installed at Crystal Dam, currently under construction inColorado (1973).

The deformation gages, which utilizeinvar-type tapes and micrometer-type readingheads as shown on figure 13-17, are installedvertically in cased wells in the base of the dam


Figure 13-11. Trios of mutually perpendicular strainmeters installed near face of dam.-P557420-7933

Tack weld cwaterproof with cut-back asphalt em”ls,o”-.

able I” ~“d~ae e l condutt

-Support bracket for stralnmeter

F i g u r e 13-12. Penstock a n d r e i n f o r c e m e n t s t r a i nmeters.-288-D-3093

4” Dia. standard steel pipef F~l~~j~;r sand-cement

and pipe cap for covernl

4 Conductor cable inflexible metalic

Pore pressure meter

4 Openings’equally spaced’ L-Wrap with burlop ’

Figure 13-13. Pore pressure meter instal led on apenstock.-288-D-3094

Figure 13-15. Resistance thermometer instal led atupstream face of a dam.-3PXl 3/10/71-3

in the maximum section. These gages extend30 to 90 feet below the surface of contactbetween the rock and the concrete fromappropriate reading stations in the foundation

Figure 13-14. Pore pressure metersinstalled in mass concrete.-HH2653

gallery. The gages show length change overtheir depths into the rock in the same manneras the deformation meter shows the amount ofvertical compressive deformation caused by the


‘/C ElectrIcal c a b l e

S u r f a c e o f c o n t a c tb e t w e e n c o n c r e t e

Wrapped w i t h p a p e r

D r i l l e d a n d c a s e dhole in rock-

f” P i p e

I f”x f” Reduf o r anch

t 3” Dia. hole

Figure 13-16. Deformation meter installed in cased wellu n d e r d a m t o m e a s u r e d e f o r m a t i o n o f f o u n d a t i o nrock.-288-D-3095

weight of the dam and by the loading on thedam.

Similar deformation gages may be installedhorizontally in tunnels which have beenexcavated into the abutment formations of adam. Figure 13-18 shows the micrometer-typereading head of one portion of a horizontalinstallation which is comprised of several1 00-foot sections.

The strain, stress, pore pressure, foundationdeformation, and reinforcement meters, andthe resistance thermometers embedded in themass concrete of a dam will furnish data over along period of time for determining the stressbehavior of the structure and conditions ofstress which develop in features that have beeninstrumented. The joint meters detect theamount of contraction joint opening forinformation during joint grouting.

All of the above-mentioned instrumentsexcept the deformation gages employ awheatstone bridge measuring circuit, and thesame portable resistance bridge as shown onfigure 13-8 can be used in common with allinstruments. Also, the same bridge is used forob ta in ing temperature from resistancethermometers.

Data supplied by the strain meters, stressmeters, joint meters, pore pressure meters,reinforcement meters, and deformation meters

Figure 13-I 7. Micrometer-type reading head for use withfoundation deformation gage.-P622B427-3916NA

are in terms of total ohmic resistance and interms of the ratio of the resistance of the twocoils contained in the meter. Data supplied bythe resistance thermometers are in terms ofohmic resistance o f t h e coil o f t h ethermometer. All d a t a a r e r e c o r d e d o nappropriate data sheets. Computations ofstress, temperature, hydrostatic pressure, jointopening, and foundation deformation are madefrom the field data by computer. Results fromthe computations are plotted as functions oftime by an electronic plotter. Distributions ofstress and temperature on gagelines of the


Figure 13-18. Micrometer reading head and invar tape usedw i t h h o r i z o n t a l t a p e g a g e i n a b u t m e n ttunnel.-P557-420-9328NA

instruments are then prepared for variousloading conditions on the dam and presented inreport form.

13-5 . S u p p l e m e n t a r y L a b o r a t o r yTests. -The determination of stress in the massconcrete of a dam or other large structurerequires a knowledge of the concrete fromwhich the structure is built. Accordingly, afterthe concrete mix for the structure isdetermined in the laboratory, and whenpracticable, prior to the beginning ofconstruction at the site, a testing program forthat specific concrete is developed ande x p e d i t e d . T h e r e s u l t s o f t h e c o n c r e t eproperties and creep tests are an important partof a behavior program, as that information isneeded for the solution of stress from theclusters of strain meters which are embedded ina dam.

The program includes creep tests, testcylinders for which are shown on figure 13-l 9,as well as the usual concrete strength tests andtests for determining elastic modulus, Poisson’sratio, thermal coefficient, autogeneous growthand drying shrinkage. All these tests are madeon specimens which are fabricated in thelaboratory and utilize materials from which thestructure will be built. The materials, which areshipped to the laboratory from the damsite, aremixed in the same proportions as the mix forthe structure, and cast into appropriate

F&we 13-19. Creep tests in progress on 18- by 36-inchmass concrete cylinders.-P557-D-34369

cylinders. The cylinders are stored and testedunder controlled environmental conditions.Reports are available on the methods of testingand on the creep tests (see references [ 171,[181, [191, [20l,and [211).

13-6. Deformation Instrumentation. -Ofequal importance to the measurements madeb y e m b e d d e d i n s t r u m e n t s a r e t h emeasurements which are made with surveyinginstruments and by mechanical devices usingp r e c i s e s u r v e y i n g m e t h o d s . Thesemeasurements involve plumblines, tangent linecollimation, precise leveling, and triangulationdeflection targets on the face of a dam. Over aperiod of several years, results from thosemeasurements show the range of deformationof a structure during the cyclic loadingconditions of temperature and water to whicha dam is subjected.

Plumblines provide a convenient andrelatively simple way to measure the manner inwhich a dam deforms due to the waterload andtemperature change. I n e a r l y B u r e a u o fReclamation dams where elevator shafts wereprovided in the structures, plumblines weresometimes contained in these shafts. Thisproved generally to be unsatisfactory and, atpresent, plumblines are suspended in verticallyformed wells which extend from the top of thedam to near the foundation at three or morelocations in the dam. Wherever feasible, readingstations are located at intermediate elevations,as well as at the lowest possible elevation to

STRUCTURAL BEHAVIOR MEASUREMENTS-&c, 13-6

measure the deflected position of the sectionover the full height of the structure. A typicalwell with reading stations is shown on figure13-3.

271

The wells are usually 1 foot in diameter andmaintained to within one-half inch of plumb asthe dam increases in elevation. In some dams,pipe or casing has been used and left in placefor forming the well, while in other dams thewells have been formed with slip-forms. Thereading stations on a plumbline are located atgalleries in the dam. A doorframe is set in theconcrete of the gallery wall at each readingstation, and doors seating against spongerubber seals are provided as closures. The doorsof the reading stations are kept locked exceptwhen readings are being made, to prevent theplumbline being disturbed. Reading stations are

Figure 13-20. Components of equipment for weighted

oriented so that measurements may be made inplumbline installation.-PX-D-74010

the directions of anticipated movements, henceavoiding the need for trigonometric resolution.In the older dams orientation of the readingstations requires that measurements be made at4S” to the directions of dam movements, thusnecessitating computation. Measurements ofdeformation are made with a micrometer slidedevice having either a peep sight or amicroscope for viewing. The measuredmovements indicate deformation of thestructure with respect to the plumbline.

Plumbline installations of two types havebeen used. These are the weighted plumblineand the float-suspended plumbline. For theweight-supporting plumbline the installationconsists of a weight near the base of the damsuspended by a wire from near the top of thedam. The suspension is located in a manhole at Figure 13-21. Tank and float for use with float-suspended

the roadway or when practicable in a utilityplumbline.-C-8163-1NA

gallery near the top. The components of station. Figure 13-22 shows the weight andequipment for the installation are shown on weight support. The support is attached to thefigure 13-20. Recent plumbline installations are plate which closes the lower end of the pipefloat suspended, using antifreeze in a tank at well prior to lowering the pipe well into thethe top of the dam with a float holding the hole in the foundation. Figure 13-23 shows awire. Figure 13-21 shows one type of float and typical reading station and reading devices.tank. When the lower end of the plumbline is I n c o n j u n c t i o n with the plumblineat a gallery reading station, the wire is fixed at installations in dams, reference monumentsthe bottom location. In other cases, where a have been established in cased wells below thepipe well is extended below the foundation, foundation near the base elevation of thethe wire is attached to a weight which is plumblines. These are used to determinelowered into that well from the lowest reading whether horizontal movement of the dam


(a) SUPPORT AND WEIGHT.

(b) WEIGHT RESTING ON SUPPORT, AND OTHERWEIGHTS.

F i g u r e 1 3 - 2 2 . A n c h o r a g e f o r f l o a t - s u s p e n d e dplumbline.-C-8170-2NA, C-8170-INA

occurs. The locations of these monuments areperiodically determined with respect to the topelevation of the well to determine whethermovement at the elevation of the measurementlocation has occurred. Figure 13-24 shows theoptical plummet and the reference grid that areused for measurements at the gallery elevationof a well which extends into the foundation ofa dam.

Tangent line, or collimation measurements,are a useful means for determining thedeformation of a dam at its top elevation withrespect to off-dam references. This method has

Figure 13-23. Typical plumbline reading station andreading devices.-P459-640-3593NA

Figure 13-24 . Foundation deformation well , opticalplummet, and reference grid.-P459-6404221


been used for measuring the deflection at thetop of some Bureau of Reclamation gravity andarch dams. It is also used at major structuresand is convenient for measurement at smalldams that have no assigned survey personnel,since the survey can usually be conducted bytwo persons.

Collimation measurements are made with atheodolite or jig-transit. An instrument pier asshown on figure 13-25 is constructed on onereservoir bank on the axis and at a higherelevation than the dam. A reference target asshown on figure 13-26 is installed on theopposite reservoir bank on the axis and atabout the same elevation as the pier. The targetand pier locations are selected so that a sightline between them will be approximately onthe axis or parallel to it at the location of a

Figure 13-25. An instrument pier for use with collimationor triangulation systems.-P526400-7877

Figure 13-26. A reference sighting target for use inobtaining collimation measurements.-P526-400-7852

movable measuring target as shown on figure13-27 on the top of the dam. Progressivedifferences in the position of the movablet a rge t f r om the s i gh t l i ne i nd i ca t e t hedeformation change in fractions of an inch atthe measurement station. Usually three to fourstations on a dam are sufficient to obtain thedesired information. The results are correlatedwith plumbline measurements to providesufficient data for charting the deformationbehavior of the structure. A typical layout fora collimation system and locations of the itemsof equipment are shown on figure 13-28.

A more elaborate installation, and one thatrequires experienced and trained personnel, isthat of triangulation targets on the face of adam from off-dam references. Although theinstallation is better suited for an arch damthan for a gravity dam, a minimal installation ise n t i r e l y s a t i s f a c t o r y f o r g r a v i t y d a mdeformation measurements. The layout oftargets on the face of the dam is madecompatible with the layout of the embeddedinstruments. Targets are l o c a t e d o n t h egagelines of instruments, and on the locationsof plumbline reading stations projected radiallyfrom the plane of the axis.

This system requires a net of instrumentpiers and a baseline downstream from the dam.The configuration is laid out to provide thegreatest strength of the geometrical figures[22] and to afford sight lines to each targetfrom as many instrument piers as is feasible.The nature of the terrain and the topography


Figure 13-27. A movable collimation target at a measuringstation on top of a dam-PX-D-74009

PLAN \

U P S T R E A M E L E V A T I O N

Figure 13-28. A collimation system layout for a gravitydam-288-D-3097

of the area are governing factors in the size ofthe net layout. The measurements are madeusing first-order equipment, methods, andprocedures insofar as feasible. The results fromthese measurements show deformation of adam with respect to off-dam references anddeformation of the canyon downstream from adam in the streamwise and cross-streamdirections. The layout of a system andlocations of items of equipment are shown onfigure 13-29. Figure 13-25 shows a pier suitable

Figure 13-29. A triangulation system layout for a gravitydam.-288-D-3099

for theodolite stations. Figure 13-30 shows thetensioning device used with the tape for precisebaseline measurements, and figure 13-3 1 showstargets used on the face of a dam and on thetheodolite piers.

Leveling measurements are u s e d t odetermine vertical displacements of a structurewith respect to off-dam references. Thesemeasurements employ first-order equipmentand procedures [23]. Base references for themeasurements should be far enough from thedam to assure that they are unaffected byvertical displacement caused by the dam andreservoir.

Combina t ions of the several precisesurveying-method measurements are includedin the behavior measurement layouts for newdams. Except for plumbline and deformationwell measurements, all are readily adaptable toolder dams, should monitoring of behaviorbecome desirable.

13 -7. Other Measurements. -Under thisgeneral category may be included types ofmeasurements which are related to and have ani n f l u e n c e o n t h e s t r u c t u r a l b e h a v i o rmeasurements, but which are not included as apart of the program for those measurements.The measurements of primary interest arethose of air temperature as recorded at anofficial weather station, air temperature as maybe recorded at certain locations on a project,


Figure 13-30. A tensioning device used with a tape forprecise baseline measurements.-P557-D-58714

Figure 13-31. A pier plate, pier targets, and damdeformation targets.-P557-D-58717

river water temperature, concrete temperatureduring the construction of a dam, reservoirwater elevation, uplift pressure under a dam,and flow of water from drainage systems. Thelatter two items are discussed more fully.

(a) Upl i f t Pressure Measurements.-Asystem of piping is installed in several blocks atthe contact between the foundation rock andthe concrete of a gravity dam as shown onfigure 13-32. The piping is installed tod e t e r m i n e w h e t h e r a n y h y d r a u l i cunderpressures may be present at the base ofthe dam due to percolation or seepage of wateralong underlying foundation seams or jointsystems after filling the reservoir. Measuredvalues of uplift pressure also may indicate theeffectiveness of foundation grouting and of

drainage. The uplift pressure gradient throughthe section of a dam used for design is anassumed variation between the upstream anddownstream faces of a dam as shown inreference [24] and in section 3-9 of thismanual.

Uplift pressures are determined by pressuregages or by soundings. When a pipe is underpressure, the pressure is measured by aBourdon-type pressure gage calibrated in feet,attached through a gage cock to the pipe. Whenzero pressure is indicated at a pipe, the waterlevel in the pipe is determined by sounding.

A n o t h e r s y s t e m f o r m e a s u r i n g u p l i f tpressure at the base of a structure where nogalleries are included near the foundation intowhich a piping system may be routed is toinstall pore pressure cells at the locations to beinvestigated. Electrical cables may be routedfrom the cell locations to appropriate readingstations on the downstream face or top of thestructure where measurements can be obtained.The installation of pore pressure cells isparticularly applicable to installations beneathconcrete apron slabs downstream from anoverflow section of a dam, spillway trainingwalls, and powerhouse structures. A typicalpressure cell installation is shown on figure13-33. Details on figure 13-34 show themanner in which contraction joints can becrossed by electrical instrument cable which isencased in electrical conduit.

(b) Drainage Flo w Measurements. -Asystem of foundation drains is installed duringthe construction of a gravity dam. The drainagesystem usually consists of 3- or 4-inch-diameterpipes placed on approximately lo-foot centersin the axis direction, in the floors of thefoundation gallery and foundation tunnels.Periodic measurements of flow from theindividual drains should be made and recorded.When f lows f rom d ra ins a r e min ima l ,measurements may be made using any suitablecontainer of known volume and noting thenumber of containers filled per minute. Whenflows are too great to measure by that method,measuring weirs may be installed as needed inthe drainage gutters of the galleries and adits ofa dam. Weirs should be located as required tomeasure flows from specific zones in a dam.


PLAN AT FOUNDATION GALLERY

Altitude gage r a n g e twice t h emaximum workmg pressure

ta f i t instollotlon - -

He’ ““‘““:~,pe extendmg Into g u t t e r

GUlk\

TYPICAL ALTITUDE GAGE INSTALLATION

E 5’~7’Foundotton goller

tly when drllllng IS

tend this pope to gallery wheno horizontal extension IS needed

Extension pipe used when nconnect with riser to gaon upgrade of o 02 towalowest possible elevate

ReInforcIng bar with offset groutedmplace Weld pipe to offset bar sothat pope clears rock surface

L I N E IST* 1C84

Figure 13-32. An uplift pressure measurement system for a gravity dam.-288-D-3101

When flows of drainage water are sufficient office to expedite the various phases of theto be measured by weirs, the measurements are entire program. Control of the program startsusually made on a monthly schedule and with the installation of the various instrumentsrecords maintained on appropriate data sheets. and measu remen t systems during theAny sudden increase or decrease in drainage construction period.should be noted and correlated with the Cooperation between the central designreservoir water surface elevation and any office, the project construction office, thechange in the percolating conditions of the contractor’s organization, and later with thedrains. All drains should be protected against operations and maintenance organization isobstructions and should be kept free-flowing. important and necessary in obtaining reliable

1 3 - 8 . M e a s u r e m e n t P r o g r a m installations of instruments and reliableManagement. -The overall planning, execution, information from the various phases of theand control of a measurement program must be measurement program.under the supervision of the central design A s c h e d u l e f o r i n s t a l l a t i o n o f

S T R U C T U R A L B E H A V I O R 277

p r e s s u r e g a g e s - - _ -

- - Riprop n o t s h o w n

ST1 8W.33

Heodworks a n d fishway-. ~.

P L A N

,-Axis o f d a mk:,y-- Operating deck

Fl P876,--. n o t s h o w n

“-Term,nol b o x

‘----1See defo,i X-’

S E C T I O N A - ALlNE 3 GAGESST* Bfll.3.3

Figure 13-33. A pore pressure meter installation for determining uplift pressure.-288-D-3102

278 DESIGN OF GRAVITY DAMSElectric hydrostotrcpressore gage andhoid;nq fu'ture-.-.-we.-->

/.-Air vent

;',-i"Dio,eieclricai conduit,

Electric hydrostaticpressure gage and holdingfixture.---_

.-A!r vent

-Tee in conduitrun OS req'dreq'd. for grout!"g.

for groutrng

Holding fixture placed

Holdrng fixture placed ,,,'in concrete sand---

D E T A I L W DETA/L X1Typ'col nstollot'o" -12" siabl Typtco! ~nstolloiton ~-slobs over 12')

&cure conduit to reinforcement/' lls necessoiy -~'D~o,holes for O,P Vents,' L)TV .~,ock out (pock with burlap1

\\ ~"Electrrcol condurt--,\,,-Type "~"rubber waterstop

-. : ,--i'"eiosflc filler

-.._

Tee for grouting- Tee for-Tee for grouting

groutrng

Plug ends ofconduitoround(rubber hose attached

'.-Tee for grouting.~, -‘,‘~;a electrlcel conduitwith steel bonds); -...

_I.' cable topreventgroutfromDETA,‘ Z enterrng exponsro" couplrng.

‘-Plug ends ofco"durtarou"dcable to prevent grout fromentering expansion coupling.

/YETA/L Y

(Typical ]ornt crossrng - 12' sfabsl

(T~~,co; ,oint crossing-slabs over 12'1

F&we 13-34. Details of pore pressure meter installation illustrated on figure 13-33.-288-D-3103

instrumentation and for obtaining readings at anew dam begins almost with the placement ofthe first bucket of concrete, continues throughthe construction period, and then extends intot h e o p e r a t i n g s t a g e , p o s s i b l y f o r a nundetermined period of time.

The information which is obtained isforwarded to the design office in the form of areport prepared at monthly intervals asexplained in reference [25]. It includes alltabulations of instrument readings obtainedduring the prior month and other pertinentinformation, such as daily records of air andwater temperature, reservoir and tailwaterelevations when the operating period isreached, any other data which may have aneffect on the structural action of a dam, andcomments conce rn ing t he ope ra t i on o fi n s t r u m e n t s o r measurement devices.Photographs and sketches should be used freelyto convey information.

The schedules for obtaining data fromstructural behavior installations are somewhatvaried. Embedded instrument readings are

required more frequently immediately afterembedment than at later periods. The readingfrequency is usually weekly or every 10 daysduring construction and semimonthly afterconstruction.

In some cases, instrument readings atmonthly intervals can be allowed, Although thewider spread of intervals is not desirable forstrain meters, it is satisfactory for stress meters,reinforcement meters, joint meters, pressurecells, and thermometers. During periods ofreservoir filling or rapid drawdown, readings atmore frequent intervals are preferred. In thiscase, schedules for readings may be acceleratedfor the periods of time involved.

Data from deflection measuring devices suchas plumblines and collimation are preferredweekly. During events of special interest, suchas a rapidly rising or falling reservoir, readingsat closer intervals may be desired.

Data from uplift pressure measurementsystems may be obtained monthly exceptduring the initial filling of a reservoir whendata are obtained at weekly or lo-day intervals.


Pore pressure gages may be read monthly. Atdams where drain flow is of a sufficientquantity to be measure, these data should beobtained at monthly intervals.

T h e t a r g e t d e f l e c t i o n a n d p i e r n e tt r i a n g u l a t i o n measurements should beconducted at least semiannually during theperiods of min imum and maximum airtemperature so as to obtain the furthestdownstream and upstream deformed positionsof a dam. During the early stages of reservoirfilling and operation, additional measurementsare desirable and are made approximatelymidway between those of minimum andmaximum air temperature conditions. Theselatter data are useful in noting deformationtrends and for correlating collimation andplumbline information.

Periodic leveling should be conducted in thevicinity of and across the top of a dam todetect possible vertical displacement of thestructure.

The planned program for measurementsshould cover a time period which will include afull reservoir plus two cycles of reservoiroperation, after which a major portion of themeasurements are suspended. Af t e r t hesuspension of a major portion of readings,some types of measurements, such as thosefrom plumblines, collimation, foundationdeformation meters and gages, and fromcertain clusters of embedded meters which areconsidered essential for long-time structuralsurveillance, are continued indefinitely. Forthese measurements, the intervals betweensuccessive readings may be lengthened.

13-9. Data Processing. -The installations ofinstruments and measurement systems in damsand the associated gathering of quantities ofdata require that a program for processing beplanned in advance. This requires definitelyestablished schedules and adherence to theprocessing plan. Otherwise, seemingly endlessmasses of data can accumulate from behaviorinstrumentation and become overwhelmingwith no apparent end point in sight. Carefulplanning with provisions for the execution ofsuch a program, possibly during a period ofseveral years , cannot b e t o o s t r o n g l yemphasized.

For some measurements, computations andplots can be made and used to advantage byconstruction or operating personnel at adamsite. Under this category are data fromr e s i s t a n c e t h e r m o m e t e r s , j o i n t m e t e r s ,extensometers, Bourdon pressure gages, andthe less complex systems for measuringd e f o r m a t i o n , s u c h a s c o l l i m a t i o n a n dplumblines. X-Y hand plotting of these datacan be maintained with relative ease, asrequired.

F o r m e a s u r e m e n t s f r o m t h e o t h e rinstruments such as strain meters, stress meters,and reinforcement meters, the obtaining ofresults is complex and time consuming.

The methods and details for computingwhich are used to reduce the instrument datato temperature, stress, and deflection arecompletely described in separate reports (seer e f e r e n c e s [6], 181, [26], and [27]). Theresults of the Bureau’s laboratory creep testprogram, which covers a period of more than20 years, are described in references [ 51, [ 181,[28], and [291.

The processing of large masses of raw data isefficiently and economically handled bycomputer methods. The in s t rumen t anddeformation data are processed in the Bureau’sE&R Center in Denver. Processing of themajority of these data is presently done bypunched cards, magnetic tape, and electroniccomputers, using programs of reference [26]for the computing which have been devised forthe specific purposes. Plotted results are fromoutput material which is fed into an electronicX-Y plotter. Reports are prepared from theseresults.

13-10. Results. -The interpretation of dataand compiled results includes the carefulexamination of the measurements portion ofthe program as well as examination of otherinfluencing effects, such as reservoir operation,air temperature, precipitation, drain flow andleakage around a structure, contraction jointg r o u t i n g , c o n c r e t e p l a c e m e n t s c h e d u l e ,seasonal shutdown during construction,concrete testing data, and periodic instrumentevaluations. All of these effects must bereviewed and, when applicable, fitted into theinterpretation. The presentation of results,

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both tabular and graphical, must be simple,forceful, and readily understood.

The interpretation of the measurementresults, as shown in references [ 271, [30], and[ 311 , progresses along with the processing ofthe gathered data. Progress reports usuallycover the findings which are noted during theperiods of construction and initial reservoirfilling stages for a dam. The resume of findings,as a final report, is usually not forthcominguntil several years after completion of thestructure, since the factors of a full reservoir,its seasonal operating cycle, the seasonal rangeof concrete temperature, and local effects oftemperature on concrete are all time-governed.

13-l 1. Bibliography.[II

VI

[31

]41

[51

[61

[71

181

[91

“Arch Dam Investigation,” vol. I, Engineering FoundationCommittee on Arch Dam Investigation, ASCE, 1927.“Arch Dam Investigation,” vol. II, Committee on ArchDam Investigation, The Engineering Foundation, 1934.“Arch Dam Investigation,” vol. Ill, Committee on ArchDam Investigation, The Engineering Foundation, 1933.Raphael, J. M., and Carlson, R. H., “Measurement ofStructural Action in Dams,” James J. Gillick and Co.,Berkeley, Calif., 1956.McHenry, Douglas, “A New Aspect of Creep in Concreteand its Application to Design,” Proc. ASTM, vol. 43, pp.1069-1087, 1943.Jones, Keith, “Calculations of Stress from Strain inConcrete,” Engineering Monograph No. 25, Bureau ofReclamation, October 29,196l.R a p h a e l , J . M . , “ D e t e r m i n a t i o n o f S t r e s s f r o mMeasurements in Concrete Dams,” Quest ion No. 9 ,Report 54, Third Congress on Large Dams, ICOLD,Stockholm, Sweden, 1948,Roehm, L. H., and Jones, Keith, “Structural BehaviorAnalysis of Monticello Dam for the Period September1955 to September 1963,” Technical Memorandum No.622, with Appendixes I and II, Bureau of Reclamation,September 1964.Carlson, R. W., “Manual for the Use of Stress Meters,Strain Meters, and Joint Meters in Mass Concrete,” secondedi t ion , 1958, R. W. Carlson, 55 Maryland Avenue,Berkeley, Calif.

[lo] Raphael, J. M., “The Development of Stress m ShastaDam,“Trans. ASCE, vol. 118, pp. 289-321, 1953.

[ 111 Copen, M. D., and Richardson, J. T., “Comparison of theMeasured and the Computed Behavior of Monticello(Arch) Dam,” Question No. 29, Report 5, 8th Congresson Large Dams, ICOLD, Edinburgh, Scotland, 1964.

[12] R i c e , 0 . L . , “In Situ Testing of Foundation andAbutment Rock on Large Dams,” Quest ion No. 28,R e p o r t 5 , 8 t h C o n g r e s s o n L a r g e D a m s , ICOLD,Edinburgh, Scotland, 1964.

[ 131 Rouse, G. C., Richardson, J. T., and Misterek, D. L.,


“Measurement of Rock Deformations in Foundations onM a s s C o n c r e t e D a m s , ” A S T M S y m p o s i u m ,Instrumentation and Apparatus for Soil and Rock, 68thAnnual Meeting, Purdue University, 1965.

(141 Technical Bulletin Series, Bulletins 16 through 23,Terrametrics Division of Earth Sciences, Teledyne Co.,Golden, Colo., 1972.

[15 ] Technical Record of Design and Construction, “GlenCanyon Dam and Powerplant,” Bureau of Reclamation,pp. 117-138 and 449453, and p. 464, December 1970.

[ 161 Technical Record of Design and Construction, “FlamingGorge Dam and Powerplant,” Bureau of Reclamation,1968.

1171 Hickey, K. B., “Effect of Stress Level on Creep andCreep Recovery of Lean Mass Concre te ,” Repor tREC-OCE-69-6, Bureau of Reclamation, December 1969.

[18] “A Loading System for Compressive Creep Studies onConcrete Cylinders,” Concrete Laboratory Report No.C-1033, Bureau of Reclamation, June 1962.

[ 191 Best, C. H., Pirtz, D., and Polivka, M., “A LoadingSystem for Creep Studies of Concrete,” ASTM BulletinNo. 224, pp. 44-47, September 1957.

(201 “A IO-Year Study of Creep Properties of Concrete,”Concre te Labora tory Repor t No. SP-38 , Bureau ofReclamation. July 1953.

1211 Hickey, K. B., “Stress Studies of Carlson Stress Meters inC o n c r e t e . ” Reuort REC-ERC-71-19 . Bureau ofReclamation, Aprii1971.

[22] “Manual of Geodetic Triangulation,” Special PublicationNo. 247, Coast and Geodetic Survey, Department ofCommerce, Washington, D.C., 1950.

[23] “Manual of Geodetic Leveling,” Special Publication No.239, Coast and Geodet ic Survey, Depar tment ofCommerce, Washington, D.C., 1948.

[24] Design Criteria for Concrete Gravity and Arch Dams,”Engineering Monograph No. 19, Bureau of Reclamation,p. 3, December 1960.

[ 251 Reclamation Instruct ions, Par t 175, Reports ofConstruct ion and Structural Behavior (L-21 Report)Bureau of Reclamation, 1972.

[26] “Calculations of Deflections Obtained by Plumblines,”Electronic Computer Description No. C-114, Bureau ofReclamation, 1961.

[27] Roehm, L. H. , “Investigation of Temperature Stressesand Deflections in Flaming Gorge Dam,” TechnicalMemorandum 667, Bureau of Reclamation, 1967.

[28] “Twenty-Year Creep Test Resul ts on Shasta DamConcrete.” Laboratorv Report No. C-805A, Bureau ofReclamation, February 1962.

[29] “Properties of Mass Concrete in Bureau of ReclamationDams,” Labora tory Repor t No. C-1009, Bureau ofReclamation, December 196 1.

[30] Roehm, L. H. , “Deformation Measurements of FlamingGorge Dam,” Proc. ASCE, Journal of the Surveying andMapping Division, vol. 94, No. SUl, pp. 37-48, January1968.

(311 Richardson, J. T., “Measured Deformation Behavior ofGlen Canyon Dam,” Proc. A S C E , J o u r n a l o f t h eSurveying and Mapping Division, vol. 94, No. SU2, pp.149-168, September 1968.

<<Chapter XIV

Concrete Construct ion

14-l . General . -Concrete control andconcrete construction operations are of vitalconcern to the designer of a concrete structure.The ideal situation would be to have theengineer responsible for the design of astructure go to the site and personally supervisethe construction to assure its intendedperformance. Since this is not practicable, itfalls on the construction engineer and hisinspection staff, the design engineer’s closestcontact with the work, to assure that theconcrete meets the requirements of the design.

The safety of any structure is related tocertain design criteria which include factors ofsafety. Only when all concrete control andconstruction operations are of high quality willthe factors of safety be valid for the completedstructure. Whereas steel used for structures canbe tested for material requirements andstructural properties, with the full knowledgethat another piece of that same steel will reactin the same manner, concrete is mixed andplaced under varying conditions. Concrete isplaced in the structure knowing what it hasdone in the past under similar circumstances.From experience, we know what concrete cayldo. Time alone will tell if it will do this. A highassurance that it will can be obtained by theconcrete inspector by making certain that theconcrete is mixed and placed, and the structureis completed, in full compliance with thespecifications.

Appendix H covers those specificationsparagraphs relating to concrete that arenormally required for construction of concretedams.

14-2. Design Requirements. -Basically, ac oncrete structure must be capable of

performing its intended use for what may be anunknown but usually long period of time. Toserve its purpose, the concrete in the structuremust be of such strength and have suchphysical properties as are necessary to carry thedesign loads in a safe and efficient manner. Theconcrete throughout the structure must be ofuniform quality because a structure is only asstrong as its weakest part. The concrete mustbe durable and resistant to weathering,chemical attack, and erosion. The structuremust be relatively free of surface and structuralcracks. Because of increasing environmentaldemands, the final completed structure mustbe pleasing in appearance. And, last but notleast , t h e c o n s t r u c t i o n p r o c e s s e s a n dprocedures should reflect an economical designand use of materials, manpower, andconstruction effort.

A number of the above design requirementsare the responsibility of the designer. Theseinclude the determination of the configurationand dimensions of the structure, the sizes andpositioning of reinforcing bars, and the finishesnecessary to minimize erosion and cavitationon the surfaces of the structure. Additionaldesign requirements are determined from fieldinvestigations of the site conditions, includingsuch items as the type and condition of thef o u n d a t i o n f o r t h e s t r u c t u r e , a n d t h eavailability of sand and coarse aggregates.Other design requirements may be obtainedfrom concrete laboratory investigations on theconcrete mix, from hydraulic laboratory modelstudies, and from environmental studies on thedesired appearance of the structure. Thefulfillment of all design requirements isdependent upon actual construction processes

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and procedures. A continuing effort musttherefore be made by all inspection personnelto assure the satisfactory construction of thedesired structure.

Aggregates for use in concrete should be ofgood quality and reasonably well graded.Usually, an aggregate source has been selecteda n d t e s t e d d u r i n g p r e c o n s t r u c t i o ninvestigations. Also, in some cases, concretemix design studies have been made as part ofthe preconstruction investigations using theaggregates from the deposit concerned. Whengood quality natural sand and coarse aggregateare available, use of crushed sand and/or coarseaggregate is generally limited to that needed tomake up deficiencies in the natural materials,as crushing generally increases the cost of theaggregates and resulting concrete. In theseinstances, crushing is usually restricted tocrushing of oversize materials and/or the excessof any of the individual sizes of coarseaggregate. Where little or no natural coarseaggregate is available in a deposit, it may benecessary to use crushed coarse aggregate froma good quality quarry rock.

14-3. Composition of Concrete.-Theconcrete for a specific concrete structure isproportioned to obtain a given strength anddurability. Concrete with a higher strengththan required could be designed by addingmore cement, and perhaps admixtures, but thishigher strength concrete is not desirable fromthe standpoint of economy of design. In coldclimates, where frequent cycles of freezing andthawing often occur, it may be advantageous touse a special mix for the face concrete of thedam to assure adequate durability. A highercement content and lower water to portlandcement ratio, or when the mix containspozzolan a lower water to portland cementplus pozzolan ratio, is often used in these outerportions of the dam. On the larger and moreimportant Bureau of Reclamation structures,trial mixes are made in the laboratories at theEngineering and Research Center not only toobtain an economical and workable mix but toassure that the required strength and durabilitycan be ob t a ined w i th t he cemen t andaggregates proposed for the construction.

Adjustments in the field are sometimes


necessary to obtain a workable mix. These maybe occasioned by variations in aggregatecharacteristics w i t h i n t h e d e p o s i t beingworked, or by a change in the characteristics ofthe cement being used.

The amount of cement to be used per cubicyard of concrete is determined by mixinvestigations which are primarily directedtoward obtaining the desired strength anddurability of the concrete. The type of cement,however, may be determined by other designconsiderations.

Considerable bad experience has beenencountered where alkali reactive aggregatesare used in concrete. Where field andlaboratory investigations of aggregate sourcesindicate that alkali reactive aggregates will beencountered, a low-alkali cement is normallyr e q u i r e d t o p r o t e c t a g a i n s t d i s r u p t i v eexpansion of the concrete which may occurdue to alkali-aggregate reaction (a chemicalreaction between alkalies in the cement and thereactive aggregates) . Ano the r means o fcontrolling alkali-reactive aggregates is by useof a suitable fly ash or natural pozzolan. If ahighly reactive aggregate is to be used, it maybe necessary to use both low-alkali cement anda pozzolan.

Another design consideration is the type ofcement to be used. Type II cement is normallyused by the Bureau of Reclamation in massconcrete dams. Limitations on the heat ofhydration of this cement are specified whendetermined necessary to minimize cracking inthe concrete structure. Use of a type II cementwill generally reduce the heat of hydration toan acceptable level, particularly since type IIcement is usually used in conjunction withother methods of heat reduction. These includeuse of lower cement contents, inclusion of apozzolan as part of the cementitious material,use of a pipe cooling system, and use of aspecified maximum placing temperature of theconcrete, which may be as low as 50’ F. Use ofall or some of these methods will usuallyreduce or eliminate the need for stringentlimitations on the heat of hydration of thecement. However, a limitation of 58 percent onthe tricalcium aluminate plus tricalcium silicate(CBA + C3 S) content of the type II cement

CONCRETE CONSTRUCTION-Sec. 14-4

may be required where heat of hydration ofcement must be kept low. Further limitationon the heat of hydration, if more stringentcontrol of heat is needed, can be obtained witha type II cement by providing a maximumlimitation on the cement of 70 calories pergram at 7 days or 80 calories per gram at 28days, or both.

If the above measures are insufficient, use oftype IV cement, an extremely low heat ofhydration cement, may be specified. This typeof cement, referred to as low-heat cement, wasdeveloped many years ago for mass concretewhen thick, very massive, high-cement-contentconcrete dams were being built. Maximumlimitations on heat of hydration of type IVcement are 60 calories per gram at 7 days and70 calories per gram at 28 days. The amountand type of cement used must be compatiblewith strength, durability, and temperaturerequirements.

Admixtures are incorporated into the mixd e s i g n a s n e e d e d t o o b t a i n e c o n o m y ,workability, or certain other desired objectivessuch as permitting placement over extendedperiods of time. Admixtures have varyingeffects on concretes, and should be employedonly after a thorough evaluation of theireffects. Most commonly used admixtures area c c e l e r a t o r s ; a i r - en t r a in ing a g e n t s ;water-reducing, set-controlling admixturesNW; and pozzolans. Calcium chlorideshould not be used as an accelerator wherea luminum o r g a l v a n i z e d m e t a l w o r k i sembedded. When accelerators are used, addedcare will be necessary to prevent cold jointsdur ing c o n c r e t e placing o p e r a t i o n s .Air-entraining agents should be used to increasethe durability of the concrete, especially if thestructure will be exposed to cycles of freezingand thawing. Use of a WRA will expedite theplacing of concrete under difficult conditions,such as for large concrete placements in hotweather. Also, use of a WRA will aid inachieving economy by producing higherstrengths with a given cement content.

Good quality pozzolans can be used as areplacement for cement in the concretewithout sacrificing later-age strength. Pozzolanis generally less expensive than cement andwill, as previously indicated, aid in reducing

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heat of hydration. Since the properties ofpozzolans vary widely, if a pozzolan is to beused in a concrete dam it is necessary to obtainone that will not introduce adverse qualitiesinto the concrete. Pozzolan, if used in faceconcrete of the dam, must provide adequatedurability to the exposed surfaces. Concretecontaining pozzolan requires thorough curingto assure good resistance to freezing andthawing.

The water used in the concrete mix shouldbe reasonably free of silt, organic matter,alkali, salts, and other impurities. Watercontaining objectionable amounts of chloridesor sulfates is particularly undesirable, becausethese salts prevent the full development of thedesired strength.

14-4. Batching and Mixing. -Inherently,concrete is not a homogeneous material. Anapproach to a “homogeneous” concrete ismade by careful and constant control ofbatching and mixing operations which willresult in a concrete of uniform qualitythroughout the structure. Because of its effecton strength, the amount of water in the mixmust be carefully controlled. This controlshould start in the stockpiles of aggregatewhere an effort must be made to obtain auniform and stable moisture content. Watershould be added to the mix by some methodwhich will assure that the correct amount ofwater is added to each batch.

Close control of the mixing operation isrequired to obtain the desired uniform mix.Sand, rock, and cement pockets will result in astructure weaker in some sections than inothers. A nonuniform concrete mix will alsoresult in stress concentrations which cause aredistribution of stresses within the structure.These redistributed stresses may or may not bedetrimental depending on where the stressesoccur.

Segregation of sand and coarse aggregatescan also result in surface defects such as rockpockets, surface scaling and crazing, and sandstreaks. These are not only unsightly but arethe beginning of surface deterioration instructures subjected to severe weathering.

14-S. Preparations for Placing.-Theintegrity of a concrete structure is dependentto a large extent on the proper preparation of


construction joints before placing freshconcrete upon the construction joint surfaces.Bond is desired between the old and newconcretes and every effort must be directedtoward obtaining this bond. All laitance andinferior surface concrete must be removedfrom the old surface with air and water jets andwet sandblasting as necessary. All surfacesshould be washed thoroughly prior to placingthe new concrete, but should be surface dry atthe time they are covered with the freshconcrete. Rock surfaces to be covered withconcrete must be sound and free of loosematerial and should also be saturated, butsurface dry, when covered with fresh concreteor mortar. Mortar should be placed only onthose rock surfaces which are highly porous orare horizontal or nearly horizontal absorptivesurfaces.

14-6. Placing. -Mass concrete placement canresult in a nonuniform concrete when theconcrete is dropped too great a distance or inthe wrong manner. The same effect will occurwhen vibrators are used to move the concreteinto its final position. All discharge andsucceeding handling methods should thereforebe carefully watched to see that the uniformityobtained in mixing will not be destroyed byseparation.

Thorough vibration and revibration isnecessary to obtain the dense concrete desiredfor structures. Mass concrete is usually placedin 5 or X-foot lifts and each of these lifts ismade up of 18- to 20-inch layers. Eachsuccessive layer must be placed while the nextlower layer is still plastic. The vibrators mustpenetrate through each layer and revibrate theconcrete in the upper portion of the underlyinglayer to obtain a dense monolithic concretethroughout the lift. Such a procedure will alsoprevent cold joints within the placement lift.

14-7. Curing and Protection.-One of themajor causes of variation in attained concretestrength is t h e l a c k o f p r o p e r c u r i n g .Laboratory tests show that strength of poorlycured concrete can be as much as one-third lessthan that of well-cured concrete. This varianceis more for some cements than for others.Curing of concrete is therefore important if

high quality is to be obtained. The fulleffectiveness of water curing requires that it bea continuous, not intermittent, operation.Curing compounds, if used, must be applied assoon as the forms are stripped, and must beapplied to completely cover all exposedsurfaces.

Poor curing often results in the formation ofsurface cracking. These cracks affect thedurability of the structure by permittingweathering and freeze-thaw actions to causedeterioration of the surface. The largerstructural cracks often begin with the crackscaused by poor curing.

Protection of the newly placed concreteagainst freezing is important to the designer,since inadequate protective measures will bereflected by lower strength and durability ofthe concrete. Protective measures includeaddition of calcium chloride to the mix andmaintaining a minimum 40’ F. placementtemperature. Although calcium chloride in aquantity of not to exceed 1 percent, by weightof cement, is normally required when weatherconditions in the area of the work will permit adrop in temperature to freezing, its use shouldnot preclude the application of more positivemeans to assure that early age concrete will notfreeze. When freezing temperatures may occur,enclosures and surface insulation should also berequired. One of the most important factorsassociated with protection of concrete isadvance preparation for the placement ofconcrete in cold weather. Arrangements forcovering, insulating, or o.therwise protectingnewly placed concrete must be made inadvance of placement and should be adequateto maintain the temperature and moistureconditions recommended for good curing.

14-8. Finishes and Finishing. -Suitablefinishing of concrete surfaces is of particularconcern to the designer. Some surfaces ofconcrete, because of their intended function,can be rough and of varying texture andevenness; whereas, others in varying degreem u s t b e s m o o t h a n d u n i f o r m , s o m enecessitating stringent allowable irregularitylimits. The Bureau of Reclamation uses aletter-number system to differentiate between

CONCRETE CONSTRUCTION-Sec. 14-9

the different types of finishes, using F 1, F2,F3, and F4 for formed surfaces and Ul, U2,and U3 for unformed surfaces. Each finish isdefined as to allowable abrupt and gradualirregularities. F o r f o r m e d s u r f a c e s , t h eparticular forming materials permitted are alsorelated to the letter-number system.

Finish Fl applies to formed surfaces thatwill be covered by fill material or concrete,which includes vertical construction andcontraction joints, and upstream faces of massconcrete dams that are below the minimumwater pool. Finish F2 applies to formedsurfaces that will be permanently exposed toview but which do not require any specialarchitectural appearance or treatment, orwhich do not involve surfaces that are subjectto high-velocity waterflow. Finish F3 is usedfor formed surfaces for which, because ofprominent exposure to public view, an aestheticappearance from an architectural standpoint isconsidered desirable. Finish F4 is for formedflow surfaces of hydraulic structures whereaccurate alinement and evenness of surfaces arerequired to eliminate destructive effects ofhigh-velocity water.

Finish Ul applies to unformed surfaces thatwill be covered by fill material or concrete.This is a screeded surface where considerableroughness can be tolerated. Screeding of anunformed surface i s p r e l i m i n a r y t o t h eapplication of a U2 finish. The U2 finish is awood-floated finish. This finish applies to allexposed unformed surfaces, and is apreliminary to applying a U3 finish, whichrequires steel troweling. A U3 finish is requiredon high-velocity flow surfaces of spillwaytunnels and elsewhere where a steel-troweledsurface is considered desirable.

When finishing the surfaces of newly placedconcrete, overtroweling is to be avoided in allinstances. Surfaces which are overtroweled aresusceptible to weathering and erosion andusually result in a requirement for early repairmeasures on the structure.

14-9. Tolerances. -The prescribed toleranceson all structures should be maintained at alltimes. Some of these tolerances are placed inthe specifications to control the overallconstruction and are necessary if the structure

28.5

i s t o b e c o m p l e t e d a s d e s i g n e d . S o m etolerances are for appearances and others are tominimize future maintenance of the structure.For example, near-horizontal surfaces withvery slight slopes are hard to finish withoutleaving depressions in the surface. Thesedepressions collect moisture and usually beginweathering at an early age.

14- 10. Repair of Concrete. -Repair ofconcrete covers not only the patching of holesremaining after construction operations butalso the repair of cracks and damaged concrete.Repair of concrete in Bureau of Reclamationstructures is required to conform to theBureau’s “Standard Specifications for Repairof Concrete.” These specifications generallyprovide for concrete to be repaired withconcrete, dry pack or portland cement mortar,or, at the option of the contractor, withepoxy-bonded concrete or epoxy-bondedepoxy mortar, where and as permitted by thespecifications for the particular repair to bemade. Repairs to high-velocity flow surfaces ofconcrete in hydraulic structures are required tob e m a d e with concrete, epoxy-bondedconcrete, or epoxy-bonded epoxy mortar.Concrete is used for areas of extensive repairwh ich exceed 6 i nches i n dep th , wh i l eepoxy-bonded concrete is used for areas havingdepths of 1% to 6 inches. Epoxy-bonded epoxymortar is used for shallow surface repairs fordepths ranging from 1% inches to featheredges.

Before making any repair, all deterioratedand defective concrete must be removed.Unsound or questionable concrete may negatethe successful repair of any concrete. Removalof the defective concrete should be followedby a thorough washing of the surfaces. Asurface-dry condition should exist at the timereplacement concrete is placed.

Cracks should not be repaired until allevidences indicate that the crack has stablized.The cause of the crack should also beinvestigated and, if possible, correctivemeasures initiated so that the crack will notreopen. All repairs should be thoroughly curedto minimize drying shrinkage in the repairconcrete. Except where repairs are made withepoxy-bonded epoxy mortar, featheredgesshould be avoided in all repair of concrete.

<<Chapter XV

E c o l o g i c a l a n d E n v i r o n m e n t a l C o n s i d e r a t i o n s

A. INTRODUCTION

15-l. General Considerations. -The rapidincrease in world population and the increasingdemands this population has made on theplanet’s natural resources have called intoquestion the long-term effect of man upon hisenvironment. The realization that man is anintegral part of nature, and that his interactionwith the fragile ecological systems whichsurround him is of paramount importance toh i s c o n t i n u e d s u r v i v a l , i s p r o m p t i n g areevaluation of the functional relationshipsthat exist between the environment, itsecology, and man.

Of increasing concern is the effect whichman’s structures have upon the ecosystems inwhich they are placed, and especially on thefish, wildlife, and human inhabitants adjacentto these structures. The need to store water foruse through periods of drought, to supplyindustry and agriculture wi th wa te r fo rmaterial goods and foodstuffs, to providerecreational opportunity in ever-increasingamounts, and to meet the skyrocketing electricpower demand has required the developmentof water resources projects involving theconstruction and use of dams and other relatedstructures. These structures help man and yetat the same time cause problems in theenvironment and in the ecosystems into whichthey are placed. Many of these problems areexceedingly complex, and few answers whichencompass the total effect of a structure on itsenvironment are readily available.

Included in the answer to these problemsmust be the development and protection of aquality environment which serves both the

demands of nature for ecological balance andthe demands of man for social andpsychological balance. The present challenge isto develop and implement new methods ofdesign and construction which minimizeenvironmental disturbances, while also creatingaesthetic and culturally pleasing conditionsunder which man can develop his mostdesirable potentialities. This challenge can onlybe answered by the reasoned, pragmaticapproach of sensitive, knowledgeable humanbeings.

The purpose of this chapter is to providepractical s o l u t i o n s t o s o m e o f t h eenvironmental and ecological problems whichconfront the designer. This discussion is notexhaustive and it is hoped that the reader willconsult the references at the end of thischapter (and numerous others available on thistopic) for a more extensive coverage. Theamount of scientific data concerning theenvironment and man’s relation to it isexpanding rapidly, and new design methodsshould become available soon. The practicalinformation presented here can provide auseful introduction to the designer and a basisfor maximizing the project’s benefits andminimizing its negative environmental andecological effects.

Recognizing the importance of man’senvironment, the 9 1st Congress passed theNational Environmental Policy Act of 1969.This act established a three-member Council onEnvironmental Quality in the Executive Officeof the President. Before beginning constructiono f a p r o j e c t , an Environmental Impact

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Statement must be prepared by the agencyhaving jurisdiction over project planning ands u b m i t t e d t h r o u g h p r o p e r channels toa p p r o p r i a t e g o v e r n m e n t a l agencies andinterested private entities for review andcomments.

The term environment is meant here toinclude the earth resources of land, water, air,and vegetation and manmade structures whichsurround or are directly related to theproposed structure, The term ecology is meantto encompass the pattern of relationships thatexist between organisms (plant, animal, andhuman) and their environment.

15-2. Planning Operations. -One of themost important aspects of dealing correctlyand completely with the ecological andenvironmental impact of any structure isproper planning. If possible, an environmentalt e a m s h o u l d b e f o r m e d c o n s i s t i n g o frepresentatives from groups who will beaffected by the structure and experts fromvarious scientific fields who can contributetheir ideas and experience. The team approachw i l l h e l p assure tha t env i ronmen ta l


considerations are placed in proper perspectivewith other vital issues such as reliability, cost,and safety, and that the relative advantages anddisadvantages of each proposal are carefullyweighed. It should also assure that the projectis compatible with the natural environment. Asuggested list of participants is given below:

( 1 ) C o n c e r n e d l o c a l a n d c o m m u n i t yofficials.

(2) Design personnel.(3) Environment and ecology experts.(4) Fish biologists and wildlife experts.(5) Building architects.(6) Landscape architects.(7) Recreational consultants.This team should be responsible for the

submittal of an ecological and environmentalreport to the designers with a list of criteriawhich the designs should encompass. Some ofthe topics which should be discussed in thereport are covered briefly in this chapter. Sinceeach site will present unique problems, only ageneral outline o f t he mos t impor t an tconsiderations is provided herein.

B. FISH AND WILDLIFE CONSIDERATIONS

15-3. General.-The placement of a dam andits reservoir within the environment should bedone with due consideration to the effects onthe fish and wildlife populations of the specificarea. These considerations often involvecomplex problems of feeding patterns andmobility, and where possible an expert in thisfield should be consulted. The Fish andWildlife Service of the Department of theInterior, the Forest Service of the Departmentof Agriculture, and appropriate State agenciescan supply considerable expertise on theenvironmental impact of a proposed structure.It should be remembered that dams andreservoirs can be highly advantageous in thatthey provide a year-round supply of drinkingwater for wildlife, breeding grounds forwaterfowl, and spawning areas for fish. At thetime of design, as many benefits as practicableto fish, wildlife, and waterfowl populations

should be included and provisions should bemade for the future protection of thesepopulations. The following sections discusssome of the items which affect fish and wildlifeand outline what can be done to aid them.

15-4. Ecological and EnvironmentalConsiderations for Fish. -Critically importantto the survival of fish population are threei t e m s : (1) w a t e r q u a l i t y , ( 2 ) w a t e rtemperature, and (3) mobility. Water quality isobviously important to the survival of fish, andan effort should be made to see that thequantity of pollutants which enter the streamduring construction and the reservoir aftercompletion is kept to the minimum. Strictregulations concerning pollutants should bei n s t i t u t e d and enforced. Quantities ofdegradable, soluble, or toxic pollutants shouldnot be left within the reservoir area afterconstruction. Heavy pesticide runoffs can cause

ECOLOGICAL CONSIDERATIONS-Sec. 15-4

fish kills, and some means such as a holdingpond or contour ditches should be used toreduce their presence and steps taken toeventually eliminate them. Substances that cancloud or darken the water interfere with theability of sight-feeding fish to forage, andshould not be allowed to enter the water.

In mining areas where heavy erosion oftenoccurs, careful consideration must be given tothe effects of siltation which may rapidlyreduce the reservoir capacity. Considerationmust also be given to the acidic character ofthe water since it can cause fish kills. Controldams may be the solution, and in one case theBureau of Reclamation has constructed ano f f - r e s e r v o i r d a m t o r e d u c e t h e r a p i dsedimentation of the main reservoir and tolimit the amount of acidic inflow to anacceptable level.

The temperature of the water controlstiming of migration, breeding, and hatchingand affects the appetite, growth, rate ofheartbeat, and oxygen requirements of all fish.Each species of fish has an optimumtemperature range within which it can survive,and consideration must be given to thetemperature range which will exist both in thereservoir and in the stream below the dam dueto the resefioir releases. For example, if a lowdam is constructed in a mountainous area, thecool water entering the shallow reservoir can bewarmed by the sun during the summer monthsto an undesirable extent. T h e w a r mtemperatures of the shallow water within thelake and also of the downstream releases couldthen prevent the spawning of cold waterspecies of fish such as trout.

To remedy this problem, care must be takento provide sufficiently deep reservoir areaswhere cold water will remain, and to use anoutlet works which is capable of selectivelywithdrawing the colder water from the lowerreservoir depths. Federal and State fish andwildlife agencies should be consulted as to thecorrect depth for the outlets in a specific area.Figure 15-l shows the selective withdrawaloutlet works to be used at Pueblo Dam inColorado. Figure 15-2 shows a selectivewithdrawal outlet works used at Folsom Damin California. Movable shutters were placed

289

Trashracks.seats.ondqmdes notshorn\

8P L A N - F I S H H A T C H E R Y O U T L E T W O R K S

. . ..-IS E C T I O N A - A

Figure 15-I. Selective withdrawal outlet at Pueblo Damin Colorado. Water can be withdrawn at any of fourlevels.-288-D-3104

upstream from the trashracks. By manipulationof the shutters water may be drawn from thedesired level. The Bureau of Reclamation hasused selective withdrawal outlet works ats e v e r a l l o c a t i o n s t o c r e a t e f a v o r a b l etemperatures for fish spawning downstream ofthe dam. Further information concerning thesestructures is available in references [ 1 I and[2] .l Another reason for providing adequatereservoir depth, in addition to creatingfavorable conditions for spawning, is to preventfish kill in the winter due to extreme cold.However, shallow reservoir areas are sometimesrequired to develop a warm water fishery or forwaterfowl habitats.

Although salmon are commonly thought ofas the only migrators, other species of fish such

‘Numbers in brackets refer to items in the bibliography,section 15-l 2.

290

, A ,--TOP Of oaraoet


tack trashrockS

UPSTREAM ELEVATION

HALF SECTION A-A

Max w s El 475 IDeck EI 18050

- superstructure

SHUTTERS ON TRASHRACK

SHGTTiRS DOWN SHCiTTERSUP

Figure 15-2. Selective withdrawal outlet at Folsom Damin California. This outlet makes use of an adjustableshutter arrangement.-288-D-3105

as shad, steelhead trout, and other trout alsorequire mobility considerations. The mostcommon method for allowing fish to pass by adam is use of the fish ladder. Figure 15-3 showsthe fish ladder used by the Bureau ofReclamation on the Red Bluff Diversion Damin California. Specific design requirements forfish ladders may be obtained from the ForestService, the Fish and Wildlife Service, orappropriate State agencies. Where practicable,fish should be prohibited from enteringspillways, outlet pipes, penstocks, and otherrestricted areas by use of fish screens.

Where fish populations are concerned, careshould be taken to avoid the destruction ofvegetation in the reservoir area since thisbecomes a food source after the reservoir isfilled. Certain amounts of standing trees or treedebris left in the reservoir area can provide ahabitat for several species of fish as can brush

Figure 15-3. Fish ladder used on the left abutment ofR e d B l u f f D i v e r s i o n D a m i nCalifornia.-P602-200-4543 NA

piles, which are staked down to prevent themfrom being washed away, Figure 15-4 shows areservoir in which trees have been left standingto benefit the fish population.

Although certain aquatic plants are desirablefor water birds, such as ducks, coots, andwading birds, they can be detrimental to fishproduction and should be controlled whennecessary. Shallow shorelines in the inletportions of the reservoir can be deepened toeliminate the growth of any plant life foundnot useful.

I n n e w l y c o n s t r u c t e d r e s e r v o i r s ,arrangements should be made for stocking witht h e a p p r o p r i a t e t y p e o r t y p e s o f f i s h .Consultation with a fisheries expert isrecommended to determine the correct type offish and the proper time for stocking them.

The oxygen content of some reservoirs candecrease with time and an examination ofavailable reservoir reaeration devices may provehelpful. The oxygen content of the reservoirwater may be increased during release from thereservoir by the use of reaeration devices suchas the U-tube [ 31. Reaeration is also aided byincreasing the contact of the water released inthe spillways and outlet works with air. A

ECOLOGICAL CONSIDERATIONS-Sec. 15-5 291

Figure 15-4. An aerial view of a small reservoir with trees left at the water’s edge to provide a fishhabitat.-288-D-2869

bibliography of reaeration devices compiled by feeding areas, (2) loss of habitat, and (3)the Bureau of Reclamation is contained in limitation of mobility. The severity of each ofreference [4] . these effects can be significantly reduced.

In some cases, fish hatcheries can be built inconjunction with the dam. Figure 15-5 showsthe hatchery below Nimbus Dam in California.Canals also may provide spawning areas forfish, although considerable cost and specialequipment may be required. Figure 15-6 showsan artist’s conception of the “grave1 cleaner”which will be provided at a salmon spawningarea in the Tehama-Colusa Canal in California.Special gravel and special gravel sizes wererequired in the canal bottom to facilitatespawning.

15 -5. Environmental Considerations forWildlife. -Three common detrimental effects ofreservoirs on wildlife involve: (1) removal of

When reservoirs inundate wildlife feedingareas, new areas should be planted to lessen theimpact and, if possible, new types of grasseswhich are suitable and which provide morefood per unit area should be planted. Inaddition, the new feeding areas can sometimesbe irrigated with reservoir water to cause rapid,heavy growth. If the reservoir water is notimmediately needed for irrigation, the waterlevel can be left below the normal watersurface to allow sufficient time for the feedingareas which are to be flooded to be replaced byareas of new growth.

Where flooding of the homes of a largenumber of smaller animals such as muskrat and


Figure 15.5. Fish hatchery at Nimbus Dam in California.-AR2964-W

Figure 15-6. An art i s t ’ s concept ion of the grave lcleaner to be used at a salmon spawning area ont h e T e h a m a - C o l u s a C a n a l i nCalifornia.-P602-D54534-520

beaver will occur, consideration should begiven to adjusting the required excavation,reducing the reservoir water levels, orrelocating the dam so that the number ofanimals affected will be minimized. It may alsobe possible to provide special dikes anddrainage conditions which can lessen the effect.Problems in this area are difficult to solve andthe advice of a specialist should be sought.

Provisions for ducks, geese, and otherwaterfowl at reservoirs can be made byplanting vegetation beneficial to nesting and byleaving areas of dense grass and weeds at thewater’s edge. If suitable areas already exist atthe damsite, an effort should be made toselectively excavate to leave the habitat inplace. Assistance concerning the appropriatereservoir treatment can be obtained from theFish and Wildlife Service of the Department ofthe Interior, the Forest Service of theDepartment of Agriculture, and appropriateState agencies.

ECOLOGICAL CONSIDERATIONS-Sec. 15-6

C. RECREATIONAL CONSIDERATIONS

293

15-6. General. -The nation’s increase inpopulation, the decrease in working hours, andthe great mobility of large numbers of peoplehave caused a significant increase in the use ofreservoirs for recreational activities. Theseactivities include fishing, boating, water skiing,swimming, scuba diving, camping, picnicking,a n d j u s t s i m p l y e n j o y i n g t h e o u t d o o rexperience of the reservoir setting. Many of thereservoirs constructed in past years havebecome the recreation centers of the present,and this will undoubtedly be repeated in thefuture. Provisions should be made to obtain themaximum recreational benefits from thecompleted reservoir, and a future developmentplan should provide for area modifications asthe recreation use increases.

15 - 7 . Recreational Development. -Considerations for recreational developmentshould start when project planning is begunand should be integrated into the total siteplan. Areas of significant natural beauty shouldbe left intact if possible, and recreationalfacilities should be developed around them.Boat ramps and boat docking facilities arebeneficial to-most reservoir areas and should beconstructed at the same time as the dam.Figure 15-7 shows the docking facilities at theBureau of Reclamation’s Canyon FerryReservoir in Montana. Camping facilities fortruck campers, trailers, and tenters, andpicnicking areas can often be provided atreasonably low costs.

Trash facil i t ies should be provided atconvenient locations to help in litter control,and the excessive use of signs and billboardsnear the reservoir area should be prohibited.The signs which are used should be blendedwith the surroundings. Toilet facilities shouldbe available at all camping grounds and propersewage disposal facilities should be installed,

especially where the possibility of reservoirpollution exists.

If the reservoir is near a population center itmay prove advantageous to provide bicyclepaths, equestrian paths, and foot paths forpublic use. At the damsite or nearby, areservoir viewing location and possibly avisitors’ center should be built . Exhibitsshowing the history of the project, localhistory, or other appropriate exhibits cane n h a n c e t h e v i s i t o r s ’ e n j o y m e n t o f t h ereservoir. These centers should be aestheticallydesigned to fit the location. Figure 15-8shows a viewing area at Glen Canyon Dam.

Buildings adjacent to the reservoir should beof low profile and blend with the reservoirsurroundings; however, in some cases it may bedesirable to contrast the buildings with theirsurroundings.

Fishing benefits can be maximized bystocking the reservoir with several types of fishand by replenishing these stocks yearly.

Proper maintenance requirements for therecreation areas should be instituted aftercompletion of the dam and reservoir complex,and should include repair of broken anddamaged equipment, repainting, and rebuildingto meet expanded facility demands. Trashshould be removed from the campgrounds anda d j a c e n t recreation facil i t ies at regularintervals, and the possibility of recyclingaluminum and other metal products should beexplored. Recreational areas which areoverused should be rotated to prevent theirdeterioration, and single areas which receiveexceptionally heavy use should be fenced offcompletely for short intervals to prevent theirruination. Protection of the reservoir banksfrom sloughing may be required for steepslopes, and excessive erosion at any part of thesite should be prevented.


15-8. General. -Design requirements should goals: (1) keeping the natural beauty of thebe devoted to the accomplishment of three su r round ing area intact, (2) creating


Figure 15 7. Boat docking facilities at Canyon Ferry Reservoir in Montana.-P296-600-949

aesthetically satisfying structures andl a n d s c a p e s , a n d ( 3 ) c a u s i n g m i n i m a ldisturbance to the area ecology. Designersshould try to accomplish these goals in them o s t e c o n o m i c a l way. The followingparagraphs discuss some items to be consideredduring design and will provide some practicalsuggestions for designers. Many of the itemsdiscussed here should be considered during theproject planning stages and the criticaldecisions made at that time.

If it is necessary to excavate rock abutmentsabove the crest of the dam, considerationshould be given to the use of presplittingtechniques since they leave clean, aestheticsurfaces. As discussed in sections 15-6 and15-7, a scenic overlook should be provided forviewing the dam and reservoir. The overlooks h o u l d h a v e a d e q u a t e p a r k i n g a n d , i fpracticable, a visitors’ center.

The diversion schemes (see ch. V), should be

such that excessive silt created duringconstruction will not find its way into thedownstream water. Materials from excavationsshould be placed in the reservoir area upstreamof the dam to prevent unsightly waste areas inthe downstream approaches. In some cases,boat ramps, picnic areas, or view locations canbe constructed with excavated material. Wherefoundation conditions permit it , spillwaystructures of a type which minimizes therequired surface excavations on the damabutments should be used. (See ch. IX.)

If a section of canal is constructed inconnection with a dam, spoil piles should beshaped to the natural landscape slopes alongthe canal length; this material can also be usedt o c o n s t r u c t r e c r e a t i o n areas whereappropriate. Pipelines should be buried asshould electrical wiring; where this is notpossible, the pipelines and electrical apparatuss h o u l d b e p a i n t e d t o b l e n d w i t h t h e i r


Figure 1.5-8. Viewing area at Glen Canyon Dam in Arizona.-P557400-1133

background. Protective railings used on the made to util ize or preserve them, anddam crest and on bridges near the site should additional right-of-way should be obtained tobe low enough so that the reservoir may be include any such adjacent areas.seen from a passenger car. Access roads to the damsite and roads used

15-9. Landscape Considerations. -As much by the contractor during construction shouldnatural vegetation as possible should be left in be kept to a minimum, and those roads notplace. If significant areas of natural beauty planned for use after completion of the damexist near the project, every effort should be

296

should be obliterated and replanted with grassor other natural vegetation. Access roadssubject to excessive erosion should haveprotective surfacing. Roads which are requiredfor maintenance of the dam or appurtenantworks should be protectively fenced ifexcessive visitor usage will cause erosion.

Erosion control should be started at thebeginning of the job. Roads and cut slopesshould be provided with terraces, berms, orother check structures if excessive erosion islikely. Exploratory trenches which are adjacentto the damsite should be refilled and reseeded.

Quarry operations and rock excavationsshould be performed with care. The minimumamount of material should be removed, correctblasting techniques should be used, unsightlywaste areas should not be left, and final rockslopes for the completed excavation should beshaped to have a pleasing appearance.Presplitting and/or controlled blasting shouldbe considered for final slope cutting to permita clean, pleasing view.

Road relocations near the dam can ofteneliminate deep cuts in hillsides, allow scenicalinements, and provide reservoir viewinglocations. Adequate road drainage should beused and slopes should be cut so that reseedingoperations will be convenient. For projectswhere power transmission lines will be requiredthe publications “Environmental Criteria forElectric Transmission Systems” [ 51 and“Environmental Considerations in Design ofTransmission Lines” [61 will provide manyhelpful suggestions which will lessen theirenvironmental impact.

1 S-10. Protective Considerations.-Atlocations where accidents are most likely tooccur, protective devices and warning systemsshould be installed. The most dangerouslocations at a damsite are near the spillway(especially if it is a chute type), the outletworks intake tower, and the stilling basins ofboth the spillway and outlet works. Anyportion of the spillway and outlet worksstilling basins which might prove hazardousshould be fenced off and marked by warningsigns.

Canals with steep side slopes which prevent aperson or an animal from climbing out are


extremely dangerous, as also are siphons.Considerable information concerning canalsafety is contained in the Bureau’s publication“Reducing Hazards to People and Animals onReclamation Canals”[ 71 .

W h e n t h e p r o j e c t e n c o m p a s s e s t h egeneration of electricity, the problems ofproviding adequate safety precautions areconsiderably increased and the advice of anexpert in that field should be sought.

15 - 11. Construction Considerations. -Thee n v i r o n m e n t a l a n d ecological designrequirements presented in the specifications areconverted from an abstraction into a reality bythe builder. The contractor and his personnelshould be informed that this is a mostimportant step in the planning, design, andconstruction sequence. In this regard, apreconstruction conference may be invaluablein assuring an understanding of the jobrequirements by the builder and in enlisting hiscooperation. T h e o w n e r should insurecompliance by having competent inspectorsand by having specifications which clearly spellout the construction requirements. Excessiveair and water pollution during constructionshould be prevented, and specificationscovering these items are included in appendix I;they should provide a framework for theinclusion of other important environmentalprovisions. The builder should also institutesafety precautions during construction, and thepublication “Safety and Health Regulations forConstruction” [ 81 will provide helpfulinformation. The builder should be encouragedto bring forward any obvious defects in theenv i ronmen ta l considerations which heencounters during construction and to suggestimprovements.

Construction campsites should be placedwithin the reservoir area below normal waterlevel. All trees, shrubs, and grassland areaswhich are to be protected should be staked orroped off. Any operations which would affecta large wildlife population should be moved toa different location if at all possible. Largevolumes of water should not be taken from thes t r e a m i f t he re are prior downstreamcommitments, and the water going downstreamshould be muddied as little as possible and kept


pollution free; siltation ponds may be neededin extreme cases. The builder should berequired to remove or bury all trash and debriscollected during the construction period and toremove all temporary buildings. Everyopportunity should be taken to use the timberin the reservoir area for commercial operations.The burning of trees cleared within thereservoir area should be prevented if excessiveair pollution will result or if State laws preventit. At Pueblo Dam in Colorado, the Bureaurequired that all brush and timber smaller than7 inches in diameter be chipped into mulch andstockpiled for future use on the reseeded areas.The chipping operation at Pueblo Dam isshown in figure 15-9. Slightly larger timber canbe cut into firewood for use at camping andrecreation areas, and still larger timber can bechanneled into some commercial use such asproduction of lumber, wallboard, or boxes.

A temporary viewing site for the project,having signs which show the completed projectand explain its purpose, is helpful in promotinggood community relations.

[II

f21

131

[41

[51

161

[71

Figure 15-9. Chipping operations at Pueblo Dam inColorado. All brush and timber smaller than 7 inchesin diameter are chipped and stored for use as a mulchon reseeded areas.-P382-700-790 NA

E. BIBLIOGRAPHY

15-12. Bibliography.“Register of Selective Withdrawal Works in UnitedStates,” Task Committee on Outlet Works, Committee onHydraulic Structures, Journal of the Hydraulics Division,ASCE, vo l . 96 , No . HY9, Sep tember 1970 , pp .1841-1872.Austin, G. H., Gray, D. A., and Swain, D. G., “MultilevelOutlet Works at Four Existing Reservoirs,” Journal of theHydraulics Division, ASCE, vol. 95, No. HY6, November1970, pp. 1793-1808.Speece, R. E. , and Orosco, R. , “Design of U-TubeAeration Systems,” Journal of the Sanitary EngineeringDivis ion, ASCE, vol . 96 , No. SA3, June 1970, pp.715-725.K i n g , D . L . , “ R e a e r a t i o n o f S t r e a m s a n d

Reservoirs-Analysis and Bibliography,” REC-OCE-70-55,Bureau of Reclamation, December 1970.U.S. Department of the Interior and U.S. Department ofAgriculture, “Environmental Criteria for ElectricTransmission Systems,” Government Printing Office,Washington. D.C., 1970.Brenman, H., and Covington, D. A., “EnvironmentalConsiderations in Design of Transmission Lines,” ASCEN a t i o n a l M e e t i n g on Transportation Engineering,Washington, D.C., July 1969.Latham. H. S.. and Verzuh. J. M.. “Reducing Hazards toP e o p l e ’ a n d A n i m a l s o n R e c l a m a t i o n C a n a l s , ”REC-OCE-70-2, Bureau of Reclamation, January 1970.

[8] Bureau of Reclamation, “Safety and Health Regulationsl for Construction,” latest edition.-> “Environmental Quality-Preservation and

Enhancement.” Reclamation Instructions. Series 350,Part 376. 1969.

U.S. DepartmentoftheInterior,“Man-AnEndangeredSpecies,”Government Printing Office, Washington, D.C., 1968.

“River of Life, Water: The Environmental Challenge,”Government Printing Office, Washington, D.C., 1970.-, “The Populat ion Challenge-What I t Means to

America,” Government Printing Office, Washington, D.C.,1966.

“The Third Wave,”T\hington, D.C., 1967.

Government Printing Office,

Benson, N. G. (editor), “A Century of Fisheries in NorthAmerica,” American Fisheries Society, Washington, D.C.,1970.

Clawson, M., and Knetsch, J. L., “Economics of OutdoorRecreation,” The John Hopkins Press, Baltimore, Md.,1966.

Dasmann, R. E., “Environmental Conservation,” John Wiley &Sons, Inc., New York, N.Y., 1968.

Dober, R. P., “Environmental Design,” Van Nostrand ReinholdCo., New York, N.Y., 1969.

“Environmental Quality,” First annual report of the Councilon Environmental Quality, Government Printing Office,Washington, D.C., August 1970.

*References without numbers are not mentioned in text.


Flawn, P. T., “Environmental Geology: Conservation,Land-Use Planning, and Resources Management,” Harper&Row, New York, N.Y., 1970.

McCullough, C. A., and Nicklen, R. R., “Control of WaterPollution During Dam Construction,” Journal of theSanitary Engineering Division, ASCE, vol. 97, No. SAL,February 1971, pp. 81-89.

Prokopovich, N. P., “Siltation and Pollution Problems inSpring Creek, Shasta County, California,” Journal ofAmerican Water Works Association, vol. 57, No. 8,August 1965, pp. 986-995.

Reid, G. K., “Ecology of Inland Water and Estuaries,” VanNostrand Reinhold Co., New York, N.Y., 1961.

“Report of the Committee on Water Quality Criteria,” U.S.Department of the Inter ior , Federal Water Pollut ionControl Administration, April 1, 1968.

Seaman, E. A., “Small Fish Pond Problem-Management Chart,”Technical Publication No. 2, West Virginia ConservationCommission, Charleston, W. Va.

Smith, G. (editor), “Conservation of Natural Resources,” thirdedition, John Wiley & Sons, Inc., New York, N.Y., 1965.

“Transactions,” American Fisheries Society, Washington, D.C.U.S. Department of the Inter ior , “Quest for Quali ty,”

Government Printing Office, Washington, D.C., 1965.Vernberg, .I. F., and Vernberg, W. B., “The Animal and the

Environment,” Holt , Reinhart & Winston. Inc . . NewYork, N.Y. 1970.

Wat t , K . E . , “Ecology and Resources Management; AQualitative Approach,” McGraw-Hill, New York, N.Y.,1968.

Wing, L. W., “Practice of Wildlife Conservation,” John Wiley &Sons, New York, N.Y., 1951.

<<Appendix A

The Gravity Method of Stressand Stability Analysis

A- 1. Example of Gravity Analysis- Frian tDam. -The example presented in this appendixwas taken from the gravity analysis of ther e v i s e d F r i a n t D a m . F r i a n t D a m w a sconstructed during the period 1939 to 1942and is located in the Central Valley ofCalifornia. A plan, elevation, and sections ofthe dam are shown on figure A- 1.

The assumptions and constants used for theanalysis are given below:

(1) Unit weight of water = 62.5 pounds percubic foot.

(2) Unit weight of concrete = 150 poundsper cubic foot.

(3) Unit shear resistance of both concreteand rock = 450 pounds per square inch.

(4) Coefficient of internal friction ofconcrete, or of concrete on rock = 0.65.

(5) Weight of l&foot drumgate = 5,000pounds per linear foot.

(6) Top of nonoverflow section, elevation582.

(7) Crest of spillway section, elevation 560.( 8 ) N o r m a l r e s e r v o i r w a t e r s u r f a c e ,

elevation 578.(9) Tailwater surface, elevation 305.(10) Horizontal component of assumed

earthquake has an acceleration of 0.1 gravity, aperiod of vibration of 1 second, and a directionwhich is at right angles to axis of dam.

Note. Figure A-2 is a graph showing valuesof the coefficient KE, which was used todetermine hydrodynamic effects for theexample given. However, this procedure is notconsistent with current practice. A discussionof the coefficient C, , which is presentIy usedto determine hydrodynamic pressures, is givenin set tion 4-3 4.

( 1 1) Vertical component of assumedearthquake shock has an acceleration of 0.1gravity and a period of 1 second.

(12) For combined effects, horizontal andvertical accelerations are assumed to occursimultaneously.

(13) Uplift pressure on the base or on anyhorizontal section varies from full-reservoirpressure at the upstream face to zero, ortailwater pressure, at the downstream face, andis considered to act over two-thirds the area ofthe section. Uplift is assumed to be unaffectedby earthquake shock, and to have no effect onstresses in the interior of the dam.

Note. This uplift assumption is no longerused by the Bureau of Reclamation. Seesection 3-9 for uplift assumptions now in use.

A-2. List of Conditions Studied. -A list ofconditions studied for Friant Dam for both thenonoverflow and the overflow section istabulated below:

( 1) Reservoir empty.(2) Reservoir full.(3) Reservoir empty plus earthquake.(4) Reservoir full plus earthquake.Loads for reservoir empty are dead loads

consisting of the weight of the dam and gates.Loads for full-reservoir operation include, inaddition to dead loads, the vertical andhorizontal components of normal waterloadson the faces of the dam.

Loads for earthquake effects with reservoirempty include inertia forces caused byacceleration of the mass of dead loads. Loadsfor earthquake effects with reservoir fullinclude, in addition to the above, the inertiaforce of the mass of water and thehydrodynamic force caused by the movement

299


t ‘O” El. 38001-,q

”

\

f

. : +

:,-Gantry crane

600 TOP

Spillway crest,r, c,-nn ,’

OP Of Parapet, El. 5850

305.0

Grout.c”rtainT-m’ySECTION B-B

DAL-r‘d

Trashmck-structure(sb,n C-C El. 452.0n D-D El.433.2t

El 450.1

SECTION C-C 6 D-D El 431.25

v-- \)I ’

li Roadway---*y/

PLAN

Figure A-I. Friant Dan-plan and sections. -288-D-3156

-7Example: To find pressure change at A CURVES FOR COEFFICIENT K,

\

General Formula : pE= K,c,A m FOR COMPUTING CHANGE IN PRESSURE

Q=400’ h = 3 0 0 A =.I O N I N C L I N E D F A C E S OFDAMS

c,l\GiT = 1 ,878 DUE TO EARTHQUAKE SHOCK

From curve for h = 300 I

\‘nd L= 40, find K= .834then pE = ,834 x 1,878 = 1,566 Ib./sq.ft.

I. = HORIZONTAL DISTANCE IN FEET TO POINT ON FACE FROM INTERSECTION OF WATER SURFACE AND FACE OF DAM

Figure A-2. Curves for coefficient KE for computing change in pressure due to earthquake shock. -288-D-3157

302

of the dam against the water of the reservoir.Uplift forces are assumed to be unaffected byearthquake shocks.

The effects of earthquake were studied foreach of the following directions of theacceleration:

(1) Horizontal upstream.(2) Horizontal downstream.(3) Vertical upward.(4) Vertical downward.(5) Horizontal upstream plus vertical

upward.(6) Horizontal upstream plus vertical

downward.(7) Horizontal downstream plus vertical

up ward.(8) Horizontal downstream plus vertical

downward.A-3. Computations and Forms. -Computa-

t ions for the gravity analysis of thenonoverflow section of Friant Dam are shownas figures A-3 to A-9, inclusive. These are forreservoir-full conditions with earthquakeaccelerations upstream and upward. Equationsused are shown at the top of the forms.Standard forms are used.A-4. Final Results. -Final results are given

on figures A-l 0 to A- 18, inclusive, which shownormal and shear stresses, stability factors, andprincipal stresses for each loading condition onthe overflow and nonoverflow sections.A-5. Summary and Conclusions. -Following

is a summary of results and conclusionsobtained from the gravity analysis of FriantDam. These are presented for the purpose ofshowing the type of information usuallyobtained from such an analysis.

( 1 ) T h e a n a l y s e s o f t h e m a x i m u mnonoverflow and spillway sections of FriantDam indicate stresses and stability factorswithin safe limits for all loading conditions.

(2) The maximum compressive stress,maximum horizontal shear stress, and


minimum shear-friction factor all occur forn o r m a l f u l l - r e s e r v o i r o p e r a t i o n d u r i n ge a r t h q u a k e accelerations “hor i zon ta lupstream” and “vertical upward.”

(3) The maximum tensile stress occurs forreservoir-empty conditions combined withe a r t h q u a k e accelerat ion “hor i zon ta ldownstream” acting alone or in conjunctionwi th e a r t h q u a k e acceleration “verticalupward. ”

(4) The maximum sliding factor occurs fornormal full-reservoir conditions combined withe a r t h q u a k e accelerations “hor i zon ta lupstream” and “vertical downward.”

(5) Points of application of resultant forceson the bases and horizontal sections of thenonoverflow and spillway sections are wellwithin the middle-third for most loadingconditions.

( 6 ) M a x i m u m s t r e s s e s o c c u r a t t h edownstream face of the maximum nonoverflowsection; the maximum compressive and shearstresses occur at the base elevation, and themaximum tensile stress occurs at elevation 400.Maximum direct stresses all act parallel to theface.

(7) The maximum sliding factor occurs atelevation 400 and the minimum shear-frictionfactor occurs at the base elevation of thenonoverflow section.

(8) The maximum compressive stress is 409pounds per square inch and the maximumtensile stress is 46 pounds per square inch.

(9) The maximum horizontal shear stress is192 pounds per square inch. The maximumsliding factor is 0.999, and the minimumshear-friction factor is 5.45.

(10) Since tensile stresses occur at pointsnot subjected to water pressure, the possibilityof uplift forces acting in tension cracks iseliminated.

Complete results for nonoverflow andspillway sections are tabulated in table A-l.

THE GRAVITY METHOD-Sec. A-5

FRIANT DAM NONOVERF

VERTICAL PLANE

)I3 921,167.32 46/,88992 51, 895.117

Y 132.3 112.3 72.3 32.3 0

y2 I( 503.29 /2,6//.29 5,22729 (043.29

Y3 2,3/5,68527 /,416,24287 37/:93307 33,698.267

Y I82 3 I47 3 I073 67.3 2 7 3 0

y 2 y233.29 Z/,69729 l/,51329 4,529.29 745 29

y 3 6>058,428.77 3,/96,0/0,82/,235,376.02 304,821.22 20,346.4/7

y 217.3 211 8 171.8 131.8 918 51 8 Il. 8 0

)I2 4<2/9.29 44,85924 29,5/5.24 l(371.24 8,42724 2,683.24 139.24

V3 10260 752 9.501.1875.0707182 2.289529.4 773620.63138.99183 1.643.032

Figure A-3. Friant Dam study-values and powers of y. -DS2-2(6)

FRIANT D A M NONOL!ERFLL?W. S E C T I O N . R E S E R V O I R W . S . EL..578. ._ T A I L W A T E R E L . .NONE.. S T U D Y N o , ..z

GRAVITY STRESS ANALYSIS OF MAXIMUM PARALLEL-SIDE CANTILEVERINCLUDING EFFECTS OF TAILWATER AND HORIZONTAL EARTHQUAKE

E A R T H Q U A K E NORMAL STRESS ON HORIZONTAL PLANES &=a+by By..J.T.R Date.?r5:.94.

./SP ,.a=0

0 = .434,03,,=f(ZW)- + (ZM)

I I I c I I_ I I I I CT7 Pounds

b =+M) Check: ( for y =T), 0,” = +(,IW) t -$xM)I

ELEV. T tJ IC _ --..-a. per Square Foot7 T3 xw EM b ’ V E R T I C A L P L A N E

us. 6 5 4 3 2 I 0.s cr,,-Reservoir Fuli

.036~630,036i008,05~55~2.0~56589,784,4 ili,R80 - 1 7 0 , 7 0 0 /00676,20 2,7084 4 , 7 3 3 5 5438 2,7‘?394__--__ _~_

500 .016,05/,364 .00(545877,7 0>%4L?626,&Y3 481r490 2,945200 i&60,38 3> I22 5 6 6 , 0 4 2 8 211,983 12,285 3,i7256

450 .OlO,277,492 0,3633,76,,04 0,%13,026,948 1,139,800 14,328,OOO ESSSO,/l 2,618 75 6,344 8 13,896 8 20,144 2,633 76

400 .00<25~57~CLl~342,792,70 $as;l82,05(3 2,086,900 -39,701,OOO 205732,62 78 4 72,115 9244 14,101 22,758O 29,204 2,164 78

350 L-__---------- l6,llE.O 23,005,~5;163,5.0~~8~54i~66 O)Ol~Yl?J7ll,6 3,594,OOO 86>900,000 1%123,84 4,028 66 10,070 0 I650 30,213.Y 35,246 4,025 6 7

315 .004,60/,932,8.0~2~066,7/ $00l,169,4504,925,000 732,780,OOO ~5+?86,875,740.60 6,646 7 lZ,889.2 19,132.6 2~5/76~/ 3i,Pi9 37704 I 3gs275 5,792.60

Figure A-4. Friant Dam study-normal stresses on horizontal planes. -DS2-2(7)

F.!?IANT.. D A M NONOVERFLOW. S E C T I O N . R E S E R V O I R W . S . EL..5?8 TAILWATER E L . N.QlvE. ., S T U D Y N o . . ? . .’ 2

GRAVITY STRESS ANALYSIS OF MAXIMUM PARALLEL-SIDE CANTILEVER m

-AINCLUDING EFFECTS OF TAILWATER AND HORIZONTAL EARTHQUAKE G)

EA R TH WA KE SHEAR STRESS ON HORIZONTAL AND VERTICAL PLANES Tzy =Tyz = a,+ b,y + c,y2 By.. J..!.!?.. ..Dote .?.mr.6rW.

Tzyv=- (9”-P’*PE)tan9, a, = Tzy,= (ozo- p’k’tp: 1 tan QD b, = - [ ~~(“)+q(~~yu’t~(~~yDl] Cl = +Jw)+$~~~y,) t $(T~yo)z=I

I I :

I (t Use (t) sign if horizontal earthquake acceleration is upstream.) (ruse t-J siqn if horizontal earthquake acceleration is upstream.)

Q=..

-137 432,33 -/36,314,55 0 3,4/55 9,919 3 /5, ///

wFigure A-5. Friant Dam study-shear stresses on horizontal and vertical planes. -DS2-2(8) z

.F.R!AN.?- .DAM NONOVE:RFCOW. S E C T I O N . RESERVOIR W.S. EL. .5.?.8.. TAILWATER EL. .!??!!6.. _. S T U D Y N O . .3

(&= 150 GRAVITY STRESS ANALYSIS OF MAXIMUM PARALLEL-SIDE CANTILEVERW0

0 = ..4%?3.J INCLUDING EFFECTS OFTAILWATER AND HORIZONTAL EARTHQUAKEm

EARTHQUAKE (ACGELI PARTIAL DERIVATIVES FOR OBTAINING CJy By. H. .9 W Da te .?.: !? r.40.

T[tUse(t)sign if horizonfol eorthquoke occelerotion is upstream) ftUse(-)sign if horizontol eorthquoke occelerotion is upstream) ( *W -omitted if water oh face is absent)1

* = tan@, (0@ auzu +* a a tan cu)+ a2 ( P -0s” +_tpE)

atanD- -

a2 - a2 azI

a ton% _ A tonQu- _ atan@D Atan@D ah _ PEA a P’E = A P’ra2 A Z a2 A Z -5-T' A Z a2 A Z

ELEV + + + -$ + -$ +- K, K, F K, K, ado;0 apE atOn+ aT--‘+J*y$!?xp& h(&+&La2 az

Reservocr Fuii

5 5 0 - 70/.140'43i55/8,/53 0 0 0 %8Ei;293 7 I5 T 2,783. 47

Note. K, , K2 a n d K3 n o t r e q u i r e d a b o v e+ +

5 0 0 Ei 4 0 0 b e c a u s e U . 5 Face IS vertlcai - - - - 642,47(85/51476,99 0 0 0 62.283>693 7 15 T 5046 36

+4 5 0 - - - - 668224>~Wl5675<77 0

+0 0 65976935 7 l5T q/9.45

--__-. - c4 0 0 - - 682646/68l56580,5?

L- - - 0 0 0 65.854399 7 15T 15,354 50

Figure A-6. Friant Dam study-partial derivatives for obtaining 0~. -DS2-2(9)

WITH EARTHQUAKE 2

ZNTERMEDIATE COMPUTATIONS FOR OBTAINING STRESSES- GRAVITY ANALYSIS OF FRIANT DAMm

FigureA-7. Friant Dam study-intermediate computations for obtaining stresses. -DSZ-2(10) z

~RWT D A M NONOVERFLOW..SECTION. R E S E R V O I R W.S. EL.??.. T A I L W A T E R EL.MY?JE .,.. S T U D Y N o . 3..

i GRAVITY STRESS ANALYSIS OF MAXI MUM PARALLEL-SIDE CANTI LEVERI N C L U D I N G E F F E C T S O F T A I L W A T E R A N D H O R I Z O N T A L E A R T H Q U A K E

EARTHQUAKE -X NORMAL STRESS ON VERTICAL PLANES Cy=a2+ b,y + c2y2 + d,y3 B y . H.PW D a t e P:?-40.,aa, a3T;' a2 s=-g y4 xv t+ &zyu[ ( ) (

(*Use(t) sign If horuontol earthquake occelerotion is upstream ) (% Use (-) sign if horizontal earthquake acceleration is upstream )

1 a,= Up= a,tan *,+ p’?*pL b = b tan+2 I 0 t da, +‘Ahoaz- c

c,= c,tan @ ti *D 2 a2 Check far y = T ; a,“=( P **&Zyutan 9,

ablELEV. 2 az ac,0y Pounds per Square Foot

az b, CL? d, VERTICAL PLANEu s 6 5 T 4 3 2 I D S Fyu

Reservoir Fu//

5 5 0 -?5.887,293~1.807,619 -683,605>49 177.356,02 32 304,768-227,868, 5 2>373.97 1914.9 2,619. 5 2373.9

5 0 0 +62.203,893 +2.957,829,61b31,935,70 23 349,901 t861,795,3 010,645,07 6,142 86 6143 9 5,941. 2 6,042.5 6,111 9

4 50 ;5 976,939 1.875,786,3 bl3,285>579 35.754.699if752,996,4 -004,428,53 9,759 95 906 9.5 9,667.6 10,171.5 9.760.0

4 00 +65856,399 %436,296,4 -007,680,134i5.346,232 +627,728,0 :002,560,05 13,393 0 13,594.1 13,493.g 13r494 5 i4,lOC8 13,370.o

3 5 0 37 f ~006,934,037~05.710,094 3 9 , 6 9 5 516,354,8 ?957,897,7 002,311, 35 15,110 7 5 15,KJ5.4 14,988.3 13,896 6 15,105 9 17,120.9 15.907.8

3 I 5 &620,433 lf219,767 005,044,313 &,099,lS3,4 .?99,784,2 .ti,681,44 18, 127.0 18,127 7 1 7 , 1 2 1 4 16,114.lJ 15,109.7 16,/12 8 18J27.1 19,135.g 18,351.O

-

Figure A-8. Friant Dam study-normal stresses on vertical planes. -DS2-2(11)

THE GRAVITY METHOD-Sec. A-5 309

LE\-

55c

. .F.!?!4.N?.. . DAM. .hQ’K?W?F4.QH!, . . SECTION. RES. W.S. E1.3.W. . . TAILWATER EL.&%?!‘E. STUDY No.3.GRAVITY STRESS ANALYSIS OF MAXIMUM PARALLEL-SIDE CANTILEVER

RESERVOIR FULL WlTH EARTHGUAKE PRINCIPAL STRESSES SY..H.P.W. Dote.4.~,6:68.

5 0 0

9

&;fj 7,469 3, I72 56 65 2,847 6,/l/ - 1 4 . 0 5 217,841 2,988 8,959.7 6 5 b3,/32.6 304

I I I I I 1 I

I&7, 2 2 2 0 1 2 4 1 2 7

UP2 6,//1.&?6 9 , 3 7 6 6 7 7 8 0 4 2 6 5 I 0

Ton2iepjI 0 b32 3 6 2 1-2745.07, I

Figure A-9. Friant Dam study-principal stresses. -DS2-2(12)

M A X I M U M N O N - O V E R F L O W S E C T I O N

UPSTREAM FACE M A X I M U M S P I L L W A Y S E C T I O N HORIZONTAL SECTION DOWNSTREAM FACE

1 Resulton+-concrete weight only.\ Resultant-water pressure and weaght. ‘, Resultant-wok pressure, weight and uploft.S,,ding f,,ctor; Horlmntal Force

Weight-UplIftSheor-fr,ct,on Factor= (Weight-UplIft) x Coefficient o f Internal Fr~ctaon + Horlzontol Areo I Umt Shear Rerlrtonce

Horizontal ForceUnat weight of concrete =I% pounds per cubic foot. Uni t sheor rewstonce ‘450 pounds per square inch.

Coefflclent of Internal frlctlon = 0 65

Upllft pressure varies 0s a straight line from reservoir water pressure ot upstream face to zero ortollwoter pressure otdownstream face, octang over two-thards the area of the horIzonto section.

Tota l l o a d corrled by vertlcol con+,lever

1 REVISED DESIGN)G R A V I T Y &NALYSES

MAXIMVM NON-OVERFLOW AND SPILLWAY SECTlONSRESERVOIR EMPTY AND NORMAL FVLL RESERVOIR OPERATION

N O R M A L CONDITIONSAll norm01 stresses ore compressive except those preceded by o negative r~gn, which ore tens!le.Positive sheor stresses ore caused by shear forces octlng thus P Negatwe sheor stress.% ore caused by shear

forces octmg th”I -.Weight of gate included in onolya~a of sp~ilroy section

Figure A-IO. Friant Dam study-gravity analyses for normal conditions.

NORMAL RES. W. S. EL. 578 IOR-MAL RES.W. S. EL. 578

-----yj

Pounds oer “are Inch

)OWNSTREA

\ Resultant-concrete weight and earthquake (horizontal upstream). \ Resuitoti-mncnte weight and earthquake (horizontal downstream)\ Aesulfont-&r pressure,w$ght,ond earthquake (horizontal upstream)i ~su~tOnt-WoHkd,~~~,~o~~g~,u~i~,U~ earthquake (hor~zon~f Upstim).

\ Resultant-water pessure, ueight,and earthquake (horizontal dounslrwm).& Resultant- voter pressure,~eight,uplift,ond ~arthquake!horlzontol dcwnstreom).

Sliding factor= Weigh-UpliftShrehidion Fahrz (Wagi+ Uplift) x Coefficient of Interml Friction + Hcwontol Are0 x Unit Sheor Res&.mce

Horizoniul ForceUnitveightof concrete : 150 pounds per cubic foot. Unit sheor rewstance 2 450 pounds persquze inch. Coefficient d inten-4 friction = 0.65Upl~fl pressure varies 05 o straight line from reserwir water pressure otupstrmm face to zero or toilwater pressure ot downstream face,

acting Over two-thuds the oreo of the horizontal section; assumed to be unaffected by earthquakeHorizontal earthquake acceleration : 0.1 gravity, period: I second.Total load carried by vertical cantileverAll normal stresses ore compressive exceptthose preceded by o negative sign, which ore tensile.Posltlve shear stressesore caused by shear forces atlng thus e. Negative shear st~~~sesoremused by shear forces acting thus-.* Including wrihquohe occelertion (horizontal upstrewn). ** Including wr+i?quake ocseleratnon (tnrizcntol downstream).Weightof gate included in analysis of spillway section.

F R I A N T D A MlRE”lSED DESIGN)

Figure A-l 1. Friant Dam study-gravity analyses with horizontal earthquake acdeleration.

r

:h

N O R M A L R E S . W . S . E L . 5 7 6 RESERVOIR EMPTYHORU. “EW,CC. STRESS “ORll

STRE.33 PARClLEL SHEAlTOt=ACE STRES

Pounds Pounds ‘Per Sauore Inch

MAXIMUM NON-OVERFLOW SECTION

c

UPSTREAM FACE M A X I M U M S P I L L W A Y S E C T I O N HORIZONTAL SECTION DOWNSTREAM FACE

b Resultant -concrete weight and earthquake (vertical upward),colncldes with 1 Resultant -concrete weight and earthquake (vertlcol downward).\rResultont-waterpress”re,welgM and eorthquoke(vertlcoI upward),coincldes wtt, \ Resultant-woterprea”Te.welgh+ and ear+hquoke(vert,cal downward).jReSult~“t-woterpressure,welght,upllft,and earthquake (vertical upward). i Resultant-woterpresure,veight,uplift,pndearthqu~ke(vert~col &wnvard)

Sliding factor = Honzontol ForceWaghi-Upllft

Shear-fr,ct,on Factor = ( Weight -UPlift) x Coefficient of Internal Frlctlon +Horizontol Area x Unit SheorResistonce.Horizontal Force

Unitwetght ofconcrete= poundspercubtcfoot. UnltsheOrreslstanCe’45Opoundspersquore~nch.Coefficientof lnternol friction =O 65.UplIft pressure vor~es oso strolght line from reservoir water pressure atupstreom face to zero or tollwater pressure ot downstream face octlng over

two-thirds theoreo of the horlzontal sectton; assumed to be unaffected byearthquake.Vertical eorthquoke occeieration = 0 I g , Perlod = I secondTotal load cowled by vertlcol contlleverAll normal stresses are Compressive except those preceded byo negotlve sign, whlchare tensilePosltlve sheor stresses ore caused by shear forces acting thus _ Negative shear Stresses ore caused by sheor forces octlng thus +===+ lncludmg eorthquoke acceleration lverticai upward). xx lncludlng earthquake acceleration (vertical downward)Weight of gote ancluded in analysis of spillway sectton.

Figure A-12. Friant Dam study-gravity analyses with vertical earthquake acceleration.

RESERVOIR EMPTY / NORMAL RES. W.S. EL.578 1 3MAL RES. W. S. EL.? 17E

Lm ; Pi

I

1 MAXIMUM NON-OVERFLOW SECTION

ijEl

z+s3RIZONTAL !

A 1 243.29’

MAXIMUM SPILLWAY SECTION DOWNSTREAM FACE

STUDY NO.5ALL RESULTANT FORCES INCLUDE VERTICAL EARTHQUAKE ACCELERATION UPWARD.I~~Resultant-Concrete weight and eorthquake(horlrontol upstream). i Resultant-concrete weight and earthquake (horizontal downstream)IResultant-water pressure, weight,and earthquake (horizontal upstream). >Resultant-water pressure weight and earthquake (horizontal downstream).{Resultant-water pressure, weight, uplift,and earthquoke(horizontal upstreoml. ‘+Resultant-voter pr&re, ieight, uplift, and earthquake (horizontal downstream).

Horizontal Force (Weight-Uplift)xCoefficient of Internal Friction +Horizontal Area x Unit Sheor ResistanceCENTRAL VlLLEY PROJECT-CILIFORWIA

Sliding factor = Weight-Up,ift Shear-friction Factor ;- -KENNETT DlVlSlON

Horizontal ForceUnit weight of concrete =I50 pounds per cubic foot. Unit shear resistonce ‘450 pounds per square Inch. Coefficient of internal friction = 0.65.Uplift pressure varies 0s 0 straight line from reservoir water pressure at upstream face to zero or tailwater pressure ot downstream face, acting over

FRIANT D A M( REVISED DESIGN 1

GRAVITY ANALYSEStwo-thirds the ores of the horizontal section; assumed to be unaffected by eorthquoke. MAXINUN NON-OVERFLOW AND SPILLWAY SECTIONS

Vertical eorthquoke acceleration and horizontal earthquake occelerotion = 0.1 gravity, period = I second. RESERVOIR EMPTY AND NORMAL FULL RESERVOIR OPERATICTotal load catraed by vertical contllever. W&T” “ORIZONTAL ,ND VERTICAL EARTHQUAKE EFFECTS

All normal stresses ore compressive except those preceded by 0 negative sag”, which ore tenslIe.“ERTtCAL ACCELERATION UPWARD

Positive shear stresses ore caused by sheor forces acting thus d Negative sheor stresses ore caused by sheor forces acting thus L*Including earthquake occelerot~on (horuontal upstream and vertlcol upword). Dn*w*

,T” U.IITlS0.d~‘

Weight of gote included in analysis of spillway section.**Including earthquake occelerotion (horizontal downstream and vertical upward). T”.CSD. .?! * .D?.’ “LCO”Ys*oco

C”fCILD..$CW.. . . . . “OYLD1 DE..*..c0~Lo~~~~*rr.. l.l..O 1 2j4-D-4,

IN

61

Figure A-13. Friant Dam study-gravity analyses with horizontal and vertical earthquake effects, vertical acceleration upward.

Pounds Per Sauc Ire Inch


i

m I

f

MAXIMUM SPILLWAY SECTION HORIZONTAL SECTIONU PSTREAY FACE DOWNSTREAM FACE

.L RESULTANT FORCES INCLUDE VERTICAL EARTHQUAKE ACCELERATION DOWNWARD.qesultont-concrete welqht ond eorthquoke ihor~zontol upstream)!. Resultant-concrete weight and earthquake (horirontol downstream).iesultant-water pressure,wght,ond earthquake (horlzontol upstream): . Resultant-water prerrure,we~ght,and earthquake (hor~zontol downrtreom)iesultant-water pressure,weight, uplift,ond ear+hquake(honzontal upstreoml.? Rerultont-rater pressure,veight,uplin,ond eorthquoke(hon~ntol downe+reoml

Horizontal Forceidlw factor= Weight-Up,,ft Shear-frltilon Factor= - -( Weight-Uplift) I Coefficient of lnternol Frxtion+Hor!zontol Area x Unit Shear ResIstonce

Hor~zontol Forcerlt weaght of concrete= 150 pounds per cublcfmt. Unit sheor res1etance=450 pounds per square Inch. Co&went of internal fr&on=0.65.llif+ presewe vorles (IS o strolght llne from resewow water pressure at uprtreom face to zero or tollwater pressure ot downstream tote, octlngover two-thirds the oreo of the horizontal sectlo”; oewmed to be unaffected by earthquake.

!TticoI earthquake occelerotion and horizontal earthquake accelemtion=O.l grovtty , penod = I second.)tol load carried b y vertlcol contllever.II normal stresses ore compresswe except there preceded by o “egotlve r,gn, which ore tenslIe.,s,twe sheor stresses ore caused by sheor forces octmg thee =c=. Negotwe sheor stresses ore caused by shear forces acting thus w

.lnclJdlng earthquake occelemtion lhorlzontol up&earn ond vertical do*n*ordl.**Includlng earthquake occ&&iinlhonzontol da&mom ondvertial do-rIcdght of gote lnclvded I” onolysns of rp~llwoy sectlo”.

G R A V I T Y A N A L Y S E SYAxlMuu NON-OVERFLOW AND SPILLWAY SECTIONS

RESERVOIR EMPTY AND NORMAL FULL RESERVOIR OPERATIO,WITH HORIZONTAL AND VERTICAL EARTHQUAKE EFFECTS

VERTICAL ACCELERATION DOWNWARD

62Figure A-14. Friant Dam study-gravity analyses with horizontal and vertical earthquake effects, vertical acceleration downward.

STRESSES IN POUNDS PER SO IN.WIN “.S 6 s 4 1 2 1 0,s

EL 1 RESLRVOIR EYPTY .-RESERVOIR w s E L 518IO.. I a. I I I. I I I Ia

RESERVOIR EMPTY NORMAL FULL RESERVOIR OPERATION ’ \ \

STRESSES IN POUNDS PER $4 IN.POINTI I us.1 6 I 5 1 4 I 3 I 2 I I IDS

Unit weight of concrete =I50 pounds per cub,c foot,Effect of upllft neglected.Total load carried by vertical cantilever.- D e n o t e s compressnon.- D e n o t e s t e n s i o n .U.S.denotes upstream face of sectlon.D.S. denotes downstream face of sectlonNumbers denote vertlcol planes.

0 3 0 0 6001 1 1 1 I I I I

SCALE OF STRESS-POUNDS PER SP.,N.

0 3 0 6 0Cl 1 1 1 1 1 I

SCALE OF FEET

OEP.“TYL”T OF 7°C II(,LI,OIa”IF.” OF “ECL.“.TIO”

CENTRALVALLE” PROJECT-CALIFORNIAF R I A N T DlVlSlON

F R I A N T( R E V I S E D OES?G!?

GRAVlI-f ANALYSES OF MAXIMUM NONOVERFLOW SECTIONPRINCIPAL STRESSES

ESERVOIR EMPTY AND NORMAL FULL RESERVOIR OPERATIO,

Figure A-1.5. Friant Dam study-principal stresses on the maximum nonoverflow section, normal conditions.

STRESSES IN POUNDS PER SQ. IN.POINTI us.1 6 S 4 3 2 I OS.

EL. 1 RESERVOlR ENPTY ~-RESERVOIR W.S. EL.578/TOP OF DAM EL. se1

NORMAL FULL RESERVO I R

- .2’4

RESERVOIR EMPTY

Unit weight of concrete: 150 pounds per cubic footEffect of upl i f t neglected.Total load carried by vertical canti lever.Vertical earthauoke acceleration ond horizontal

0aSCALE OF STRESS

POUNDS PER SQUARE INCH

earthquoke’acceleratlon: O.lg , period=one secondw Denotes compression.C--, Denotes tensionU.S denotes upstream face of s&ion

0

SCALE OF FEET

D. S. denotes downstream face of sect6on.Numbers denote vertical planes

O P ER AT I O N STUDY No.3““ITED ,,.,E,

GRAVITY ANALYSES OF MAXIMUM NONOVERFu,WSECT,ONP R I N C I P A L STRESSES

RESERVOIR EMPTY AND NORMAL FULL RESERVOIR OPERATIONWITH HORIZ AND VERT EARTHOUAKE ACCELERAllONS INCLUDED

Figure ~-16. Friant Dam study-principal stresses on the maximum nonoverflow section, horizontal and vertical earthquake accelerationsincluded.

+

NORMAL FULL RESERVOIR 6PERATION ’ \ \

Unit wght of concrete = 150 pounds per cubic FootEffect of uplIFt neqlectedTotal load carried by vertical cantMever.- Denotes compresslo”t-+ Denotes tensIon

U S denotes upstream Face of section.0 S denotes downstream Face of sectton.Numbers denote vertical planes.

0 300 600I I I

SCALE OF STRESS-POUNDS PER so IN.

0a

SCALE OF FEET

Figure A-l 7. Friant Dam study-principal stresses on the spillway section for normal conditions.

!3- 3

STRESSES IN POUNDS PE R sa INI

1.5.

RESERVOIR EMPTY NORMAL FULL I~ESERVOIR OPERATION \-\ \

unit weight of concrete = 150 pounds per WbOC foot.E f fec t o f uplIft neg lec ted .To ta l l oad ca r r i ed by vcrtncol contblever.Ver t i ca l ea r thquake occelerotion end horuzontol.

earthquake 0CCClC~,tl0n = 0 Ig , per,od=onc second.

04

SCALE OF STRESS

-Denotes compre*s,o”.*----c Denotes tensmn.U S . denotes upstream face o f section.D S. denotes downst ream face o f eectbon.Numbers denote vertlcol planer.

POUNDS PER SQUARE INCH

auSCALE OF FEET

STVDY NO 3 .“NlTFO S~.IL,

OIP.“TYL”T or T”E ,“rL”,oIlUlLA” OF “LCL.“.TIOY

CENTRAL “ALLEY PROJECT-GALIFORNIAFRIANT DlYlSlON

F R I A N T D A M(REVISED D E S I G N )

GRAVITY ANALYSES OF MAXIMUM SPILLWAY SECTlOt,PRINCIPAL STRESSES

RESERVOIREMPTY AND NORMAL FULL RESERVOIR OPERATIONWITH HORIZ ANDVERT EARTHQUAKE ACCELERATlWS ,NCLUDED

o”aw* J.1.R. S”.“I ITTO H&7&

Figure A-18. Friant Dam study-principal stresses on the spillway section, horizontal and verticai earthquake accelerations included.

Table A-I.-Friant Dam, nonoverflow and spillway sections (revised design)-maximum stresses, sfactors. DS2-2(22)

I Nonoverf low section

Loading conditions

A. Normal conditions:

I. Reservoir empty 2 3 2 2 64 - -2. Normal full reservoir operation 2 9 7 none I40 0.704 7. 50

8. Including eorthquake effect:

I . Reservoir empty 291 46 80- -2. Normal full reservoir operotion 4 0 9 none I92 0.999 545

ding factors, and minimum shear-friction

Spillwoy section

Stre s s,Ibs. per sq. in. M O X . Min.

shear-I D i r e c t Max.

slidingfactor

fr ic t ion

Corn p r. Tens. shear factor

2 3 9 none 66 - -2 9 7 none 139 0.643 7.59

298 24 82 - -4 0 7 none I90 0 . 9 2 6 5 4 6

<<Appendix B

T r i a l - l o a d T w i s t A n a l y s i s - J o i n t s G r o u t e d

B-l. Example of Twist Analysis, JointsGrouted-Gmyon Ferry Dam. -Illustrationsfrom a trial-load twist analysis, joints grouted,of a gravity dam are given on the followingpages. The dam selected is Canyon Ferry Dam,and the plan, elevation, and selected elementsare shown on figure B-l.

B-2. Design Data. -The following designdata and assumption are presented for CanyonFerry Dam:

(1) Elevation top of dam, 3808.5.(2) Elevation of spillway crest, 3766.0.(3) Maximum and normal reservoir water

surface, elevation 3800.0.(4) Minimum tailwater surface with gates

closed, elevation 3633.0.(5) Concentrated ice load of 7 tons per

linear foot at elevation 3798.75. Provision is tobe made so that no ice will form against theradial gates.

(6) Sustained modulus of elasticity ofc o n c r e t e i n tension and compression,3,000,OOO pounds per square inch.

(7) Sustained modulus of elasticity offoundation and abutment rock, 3,000,OOOpounds per square inch.

(8) Maximum horizontal earthquakeassumed to have an acceleration of 0.1 gravity,a period of vibration of 1 second, and adirection of vibration normal to the axis of thedam.

(9) Maximum vertical earthquake assumedto have an acceleration of 0.1 gravity, a periodof vibration of 1 second, and a direction thatgives maximum stress conditions in the dam.

Note. Figure A-2 is a graph showing valuesof the coefficient KE, which was used todetermine hydrodynamic effects for the

example given. However, this procedure is notconsistent with current practice. A discussionof the coefficient C, , which is presently usedto determine hydrodynamic pressures, is givenin section 4-34.

( 10) Poisson’s ratio for concrete andfoundation rock, 0.20.

(11) Unit weight of water, 62.5 pounds percubic foot.

(12) Unit weight of concrete, 150 poundsper cubic foot.

(13) Weight of radial gates, 3,000 poundsper linear foot.

(14) Weight of bridge, 5,500 pounds perlinear foot.

(15) Unit shear resistance of concrete orconcrete on rock, 400 pounds per square inch.

(16) Coefficient of internal friction ofconcrete on rock, 0.65.

( 17) Uplift pressure on the base orhorizontal sections above the base varies fromfull-reservoir water pressure at the upstreamface to zero or tailwater pressure at thedownstream face and acts over two-thirds thearea of the base or horizontal sections.

Note. This uplift assumption is no longerused by the Bureau of Reclamation. Seesection 3-9 for uplift assumptions now in use.

(18) Effects of spillway bucket are includedin the analyses.

(19) Effects of increased horizontalthickness of beams in spillway section areincluded.

B-3. Abutment Constants. -The method ofdetermining abutment constants for elementsof a concrete dam is shown in section 4-14.

B-4. Deflections and Slopes Due to UnitLoads.-Certain data pertaining to unit loads

321

M I S S O U R I

P L A N

ABUTMENT SECTION SPILLWAY SECTION

DOWNSTREAM ELEVATION,100KIN‘ UPSTREAM,

/ 172 95 I7295 MAXIMUM ABUTMENT SECTIONMAXIMUM ABUTMENT SECTION MAXIMUM SPILLWAY SECTION (RIGHT SlDE LOOKING “PSTREIY,

ABUTMENT SECTION

F&ure B-I. Canyon Ferry Dam study-plan, elevation, and maximum sections. g

TWIST ANALYSIS-JOINTS GROUTED-Sec. B-5 323

are required prior to starting an adjustment.These include beam deflections for each unittriangular load, uniform load, and concentratedload and moment at the dividing plane; theslope of the beam at the abutment and at thedividing plane, due to unit loads; shears andtwisted-structure deflections due to unittriangular, uniform, and concentrated shearloads on horizontal elements of the twistedstructure; deflections of the vertical elementsof the twisted structure due to unit triangularloads; cantilever deflections due to unittriangular normal loads; and shears androtations of vertical elements of the twistedstructure due to unit loads. Typical tabulationsof these values are shown on figures B-2through B-7. Calculations were by equationsgiven in sections 4-29, 4-17, and 4-19. Foridentification of the cantilevers and beams inthese drawings, see figure B-l. In the beamsymbols, L means the left portion of the beamand R the right. A aG load is a triangular loadwith a value.of 1,000 pounds per square foot atthe abutment and zero at G, and so on forother loads. Cantilever loads are designated bythe elevation at which the load is peaked.

B-5. Deflections of Cantilevers due to InitialLoads. -Cantilever deflections due to initialloads must be calculated prior to making adeflection adjustment. These deflectionsrepresent the position from which deflectionsof the cantilevers are measured when subjectedto trial loads. Figure B-8 shows a tabulation ofdeflections due to initial loads on thecantilevers. These were computed by means ofequation ( 17) in section 4-l 7. The initial loadsare not shown but include loads of the typediscussed in the latter part of section 4-16.

B-6. Trial-Load Distribution.-The totalhorizontal waterload is divided by trialbetween the three structures. However, it mustbe remembered that the twisted-structure loadis split in half (see sec. 4-25), one-half to beplaced on the horizontal elements and one-halfon the vertical elements. In order toaccomplish the trial-load distribution, thehorizontal load ordinates must be determinedat locations of the vertical elements, asillustrated on figure B-9. By multiplying theseordinates by loads on the horizontal elements,

the equivalent loads on the vertical elementsare obtained. The first trial-load distribution onelements of the left half of the dam is given onfigure B-10, and the sixth and final trial-loaddistribution for these elements is shown onfigure B-l 1.

The total waterload at any point must equalthe cantilever load plus the loads on thehorizontal and vertical twisted elements (ortwice the load on the horizontal twistedelement) plus the beam load. Accordingly, atelevation 3680 for cantilever G, the totalwaterload in kips is equal to 7.269 plus (1.9 x2 x 0) plus (0.8 x 2) plus 0.2, or 9.069.

The values for P and M for beam loads arerequired to provide slope and deflectionagreement at the dividing plane. These may beestablished by trial, or more easily bycalculation by assuming approximate values ofdeflection components from previous trials,and computing the P and M necessary to givethe same slope (not equal to zero) anddeflection of left and right portions of thebeam at the crown. Two equations involvingV, and M, are obtained from the conditionsthat the slope and deflection of the two halvesof the beam must be in agreement at thedividing plane. The simultaneous solution ofthese two equations gives the amount of shearI’, (or P) and moment MC necessary at thecrown of the beam to restore continuity in thebeam structure.

B-7. Cantilever Deflections. -Cantileverdeflections due to final trial loads are shown onfigure B-l 2 for the left half of the dam. On theupper half of the sheet are deflections due tonormal loads. These are obtained bymultiplying loads given in the upper right-handsection of figure B-l 1 by correspondingdeflections for unit normal loads. On the lowerhalf of the figure are deflections due to shearloads on vertical elements of the twistedstructure. These loads are given in the lowerright of figure B-l 1. The loads are multipliedby cantilever deflections due to unit shearloads (see fig. B-4) to obtain the values shown.At the bottom of figure B-12 are inserted thevalues for abutment movements due to beamand twisted-structure elements which havecommon abutments with the cantilever

tCANYON FERRY PAM..* .___________.____ __..______._ SECTION. STUDY NO I. . . _ . . . . . . . . . . . ._.__________.___________

_._____. PA.RAL.LEL.r.S~DE CANT~LEVER--STRESS ANALYSlS -rr.-~~!A--L.clA.r2.TWISr...~ _.._D E F L E C T I O N O F B E A M D U E T O U N I T N O R M A L L O A D S - L E F T S I D E.._. __.______________._ ____._.__.__ . . . . _ . . . . ..__ _ ___._ __ ______ ____ _._..____...____ ______._ _____.__ _ _...______.__._.__...............~..~~.-_ _ . . ..-_..-... _ ._....F _.-._--- --.I-- _-.

B E A M 3 7 2 5 L. . . . . _...._-__-.._. ___ ___. __-___ _....__. ___ ._-...._.-.-....- _ . . ..I __ -...-... _.._-_-_ .---.. -.-~..---.-.------.._....--.....-..~-----. _______ By.&:!??: .-Dote...???!..

QY 4

B G D E F G B G

i

QG -Of562 79 1015,269 -.039,130 -.07j;211 -.086,60% :128,414 ~0~048,408 :0,*379,7t3

OF :0;380,22 bO7,927,0 - .018,741 -.033,597 -.038,074 -.054,736 :0;025,474 :0,=151 ,48

OE :0;333,95 :006,335,5 - .014,5/l - .025,413 - .026.741 -.040.941 :0;020,486 -0;I IO,9 I

,A0 :0:193,j3 -002,368,3 :004,647,4 TOO;: 519,9 :008,399,3 - 0 1 1 , 6 2 4 -0foo~975,o :o,3o29,3ll

_ QG ,0;094,75 -.(SOl, 4 7 :Cf998, 3 9 :OOl, 506,9 :OOl,662,5 .002,233,3 :0:002 234) :0@5,188,6

Unif :OU/,257.5 -,OSS,OOO ,126,530 y258.534 :30/,761 :46!,466 @44, 2 3 :001,450,34

Cone. P :@04,169,4 :0:232,51 -.Of692,17 :cOl,534,8 :OOl,@t3,4 :002,945$ :0,6722, 4 6 :O;OlO,l90

Figure B-2. Canyon Ferry Dam study-deflection of a beam due to unit normal loads. -DS2-2(32)

Figure B-3. Canyon Ferry Dam study-deflection of a horizontal element due to unit shear loads.-DS2-2(33)

PHMLLEL-SIDE CANTILEVER-STRESS. . . . . . . . ._ . ..__._...._ _ .._._. __ .!?EELE~~T?ON~ _ OF .ca! T!

Figure B-4. Canyon Ferry Dam study-deflection of a cantilever due to unit shear loads. -DS2-2(34)

I 36053808.5 3762 3725 3680 3635 2

Y&z

38085 ,003,552,6 :ool,a53,5 -.0,'9tJ2, 3 -.0,'477, 6 -.0:220, 3 -.o,3/19, 5 2l

c)

3762 TOO3,904,7 :002,444,7 TOOI, 49/: 9 -.$773,3 -.Of370,9 -.0,"20<6 - z

3725 ml,7/6,5 700/,352,0 T001,032,5 -@632, I -.0,'327, 2 -.0,793, 3 5

Figure B-5. Canyon Ferry Dam study-deflection of a cantilever due to unit normal loads. -DS2-2(35)

W

I

h,____ CANY.C?N...KRR.Y . ..DAM . .._..__.... _.._ ____ _.. ._ _. ___. SECTION. STUQY NO. l_.______. _ __._________ cc

IAG -198,250 -124,729 -97,108 -71,430 -24,716 - 15,259 0 396.5A F -143,250 - 72,985 -48,964 -28,593 - 1,571 0 286.5AE -128,250 -59,357 -36,854 -18,721 0 256.5A D -,79,250 -18,461 - 4,922 0 158.5 - ^.oc -41,000 0llnif -396,500 -314,500 -277,500 -238,000 -140,000 -110,000 0-I_

Cont. P - ~000. 3 --1ooo

l----t- II

II I, I I I I i---lI / I- E l e m e n t 3 6 8 0 L I

At;I

-157.250 -M2.426 l-90.054 I-331.161 -19.237 0 319 52 -102,250 - 68,597 -40,059 - 2,200 0 204.5A E - 87,250 - 54,173 -27,519 0 174.5Al7 l-38 250 -/lo./98 I 0 I 76.5

I llnif l-3/4.500 ~-277.500 i-238.000 I--140.000 I--110.000 ! 0 /-. -...

Cont. PI

I- 1,000. I w 1 - 1.000 I -I I r/

I I I IE l e m e n t 3 6 3 5 L I

AG -138,750 -/02,06/ - 35,315 - 21,802 0 277.5 IOF -83,750 - 48,907 - 2,687 0 167.5 ----J-

A E -68,750 -34‘9 24 0 137.54D - 19,750 0 39.5

Un if. -277,500 -238,000 -/40,000 - 110,000 0

v)nz0n

(Cont. P 1 I--1,000. ) I II I *I-lOO0. )

Figure B-6. Canyon Ferry Dam study-shears in twisted structure due to unit loads. -DS2-2(36)

CANYON FERRY DAM.2 ___.__________________________ SECTION. STUDY NO I. . . . . . _ . . . . . _ . . . . . _. * . . ..- __ _.._. ~_ ._..__._.

Figure B-7. Canyon Ferry Dam study-rotations of vertical twisted-structure elements due to unit couple loads. -D,Q-2(37)

.___ C.A.NYQ.l!..FERffY . ..DAM . . . .._...._. .__......_._ SECTION. STUDY NO..! . ..____.____...__._PARALLEL-SIDE CANTILEVER--STRESS ANALYSIS_-.~.~~AL_LOAD..-T.~!ST:..-..-..._ _ _ _ _ ...__ .D.~FLECTI!!N..OF..CA.I\!T!LE.VERS ____ 5!u.E.-To.-!.N!.!:!.AL...r_oaos ______._____.________.______________ _____.

__. ..__.__._ _ ~._~______~______.~.~~______~___~.__._~_~~~~__.__.~.~..............~~..~~. ------...---.--.-- _ . . _. . . . - . . - - . . - . ____ ...13y..&mf?e?I . ..Date???!6I I

Cantilevers

Elev. A B c D E F G H I J K L M

-

Bose of-36351.

:0:5/7, I

Figure B-8. Canyon Ferry Dam study-deflections of cantilevers due to initial loads. -DS2-2(38)

ww0

.__.__ CAN.VQN...F.ER.R.Y.-.DAM .._........_ _._. ._.. __.. __..._.. SECTION. STUDY NO.../. _____.____.___._.___CANTILEVER--STRESSI.. PARALLEL-SIDE. . . . . . . . . . . .._..._._.._.. ANALYSIS_.TRlAL--.C.OAD ?-J’!-:.r.__. ____.__

.__.. LQA.D..QRDiNA.T:ES.. .A7:._CA.N.TILE~E.R~..~.OJ~.T.S..~.LE.~.T...SlD.E ____________ ___ ____ __________ ______BEAM OR TWISTED- STRUCTURE LOADS .._._. By-.L:fil.S~..Date3-5.~f.6.

C a n t i l e v e r s

3eam L o a d Abf. A B c 3635L D E F Gn 4-Ew 1 . 0 765,i2 .596,5! .405,Bl .319,77 .227,9/ 0-~.cd dD 1 . 0 .‘2o- .695,78 .477,41 30,42 J/8,98 0

z AC 1. 0 604,70 .320,94 0

AB 1 . 0 .4 17,87 0

A G 1 . 0 .845,42 .591,686 70,58 ,507,46 .298,5/ .234,54 0

c\l - - - A L - /. 0 .7 98,05 .569,64 .466,5 7 .3 56,55 .083,57 0

co .-..-4 E 1 . 0 .‘7~E3 .530,40 .4/7,93 .2 9 7,87 0hv---- 4-D 1 . 0 .666,15 .33/,/7 .171,00 0

--AC 1 . 0 .530,74 0

A B 1 . 0 G

AG 1 . 0 .793,/5 .699,87 .6@0,25 .277,43 0353,09

Ir, AF 1 . 0 .713,75 .584,64 .446,77 ,104,71 0

(\1 IJE 1. 0h .680,3l .536,06 .3 082,0/

m .-AD 1 . 0 .482,65 .249,2 1 0

AC 1. 0 0

AG 1 . 0 .882,35 .756,:6 .4 15,i 5 .349,76 002 - - A F 1 . 0 B/9,07 .625,92 .I 46,70 0

v - - - - - AE I. 0 .787,97 , .56/,60 0

AD I. 0 .516,34 0

AG 1 . 0 .657,66 .504,50 .3 96,40 0

G AF I. 0 .764,/a .I 79,/o 0...~g AE 1. 0- - .712,73 0

AD 1. 0 0

Figure B-9. Canyon Ferry Dam study-load ordinates at cantilever points. -DS2-2(39)

-.__. GU!‘.??i?N...F.E!?.t?Y . ..DAM . . . . . . . . .._. _... _._ __ __ . SECTION. STUDY NO. PARALLEL-SIDE CANTILEVER--STRESS ANALYSIS_.T~!ALTLOAD _. ..- . . . . . . . . . . . . . . . ..___.....

. . ..TR!AL:.LOADMs ~!.5‘TR!.~.~L!C!N_.I,EF.T...S!~!E . . . . . .._.__. . ..__ mc!A.L...NO..!2. _ _. . . _ _ _ _. __.. __ ___ ______ __

1 IHorizontal twisted-structure l o a d s 1 Normal can t / lever loads

Unif OB’OC dD OE AF LIG Cone, A B G 36351. D

38085

3 7 6 2 + 1.0 +,973 1.397 1.877 2.093 2.324

3 725 +2 4 +.203 I.806 2.529 3.30/

3 6 8 0 +3.5 +.069 I. 697 t3.436

3 6 3 5 1t4.0 +.25/ t3.081

3 6 0 5 I i-3.0

t3 7 6 2 +.I -565. + 1. 0 1.798 +.570 +.467 +.357

I3 7 2 5 +a -3,645 t2.4 +I.713 1 'I.403 +1.072

3 6 8 0 c2.0 -6,060 +3.5 f2.867 +2.191

3 6 3 5 +40 -9,478 +4.0 +3 057

3 6 0 5 +35

3592 I

Figure B-IO. Canyon Ferry Dam study-trial-load distribution (trial NO. 1). -DS2-2(40)

r CANYON FERRY DAM ..__....___.____ ____ __.__ _ ._____ SECTION.-..._ . . . . . . ~ . . . . . . . . . . . . . . . . . . . . ._. STUDY NO I* . . . ___._ ._.. ___ .____ __PARALLEL-SIDE CANTILEVER--STRESS ANALYSIS--.-T.~!AL_LOAD.-.~W!.~T-~..--..

“1. . . . - . . . . _ _ _. _ _ _ _. . -I

TRIAL-LOAD DISTRISUTION-LEFT SIDE. . . . . . . . . . . . ..~....~~.......~......... _ . ..- _ .-....-._....- _ __-......--........ (FiNAi) -..-...--.- _ .-... _ __................._.____________ _.__.__._..____._ ___.._________. . . ~___________~..____.____.~~~.....~~. _ _.-_._.-..-...... _ _.... -- -.... ---.-_-_..__.--_..----_ . . . ..-... -- -... -..--__-_ .-.-. -_ ---._.- - .---.By.C..R;.S,..Date.4.16.46

2

Horizonfol t w i s t e d - s t r u c t u r e l o o d s Normal Cant i lever loads-2

LIG .!lF’DE AD 1lC bB Unif Cont. A B c 3635L D E F tsG I

3808.5 +.I5 - --./61 -.I35 -.I05 -.066 -.024 +.04 - - &

3762 - t4.0 -4.5 t.2 +.25 +o.os -5. 3.033 3.027 3.020 2.897 2.766 2.296 2.973 -?2.973 cn4 -_

37251+.3 $3.0 -2.0 -2.5 +l.O + .45 -30. 5.053 5.060 4.161 3.200 3.9 10 4.595 +II I I

3680 t1.9 t3.5 -3.0 - .5 + .e -50. t 1.469 i-1.789 i2.130 + 4.257 +5.940 +..--- ,,,

3635 +4.0 -2.5 + 1.7 --I/O. -+I 151 7+2.662 -+6.4/Z

3605f8.651 +8.65/ f+

t,3.000 r,

3592 Esttmated-” i/5.288 t12.469 t12.469 z

3762 t.10 -.06 t . 5 9 6 - 5 7 0 . 8 0 +.004 + ,008 + ,070 + ,136 + .384 -t .050 +.050

3725 f. 15 +.I -.I3 6 -5.324.3, t ,250 t ,262 t ,719 jl.206 f .a70 t ,533 + .450

3680 +w +.2 t 2 . 4 7 4 - 1 2 , 7 9 3 +2.700 f- 2.721 +2.744 +2.159 t 1.465 t .800

3635 +4.5 i.2 0 -I;:953 t3.200 t2.975 t-2.416 + 1.700 + 1.700360535921

c,3.500i E s t i m a t e d - . ’ 0 0 0

Figure B-II. Canyon Ferry Dam study-trial-load distribution (final) -DS2-2(41)

,W

CANYON F E R R Y . ..DAM . . . . . . . . .._....._... ._____.____. SECTION. STUDY NO...! ______._____________. wP._........._......._..____.____.

PARALLEL-SIDE CANTILEVER--STRESS ANALYSIS~T: _______________....TRIAL-LOAD.TW!eST __..______.._..._ . . . ..___...... _. ._..______ UNTILE.VeER. ..~-~.~~.ECTlON-.COM~(!NEN.~~-rLEE.T..S!DE. _______ _________ ___ ____ __________ __-__.

(FINAL)_ _ _ _ .__._._._.________ _ _________._._._________._____....________...__________________. .____._._. .____...__..._._... _ ._._...._ . ..By __._._ . . . ..Date.... _._.-...I I I

Canfilever Oy d u e i - o norirol l o a d s

A 6 C 3635L D E F G3808.5 !7lO~SS - 3 0 6 , 3 0 9 -J/3,045 - :019,684 .029,482 ~ -

I

structure element.

F&we ~-12. Canyon Ferry Dam study-cantilever deflection components (final). -DSZ-2(42) 2


structure. The three component deflectionsgiven on figure B-12 represent the deflectionsdue to trial loads on the structure which mustbe added algebraically to the deflections due toinitial loads (see fig. B-8) to obtain the totaldeflection of the cantilever structure. Thesevalues are shown on Figure B-l 3. It should ben o t e d a t t h i s p o i n t tha t t he abu tmen tmovements of each structure are equal.

B-8. Twisted-Structure Deflections. -Shearsdue to loads on the horizontal elements of thetwisted structure and angular rotations ofvertical elements due to these shears are shownon figure B-14. Loads on horizontal twistedelements in the upper left of figure B-l 1operate on unit shears to give the shear at eachp o i n t i n the horizontal twisted-structureelement. The shear is divided by negative 1,000to get units of twist load to operate on the unitrotations given on figure B-7 because themaximum ordinate for a unit twist load wasassumed to be minus 1,000 foot-pounds persquare foot. At each point where the verticalelement and beam have a common base andabutment, it is desirable to note the value ofabutment rotation of the vertical element dueto load on the beam. These values are obtainedfor each element from figure B-l 6 and areindicated by asterisks (*) on figure B-14. Atthe base of element D there is no beam and avalue is estimated.

In the upper half of figure B-l 5, rotations ofvertical elements are integrated from theabutment to the crown using values calculatedin figure B-14. Here the abutment rotations ofthe beams have been included. These aredeflections of the horizontal elements due torotation of vertical elements and abutmentrotation of the beams. In the lower half of thefigure are given the shear detrusions ofhorizontal elements due to loads on the beams(see the lower left-hand section of figure B-l 1).Detrusions are obtained by using deflectionsdue to unit shear loads on horizontal elementsas shown on figure B-3.

The lower half of figure B-16 shows valuesof shear detrusions due to twisted-structureloads. These are calculated by using deflectionsdue to unit shear loads on horizontal elements,from figure B-3. Not only are these values

componen t s o f t h e twisted-structuredeflections, but they are also components ofdeflections of the beam structure, as will beshown later.

At the base of the deflection columns forcantilevers A to D, inclusive, on the lower halfof figure B-16, the abutment movements of thecantilever and of the beam due to momentonly, Jh, are entered for inclusion in thetotal twisted-structure deflection. Thus, theabutment movement at the base of cantilever Ais equal to -.03 ,023 (fig. B-15) plus -.03 ,086,plus -.03 , 4 3 0 ( f i g . B - 1 6 ) o r e q u a l t o-.03 ,539. This is equal to the abutmentmovement at the base of the cantileverstructure at A (see fig. B-13). Finaltwisted-structure deflections are given on figureB-13. These are compared with beam andcantilever deflections given on this same sheet.

B - 9. Beam-Structure Deflections. -Deflections of beams due to bending arecalculated in the upper half of figure B-16.These are determined by means of beam loadsgiven on figure B-l 1 and unit deflections givenon figure B-2. Slopes at the abutment and atthe crown are also shown. Slopes at the crowninclude rotation of the common abutment dueto twist loads on the vertical elements, but theslope shown at the abutment is only therotation due to beam loads. Immediately aboveeach deflection due to bending, the deflectionof the beam due to rotation of the verticalelement at the abutment is entered. Deflectionsare calculated by multiplying the slope at theabutment by the horizontal distance to eachcantilever. At the abutment of each beam thereare also additional movements due to initial,trial normal, and trial shear loads on thecantilevers which are entered at the bottom offigure B-16. Another component of the totalbeam deflection is due to shear detrusion fortwisted-structure loads on horizontal elements.These values were previously calculated for thetwisted structure and are shown in the lowerhalf of figure B-16. Total deflections of beamsmay now be calculated by adding deflectionsdue to bending, rotation, shear detrusion, andabutment movement. For example, the totaldeflection at the abutment of beam 3762,which coincides with the base of cantilever A,

___. ~.~.N.‘CI!N...F~.~.~Y...DAM ._____........______ ._....____._ SECTION. STUDY NO...!PARALLEL-S IDE CANTILEVER- -STRESS ANALYSIS-. . .____ _. . . . _ _ __._ _... TR!AL.a?mTW!SI.

._. . __ . . . . _. . . . . . . . . . __ . . ._ _ .?x?TAC . .DEFCECT!ONS 7 . . - . . .L EF.Te.S!DE ____.._______._________...~~~...~..~.

. . __._. ._ . ___ ______ .___ __ _.__ .._ _ _ __ . . ..___. . . .._. . . ..--. . . (NNAL) __________________.___ ___________ _________ _____I

Beam deflection

Abf A B G 0 E F G A

Eli.5 -.0:034 YOOa49 -.OlO,225 7020,639 -029,166 -037,843 - - -,002,503

3 762 : Of539 -005,198 7013,444 ~021,169 -.028,365 7029,707 1031,175 7oy539

3 7 2 5 -.00/,895 :009,/Z/ -,016,82/ 7023,437 -.024,414 ~025,152

3 6 8 0 :004,6/l -YO/2,097 ‘7017,796 -019, I23 -.0/9,594

Figure B-13. Canyon Ferry Dam study-total deflections (final).-DS2-2(43)

3 7 6 2

3 7 2 5

A t a n y p o i n t i n s t r u c t u r e - (000 p o u n d sshear represents one unit of twist load.

-38,613 $014,22 -38,479 :03055,688 *Rota t ion o f abu tment due to beam loads .

-224,025 T~5020,019

Figure B-14. Canyon Ferry Dam study-shears in horizontal elements and rotations of vertical elements due to twistedsbucture load (final). -DS2-2(44) ww-..I

w

I CANYON !W?RY. e..DAM .__...__________ ____ ._______.._. SECTION. STUDY NO.../ .._______________._ _. E. . . . _ _

.-, ..IV * b” Y I ..Y” s -o.- VT. -e-y. ..:.-r...:...-.---.:--..--.-r.-.:.-.; ____ Y-:.-.:.7_; _______.~_____.______ e-w’-,-e ._._.__._ - -.-....---. _...

Elev. 3 8 0 8 . 5 3 7 6 2 3 7 2 5 3 6 8 0 3 6 3 5

a+ f.lPX J-09 II9 * Jo9 09* / J - 0 9 d9 * 1 Jn9 n+

A b f.

A

I .I I 1 *NntP: n d incl~~des rafotions d u e t o -I :/+.0* 0 I .“.” - - - - _ _ _5 0 . 5 bezri a b u t m e n t forces

:@049,240 :002,474 :0,3022,02 07fi 36

-.,-- ___ -___ __^ -2^ -, ^ - 0D I _” “aI I/./.?, . “ “ I ,,7/ 1 .qO67,640 ~,UU5, iis0 pJ,U3l,Y// 1 lJ I

1. ^ I I I I I

0 ALIT ?3,‘0 2 7,72 0t c II - ! 4’.u I- .1.-- __ I-_ ._

1.0;/33, 46 1 .U 16, /t- 3 9 :0,‘//2,36 :0/0,630 :#080,209 304,599 :@040,68I 1 3 8 . 2 5 1 1 9 . 7 5

1 D 1 ~0:130,09 1026,870 .0,3//2 6 3 b/9, 2 3 6 :0;087, /I a/O, 9 9 9 -&;058,69 TbO3,S 01 ‘ -3034 I7 ao/ 2 2 2, .I > .tt Idan I I I

._ _49. a

L , .“,YrV>I” .“” ,$, &. ,.“,“-J,Io ,.VL”,LJ-T ,.V,“L,,7J ,.“,“,“,L ,.v,vt,,vT 307,639,6 .O;O/l, 8 2 DO3, 4 7 6

I I5fl I 15 .0I I I 1

bv,v,r.av ,.,,J,87/ Iz:O//,7.2 1^017, 199 lIb:OO9,37 i-h& 0 7 4 .-$OOS, 2 5 303. 74 7I I I I I 5 5 . 0

1,060 x006,66 :003,724I I I

Tluic)nd- s t r u c t u r e f l y f o r b e a m loadsI c D E F G161 -.o:oo 7 -.ofo I 4 +0;0/7 - -

3762 - 0,‘023 - 0 , 9 8 2 -.0,‘309 -.0:3 8 0 -,0;4/3 -@4/7 -.0:4 3 I 0n

3 7 2 5 - .c:15/ -.of7 14 - 0 0 1 , 0 9 4 bO/,378 :00/,420 -00/,48/ t)

3 6 8 0

3 6 3 5

-.0;752 TCO/, 8 5 8 - 0 0 2 , 4 0 1 :002,4 56 :002,5 51

TOO/, 5 7 7 :002,285 :002,957 202,999 :003,057

Figure B-1.5. Canyon Ferry Dam study-twistedstructure deflection due to rotations of vertical element, and twisted-structure deflection due tobeam loads (final). -DSZ-2(45)

I- CANYON F E R R Y DAM .__.______.._._...__ .__.__._.___ SECTION. STUDY. . . NO.../ .._____..____ _ ______. 12-

I 1 Rotation 1 Beom Ay due to bend ing and sheardue to Beam Ay due to rotation of abutment caused by twist on vertical elements. 2

twist Abf. 1 A ! B c I D 1 E .F -1 G,b$$[~ds a?c?-?)i?

_ #OCR. -G

. !po851 0 \+.O;Or4 ! T032,216 ldO9, 324 IT019,646 17028,161 /TO36,838 1 -1 - p.op 25 ~~0,~085 1 15-

#XL 0 bO/, 031 :002,/9 7 :003,285 :004,678 TOO5,/05 :OC'6,6693762 :0,30/4 TO7034 :003, 061 :009,465 T0/5,508 :020,851 TOP/,747 :021,708 ~0,'008 fo;ol I4xL 0 '001,642 ~003,173 7005,134 TOO5,735 -007,938 c,3725 :0:020 TO:183 :003,740 :008,274 TO//,904 TO/2,187UJXL 0 302, i63 TOO4,934 :005,7823680 :0:01028 -0;815- ~003,455 :004,609 TOO4,8964XL ABT. -,0:744 :002,591 :003,1563635 1 :O:OlY 1 1:001,655 /DO&756 1!003,943 ~rOO3,850

I I II I I I I I ,

Beam dy, a lso twlsfed-structure ily (shear detrusionl due to tw is ted-s t ruc ture loads .

A b f B c D E F G?yO48 -.0:9Of -.0,'993 ~OOf,OO5 ~001,005 - -

3762 YOTO86 -.0T687 TOO/,363 :001,957 fOO2,417 1002,436 ~002,383

3725 -.0,%87 TOO2,514 :004,149 :005,174 305,267 -005,235

I

3680 I 301,609 x04,292 TOO6,066 ~066,258 7006,301I I I 1 I I I 1 I I I I I

3635 1 PO/,915 1:002,86/ jPO4,2// 1:004,365 lr004,277 1_.. _ IAbufmen? movemeqts o f b e o m d u e ,‘s loads o n o t h e r elpnenfs

1 (37621 1 f37251 1 (3680) 1 (3635) 11 :0;74/9 /:001,225 1:002,187 [TQ2,428 1

Abutment movements of twlsted structure due to loads on other elements.1 TO:430 ~'001,257 /1)02,250 ]ToO2,505 !

Figure B-16. Canyon Ferry Dam study-beam deflection due to beam loads and abutment rotations, and deflection of horizontal elements dueto twisted-structure loads (final).-DS2-2(46)

340

is equal to -.03 ,033,974, plus -.03 ,419, plus-.03 ,085,64 ( f i g . B - 1 6 ) , o r -.03,539.Inspection of figure B-13 shows that this agreeswith the cantilever and twisted-structuredeflections at the same point.

B-10. TotaZ Deflections. -Total deflectionsfor the right side of the dam are given on figureB-17. Note that at the crown point, G, thedeflections agree closely with those computedfor G for the left side of the dam (see fig.B-13).

B-l 1. Moment and Shear due to Trial Loadson Beams.-Total bending moments for eachbeam are calculated by multiplying final beamloads by bending moments in beams due tounit loads. The total shear is obtained byadding the beam load and the twisted-structurel o a d o n the ho r i zon ta l e l emen t , andmultiplying the result by the shear due to unitload. These moments and shears are tabulatedfor the left side of the dam on figure B- 18.

B-12. Beam Stresses.-Stresses at the facesof beams due to pure bending are calculatedfrom the well-known formula, uX = + MC/I. Noweight is carried by the beams, since it hasbeen assumed that weight is assigned to thecantilevers. Beam stresses are calculated inpounds per square foot, but are tabulated inpounds per square inch. These calculations arenot shown due to their simplicity.

B- 13. Canti lever Stresses. -Verticalcantilever stresses at the faces are calculated bymeans of the usual formula, W/A +- Me/I. Theinclined cantilever stress parallel to either faceof the dam at any point is calculated bydividing the corresponding vertical cantileverstress by the square of the cosine of the angle,#, between the face and a vertical line, andsubtracting from this quotient the product ofthe net normal water pressure and the squareof the tangent of the angle 4. (See the lowerpart of figure 4-2 for equation and method ofallowing for earthquake effect.)

In the example given here, an upwardvertical earthquake acceleration was assumed.Consequently, the effective weight of the damis found by multiplying by 1.1. The totalmoment is found by adding algebraically themoments due to weight, horizontal earthquake,vertical waterload, vertical earthquake, ice


load, and trial load on the cantilever. Stressesat the faces are then calculated, using thefo rmu la s men t ioned i n t he p r eced ingparagraph. Principal stresses are calculated bymeans of equations given on figure 4-3.

Stability factors on horizontal planes arecomputed by formulas previously given insection 4-10. In computing the stability factorson inclined abutment planes, the equivalenthorizontal force is the total shearing force dueto the sum of the shears from the cantileverelement and the abutting horizontal element ofthe twisted structure.

Assuming a unit area on the sloping surface,the total inclined abutment shear is computedby the equation,

where :

C V= total inclined abutment shear onunit area,

V, = shear in horizontal plane at baseof cantilever,

V, = shear in vertical plane at abutmentof horizontal element, and

$ = angle between vertical and inclinedplane of contact.

The total force normal to the inclinedabutment plane is equal to the resultant of thetotal vertical force and horizontal thrusttransferred from the vertical cantilever andhorizontal element, respectively. This force(see fig. B-l 9) is equal to

where :

FN = total force normal to inclinedabutment plane,

U= uplift force, and$J = angle between the vertical and the

inclined abutment plane.

After the above values have been obtained,the sliding factor is computed by dividing thetotal inclined abutment shear by the normal

. ..CA.A!.YON..F.ERRU. . ..DAM .._.....__.. ____ ..__ ._.. __ ._ .___ SECTION. STUDY NO I* . . _ _ . . - . . . . . _ . . _PARALLEL-S IDE CANTILEVER- -STRESS ANALYSIS--~/AL-LOAD TWIST. . . . . . .._..__..___. .._____._ .--__ . . ..___..___........._.___ _ .___._____ ____

_ _ . ..TQ nlL. _ BEI4 -4. d.Jvl. _ r-~!s.r.~o_sr-~clCr~~ .~~.~~~X.~.~~Q.lw. .y.mRT--. _ s!QE- ___ _ _ _ . _ _ __ _ _ _ _ _ __ ____._...__.__.. _ .__.___.__ _ __...__ _ __.__ _ .__._._.._....... _ . . . .._....... m!MLZ _ . . _ . . . . . . _ . . . _ . _. . . _. __ ._. _. . . _ _ . . _. __._ . ..B~..C..R~S.-Date..4~!(?-46

B e a m d e f l e c t i o n Can/i/ever d e f l e c t i o n

Abf. ! M 1 K J 1 I H G M L K J

808.5 ~0,3006 7002,408 ~008,/62 -.017,065 T025,7/1 1031,664 - - Too2,9/5 ,009,264 7016,625 7024,270

3762 -.O;ls49 7004,945 :012,494 -Yo20,04/ 7024,672 7026,983 '~031,495 - .Of649 7004,820 :0/l, 121 ~018,237

3725 -.002,/68 7009,2/5 ~016,377 -020,372 ~022,163 ~025,882 -~002,168 :00<379 7013,896

3680 7004,0!8 ~010,172 :014,003 ~015,831 7019,603 r004,OIB 7OOq547

3635r I ~006,033 :009,327 :0/0,912 70/4,019 ?W6,033

Twlsted -s t ruc tu re de f lec t ion

Abt. M L K J I j H G I H G

3808.5 -.O:OOS Tool,993 TOO7;178 :016,576 :026,/67 ~031,239 - - f031,092 - -

3762 -.Of649 TOO4,670 ~012,365 ~020,548 ~025,360 ~027,278 ~030,503 ~024,027 ~026,447 -030,919

3725 7002,168 :008,698 ~015,580 :020,008 ~021,963 ~025,401 :Ol8,920 7021,739 ~025,570

3680 7004,018 7009,820 ~0013,695 ~015,571 ~018,667 ~013,642 ~016,673 :Ol9,685

3635 7006,033 :009,644 7011,393 -014,419 ~009,2 553603

.:011,856 7013,9177006,758

3592 7007,434 ~008,652

Figure B-I 7. Canyon Ferry Dam study-total beam and twistedstructure deflections (final). -DS2-2(47) wP

wt-5

. ..__._._..... _.._.

PARALLEL-SIDE CANTILEVER--STRESS A

CJY20z

2c,

M = B e a m ffia: lOad5 tim2s unl? m o m e n t (5

‘mes unit s h e a r (!I,) in =Ii

iz~~~~~ ~-18. canyon Ferry Dam study-bending moments in beam due to trial loads (final), and total shear in horizontal elements due to trialloads (final). -DS2-2(48) cn


Figure B-l 9. Force normal to an inclined abutmentplane. -DS2-2(49)

resisting force. The shear-friction factor is alsocomputed. See section 4-10 for equations and adiscussion of these factors. If the computedfactors are not within the allowable values, the

B-14. Final Results. -Final results of thetrial-load twist analysis of Canyon Ferry Damare given on figures B-20 to B-25, inclusive.

dam must be reproportioned to correct this

These show load distribution and adjustmenton horizontal and vertical elements; stresses in

condition.

horizontal beams and cantilevers; principalstresses at the faces of the dam; and stabilityfactors for both the twist analysis and thegravity analysis.

The following conclusions were made fromthe twist analysis:

(1) Results determined from the trial-loadtwist analysis show tha t t he max imumcompressive principal stress is 263 pounds persquare inch and occurs at elevation 3680 at thedownstream face of cantilever C.

(2) The maximum tensile principal stressoccurs at the upstream face of the rightabutment of the beam at elevation 3725 and

amounts to 146 pounds per square inch.(3) The maximum rock-plane shearing stress

occurs at the base of cantilever G, elevation3592, and also at the left abutment of thebeam at elevation 3635, and amounts to 101pounds per square inch.

(4 ) The max imum s l i d ing f ac to r onhorizontal planes is 0.812 and occurs atelevation 3725 in cantilever G. The maximumsliding factor on inclined abutment planesoccurs at the base of cantilever L and is 1.197.

(5) The minimum shear-friction factor ofsafety on horizontal planes is 6.78 and occursat the base elevation of cantilever G. Theminimum shear-friction factor on inclinedabutment planes is 6.32 and occurs at the baseof cantilever C.

( 7 ) I n o r d e r t o r e d u c e t h e e x t e n t o fdiagonal cracking, it is recommended that theconcrete in the dam be subcooled 8O F. orm o r e , if possible, be low mean annua ltemperature prior to grouting the contractionjoints.

(6) Tensile principal stresses which occur atthe left and right abutments of the dam atpractically all elevations at the upstream faceindicate that some diagonal cracking may occurin the concrete in these regions.

(8) Maximum compressive stresses in thebeams and cantilevers, principal compressivestresses, and rock-plane shear stresses areconservative and well within allowable designlimits for good concrete.

(9) The maximum sliding factor of 1.197that occurs at the inclined base of cantilever Li n d i c a t e s t h a t s o m e w h a t u n s a t i s f a c t o r ystability conditions may be considered to existat higher elevations along the abutments of thedam if sliding factors are used as the criterionfor judging whether or not the dam is safeagainst failure by sliding. However, ifshear-friction factors are used as the criterioninstead of the sliding factors, stabilityconditions in the dam can be considered asbeing satisfactory. The minimum value for theshear-friction factor calculated from thetrial-load twist analysis was 6.32.

BEAM AT ELEVATION 3606 .5

BEAM AT ELEVATION 3660

E F G




NOTES0 = Cant,Iever deflecttonsx = Deflection of twIsted structureA = Deflectton o f horlzontol beam

and stresses

Figure B-20. Canyon Ferry Dam study-load distribution and adjustment on horizontal elements.

H

N O T E SFor constants,ass”mp+,o”s,ond

loadmg candhans see DenverOfflce Drawng No 296-O-66

O=Cantllever deflehona*?rlrted structure deflectlo”x’Hmzontal beam deflecbn

TRI&L LOAD TWIST AN0 BEAM ANALYSISRESERVOIR FULL-EARTHWAKE INCLUDED-JOINTS GROUTEL O A D D I S T R I B U T I O N A N D A D J U S T M E N T

CHECKED j&&q. A~~RO”ED,“‘““~“““:,“p,qP”,,:“‘“,“.‘,296-D-6fFigure B-21. Canyon Ferry Dam study-load distribution and adjustment on cantilever elements.

1CANTILEVER STRESSES

Figure B-22. Canyon Ferry Dam study-stresses in horizontal beam elements and in cantilever elements.

\ ’ AP R O F I L E L O O K I N G U P S T R E A M /

n D I R E C T I O N S O F P R I N C I P A L S T R E S S E S

P R O F I L E L O O K I N G U P S T R E A MV A L U E S O F P R I N C I P A L S T R E S S E S

STUDY NO I -TN O T E S

Principal stresses areoctlng parallel tothefoceof thedamOPI : First princepal stress Ope=Second pr~nupalstressa=Angletlrstpr~ncipoi stress(uPllmokes wth the vert,co,,

posltlve angle measured in 0 cltiw~se dlrectlon on theleftsldeof thedom,and I” o counter-clockwise dIrectionon the right sIdeof thedam.

f Indicates ( I compressive stress-: Compression - : Tensmn.All stresses are I” pounds persquore Inch

Figure B-23. Canyon Ferry Dam study-principal stresses at upstream face of dam.

/ / IIPROFILE LOOKING UPSTREAMDIFEC;TIONS O F PRI,NCIPAL

N O T E S

Pr~nclpal stresses are acting porollel to thefaceof the dam.opt : First prlnclpal stress. up2 ~Second prlnclpol stressO::Anqlefint principal stress(Upl)makes withthe vertical,

poslt~veangle measured I” o clockwise direction on thelefts1deofthedam,ond ~nocounter-clockwse dlrectiononthe r,ght sdeofthe dam

P R O F I L E L O O K I N G U P S T R E A MVALUES OF PRINCIPAL STRESSES

Figure B-24. Canyon Ferry Dam study-principal stresses at downstream face of dam.

Cantilever restrolned by thruston odlocent element

Welqht of concrete:l5Opounds percub,c footSlldlng factors ore forcond~tlon of reserwr

wotersurfoce at elevatlon3800Oeorthquokeeffect \nc,uded and%uplift assumed

Ice load 7 tans, II” ft

Jomts assumed groufed so thatdom con act us monolith

NOTESSlldtnq factors and shear frlctlon toctors of safety for grovlty onalysls oreshown on ups+re,,m s,de.Slldlnq factors and sheor friction factors of safety fortrial loadanalysis ore shownondownstream s,de.Shding factors are shown above elevotlonlmes of cantilever Sbeor friction factors ore shown below

elevotlon lhnes of canfllever Factors deslgnoted byi:- ore for lncllned abutment pionesSItdIng factors,S= Horlzon+o’ Force (for horIzonto planes)

Weight - UplIftShding foctars,S= ~~~?f~~~~~;;;secm lfor abutmentpiones)

Sheor trlctlonfoctors of sofety,Q,two-thirds upl,fi=[Weight-UpiMt)x Coefflclent of Internal Friction+BaseAreo x Umt Shear Resistance CANION FERR” PROJECT-YOITAUA

Horlzontol Force (for hortzootal planes) C A N Y O N F E R R Y D A MSheor frtctioo factors of sofety,Q,two-thirds uplIft =(Weight -Upllft)Sec 0xCoefficlent of lnternol Frlctlon + Bose Area x Unit Shear Resistance (fo, abutment p,ones,

TRIAL LOAD TWIST AND BEAM ANALYSlSRESERVOIR FULL-EARTHQUAKE INCLUDED-JOINTS GROUTEC

Horizontal ForceCwfflclent ot Internal Frtctloo=065,UnttShear ReslstanCe=7OOpounds per squore,“ch

SLIDING FACTORS AND SHEAR-FRICTION FACTOR!OF SAFETY FOR TRIAL LOAD AND GRAVITY ANALYSE:

Figure B-25. Canyon Ferry Dam study-sliding factors and shear-friction factors of safety for trial-load and gravity analyses.

<<Appendix C

F i n i t e E l e m e n t M e t h o d o f A n a l y s i s

A. TWO-DIMENSIONAL FINITE ELEMENT ANALYSIS

C- 1. Introduction. -The two-dimensionalfinite element analysis, discussed in sections4-36 through 4-44, is illustrated by thefollowing foundation study of the GrandCoulee Forebay Dam. Figure C-l shows apartial grid of section DG through the dam,reservoir, and foundation.

C-2. Description of Problem. -Foundationrock under Grand Coulee Forebay Dam andreservoir has a wide range of deformationmoduli, with several faults or planes ofweakness. One fault area, because of its lowmodulus, causes the concrete in the damimmediately above it to bridge over the faultcausing horizontal tensions. By treating thisfault (replacing part of the low-modulus faultmaterial with concrete) these stresses in thedam will be minimized. This study was made todetermine the depth of treatment necessary toobtain satisfactory stress.

C-3. Grid and Numbering System. -FigureC-l shows a portion of the grid used in thisstudy. The nodes are numbered starting in theupper right corner and from left to right ateach elevation. The entire grid has 551 nodalpoints. The elements are designated by anumber in a circle. The numbering starts in theupper right corner and proceeds from left toright in horizontal rows. The entire grid has517 elements. Numbers in squares designatethe material numbers. The boundaries for eachmaterial are defined by elements. There are 23materials assumed in this study.

C-4. Input.-Printouts of portions of theinput are shown on figures C-2, C-3, and C-4.

Figure C-2 shows the number of nodal points,the number of elements, and the number ofdifferent materials as indicated above. Anacceleration of - 1.0 in the Y-direction is ameans of including the weight of the materials.Each material is defined for mass density,moduli of elasticity in compression andtension, and Poisson’s ratio. Figure C-3 is alisting of the nodal points showing type ofrestraint (if any), X and Y coordinates, load ordisplacement in the X or Y direction, andtemperature. As an example node 19 is free tomove in either direction; it is 653.0 feet to theright of the X reference line and 799.0 feetupward from the Y reference line; and ahorizontal load of 27.0 kips is acting on thenode in a direction to the left. There is no loadin the Y direction and no temperature change.

Figure C-4 is a listing of the nodes enclosingan element and the element material. As anexample, element 45 is bounded by nodes 53,52, 63, 64 and is composed of material number6.

C-5. Output.-The results of an analysis aregiven as the displacements of the nodes in theX and Y directions and the stresses in theelements.

A printout of displacements for nodes 51through 100 for the condition of no treatmentof the foundation is shown on figure C-5. Asimilar printout for a loading condition wherethe foundation is treated for 25 feet is shownon figure C-6. Without treatment, node 69 isdisplaced 0.007,05 foot in the X direction tothe left and 0.037,6 foot downward. After the

351

Y+

t -+

X

/RES. W A T E R S U R F A C E1 2 9 0

M A T E R I A L S

E = 1.0 x IO~PSL - Bounded by elements58,60, 113, 112, 136, 165.

E = 2.0 x 10~ psi - Bounded by elements1 3 9 , 1 6 6 , 2 0 2 .

E = 3 o x 106 psi - Bounded by elements65,78,283,270 a n d 1,82,287,288,2.

E = 0.5 x 106 psi - Bounded by elements1 4 0 , 2 3 5 ; 7 9 , 2 8 4 ; 81, 2 8 6

E = 5 , 7 5 0 p s i - B o u n d e d b y e l e m e n t s86, 2 8 5 .

E = 3.0 x 10~ psi - Bounded by elements5 . 6 . 5 5 . 4 8 .

E = 310 ; 106’psi -Bounded by elements6 8 , 2 7 7 .

E = 3.0 I 10~ ps~ - Bounded by elements6 4 , 2 6 9 .

*NO. E L E M E N T N O .

21

57 - I I I I 1 64 * c ..“r.,.. ,.., cl. +ran+“.an+ -4 a,nm,%n+r H2 2

6 9 w I I I I-I17 78 79 80 BI 82 03 84 8 5 8 6 87 BB 89- - I.. .I I , I I , \ \ \ \\\\

/ 9il/99Yoo"/ /-/ / 105V

-I I Ill0 \- \ \

// IlOl/ (9oh / / I A \ I I

6 5 \

L N O D E S A T B A S E

I \ \255

290

@320

A R E F I X E D I

F i g u r e C-l . Grid layout for section DG of Grand Coulee Forebay Dam, including excavated cut slope along canyon wall at right.

ANALYSIS OF PLANE PROBLEMS PAGE NUMBER 1 z

DATE 05/27/70 -ICOULEE 3RD “::FOUNDAT I ON= SEC. DG, GRID 9, HYDRO LOAD, NO TREATMENT m

zXXXX::XXXYX INPUT DATA XXXXXXXX:::: NOTE-- INPUT UNITS MATCH OUTPUT UNITS UNLESS SPECIFIED

1

DATA PREPARED BY----

DATA CHECKED BY- - - - -

COULEE 3RD ““FOUNDATIONX” SEC. DG, GRID 9, HYDRO LOAD, NO TREATMENT

NUMBER OF NODAL POINTS------551

N U M B E R O F E L E M E N T S - - - - - - - - - - 5 1 7

NUMBER OF DIFF. MATERIALS--- 23

NUMBER OF PRESSURE CARDS---- -3

X - A C C E L E R A T I O N - - - - - - - - - - - - - - -O.OOOO+OOO

Y - A C C E L E R A T I O N - - - - - - - - - - - - - - -1.0000+000

REFERENCE TEMPERATURE------- -O.OOOO+OOO

NUMBER OF APPROXIMATIONS-- - - 1

MATERIAL NUMBER = 1, NUMBER OF TEMPERATURE CARDS q 1, MASF DENSITY = - O . O O O O + o o o

TEMPERATURE E(C) NU E(T) G/H2 ALPHA X-STRESS Y-STRESS- 0 . 0 0 0 1 4 4 0 0 0 . 0 0 0 0 0 0 0 0 . 1 3 0 0 0 0 0 1 4 4 0 0 0 . 0 0 0 0 0 0 0 - 0 . 0 0 0 0 0 0 0 - 0 . 0 0 0 0 0 0 0 - 0 . 0 0 0 0 0 0 0 - 0 . 0 0 0 0 0 0 0

MATERIAL NUMBER = 2 , NUMBER OF TEMPERATURE CARDS = 1, MASS DENSITY q -o.oooo+ooo

TEMPERATURE E(C) NU E(T) G/H2 ALPHA X-STRESS Y-STRESS- 0 . 0 0 0 2 8 8 0 0 0 . 0 0 0 0 0 0 0 0 . 1 3 0 0 0 0 0 2 8 8 0 0 0 . 0 0 0 0 0 0 0 - 0 . 0 0 0 0 0 0 0 - 0 . 0 0 0 0 0 0 0 - 0 . 0 0 0 0 0 0 0 - 0 . 0 0 0 0 0 0 0

MATERIAL NUMBER q 3 , NUMBER OF TEMPERATURE CARDS = 1, MASS DENSITY = - o . o o o o + o o o

TEMPERATURE E(C) NU E(T) G/H2 ALPHA X-STRESS Y-STRESS- 0 . 0 0 0 4 3 2 0 0 0 . 0 0 0 0 0 0 0 0.1300000 4 3 2 0 0 0 . 0 0 0 0 0 0 0 -0 .ooooooo - 0 . 0 0 0 0 0 0 0 - 0 . 0 0 0 0 0 0 0 - 0 . 0 0 0 0 0 0 0

MATERIAL NUMBER = 4 , NUMBER OF TEMPERATURE CARDS = 1, MASS DENSITY = - o . o o o o + o o o

TEMPERATURE E(C) NU E(T) G/H2 ALPHA X-STRESS Y-STRESS- 0 . 0 0 0 7 2 0 0 0 . 0 0 0 0 0 0 0 0 . 1 3 0 0 0 0 0 72000 .OOOOOOO -0 .ooooooo - 0 . 0 0 0 0 0 0 0 - 0 . 0 0 0 0 0 0 0 - 0 . 0 0 0 0 0 0 0

MATERIAL NUMBER q 5 , NUMBER OF TEMPERATURE CARDS q 1, MASS DENSITY q -0. oooo+ooo

TEMPERATURE E(C) NU E(T) G/H2 ALPHA X-STRESS Y-STRESS- 0 . 0 0 0 8 2 8 . 0 0 0 0 0 0 0 0 . 2 5 0 0 0 0 0 8 2 8 . 0 0 0 0 0 0 0 - 0 . 0 0 0 0 0 0 0 - 0 . 0 0 0 0 0 0 0 - 0 . 0 0 0 0 0 0 0 -0 .ooooooo

Figure C-2. Two-dimensional input data-control data and material properties. -288-D-3160 zw

NODAL POINT T Y P E X - O R D I N A T E Y - O R D I N A T ECFT) (FT)

1 1 . 0 0 1081 .DOD 8 8 0 . 0 0 02 0 . 0 0 1072 .OOO 859 .DOO3 0 . 0 0 1 0 7 6 . 5 0 0 8 5 9 . o o o4 1 . 0 0 1081 .OOD 8 5 9 . o o o5 0.00 6 2 3 . 0 0 0 8 3 6 . 0 0 0

X L O A D O R D I S P L A C E M E N T Y L O A D OR D I S P L A C E M E N T(KIPS) (FT) (KIPS) (FT)

-O.DOOOOOO+DOO -D.DODDODD+OOO-O.OOODOOO+OOO -O.DDOOOOO+OOO

o . o o o o o o o + o o o D.DDOODDO+OOO-O.OOOOOOO+OOD -0 .OOOOOOO+ODO-O.OOOODOO+DOO -O.DOOOODO+OOO

TEMPERATURE(DEG F)

-0. DOD- 0 . 0 0 00.000

- 0 . 0 0 0- 0 . 0 0 0

6 0 . 0 0 6 3 7 . 5 0 0 8 3 6 . 5 0 0 D .OOOOOOO+OOO D.OOOOOOO+OOD 0 . 0 0 07 0.00 6 5 2 . 0 0 0 837 .ODO -O.OOOOODO+OOO -O.OOOODOO+OOO - 0 . 0 0 0a 0 . 0 0 1 0 6 0 . 0 0 0 837 .OOO -0 .DOOOODO+DOO -O.OOOOODD+ODD - 0 . 0 0 09 0 . 0 0 1 0 7 0 . 0 0 0 8 3 7 . 0 0 0 D .OOODOOO+ODO o . o o o o o o o + o o o 0 . 0 0 0

10 1 . 0 0 1080.000 8 3 7 . 0 0 0 -D.OOOODOO+DOD - o . o o o o o o o + o o o - 0 . 0 0 0

11 0 . 0 0 6 2 3 . 0 0 0 8 1 9 . 0 0 0 - o . o o o o o o o + o o o -O.OOODOOO+OOO - 0 . 0 0 012 0 . 0 0 6 3 8 . 0 0 0 819 .ooo 0 .OOOODOO+OOD O.ODDDODD+OOO 0 . 0 0 013 0 . 0 0 653 .DDO 819.000 -1.1250000+000 -D.DOODDOO+DOO - 0 . 0 0 014 0 . 0 0 1051 .DDO 819 .ODO 1.1250000+000 -5.06ODDOO-001 - 0 . 0 0 015 0.00 1 0 6 5 . 5 0 0 819 .DOO O.DODODDD+OOO O.OOOOOOO+ODO 0 . 0 0 0

16 1 . 0 0 108D.ODO 8 1 9 . 0 0 0 -O.OODODOD+OOO -O.OOOOOOD+OOD - 0 . 0 0 017 0 . 0 0 623 .OOO 7 9 9 . o o o -O.OOOOOOD+OOO -O.DODDODO+OOD - 0 . 0 0 018 0 . 0 0 6 3 8 . 0 0 0 7 9 9 . o o o o . o o o o o o o + o o o O.OOOOOOO+OOD 0 . 0 0 019 0 . 0 0 6 5 3 . 0 0 0 7 9 9 . 0 0 0 -2.7ODOODD+ODl - o . o o o o o o o + o o o - 0 . 0 0 02 0 0 . 0 0 1042 .ODD 7 9 9 . o o o 2.7DOODOO+DOl -1.2938000+001 - 0 . 0 0 0

2 1 0.00 1 0 6 1 . 5 0 0 7 9 9 . 0 0 0 O.OOOOOOO+DOO O.OOOODDO+OOD 0 . 0 0 02 2 1 . 0 0 1081 .DOO 7 9 9 . 0 0 0 -0 .OODDOOO+ODO -O.OOODODO+OOO - 0 . 0 0 02 3 0 . 0 0 6 0 6 . 0 0 0 7 7 1 . o o o -D.OODOOOO+DDD -O.OOOOOOD+ODO - 0 . 0 0 02 4 0 . 0 0 6 2 1 . 6 6 7 7 7 1 . 0 0 0 O.OOODDOO+OOO O.OOOOOOO+ODO 0 . 0 0 02 5 0 . 0 0 6 3 7 . 3 3 3 7 7 1 . 0 0 0 O.DOODODO+OOO O.OOOOOOO+DOO 0 . 0 0 0

2 6 0 . 0 0 6 5 3 . 0 0 0 7 7 1 . 0 0 0 -7.7000000+001 -O.OOOODDD+DDD - 0 . 0 0 02 7 0 . 0 0 1 0 2 8 . o o o 7 7 1 . o o o 7.7OOODDD+DOl -3.85DOOOO+ODl - 0 . o o o2 8 0 . 0 0 1 0 5 4 . 5 0 0 7 7 1 . 0 0 0 D.OOOOOOO+OOO O.OOOOOOO+ODD 0 . 0 0 02 9 1.00 1081 .DOO 7 7 1 . 0 0 0 -O.DOODOOO+OOO -O.OODOOOO+DOD - 0 . 0 0 03 0 0.00 5 8 7 . 0 0 0 7 4 3 . o o o - o . o o o o o o o + o o o - o . o o o o o o o + o o o - 0 . 0 0 0

3 1 0 . 0 0 6 0 3 . 5 0 0 7 4 3 . o o o O.OODOOOO+OOO D.DOOODDO+OOO 0 . 0 0 03 2 0 . 0 0 6 2 0 . 0 0 0 7 4 3 . 0 0 0 0 .DODODOO+OOO O.ODDDDDO+DDD 0 . 0 0 03 3 0.00 6 3 6 . 5 0 0 743 .DOO O.OODDOOO+DOO O.OOOOOOO+OD’J 0 . 0 0 03 4 0 . 0 0 653 .OOO 743 .ODD -1.2867800+002 -0. DOODDOO+OOO - 0 . 0 0 03 5 0 . 0 0 1 0 1 4 . 0 0 0 7 4 3 . 0 0 0 1.28678OO+ODZ -6.3210000+001 - 0 . o o o

3 6 0 . 0 0 1 0 4 7 . 5 0 0 7 4 3 . 0 0 0 o . o o o o o o o + o o o D.OOOODDO+ODO 0 . 0 0 03 7 1 . 0 0 1081 .OOD 743 .OOD -D.OOOOOOO+DOD -O.DOOOODD+OOO - 0 . 0 0 03 8 0 . 0 0 5 7 0 . 0 0 0 7 1 4 . 0 0 0 -O.DDOOOOO+ODO -O.OOOOOOO+ODO - 0 . 0 0 03 9 0.00 5 8 6 . 6 0 0 7 1 4 . 0 0 0 D.DOOOODD+OOO O.OOOOOOD+OOO 0 . 0 0 04 0 0.00 6 0 3 . 2 0 0 7 1 4 . 0 0 0 D.DODDOOD+OOO O.OODOOOD+OOO 0 . 0 0 0

4 1 0 . 0 0 6 1 9 . 8 0 0 7 1 4 . 0 0 04 2 0.00 6 3 6 . 4 0 0 7 1 4 . 0 0 04 3 0 . 0 0 6 5 3 .DOO 7 1 4 . 0 0 04 4 0 . 0 0 1000.000 7 1 4 . 0 0 04 5 0 . 0 0 1040.500 7 1 4 . 0 0 0

1 . 0 0 1081 .DOO 7 1 4 . 0 0 00.00 552 .DDO 6 8 7 . 0 0 00 . 0 0 5 6 5 . 0 0 0 687 .OOO0 . 0 0 5 8 2 . 6 0 0 687 .OOO0 . 0 0 6 0 0 . 2 0 0 687 .OOO

D.ODDDOOD+OOO o . o o o o o o o + o o oo . o o o o o o o + o o o D.OOODOOO+DDO

-1.7586800+002 -O.OOOOOOO+OOD1.7900900+002 -8.7934DOD+DDl0 .DDOOOOO+DOO O.DOOOOOO+OOO

-O.ODOODOO+OOO -O.OOOOOOO+DDO-D.ODOOODD+OOO -O.OODOOOO+OOO-D.OODDOOO+OOO -O.OOOOOOO+ODD

0 . o o o o o o o + o o o o . o o o o o o o + o o oD.OOODDOO+OOO O.OOOOOOO+ODO

0 . 0 0 00 . 0 0 0

- 0 . 0 0 0- 0 . 0 0 0

0 . 0 0 0

4 64 7

:;50

- 0 . 0 0 0- 0 . 0 0 0-0.000

0 . 0 0 00 . 0 0 0

A N A L Y S I S O F P L A N E P R O B L E M S

C O U L E E 3 R D “::FOUNDATION:::: S E C . D G , G R I D 9 , H Y D R O L O A D , N O T R E A T M E N T

P A G E N U M B E R 4D A T E D5/27/70

Figure C-3. Two-dimensional input data-loading and description of section by nodal points. -288-D-3161

FINITE METHOD-Sec. C-5 355

A N A L Y S I S O F P L A N E P R O B L E M S P A G E N U M B E R 1 6DATE 05/2?/?0

COULEE 3RD ::::FOUNDAT I ON::” S E C . D G , G R I D 9 , H Y D R O L O A D , N O T R E A T M E N T

E L E M E N T N O I J K L M A T E R I A L

ia9

1 1

I9

1 01 2

6 7 6 1 2 1 37 9 a 1 4 1 5a 10 9 1 5 1 69 1 2 1 1 1 7 ia

10 1 3 1 2 l a 1 9

1 1 1 5 1 4 20 2 11 2 1 6 1 5 2 1 2 21 3 1 7 2 3 24 2414 l a 1 7 24 2 51 5 19 l a 2 5 2 6

1 6 2 1 20 27 2 8 31 7 2 2 2 1 28 2 9 3ia 2 3 30 3 1 3 1 619 24 23 3 1 3 2 620 2 5 24 3 2 3 3 6

2 1 2 6 2 5 3 3 342 2 2 8 27 35 3 62 3 2 9 2 8 36 3 724 30 38 3 9 3 92 5 3 1 30 3 9 40

25 3 2 3 1 40 4 1 627 3 3 3 2 4 1 42 62 8 34 3 3 42 43 62 9 36 35 44 4 5 330 3 7 3 6 45 46 3

3 1 38 4 7 48 483 2 3 9 3 8 4 8 4 93 3 40 3 9 49 5034 4 1 40 50 5 135 42 4 1 5 1 5 2

3 6 4 3 42 5 2 5 33 7 45 44 54 5 53 8 46 4 5 5 5 563 9 47 57 5 8 584 0 48 47 5 8 5 9

4 1 4 9 4842 5 0 4 94 3 5 1 S O44 52 5145 5 3 5 2

5 9606 1

i:

606 1

66:64

46 55 5447 5 6 5 548 57 694 9 5 8 5 7S O 5 9 5 8

270707 1

666 7707172

Figure C-4. Two-dimensional input data-elements defined by nodal points with material. -288-D-3162


A N A L Y S I S O F P L A N E P R O B L E M S P A G E N U M B E R 2 8DATE 05/27/70

C O U L E E 3 R D z=FOUNDATION”” S E C . D G , G R I D 9 , H Y D R O L O A D , N O T R E A T M E N T

N O D A L P O I N T D I S P L A C E M E N T - - X D I S P L A C E M E N T - - Y<FT) (FT)

5 1 -1.9811064-002 - 2 . 0 6 6 7 8 7 8 - 0 0 25 2 -1.9941570-002 - 1 . 6 6 0 7 7 3 6 - 0 0 25 3 -2.0141816-002 -1.2279052-0025 4 1.2091843-003 -2.4071188-0025 5 5.5973499-004 -2.3599376-002

5 65 75 85 96 0

o.ooooooo+ooo-1.2884864-002-1.3239801-002-1.3559575-002-1.3979795-002

-2.3429267-002- 3 . 7 5 6 1 1 3 8 - 0 0 2- 3 . 5 2 8 8 5 6 7 - 0 0 2- 3 . 2 8 1 2 6 3 7 - 0 0 2-2.8402294-002

6 1 -1.3880246-002 - 2 . 4 0 4 6 1 1 2 - 0 0 26 2 -1.3516598-002 -1.9974260-0026 3 -1.3437772-002 -1.6478346-0026 4 -1.3871664-002 -1.2207339-0026 5 1.2985815-003 - 2 . 4 0 4 4 6 7 7 - 0 0 2

i!6 86 97 0

5.8831362-004 - 2 . 3 5 2 3 8 8 6 - 0 0 2o.ooooooo+ooo - 2 . 3 3 0 3 2 7 7 - 0 0 2

-2.9159215-003 - 3 . 2 2 5 4 7 6 6 - 0 0 2-7.0522162-003 - 3 . 7 5 9 7 5 8 3 - 0 0 2-7.6117066-003 - 3 . 5 8 2 3 4 9 4 - 0 0 2

7 1 -7.5138281-003 - 3 . 4 7 4 2 0 8 0 - 0 0 27 2 -7.3896957-003 - 3 . 3 5 7 0 8 7 0 - 0 0 27 3 -7.0165442-003 -2.8818410-0027 4 -6.7566923-003 -2.1328360-0027 5 -6.9195435-003 -1.8176320-002

7 6

:i7 98 0

- 6 . 8 4 6 7 2 5 4 - 0 0 3 -1.5494703-002- 6 . 2 6 4 2 4 8 6 - 0 0 3 -1.3235448-002-6.1773772-003 -1.3248088-002- 5 . 0 5 4 6 5 6 2 - 0 0 3 -1.3404921-002-3.9716033-003 -1.3389674-002

8182838 48 5

-3.5272857-003-3.2858108-003-3.1882931-003-3.1574305-003-3.1735731-003

- 1 . 3 4 2 8 1 5 3 - 0 0 2-1.3391417-002-1.3314550-002-1.3196625-002-1.2980730-002

8687888990

-3.2264351-003-3.2859588-003-3.2372784-003-2.8409063-0031.1806029-003

-1.2680855-002-1.2212955-002-1.1813686-002-1.2637024-002- 2 . 5 4 2 6 7 7 7 - 0 0 2

91 1.0295768-003 - 2 . 4 3 5 8 2 4 5 - 0 0 292 1.0241282-003 -2.4091306-00293 5.8904893-004 -2.3338998-00294 0 .ooooooo+ooo -2.3113335-00295 - 4 . 0 6 0 0 3 0 6 - 0 0 3 -3.1606605-002

96 - 4 . 5 3 0 8 0 2 7 - 0 0 3 - 3 . 3 7 8 3 5 3 3 - 0 0 297 - 5 . 0 3 8 6 2 4 2 - 0 0 3 -3.5799620-00298 - 5 . 0 9 2 1 5 9 4 - 0 0 3 - 3 . 5 0 5 2 2 3 5 - 0 0 299 -3.9714688-003 - 3 . 2 6 3 8 1 0 1 - 0 0 2

100 -3.9967861-003 -3.1880739-002

Figure C-5. Nodal point displacements (no treatment). -288-D-3163


A N A L Y S I S O F P L A N E P R O B L E M S P A G E N U M B E R 3D A T E 05/27/70

C O U L E E 3 R D ::XFOUNDATION= S E C . D G , G R I D 9 , H Y D R O L O A D , 2 5 F T T R E A T M E N T

N O D A L P O I N T D I S P L A C E M E N T - - X

::535455

-1.8724543-002-1.8937366-002-1.9147395-002

1 . 2 0 3 1 7 2 1 - 0 0 35 . 5 5 8 1 5 5 0 - 0 0 4

- 2 . 0 4 1 5 8 0 4 - 0 0 2-1.7466395-002-1.4287073-002-2.4049716-002-2.3582274-002

565758

6':

o . o o o o o o o + o o o -2.3412686-002-1.3924929-002 -3.1812965-002-1.4099223-002 -3.0061762-002-1.4272226-002 -2.8128268-002-1.4290854-002 -2.5340594-002

-1.4190080-002 -2.2586042-002-1.4060031-002 -1.9924903-002-1.4032529-002 -1.7248892-002-1.4441423-002 -1.3770922-0021.2863362-003 -2.4022650-002

i;686970

5.8064917-0040. ooooooo+ooo

-4.8971975-003-8.6758414-003-9.3259331-003

-2.3506172-002-2.3285657-002-2.9753268-002-3.2517384-002-3.0508820-002

71 -9.5034153-003 -2.9319722-00272 -9.5773006-003 -2.8390606-00273 -9.7625006-003 -2.4257549-00274 -9.2909087-003 -2.1070602-00275 -8.8710655-003 -1.8504728-002

7677787980

-8.4077281-003-7.6451459-003-7.5582207-003- 6 . 2 9 3 4 3 3 2 - 0 0 3-5.0034774-003

-1.6204246-002-1.4086363-002-1.4071215-002-1.3983721-002-1.3774928-002

81 -4.4302627-003 -1.3719672-00282 -4.0935786-003 -1.3606782-00283 -3.9344774-003 -1.3477032-00284 -3.8588070-003 -1.3316513-00285 -3.8335854-003 -1.3053523-002

86 -3.8570314-003 -1.2710341-00287 -3.8942547-003 -1.2192559-00288 -3.8333803-003 - 1 . 1 7 4 7 1 1 2 - 0 0 289 -3.4139745-003 - 1 . 2 5 5 5 0 2 3 - 0 0 290 1.1148291-003 - 2 . 5 4 1 1 8 3 0 - 0 0 2

91 9.9502980-004 -2.4338743-00292 9.9658980-004 -2.4071306-00293 5.7744601-004 -2.3319313-00294 0 .ooooooo+ooo -2.3094178-00295 -5.1226583-003 -2.9567080-002

96979899

100

-5.5237841-003 - 3 . 0 4 2 2 8 9 3 - 0 0 2-5.9118189-003 -3.1153132-002- 5 . 6 4 0 4 3 7 9 - 0 0 3 -3.0135814-002-5.5543256-003 -2.9776455-002-5.1357266-003 -2.6788933-002

<FT)D I S P L A C E M E N T - - Y

(FT)

Figure C-6. Nodal point displacements (25foot treatment). -288-D-3164

358

25-foot t r e a tmen t , node 69 is displaced0.008,67 foot to the left and 0.032,5 footdownward.

Printouts of stresses for the analysis with theno-treatment condition are shown on figureC-7. This listing gives the element number, thelocation of the stresses in X and Y ordinates,stresses in the X and Y planes, the shear stressin the XY plane, and the principal stresses withthe angle from the horizontal to the maximumstress. In this case, a shear stress along aspecified plane and a stress normal to thatplane were found. A similar printout for thecondition with the foundation treated for 25feet is shown on figure C-8. Stresses inelement 51 are the key to this foundationproblem. By treating the foundation, thecompressive stresses in e l e m e n t 5 1 a r eincreased from 8 to 33 pounds per square inchin the horizontal direction, and from 26 to 120


pounds per square inch in the verticaldirection.

Microfilm plots of the grid and stresses arealso provided by the computer as part of theregular output. Principal stresses in the dam forthe no-treatment condition are shown on figureC-9. Principal stresses shown on figure C- 10 arefor the condition where the foundation istreated for 25 feet. These latter principalstresses are derived from the vertical stressesshown on figure C-l 1, the horizontal stressesshown on figure C-12, and the shear stressesshown on figure C- 13.

Occasionally the finite element mesh is sofine that sufficient detail cannot be portrayedon the microfilm. In order to gain greater detailof a particular area and its stresses, the area canbe plotted to an enlarged scale and moreaccurate stresses thus obtained.

B. THREE-DIMENSIONAL FINITE ELEMENT ANALYSIS

C-6. Introduction. -The analysis of theGrand Coulee Forebay Dam demonstrates thecapabilities of the three-dimensional finiteelement system of stress analysis, discussed insections 4-45 through 4-48. Distribution ofstresses around the penstock is of specialinterest because of the large size of the openingin relation to the size of the block.

C-7. Layout and Numbering System.-Athree-dimensional drawing of half of a blockwith the opening for a penstock is shown onfigure C-14. To clarify the penstock area,vertical sections normal to the penstock arealso shown. Although no foundation is shown,a treated foundation was assumed in theanalysis. The block is divided into hexahedronelements. N o d a l p o i n t s a r e n u m b e r e dconsecutively from left to right starting at thetop. There are 588 nodes in the exampleproblem. The elements are numbered startingat the top and follow the general pattern set upfor the nodes. There are 374 elements in thisexample.

C-8. Input. -Examples of the required inputdata are shown on the printouts in figures C-15

through C-l 8. Figure C-l 5 shows the numbersof elements, nodes, boundary nodes, loadednodes, and different materials. Also shown isthe maximum band width expected. Data givenfor each of the materials are modulus ofelasticity, Poisson’s ratio, and the mass density.The nodal points are described using ordinatesin the X, Y, and 2 directions as shown onfigure C-l 6. For example, node 45 is 14.0 feetfrom the centerline of the block in the Xdirection, 19.58 feet from the upstream face inthe Y direction, and at 273.0 (elevation 1273)in the 2 direction. The nodal points thatenclose the elements, the element material, andthe integration rule are shown on figure C-17.Element 41 is bounded by nodal points 49, 55,103, 97, 50, 56, 104, and 98. It containsmaterial number 1 and is to be integrated byrule 2.

Forces or loads are applied at the nodalpoints. In this problem the loads are due toweight of the concrete, the hydraulic pressureon the upstream face, the uplift pressure at thebase of the dam, and the internal pressure inthe penstock and gate shaft. An example of


C O U L E E 3 R 0 xxFOUNOATION”:: S E C . OG, G R I D 9 , H Y D R O L O A D , N O T R E A T M E N T

P A G E N U M B E R 4DD A T E OS/271 70

E L . N O .X - S T R E S S Y - S T R E S S X Y - S T R E S S MAX-STRESS M I N - S T R E S S A N G L E S H E A R - P L A N E N O R M A L - P L A N E(PSI) (PSI 1 (PSI) (PSI) (PSI) (DEG) <PSI) <PSI)

5 1 5 6 9 . 2 5 6 4 9 . 5 0 - 8 2 . 9 4 1 3 - 0 0 1 -26.5010+000 -10.1157+000 - 3 7 . 8 8 7 4 - 0 0 1 -31.0064+000 - 2 4 . 0 1 -13.3122+000 -20.2235+0005 2 5 8 8 . 2 5 6 4 9 . 2 5 -18.2965+000 -18.0532+001 81.2799+000 15.4183+000 -21.4246+001 2 2 . 5 3 29.8317+030 -21.0304+0015 3 6 0 6 . 7 5 6 4 9 . 0 0 -22.4601+000 -25.5836+001 -65.2115+000 - 5 4 . 7 4 4 9 - 0 0 1 -27.2822+001 - 1 4 . 6 0 -11.4819+001 -20.7597+0015 4 6 2 5 . 2 5 6 4 9 . 0 0 - 9 2 . 6 9 6 7 - 0 0 1 -14.1428+001 -89.3897+000 35.8131+000 -18.6511+001 - 2 6 . 7 6 -11.0453+001 -87.8800+0005 5 6 4 3 . 7 5 6 4 9 . 0 0 16.2583+000 33.5292+000 -10.0265+001 12.5530+001 -75.7425+000 - 4 7 . 4 6 -82.5144+000 82.5048+000

5 6 995.1s 6 4 8 . 7 5 -33.7595+000 -26.2658+000 27.2580+000 - 2 4 . 9 8 3 4 - 0 0 1 -57.5269+000 48.915 7 1051.38 6 4 8 . 2 5 -34.9132+000 -27.1232+000 68.5384-001 -23.1349+000 -38.9015+000 5 9 . 8 05 8 4 8 0 . 0 0 6 2 3 . 0 0 -47.9419+000 -14.3210+000 -24.0107+000 - 1 8 . 2 0 9 9 - 0 0 1 -60.4419+000 - 6 2 . 5 05 9 5 1 9 . 0 0 6 2 3 . 0 0 -29.7315+000 -72.1687+000 -32.0523+000 -12.5108+000 -89.3894+000 - 2 8 . 2 56 0 5 4 0 . 0 0 6 2 3 . 0 0 - 3 5 . 8 9 6 8 - 0 0 1 -33.0459+000 - 9 3 . 5 0 1 7 - 0 0 1 - 8 7 . 2 3 6 4 - 0 0 2 -35.7632+000 - 1 6 . 2 0

25.4795+00078.8312-001

-12.3886+000-38.3674+000-15.4615+000

-40.3968+000-31.0719+000- 4 5 . 6 7 8 5 - 0 0 1-53.2998+000-26.3976+000

61 5 4 8 . 7 5 6 2 3 . 0 0 5 6 . 7 4 6 6 - 0 0 2 - 8 6 . 0 3 1 7 - 0 0 2 5 4 . 4 9 9 6 - 0 0 2 7 5 . 1 7 1 8 - 0 0 2 - 1 0 . 4 4 5 7 - 0 0 1 1 8 . 6 8 1 1 . 5 0 3 5 - 0 0 2 - 1 0 . 3 7 1 7 - 0 0 16 2 5 6 0 . 9 0 6 2 3 . 0 0 28.7067-001 -14.7545+000 19.5284-001 3 0 . 8 4 4 5 - 0 0 1 -14.9683+000 6 . 2 5 - 2 7 . 1 5 0 9 - 0 0 1 -14.5503+0006 3 5 8 0 . 2 0 6 2 2 . 7 5 - 4 8 . 5 8 7 0 - 0 0 2 - 2 1 . 8 7 3 7 - 0 0 1 10.5970-001 2 2 . 3 2 7 7 - 0 0 3 -26.9556-001 2 5 . 6 2 4 9 . 2 3 5 2 - 0 0 2 - 2 6 . 0 3 2 4 - 0 0 16 4 5 9 9 . 0 0 6 2 2 . 5 0 -76.1447+000 -43.0465+001 -65.8382+000 -64.3064+000 -44.2303+001 - 1 0 . 1 9 -14.5598+001 -37.3811+0016 5 6 1 7 . 8 0 6 2 2 . 5 0 -30.8871+000 -21.0267+001 -11.7020+000 -30.1269+000 -21.1027+001 - 3 . 7 2 -54.9792+000 -19.2400+001

6 6 6 3 6 . 6 0 6 2 2 . 5 0 21.3056+000 -85.4769+000 - 5 9 . 5 0 0 0 - 0 0 1 21.6361+000 -85.8074+000 - 3 . 1 8 -31.8485+000 -75.3488+0006 7 6 5 3 . 5 0 6 2 2 . 5 0 14.2442+000 37.3463+000 -44.3987+000 71.6720+000 -20.0815+000 - 5 2 . 2 9 -32.6749+000 57.9981+0006 8 6 6 1 . 0 0 6 2 2 . 5 0 11.4532+001 -18.7765+000 -73.9562+000 14.7438+001 -51.6827+000 - 2 3 . 9 9 -97.3751+000 27.1316+0006 9 6 6 5 . 6 7 6 2 6 . 6 7 17.2429+001 -37.2502+000 -77.6679+000 19.8064+001 -62.8853+000 - 1 8 . 2 7 -11.9682+001 15.6296+0007 0 6 8 5 . 7 8 6 2 2 . 5 0 66.0723+000 -63.1979+000 -33.8962+000 74.4211+000 -71.5467+000 - 1 3 . 8 4 -61.6725+000 -37.5903+000

7 1 7 1 5 . 0 8 6 2 2 . 5 0 32.9545+0007 2 7 4 4 . 6 4 6 2 2 . 5 0 13.9267+0007 3 7 7 3 . 6 9 6 2 2 . 5 0 26.2043-0017 4 8 0 1 . 2 5 6 2 2 . 5 0 - 4 3 . 5 2 3 1 - 0 0 17 5 8 2 9 . 5 6 6 2 2 . 5 0 - 9 3 . 4 9 6 7 - 0 0 1

34.4280+000 -74.1262+000 - 6 . 6 9 -37.2800+000 -59.2979+00014.4141+000 -77.2925+000 - 4 . 1 8 -28.4576+000 -67.3932+0002 8 . 4 1 1 6 - 0 0 1 -77.6657+000 - 3 . 0 0 -23.6621+000 -69.9767+000

- 4 2 . 4 0 6 3 - 0 0 1 -78.0334+000 - 2 . 2 3 -20.8766+000 -71.5592+000- 9 2 . 9 2 6 5 - 0 0 1 -77.8196+000 - 1 . 6 5 -18.8145+000 -72.1917+000

7 67 77 8

EJ

8 5 8 . 8 6 6 2 2 . 5 0 -12.3082+0008 8 8 . 6 7 6 2 2 . 5 0 -12.6495+0009 1 7 . 7 2 6 2 2 . 5 0 - 9 0 . 0 4 4 7 - 0 0 19 3 6 . 0 0 6 2 2 . 5 0 5 4 . 4 7 6 7 - 0 0 19 4 1 . 7 5 6 2 2 . 5 0 4 6 . 3 7 1 3 - 0 0 1

-12.3011+000 -77.7480+000 - 0 . 6 0 -16.9486+000 -73.0169+000-12.6258+000 -75.7409+000 1.11 -14.7083+000 -72.1037+000- 8 0 . 9 2 6 9 - 0 0 1 -83.1658+000 6 . 3 3 -1l.l9lO+DOO -81.4587+00067.8562-001 -43.9310+000 - 9 . 3 5 -19.0493+000 -35.3109+0008 0 . 7 8 8 9 - 0 0 1 -20.6953+000 - 2 0 . 2 3 -13.5592+000 -11.1185+000

81 9 4 7 . 7 5 6 2 2 . 5 0 - 6 3 . 9 9 9 0 - 0 0 18 2 9 7 1 . 0 0 6 2 2 . 5 0 -23.7352+0008 3 9 9 9 . 5 0 6 2 6 . 6 7 -26.3419+0008 4 1049.88 6 2 2 . 5 0 -30.7179+0008 5 4 5 8 . 5 0 6 0 2 . 5 0 -14.0753+000

- 2 6 . 5 1 3 1 - 0 0 1 -24.1297+000 2 4 . 6 9 3 5 . 6 4 8 8 - 0 0 1 -23.5208+000-11.6653+000 -68.3369+000 2 7 . 4 8 11.9607+000 -65.6888+000- 8 2 . 1 4 4 9 - 0 0 1 -54.8025+000 3 8 . 5 9 17.0874+000 -47.3397+000-24.7872+000 -39.6944+000 39.11 5 5 . 5 7 4 1 - 0 0 1 -37.2079+000

90.6109-001 -38.7298+000 - 4 4 . 0 9 -21.0631+000 - 3 5 . 4 9 9 7 - 0 0 1

8 6

8”:8 99 0

4 9 7 . 5 0 6 0 2 . 5 0 -17.5592+0005 2 8 . 0 0 6 0 2 . 5 0 - 6 7 . 8 6 6 6 - 0 0 15 3 9 . 7 5 6 0 2 . 5 0 8 8 . 7 6 8 7 - 0 0 25 5 0 . 8 0 6 0 2 . 5 0 -13.1075-0015 6 9 . 4 0 6 0 2 . 5 0 -49.3957-002

2 1 . 0 5 8 7 - 0 0 1- 1 1 . 3 6 0 8 - 0 0 1

1 5 . 2 7 4 2 - 0 0 1- 1 3 . 0 9 7 8 - 0 0 1

5 6 . 2 3 4 5 - 0 0 2

-63.7692+000 - 3 3 . 1 2 -32.7426+000 -27.2534+000-47.2241+000 - 2 0 . 5 0 -21.7876+000 -31.6852+000-29.5864-001 2 2 . 1 9 5 5 . 6 8 3 7 - 0 0 2 -28.8843-001-14.0092+000 0 . 5 0 - 3 0 . 7 8 1 1 - 0 0 1 -13.2132+000- 3 7 . 0 9 4 9 - 0 0 1 2 9 . 8 2 1 0 . 5 6 2 6 - 0 0 1 - 3 4 . 3 0 0 4 - 0 0 1

9192939495

96979899

100

5 8 8 . 0 0 6 0 2 . 5 0 -50.9808+0006 0 6 . 6 0 6 0 2 . 5 0 -41.9202+0006 2 5 . 2 0 6 0 2 . 5 0 -4i.j499+0006 4 8 . 2 5 6 0 2 . 5 0 -20.0766+0006 6 6 . 6 7 6 0 0 . 0 0 -16.8373+000

-72.6528+000 -12.5610+000-76.8051+000 -66.6803-001-77.4449+000 -42.0971-001-77.9217+000 - 2 8 . 6 8 5 9 - 0 0 1-77.7625+000 - 1 9 . 7 6 0 1 - 0 0 1

-77.7409+000 -68.1714-002-75.7173+000 12.2243-001-82.2540+000 8 2 . 2 3 0 6 - 0 0 1-42.5930+000 - 8 1 . 2 8 1 1 - 0 0 1-17.2536+000 - 9 3 . 3 7 4 7 - 0 0 1

-20.3811+000 81.5241-001-56.2670+000 23.2021+000-36.6750+000 22.7138+000-33.7637+000 72.9640-001-15.5933+000 -23.8834+000

-44.1041+000 -30.1450+000-41.5736+000 -15.1161+000- 2 3 . 1 8 9 1 - 0 0 1 15.6864-001-14.0082+000 1 1 . 1 1 4 5 - 0 0 2- 2 6 . 5 3 1 9 - 0 0 1 18.4298-001

-27.7548+001 -10.2420+001-27.4568+001 - 7 1 . 6 4 6 3 - 0 0 1-14.6202+001 18.9042+000-54.3948+000 - 6 3 . 2 3 3 9 - 0 0 1

87.1260-002 -27.6822+000

-14.0913+000 -38.3291+000-44.9724+000 -39.9128+000-62.8762+000 -26.3745+000-73.2695+000 -15.3108+000-75.7009+000 - 9 6 . 2 4 7 7 - 0 0 1

Figure C- 7. Stresses in elemen

-11.5456+000 -31.6983+001 - 2 1 . 0 6 -14.5340+001 -21.1161+001-41.6998+000 -27.4788+001 - 1 . 7 6 -64.3666+000 -25.5401+001-38.4338+000 -14.9518+001 9 . 9 5 - 9 7 . 4 1 5 9 - 0 0 1 -14.8657+001-18.9485+000 -55.5229+000 - 1 0 . 1 1 -14.0558+000 -48.9342+000

21.0808+000 -37.0468+000 - 5 3 . 8 7 -19.5464+000 13.5261+000

6 7 2 . 0 0 6 0 2 . 5 0 -78.4602-0016 8 4 . 2 8 6 0 2 . 5 0 21.0208+0007 1 1 . 5 2 6 0 2 . 5 0 19.3361+0007 4 2 . 4 5 6 0 2 . 5 0 11.4645+0007 7 3 . 3 8 6 0 2 . 5 0 35.1875-001

27.4874+000 -49.4247+000 - 4 2 . 6 7 -34.7553+000 54.9163-00139.8104-000 -63.7620+000 - 2 5 . 2 1 -51.0638+000 -20.5953+00027.0697+000 -70.6098+000 - 1 6 . 3 4 -43.3940+000 -44.1818+00014.1461+000 -75.9512+000 - 9 . 9 3 -34.4430+000 -59.938D+ODD4 6 . 7 1 3 4 - 0 0 1 -76.8535+000 - 6 . 8 3 -28.1402+000 -65.5818+000

ts (no treatmenth-288-D-3165


C O U L E E 3 R D =FOUNDATION:‘:: S E C . D G , G R I D 9 , H Y D R D L O A D , 2 5 F T T R E A T M E N T

E L . N O .X - S T R E S S Y - S T R E S S X Y - S T R E S S MAX-STRESS M I N - S T R E S S ANGLE

(PSI) < P S I > (PSI) (PSI) (PSI) CDEG)

5 1 569.25 649.505 2 5 8 8 . 2 5 6 4 9 . 2 55 3 6 0 6 . 7 5 6 4 9 . 0 05 4 6 2 5 . 2 5 6 4 9 . 0 05 5 6 4 3 . 7 5 6 4 9 . 0 0

5 65 75 8

i:

9 9 5 . 1 3 6 4 8 . 7 51 0 5 1 . 3 8 6 4 8 . 2 5

4 8 0 . 0 0 6 2 3 . 0 05 1 9 . 0 0 6 2 3 . 0 05 4 0 . 0 0 6 2 3 . 0 0

616 26 3

::

5 4 8 . 7 5 6 2 3 . 0 05 6 0 . 9 0 6 2 3 . 0 05 8 0 . 2 0 6 2 2 . 7 55 9 9 . 0 0 6 2 2 . 5 06 1 7 . 8 0 6 2 2 . 5 0

6 6 6 3 6 . 6 0 6 2 2 . 5 06 7 6 5 3 . 5 0 6 2 2 . 5 06 8 6 6 1 . 0 0 6 2 2 . 5 06 9 6 6 5 . 6 7 6 2 6 . 6 77 0 6 8 5 . 7 8 6 2 2 . 5 0

7 1 7 1 5 . 0 8 6 2 2 . 5 07 2 7 4 4 . 6 4 6 2 2 . 5 07 3 7 7 3 . 6 9 6 2 2 . 5 07 4 8 0 1 . 2 5 6 2 2 . 5 07 5 8 2 9 . 5 6 6 2 2 . 5 0

7 67 77 87 98 0

8 5 8 . 8 6 6 2 2 . 5 0 -93.7148-001 -77.7381+0008 8 8 . 6 7 6 2 2 . 5 0 -1D.S079+DOO -75.6816+000917.72 6 2 2 . 5 09 3 6 . 0 0 6 2 2 . 5 09 4 1 . 7 5 6 2 2 . 5 0

8 1 9 4 7 . 7 5 6 2 2 . 5 08 2 971.00 622.508 3 9 9 9 . 5 0 6 2 6 . 6 78 4 1049.88 622.508 5 4 5 8 . 5 0 6 0 2 . 5 0

8 68 78 88 99 0

4 9 7 . 5 0 6 0 2 . 5 0 -13.6288+000 -35.8360+0005 2 8 . 0 0 6 0 2 . 5 0 29.1846-001 -30.7301+0005 3 9 . 7 5 6 0 2 . 5 0 68.9677-002 -75.2481-002 3 15 5 0 . 8 0 6 0 2 . 5 0 4 5 . 0 9 4 5 - 0 0 1 -13.2139+000 17

9192

i195

5 6 9 . 4 0 6 0 2 . 5 0 -22.6987-002 -15.5964-001 77

5 8 8 . 0 0 6 0 2 . 5 0 -87.3317+000 -47.8188+001 - 3 76 0 6 . 6 0 6 0 2 . 5 0 -69.8602+000 -19.5830+001 -10 1.625.20 602.50 -41.3323+000 -12.2190+001 -98648.25 602.50 -83.1921-001 -54.0970+000 -216 6 6 . 6 7 6 0 0 . 0 0 -85.5344-001 -41.6698-001 - 3 3

96979899

100

6 7 2 . 0 0 6 0 2 . 5 0 31.5872-001 -17.2564+000 -42.5064+000 36.6660+000 -50.7637+000 - 3 8 . 2 56 8 4 . 2 8 6 0 2 . 5 0 28.6650+000 -46.0280+000 -43.3399+000 48.5297+000 -65.8926+000 - 2 4 . 6 27 1 1 . 5 2 6 0 2 . 5 0 26.3567+000 -61.4328+000 -29.6761+000 35.4470+000 -70.5231+000 - 1 7 . 0 37 4 2 . 4 5 6 0 2 . 5 0 17.7289+000 -72.5470+000 -17.8019+000 21.1125+DOO -75.9306+000 - 1 0 . 7 67 7 3 . 3 8 6 0 2 . 5 0 86.6945-001 -75.3200+000 -11.3828+000 10.1848+000 -76.8353+000 - 7 . 5 8

-32.7145+000 -12.0034+00174.9617-001 -16.6625+00120.2207+000 -16.1694+00121.3625+000 -12.1475+00126.5266+000 -10.3843+000

-33.1891+000 -26.1342+000

94.2840-001 -31.7080+000 -12.1D41+001 6 . 0 9-16.8468+000 91.1118-001 -16.8240+001 - 5 . 4 8-51.0114+000 33.5486+000 -17.5022+001 - 1 4 . 6 4-76.0907+000 54.3011+000 -15.4413+ODl - 2 3 . 4 1-91.318O+DOO 10.1235+001 -85.0932+000 - 3 9 . 2 9

27.5627+000 -18.7407-001 -57.4492+000 4 8 . 6 569.1634-001 -23.0456+000 -38.6227+000 5 8 . 6 9

-21.7198+000 -88.7067-002 -54.3230+000 - 6 2 . 8 1-34.0554+000 - 3 0 . 5 6 4 6 - 0 0 1 -75.8422+000 - 3 4 . 6 8-22.0893+000 14.6001+000 -32.9311+000 -34.18

-13.3666+000 16.1279-00112.8563+000 14.2610+00057.3429+000 27.2540+000

-42.8305+000 -12.2501+000-48.8801+DOO 12.7676+000

-49.6909+000 - 1 5 . 7 0-49.3844+000 11.91-25.8539+001 11.83-25.4292+001 -10.36-17.8675+001 -15.35

-92.1177+000 - 1 2 . 4 0-31.5615+000 - 4 1 . 1 4-50.5182+000 - 2 2 . 0 4-65.1781+000 - 1 6 . 3 8-72.8911+000 -13.52

-29.8111+000 49.9952+000-54.1453+000 77.7183+000-70.6748+000 15.2636+001-76.2355+000 21.6555+001-37.0082+000 89.9309+000

-14.5382+000 45.9591+000-78.5996-001 22.9293+000- 5 0 . 2 4 7 2 - 0 0 1 92.8327-001-34.8766-001 78.7417-002- 2 4 . 6 5 0 0 - 0 0 1 - 5 3 . 7 2 4 6 - 0 0 1

-10.8770-001 -93.5418-00188.8498-002 -10.4958+00080.6889-001 -66.0970-001

-79.2355-001 78.6046-001

-73.6713+000 - 7 . 0 3-77.2372+000 - 4 . 5 1-77.5939+000 - 3 . 3 2-78.0140+000 - 2 . 5 4-77.8199+000 -1.95

-77.7554+000 -0.91-75.6937+000 0 . 7 8-82.8772+000 6 . 1 1-43.7128+000 - 8 . 9 5-20.2725+000 -19.30-91.3237-001 90.0933-001

84.1768-001 -13.9780-001 -23.9913+000 24.0923.3454+000 -10.7926+000 -68.1687+000 2 7 . 2 322.8377+000 - 7 6 . 3 4 7 1 - 0 0 1 -54.6568+000 3 8 . 1 37 3 . 6 3 1 2 - 0 0 1 -24.4033+000 -39.6156+000 3 7 . 7 4

-21.4961+000 77.2229-001 -35.3540+000 - 4 3 . 2 1

-25.7387+000 32.9915-001-10.9243+000 61.5399-001

.5427-002 7 5 . 5 6 4 9 - 0 0 2

:7242-DO2 1196-001 46.7330-001 13.0444-002

-52.7640+000 - 3 3 . 3 3-33.9657+000 - 1 6 . 5 0-81.8453-002 11.81-13.3777+000 5 . 4 7-19.1712-001 2 4 . 7 0

-34.4if4+000 -27.2529+000-43.1646+000 -12.0455+000-26.6169+000 -52.2818+000-39.8110-002 -17.9328+000

-21.4494-001 -45.9332+00011.5484+000 -46.6719+00015.2437+000 -24.6529+001

-20.0826+000 -24.6460+001- 6 5 . 3 6 5 1 - 0 0 2 -16.5254+001

43.4393+000 -85.5618+00030.4139+000 15.7429+00012.4017+001 -21.8999+00019.4144+001 -42.7663+0008l.D329+DOO -63.9932+000

44.1654+000 -71.8777+00022.3087+000 -76.6165+00089.9168-001 -77.3023+0006 3 . 2 7 5 4 - 0 0 2 -77.8593+000

- 5 4 . 5 6 4 3 - 0 0 1 -77.7359+000

- 7 4 . 7 3 1 4 - 0 0 1 -82.0137+00066.1293-001 -42.4652+00058.1203-001 -17.0752+000

- 5 1 . 6 0 6 7 - 0 0 1 -20.2284+000-22.8074+000 -56.1539+000-25.5592+000 -36.7323+000-30.1020+000 -33.9169+000-12.4712+000 -15.1605+000

7765+000 -83.7141+OOD -48.1806+ODl - 5 . 4 75696+000 -68.9795+000 -19.6711+001 - 4 . 7 64612-001 -4D.l5D6+000 -12.3372+001 - 6 . 8 42528+000 26.1804-003 -62.4424+000 - 2 1 . 4 4 9891+000 27.6996+000 -40.4200+000 - 4 6 . 8 5

Figure C-8. Stresses in elements (25-foot treatment). -288-D-3166

F I N I T E M E T H O D - S e c . C - 9 361

PRINCIPAL STRESSES(4~) Indicates tension

1000 PSI.Scale 50 Feet

Figure C-9. Grand Coulee Forebay Dam foundationstudy-microfilm printout showing principal stresses(no treatment). -288-D-3167

load vectors is shown on figure C-18. Nodalpoint 10 has a load of 4,105 pounds in thepositive X direction, 2,711 pounds in thepositive Y direction, and 143,590 pounds inthe negative 2 direction.

C-9. Output. -Displacements of the nodesare given in X, Y, and 2 directions. Shearstresses and stresses normal to each of the three

PRINCIPAL STRESSES($:) Indicates tension

1000 PSI.Scale 50 Feet

F i g u r e C - I O . G r a n d C o u l e e Forebay D a mstudy-microfilm printout showing principal stresses(25foot treatment). -288-D-3168

planes are computed at each node.Some of the stresses of interest at the base

of the dam and around the penstock are shownon figure C-19. The maximum compressivestress is about 255 pounds per square inch andthe maximum tensile stress, 98 pounds persquare inch.

3 6 2 DESIGN OF GRAVITY DAMS

-29

VERTICAL STRESSES HORIZONTAL STRESSES(-) lndlcates compress ion (-) Indicates compression

Scale 50Feet Scale 50 Feet

-9

- 2 8

- 5 0

- 7 0

- 8 3

- 9 0

-84

-10

F i g u r e C - 1 1 . G r a n d C o u l e e Forebay D a m F i g u r e C - 1 2 . G r a n d C o u l e e Forebay D a mstudy-microfilm printout showing vertical stresses study-microfilm printout showing horizontal stresses(25-foot treatment). -288-D-3169 (25foot treatment). -288-D-3170


SHEAR STRESSESScale 50 Feet

F i g u r e C - 1 3 . G r a n d C o u l e e Forebay D a mstudy-microfilm printout showing shear stresses(25foot treatment). -288-D-3171


199 2 0 4

2 4 7 252

2 9 53 0 0

3 6 4

3 9 6

4 3 9 4 4 4

4 8 7 4 9 2

S E C T I O N A - A SECTION B - B

NUMBER CODE :148 N o d e N u m b e r

@ Element Number

q Material Number

IBI 186

2 2 9 2 3 4

2 7 7 2 8 2

3 2 0

3 5 2

3 8 4

421 4 2 6

4 6 9 4 7 4

W a t e r t h r e eelements deco

NOTE :All volume shown is Material Number I, except

M a t e r i a l N u m b e r 2, w a t e r , w h i c h rose i nt h e aate s l o t a s s h o w n .

175~180 co,. \ I \

2 2 3 2 2 8

271 2 7 6

316

3 4 8

3 8 0

415 4 2 0

4 6 3 4 6 8

4 8 7

JA

I33 i d

SECTION C -C HALF-BLOCK, THREE- DIMENSIONAL VIEW

Figure C-14. Grand Coulee Forebay Dam study-threedimensional finite element grid. -288-D-3172


G R A N D C O U L E E FOREBAY--FAULT U / S O F H E E L - - L O A D S D U E T O G R A V I T Y , H Y D R O S T A T I C , U P L I F T

N U M B E R O F E L E M E N T S - - - - - - - - - - - 3 7 4N U M B E R O F N O D E S - - - - - - - - - - - - - - 5 8 8N U M B E R O F B O U N D A R Y N O D E S - - - - - 1 9 4M A X I M U M B A N D W I D T H - - - - - - - - - - - 1 6 8N U M B E R O F M A T E R I A L S - - - - - - - - - - 5N U M B E R O F L O A D E D N O D E S - - - - - - - - 0

M A T E R I A L N U M B E R MODULUS PO1 S S O N D E N S I T Y

1 4.320+008 0 . 1 5 1 5 0 . 0 02 0 . o o o + o o o 0 . 0 0 0 . 0 0I 2.880+008 3.880+008 0.13 0.13 0.00 0.00

5 1.728+008 0 . 1 3 0 . 0 0

Figure C-15. Threedimensional input data-control data and material properties. -288-D-3173


NODE XORD YORD ZORD

0 .oooo 30.0000 311 .oooo7.0000 30.0000 311 .oooo

14.0000 30.0000 311 .oooo27.0000 30.0000 3 1 1 . 0 0 0 028 .oooo 30.0000 311 .oooo

67a9

10

35.00000.00007.0000

14.000017.5000

28 .oooo35.00000.00007.0000

14.0000

30.000019.580019.580019.580019.5800

3 1 1 . 0 0 0 03 1 1 . 0 0 0 0311 .oooo311 .oooo311 .oooo

1112131415

19.5800 3 1 1 . 0 0 0 019.5800 311 .oooo14.2800 311 .oooo14.2800 311 .oooo14.2800 311 .oooo

1617la1920

17.500028 .oooo35.00000 .oooo7.0000

1 4 . 0 0 0 021 .oooo28 .oooo35.00000.0000

14.2800 311.000014.2800 311.000014.2800 311.00000.0000 311.00000.0000 311.0000

2122232425

0.0000 311.00000 * 0000 311.00000.0000 311.00000 .oooo 311.0000

57.9500 230.0000

2627282930

57.950057.950057.950057.950057.9500

230.0000230.0000230.0000230.0000230.0000

3132333435

7.000014.000021.000028.000035.0000

0 .oooo7.0000

14.000021.000028.0000

44.9500 250.000044.9500 250.000044.9500 250.000044.9500 250.000044.9500 250.0000

3637383940

44.950030.000030.000030.000030.0000

250.0000273.0000273.0000273.0000273.0000

4142434445

35.00000 .oooo7.0000

14.000021.0000

28.000035.00000 .oooo7.0000

14.0000

30.0000 273.000030.0000 273.000019.5800 273.000019.5800 273.000019.5800 273.0000

4647484950

17.50002 8 . 0 0 0 035.00000 .oooo7.0000

14.000017.500028 .oooo35.00000 .oooo

19.5800 273.000019.5800 273.000019.5800 273.000014.2800 273.000014.2800 273.0000

5152535455

14.280014.280014.28001 4 . 2 8 0 0

0 . 0 0 0 0

273.0000273.0000273.0000273.0000273.0000

56 7.0000 0 .oooo 273.000057 14.0000 0 . 0 0 0 0 273.0000

Figure C-16. Threedimensional input data-descriptionof section by nodal points. -288-D-3174


ELEMENT CONNECTED NODES MATERIAL INT. RULE

ii9

1011

4 3 3 74 4 3845 3946 4 04 7 41

8 4 4 389 45 39

10 46 4 011 47 4112 48 42

678

1:

;9

1011

1314151617

495051

::

4344

z;47

8 149 1 5

10 1611 1712 18

505152

::

4 4454 64748

11 13 19 5 5 49 14 2 0 5 6 5012 14 2 0 56 5 0 15 21 5 7 5113 15 21 57 5 1 16 22 5 8 5214 16 2 2 5 8 5 2 17 23 59 5 315 17 23 5 9 5 3 18 24 6 0 54 3

1617181920

6162

6”:65

2 5 7 3 67 62 2 6 74 6826 74 68 63 27 75 6927 75 69 64 2 8 76 7 028 76 7 0 65 29 77 7129 7 7 71 66 30 78 72

33

21 2522 2 62 3 2 724 2825 29

31

::343 5

79 73 26 3 2 8 0 7 480 74 27 3 3 81 7 581 75 28 3 4 8 2 768 2 7 6 29 3 5 83 778 3 77 30 3 6 84 78

26 3127 3228 332 9 3430 3 5

373 8

241

85 79 3 2 3886 8 0 33 3987 81 34 4 08 8 8 2 35 4189 8 3 3 6 42

86 8 087 81

i: i:9 0 84

4444

31 3 7 433 2 38 4 43 3 3 9 4534 4 0 463 5 41 47

8586

8”;89

3 8

1:4142

2 z:46 9 447 9548 96

868 7888 99 0

3333

3 63 738

2

4344454647

495051

::

97 91 44 50 98 9298 92 45 51 99 9399 93 46 5 2 100 9 4

100 94 47 5 3 101 95101 95 48 54 102 96

4142434445

495051

::

5 5 103 97 5056 104 9 8 5 15 7 105 99 5 25 8 106 100 5 35 9 107 101 54

5 65 758

z:

104 98105 99106 100107 101108 102

46 6147 6248 6 349 6 450 65

6 7

27071

115 109116 110117 111118 112119 113

kfz707 17 2

116 110117 111118 112119 113120 114

515 25 3545 5

67

6”;7 07 1

7 3 121 115 68 7 4 122 11674 122 116 69 7 5 123 1177 5 123 117 70 7 6 124 1187 6 124 118 71 7 7 125 1197 7 125 119 72 7 8 126 120

56 7 3 7 9 127 121 74 80 128 1225 7 74 80 128 122 7 5 8 1 129 123

11111

22211

11111

11111

11111

11111

11111

22211

11111

11111

11111

11

44

Figure c-17. Three-dimensional input data-elements defined by nodal points with material.-288-D-3 175

368 DESIGN OF GRAVITY DAMSL O A D V E C T O R

N O D E X - L O A D Y - L O A D Z - L O A D

o . o o o o + o o o o . o o o o + o o o -5.1970+004o . o o o o + o o o o . o o o o + o o o -1.0394+005o.oooo+ooo o . o o o o + o o o -1.1508+005o . o o o o + o o o 0 . o o o o + o o o -1.0394+005o . o o o o + o o o o . o o o o + o o o -9.2803+004

6 o . o o o o + o o o o . o o o o + o o o -5.1970+0047 - 2 . 6 4 9 4 - 0 0 7 5.4220+003 -5.1970+0048 - 5 . 2 9 8 8 - 0 0 7 1.0844+004 -1.0394+0059 - 5 . 2 9 8 8 - 0 0 7 8.1331+003 -9.6515+004

10 4.1053+003 2.7110+003 -1.4359+005

11 o . o o o o + o o o o.oooo+ooo -1.7745+0051 2 o . o o o o + o o o o.oooo+ooo -7.8403+00413 o . o o o o + o o o -5.4220+003 -7.1221+00414 o . o o o o + o o o -1.0844+004 -1.4244+00515 o . o o o o + o o o -8.1331+003 -1.1870+005

16 4.1053+003 -2.7110+00317 o . o o o o + o o o o.oooo+ooo18 o . o o o o + o o o 0 .oooo+ooo19 o . o o o o + o o o 5.4220+00320 o . o o o o + o o o 1.0844+004

-1.8209+005-2.322j+OOi-9.7655+004-7.1221+004-1.4244+005

21 o . o o o o + o o o 1.0844+004 -1.3057+00522 o . o o o o + o o o 1.0844+004 -1.4244+00523 o . o o o o + o o o 1.0844+004 -1.5431+00524 o . o o o o + o o o 5.4220+003 -7.1222+00425 o . o o o o + o o o o.oooo+ooo -3.5017+004

26 o . o o o o + o o o o.oooo+ooo -7.0035+00427 o . o o o o + o o o o.oooo+ooo -7.0035+0042 8 o . o o o o + o o o o.oooo+ooo -7.0035+0042 9 o . o o o o + o o o o.oooo+ooo -7.0035+00430 o . o o o o + o o o o.oooo+ooo -3.5017+004

31 o . o o o o + o o o o.oooo+ooo -5.6622+00432 o . o o o o + o o o o.oooo+ooo -1.1324+00533 o . o o o o + o o o o.oooo+ooo -1.1324+00534 o . o o o o + o o o 0 .oooo+ooo -1.1324+00535 o . o o o o + o o o o.oooo+ooo -1.1324+005

363738

I:

o . o o o o + o o oo . o o o o + o o oo . o o o o + o o oo . o o o o + o o oo . o o o o + o o o

0 .oooo+ooo0. oooo+oooo.oooo+oooo.oooo+oooo.oooo+ooo

-5.6622+004-1.4149+005-2.8299+005-2.7593+005-2.8299+005

41 o . o o o o + o o o o.oooo+ooo -2.9005+00542 o . o o o o + o o o 0 .oooo+ooo -1.4149+00543 -4.5776-006 1.2828+005 -1.0176+00544 -9.1553-006 2.5656+005 -2.0353+00545 -9.1553-006 1.9242+005 -1.7456+005

46 9.7124+004 6.4139+00447 o.oooo+ooo o.oooo+ooo48 o.oooo+ooo o.oooo+ooo49 -9.3561-008 -1.2828+00550 -1.8712-007 -2.5656+005

-2.7761+005-3.5597+005-1.5115+005-1.3307+005-2.6614+005

51 -1.8712-007 -1.9242+005 -2.2179+00552 9.7124+004 -6.4139+004 -3.4023+00553 0. oooo+ooo 0 .oooo+ooo -4.3397+00554 o.oooo+ooo o.oooo+ooo -1.8246+00555 o.oooo+ooo 1.2828+005 -1.3307+005

Figure C-18. Threedimensional input data-load vectors. -288-D-3176

FINITE METHOD-Sec. C-9r--trVERTICAL S T R E S S

369

ELE

HORIZONTAL AND VERTICALSTRESSES

AT DOWNSTREAM FACE

HORIZONTALSTRESS

3 s psr I ITENSION

HORIZONTAL STRESSES

/2 5 5 p s i AT VERTICAL SECTION

62 FEET FROM UPSTREAM FACE62 FEET FROM UPSTREAM FACE

TALVERTICAL STRESS ON HORIZONVERTICAL STRESS ON HORIZONTALPLANE -PLANE - ELEVATION II40ELEVATION II40

E L E V A T I O N II40E L E V A T I O N II40

Figure C-19. Grand Coulee Forebay Dam study-stresses at nodal points. -288-D-3177Figure C-19. Grand Coulee Forebay Dam study-stresses at nodal points. -288-D-3177

<<Appendix D

S p e c i a l M e t h o d s o f N o n l i n e a r

Stress Ana lys is

D- 1. Introduction. -The systems fordetermining nonlinear stresses presented hereare the “Slab Analogy Method,” “LatticeAnalogy Method,” “Experimental Models,”and “Photoelastic Models.” None of thesemethods, except photoelastic models, are usedpresently in the Bureau of Reclamationbecause of their complexity and the timeconsumed in performing the analyses. Thesemethods are included in the discussion sincethey were used in some of the examples shownin this manual.

M o d e r n t w o - d i m e n s i o n a l a n d three-dimensional finite element methods providemore sophisticated and more economicalanalyses for the determination of nonlinearstress distribution than the methods mentionedabove. T h e f i n i t e e l e m e n t m e t h o d s a r ediscussed in subchapter E of chapter IV and inappendix C.

D-2. Slab Analogy Method. -Although theexact law of nonuniform stress distribution isu n k n o w n , a n a p p r o a c h t o w a r d s adetermination of true stresses can be made bymeans of the theory of elasticity. The “SlabAnalogy Method” was developed as a result ofa suggestion by H. M. Westergaard in 1930, inconnection wi th the des ign of Hoover(formerly Boulder) Dam. This method isdescribed in detail in one of the BoulderCanyon Project Final Reports.’ Consequently,the method will be only briefly described here.

“‘Stress Studies for Boulder Dam,” Bulletin 4 of Part V,Boulder Canyon Project Final Reports, Bureau of Reclamation,1939.

It is a lengthy, laborious method and isjustified only for unusually high and importantdams. The analysis is based upon an analogybetween an Airy’s surface, which defines thestresses in a two-dimensional elastic structure,and the deflections of an unloaded slab bent byforces and couples applied around its edges.The slab has the same shape as a cantileverset tion including a large block of thefoundation. The edges of the slab are bent intoa form which corresponds to the stresses at thesurface of the structure. The analysis is madeby dividing the analogous slab into horizontaland vertical beams which are brought intoslope and deflection agreement by trial loads.T h e c u r v a t u r e s in the slab are thenproportional to the shears in the structure, andconsequently the moments in the horizontaland vertical beams are proportional to thestresses in the vertical and horizontaldirections, respectively.

Nonlinear stress investigations by the slabanalogy method have been made for three largedams: Hoover, Grand Coulee, and Shasta.Conclusions drawn from several studies ofmaximum cantilever sections are that stressesin the vicinity of the upstream and downstreamedges of the base are greater than those foundby the gravity method and warrant specialconsideration in design. These studies alsoindicated that nonlinear effects are importantwithin approximately one-third the height ofthe cantilever, and reach a maximum at thebase.

The maximum nonlinear effects which werefound in the vicinity of the bases of Hoover,

371


Grand Coulee, and Shasta Dams are shown intable D-l. The table also shows a comparisonbetween stresses based on linear and nonlineardistribution for the vertical, horizontal, andshear stresses in the regions of the upstreamand downstream toes. Since the nonlinear (slabanalogy) method bears out the proof by thetheory of elasticity that the theoreticalmaximum shear stresses are infinite at thereentrant corners of the base, the values givenare for the maximum computed shear stressesat conjugate beam points nearest the corners.The vertical stresses were the ones whichshowed the greatest changes when computedby the nonlinear method. The maximumincrease in vertical upstream stress was 18percent, and occurred for Hoover Dam; whilethe maximum increase in vertical stress at thedownstream toe was 64 percent and occurredfor the maximum nonoverflow section ofGrand Coulee Dam.

The studies of Shasta Dam showed the leastdeparture of stresses from the linear law of anynonlinear studies completed to date. Theupstream vertical stresses were decreased byapproximately 12 percent and the downstreamstresses were increased by correspondingamounts. This close agreement of linear andnonlinear stresses was believed to be due to thefact that the batter of the upstream face at thebase of the cantilever was 0.5 to 1, whichallowed for a better introduction of stressesfrom the dam into the foundation than woulda sharper reentrant.

Table D-l shows that horizontal stresses ascomputed by the nonlinear method may beover twice the values computed by theordinary linear assumption. This is animportant consideration in the design of galleryand drainage systems, outlet works, powerpenstocks, elevator shafts, and other openingsin the dam. The studies show that shear stressescomputed by the nonlinear method followrather closely the parabolic distributionobtained by an ordinary gravity analysis,except of course, at the reentrant corners.

D-3. Lattice Analogy Method. -Many of thetwo-dimensional problems encountered inengineering are difficult or impossible ofs o l u t i o n when treated mathematically.

Necessity has fostered the approximate“Lattice Analogy Method” of dealing withsuch problems. This section will describe themethod and some of its applications ratherthan the derivation of formulas involved in itsuse. As far as practical engineering problemsare concerned, the field of application isrestricted only by two limitations: (1) Theshape of the section must be such that it can bebuilt up, exactly o r t o a s a t i s f a c t o r yapproximation, from a limited number ofsquare elements; and (2) the value of Poisson’sratio must be equal to one-third. The limitationupon Poisson’s ratio is usually unimportant. Inmany cases, stress distribution is independentof the values of the elastic constants, and incases where these constants affect the results,the value of one-third will ordinarily be closeenough to the true value that only smalldifferences w i l l e x i s t i n stresses ordisplacements.

As in the usual treatment oftwo-dimensional problems in elasticity, asection of the structure to be analyzed isconsidered as though it were a slice or plate ofunit thickness, in accordance wi th thegeneralized theory of plane stress. The plate issimulated in size and shape by a latt icen e t w o r k c o m p o s e d of interconnectedelemental square frames, each diagonallyconnected at the corners. When the plate hasirregular boundaries, i ts outline may bea p p r o x i m a t e d t o a n y d e s i r e d d e g r e e o faccuracy depending on the number of frameschosen. As the number is increased, however,the solution becomes more involved so that forany problem a practical decision must be madeas to the refinement desired. The validity ofthe simulation may be shown by demonstratingthat in the limit, as the dimensions of thesquare frames approach zero, the differentialequations of equilibrium and compatibilitybecome identical for the lattice and the plate,and t h e b o u n d a r y conditions becomeexpressible in the same form. Thus the twosolutions become identical and for obviousreasons the lattice is referred to as analogous tothe plate.

(a) Condit ions to be Satisf ied.-In theanalogy between the lattice and the plate, three

TABLE D-l .-Maximum nonlinear stress effects in sections Of various dams.-DS2-2(U)

Dam

Cant i lever Sect ion

Loading Condition

Reg ion neor Ups t ream Edge o f Base

BOULDER GRAND COULEE S H A S T A

MaximumMax imum

C r o w n Sp i l lwoy Maximum Maximum MaximumNon-Overflow

With BucketNon-Overflow Spillway Non-Overflow

Dead Load Dead Loadp lus

Dead Load Dead Load Dead Load Dead Load plus

T r i a l Load?plus plus plus plus Full Water Load

Water Load Full Water Load Full Water Load Full Water Load Full Water Load plus Eorthquake

Maximum Change, ver t i ca l normal s t ress 5 5 5 t o 6 5 4 261 t o 3 0 2 2 4 5 t o 2 6 0 2 2 7 to 204 239 to 172 155 t o I I I

Maximum Chonge, hor izon ta l normal s t ress 2 3 0 t o 4 0 5 221 t o 7 2 198 to194 2 0 0 t o 120 2 1 9 t o 4 8 198 t o 5 4

Maximum C h a n g e , s h e a r stress’. 6 8 t o 3 2 0 t o 160 5to95 -15 t o - 4 8 -9 to -72 3 6 t o 7 3

Reg ion near Downs t ream Edge o f Base

Maximum C h a n g e , vertical normoi s t r e s s 271 t o 3 7 7 3 3 2 t o 5 4 6 289 to 196 2 4 8 to 282 339 to 371 3 5 6 to 3 9 7

Maximum Change, hor izon ta l normal s t ress 139 t o 2 9 9 2 2 6 to 4 0 6 184 to 369 179 to 256 199 to 310 2 2 2 to 317

Maximum C h a n g e , s h e a r stress?’ 140 t o 120 190 to 216 195 t o 2 4 0 213 to 297 240 to 109 271 to 318

Notes:’ Based on t r ia l - load a rch dam ana lys is .++ T h e o r e t i c a l m a x i m u m s h e a r i s i n f i n i t e a t r e e n t r a n t c o r n e r ; t h e r e f o r e v a l u e g i v e n i s t h e

max imum computed s t ress in v ic in i ty o f corner .F i g u r e s t o l e f t b a s e d o n g r a v i t y s t r e s s a n a l y s i s ; f i g u r e s t o r i g h t b a s e d o n n o n l i n e a r

Stress OnOlYSiS. (S lab Ana logy Method)


equilibrium in a second region disturbs thefirst, but still leaves it approaching finalequilibrium. The operations of adjustment areeasily applied when each step is confined to asingle joint.

To illustrate the method, consider thesimplest case where the boundary conditionsare given in terms of displacements. Theprocedure of adjustment may be visualized asfollows: Consider a lattice actually constructedto a given scale, with elastic members comingtogether at the corners to form frictionlesshinged joints. Lay this lattice out on ahorizontal board, and before applying anydisplacements, completely restrain all joints bynailing them to the board. Next, displace andsecure again, the various boundary jointsthrough distances corresponding to theirassigned displacements. Then, working in a lineof joints adjacent to a displaced boundary, freeone joint and allow it to move to a newposition of equilibrium and resecure it. Repeatthe process at successive joints until all havebeen adjusted (keeping only the boundaryjoints fixed in conformity with the givendisplacements) as many times as is required togive a satisfactory approach to the condition ofcomplete transfer of forces from the interiornails to the members of the lattice. Simplerelationships then exist between displacementsand stresses.

(c) Equations. -Lattice equations for thedisplacement of an interior joint, an exteriorcorner joint, a reentrant corner joint, and aboundary joint have been developed in termsof loads at the joint and in terms ofdisplacement of the surrounding joints. Theseequations are shown on figure D-l.

( d ) B o u n d a r y C o n d i t i o n s . - B o u n d a r yconditions for the problem can be given eitherin terms of loadings or displacements. For thedesign of structures, estimated or computedloads would probably comprise the boundaryconditions, but for structures already built it ismore likely that boundary conditions would begiven in terms of measured displacements. Ineither case, the loads or displacements for theplate must be expressed in terms of loads ordisplacements for the boundary joints of thelattice. However, the adjustment of the lattice

fundamental conditions must be satisfied inorder that an assemblage of elemental latticesmay constitute a plate. These conditions are:

(1) The normal and tangential stresses mustbe distributed throughout the plate in such away that the forces acting upon each elementare in equilibrium with respect to translationand rotation of the element.

(2) The extensions and detrusions of thee l emen t s r e su lting from these stressesc o n s t i t u t e a single-valued s y s t e m o fdisplacements.

(3) Any special conditions of stress ordisplacement which are specified at theboundaries must be satisfied.

(b) Solution. -Having replaced the plateprototype by a lattice framework, a solutionmay be devised for the lattice and applied tothe plate. The essential concept involved in thissolution is a systematic relaxation of restraintsat the joints. A description of a relaxingprocess to aid in an understanding of theadjustment will be given subsequently. Afterthe adjustment of the lattice to removerestraint has been completed, the strains arededuced from relative displacements betweensuccessive joints and from these the stressesmay be computed.

The fundamental device employed in thelattice analogy is the elemental square framewhich is composed of six elastic members, twoof which are horizontal, two vertical, and twodiagonal. The length of the sides is consideredunity in the derivation of the lattice formulas.The six members are assumed to be connectedat the corners by frictionless joints. The elasticproperties of the frame members are sodetermined that the behavior of the frameu n d e r g i v e n b o u n d a r y c o n d i t i o n s w i l lcorrespond exactly to the square element ofthe plate section with respect to axialelongation, lateral contraction, and sheardetrusion. In a lattice network composed ofmany frames, the amount of work involved in aconventional solution would be tremendous.However, by using a relaxation method, onemay deal with a small region in whichequilibrium is easily established and themethod can consequently be applied tointricate latt ice systems. Adjustment of

SPECIAL NONLINEAR STRESS METHODS-Sec. D-3 375

h b

dINTERIOR- JOINT

ha=$Ha+,~’ h( bf bv +4h,+hd-v,+hf+ fv +4h, + h&/h)va=&va+& (4va+ b+ b d+ d + e+ f+ f hh v -h v 4v h v -h +vn)

b

a

BOUNDARY JOINTho=&,+~(hb+Vb +dh,+ h,j -Vd)

Va&Va+&( ha+ hb +Vb - ha +vd + 2Ve)

MCEXTERIOR CORNER

meREENTRANT CORNEI

ho.31 (3Ho-Vo)+$-vd t hb+Vb +3ho) h,~~a~V~)+~~~+4hb+4Vb+I8h,+5hd-5Vd-2V,+4hf+4vf+ghgV,=32E(3V,-H,)C~(3Va+hbtVb-h~) v,=,3,~~-~H~~~~4hb~Vb-2hc-5hd+5Vd +18ve +4hf +4vf-ha)

h,v indicate displacements of jo int 0.

H,V indicate forces per uni t th ickness at0 represent ing body forces at 0 inplane of lat t ice.

E is elast ic modulus of prototype mater ial .

Figure D-I. Lattice analogy-equations for displacement of joint 0.-103-D-274

is always made by adjusting displacements at the lattice to remove restraint having beenthe interior joints to remove restraints. completed, the resulting displacements may be

( e ) Stresses.-Normally, t h e p u r p o s e o f a p p l i e d t o t h e p l a t e . T h e d i f f e r e n c e i ncomputing a lattice would be to determine displacements between successive lattice jointsstresses in the prototype. The adjustment of will yield strains, and stresses may be


The principal limitations placed on applicationto gravity dam design or other purposes are thetime and labor involved in the calculations. Themethod has been found useful in determiningthe stress distribution in a body composed oft w o o r m o r e different materials. Thisrepresents a problem of great practicalimportance, e s p e c i a l l y i n t h e d e s i g n o fr e i n f o r c e d concrete structures. Anotherproblem which is fundamental in the study ofconcrete structures is that of uniform shrinkageof a two-dimensional section on a rigidfoundation. This problem has been analyzedsuccessfully, using the lattice analogy.

D-4. Experimental Models. -The use ofmodels is a very valuable addition to theanalytical methods used in the design of damsand similar structures. Models are necessary forany careful design development and can beused for checking of theory. All models comeunder one of two major classifications: (1)similar models, or those that resemble theprototype; and (2) dissimilar models. Principala m o n g t h e f o r m e r g r o u p a r e t h etwo-dimensional and three-dimensional typesof elastic displacement models; photoelasticmodels; and models used in studies employingthe slab analogy. In the dissimilar group arethose employing such analogies as themembrane, electric, and sand-heap analogies.T h e s e l a s t - m e n t i o n e d t y p e s , w h i l e o fconsiderable value to stress studies of specialproblems, do not concern us here, and it isonly those model types which have provedadaptable to experimental studies of masonrydam structures that will be discussed.

( a ) T h r e e - D i m e n s i o n a l Models.-Three-dimensional displacement models arethose constructed of elastic materials top r o p o r t i o n a t e s i z e a n d l o a d i n g o f t h eprototype so that deformation, structuralaction, and stress conditions of the latter canbe predicted by measurement of displacementsof the model.

The following conditions must be fulfilled,in order to obtain similarity between a modeland its prototype, while at the same timesatisfying theoretical considerations and ther e q u i r e m e n t s o f p r a c t i c a l l a b o r a t o r yprocedure:

computed from the conventional stress-strainrelationship.

(1) Restraining forces.-At any time duringadjustment of a lattice, the restraining forces atthe joints may be computed. For an exactsolution, these forces will reduce to zero, andthey are, therefore, a measure of the accuracyof the adjustment at any stage. Ordinarily, thecomputation of the restraining forces involvesconsiderable work so that other methods areused to judge the end of an adjustment. Theeasiest way is to overadjust the displacementsso that reversal occurs in their directionbecause of passing the end point.

(2) Body forces. -The equations previouslymentioned concerning displacement at certainjoints due to loads at these joints, will apply tothe body forces of the structure. Such loadscan be introduced into the lattice adjustmentby computing the horizontal and verticalcomponents, computing the displacements, andadding these displacements to those producedby displacements of the surrounding joints.Certain limited types of body forces, includinggravity forces, may also be handled by Biot’smethod of applying fictitious boundarypressures.

(3) Thermal stresses. -A system has beendevised in which displacements due totemperature change are computed by theapplication of fictitious body and boundaryforces. The determination of the fictitiousforces is somewhat involved and will not begiven here, and the application of body andboundary forces to a lattice system has alreadybeen discussed.

( f) Applicatiotu and Limitations.-Thelattice analogy method is used for solvingtwo-dimensional nonlinear stress problems inengineering and has many applications that areinvolved in the design of masonry dams. Themethod is adaptable to the computation ofstresses in a gravity dam. A section from agravity dam is normally computed of unitt h i c k n e s s a n d its ou t l i ne c o u l d b eapproximated by a lattice network made up ofsquares. As has been pointed out, boundaryforces (waterloads), body forces (dead loads),and thermal forces cause no particulardifficulty in adjusting lattice displacements.


(1) The model must be a true scalarrepresentation of the prototype.

(2) The loading of the model must bep r o p o r t i o n a l t o t h e l o a d i n g o f t h eprototype.

(3) Upon application of load, resultingstrains and deflections must be susceptibleof measurement with available laboratoryequipment. Because of reduced scale thiscondition ordinarily requires a higherspecific gravity and greatly reducedstiffness in the model compared with theprototype.

(4) Because of influence of volumestrains on the stress distribution, Poisson’sratio should be the same for both modeland prototype.

( 5 ) T h e m o d e l m a t e r i a l m u s t b eh o m o g e n e o u s , i s o t r o p i c , a n d o b e yHooke’s law within the working-stresslimits, since these conditions are assumedto exist in a monolithic structure such as aconcrete dam.

(6) Foundations and abutments mustbe sufficiently extensive to allow freedomfor the model to deform in a mannersimilar to the prototype.

(7) If effects of both live load andgravity forces are to be investigated, theratio of dead weight to live load should bethe same in both model and prototype. Ifthe effects of live load only are to beinvestigated, the results are not affectedby the specific gravity of the model,providing Hooke’s law is obeyed and nocracking occurs.

If all requirements of similarity are fulfilled,the relations between model and prototypemay be expressed in simple mathematical termsof rat ios. Overall compliance with thisrestriction is not always possible in model testsof masonry dams, but since the purpose ofmany tests made on dam models, such as theHoover Dam model tests, is to obtain data forverifying analytical methods, some variationfrom true similarity does not detract greatlyfrom the value of the test. Complete details ofmodel tests for Hoover Dam are given in the

Boulder Canyon Project Final Reports.’(b) Two-Dimensional Displacement

Models. -Two-dimensional displacementmodels are often referred to as cross-sectionalor slab models. Acting under two-dimensionalstress such a model can be compared directlyonly to a similar slice through the prototypeacting as a separate stressed member, since inthe actual structure all interior points are underthree-dimensional stress. The model slab,having no forces applied normal to the section,is considered to be in a state of plane stress. Across-sectional element or cantilever acting asan integral part of a masonry dam is stressed bya more complex system of forces, and is underneither plane stress nor plane strain. A state ofplane strain is closely approached, however, inthe central cantilever element in a long, straightgravity dam and also in a vertical slice throughthe foundation under the crown cantilever ofan arch dam. Assuming a state of plane straincan be realized, similarity of stress and straincan be had if Poisson’s ratio is the same formodel and prototype. For fairly reliable resultsin the evaluation of stress distribution in thecantilever section of a dam, the usefulness ofthe two-dimensional model is limited to thestraight gravity type of dam, and then onlywhen applied to the central cantilever element.This usefulness is further limited in itsapplication to arch dam cantilevers, to theimmediate neighborhood of the base of thecrown cantilever, and to that part of thef o u n d a t i o n s l a b c o n t i g u o u s wi th i t .Two-dimensional arch models, while usuallyfailing to give stress and deformation valueswhich can be taken as representative of thoseoccurring in the prototype, have furnishedvaluable information in connection with theevaluation o f a b u t m e n t r o t a t i o n anddeformation for use in analytical studies.

D-S. Photoelastic Models.-Photoelasticmodels are used extensively by the Bureau for

‘Bulletin 2, “Slab Analogy Experiments,” Bulletin 3,“Model Tests of Boulder Dam,” and Bulletin 6, “Model Testsof Arch a n d C a n t i l e v e r E l e m e n t s , ” P a r t V , T e c h n i c a lInvestigations, Boulder Canyon Project Final Reports ,1938-40.


stresses acting at a point within the model,optical instruments such as the photoelasticinterferometer or the Babinet compensator areused. The determination of stress fromphotoelastic models and the techniques used inthis type of investigation are subjects toocomplex to properly come within the scope ofthis appendix.

M u c h v a l u a b l e i n f o r m a t i o n h a s b e e nobtained through photoelastic studies inconnection with stress distribution andmagnitude in dam and foundation structures.The photoelastic studies made on Shasta Damfurnish a good example of the application ofthe method. These studies were made todetermine what effects would be produced ondam and foundation stresses by severalweak-rock conditions which had been exposedin the foundation during the excavation forconstruction. A 5-foot clay-filled fault seamwas discovered lying in a direction making anapproximate 60’ angle with the proposed axisof the dam. It was desired to determine thedepth, if any, to which the seam in questionshould be excavated and backfilled withconcrete in order to keep stresses withinallowable limits. Because of the direction ofthe seam with respect to the dam, threepossible locations of the seam were assumedfor the tests. Photographs of the photoelastics t r e s s p a t t e r n s w e r e t a k e n o f m o d e l sconstructed and loaded to represent the criticalcantilever section under full reservoir load withthe fault seam at the three alternate locationsand at varying depths under the cantilever.These stress patterns were studied with regardto the effect of the various depths of seamrepair on the stress at the downstream-toefillet; where the most critical stress conditionexisted. Figure D-2 shows two photographs ofthe photoelastic model under stress. Figure D-3gives curves showing the relation between thevalues of downstream-toe fi l let stressesobtained from the photoelastic stress patterns,and the depth of the 5-foot clay-filled faultseam.

design and analysis of localized portions ofmasonry dams and their appurtenant works.Stresses in photoelastic models are determinedby means of the visible optical effects whichare produced by passing polarized light throughthe model while it is under load. The modelmaterial must be elastic, transparent, isotropic,and free from initial or residual stresses.Bakelite, celluloid, gelatin, and glass have beens u c c e s s f u l l y u s e d . Studies employingphotoelastic models are usually limited toconditions of plane stress or strain, and may besaid to have their most important applicationin the determination of regions of stressconcentrations.

Effects of stress in a photoelastic model aremade visible by means of an optical instrumentk n o w n as the photoelastic polariscope.Through a system of Polaroids, the polariscopedirects a beam of light through the model sopolarized than when the material of the modelbecomes doubly refractive under stress, thefamiliar photoelastic pattern is projected to theobserver on a screen or photographic plate. Thealternate color bands of the pattern, or fringesas they are called, furnish a means of measuringthe stress quantity, by a known relationbetween principal stresses and their retardativeeffect on polarized light-waves passing throughthe stressed model. This “unit” of measure,called material fringe value, is readily evaluatedin the laboratory. For bakelite, the mostextensively used material, the value is 87pounds per square inch per inch of thickness,and represents the stress corresponding to onefringe. Values for any number of fringes, orfringe order, are found by direct proportion;and by applying a suitable factor ofproportionality, corresponding values of thestress quantity in the prototype structure maybe determined. This stress quantity is thedifference in principal stresses at any point(twice the maximum shear stress), and hasparticular significance along free boundaries,where one of the principal stresses is zero.

Where it is desirable to know the magnitudeand direction of the individual principal


(a) F A U L T S E A M U N D I S T U R B E D

lb) F A U L T S E A M E X C A V A T E D , B A C K F I L L E D 5 2 F E E T

Figure D-2. Photoelastic study of foundation fault seam near downstream face of ShastaDam-reservoir full.-PX-D-74424

; 1400~STRESSES OBTAINED FOR COMBINED

aa DEAD LOAD AND W A T E R LOAD

22ulul

(L2 1200

cn2

III I I I I I Iz3

2

’ 1000W

;: \ \0 \

m \,,- FAULT ZONE IN POSIT10

?I$

- -800-- --_

=;ii

‘--FAULT ZONE IN POSIT ION1 “.. FjULT ZjNE I N rOSITI0,

I4 0 8 0 I20 180 2 0 0 2 4 0

C U R V E S I N D I C A T ESTRESSES EXISTING

ALTERNATE FAULT

POSIT ION OF FAULT FOR CURVE

CROSS-SECTION OF DAM AT STATION

DEPTH”D” TO WHlCH FAULT ZONE IS EXCAVATED AND BACKFILLED WITH CONCRETE

S H A S T A D A MPHOTOELASTIC STUDY OF FOUNDATION

Figure D-3. Relation of stress at toe of dam to depth and location of fault zone.-DS2-2(58)

<<Appendix E

Comparison of Results by Gravity andTrial-load Methods

E- 1. Stresses and Stability Factors. -Stressesand stability factors for normal and maximumloading conditions for 12 gravity dams aregiven on figures E-l to E-29, inclusive. All ofthese dams were analyzed by the “GravityMethod,” and, in addition, three were analyzedby the “Trial-Load Twist Method” and one bythe “Trial-Load Arch and Cantilever Method.”These are Grand Coulee, Kortes, and AngosturaDams; and East Park Dam, respectively. Forthese four dams, stresses obtained by thegravity analysis are shown on the same sheetwith stresses obtained by the trial-load analysis.The same arrangement is used for showingstability factors. This facilitates comparison ofresults obtained by the two methods.

E-2. Structural Characteristics of Dams andMaximum Stresses Calculated by the Gravityand Trial-Load Methods. -A tabulation ofstructural characteristics, maximum stresses,and maximum stability factors for the 12gravity dams mentioned in the precedingsection is shown in table E-l. The 12 dams aredivided into four groups in accordance withtheir relative heights. Structural characteristicsare given in the upper half of the sheet. Theratios of crest-length to height, base to topwidth, and base to height of the crowncantilever define the relative characteristics ofeach dam. The cantilever profiles are shown forwhich the maximum stresses are tabulated inthe lower half of the figure. The cross-canyonprofile is shown for those dams for which atrial-load analysis was made.

In the lower half of table E-l is shown thecritical stress at the upstream face of each dam.

This critical stress is considered to be thatstress at the upstream face which is less thanwater pressure at the same point. In most casesthis stress occurs at the base of the crowncantilever. These critical stresses are tabulatedfor normal loading conditions and maximumloading conditions. The water pressure at thesame point is also shown. Examination ofcritical cantilever stresses at the upstream facefor maximum loading conditions reveals that inall cases the water pressure exceeds the stressshown for the designated loading. Tensilestresses are indicated at the upstream face forthree dams; namely, Black Canyon, East Park,and Keswick. However, it is felt that this is anexceptional condition with little likelihood ofoccurrence. The criterion to be used, therefore,is the normal loading condition, for which inno case is the stress at the upstream face belowa value of about 40 percent of the waterpressure at the same point.

M a x i m u m s t r e s s e s p a r a l l e l t o t h edownstream face for normal operating reservoirload and for maximum loading are also shownin table E-l. Maximum stresses computed bythe trial-load analysis are given for comparisonwith gravity stresses. Generally, the twomethods show very little stress disagreement inthe central section of the dam, but usuallyshow significant differences in stress andstability factors in the region of the abutments.

Maximum sliding factors and minimumshear-friction factors are also shown in tableE-l for the 12 dams as computed by thegravity and trial-load analyses. These factorsare for maximum loading conditions. For

381

lESERVOlR EMPTl S. EL 4354.5 RMAL RES. W.S. EL.4354.5 ESERVOtR EM’T

unds PerPO

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+

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+-

+

6I.

**

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:L 4282 60’ i 1.J \vk 81 co’19 60’

MAXIMUM NONOVERFLOW SECTION

:Resultont-c~,ete41ght only \Resultant-water pressure ond welght\Resuttont-water p,essu,e,re,ght and uplift‘a Resultant-concrete welght md eo,thquoke(vert~cal uprmtd and horIzonto downstream). ‘*Resultant- note, presw,e,we,ght ond

earthquake (vertlcol upward and hor~rontot upstreaml.~‘~Resultont-rater p,essu,e,weight,uphft and eorthquoke (vertbcot up*o,d andhorizontot upstream)Uplift pressure vo,,es os o straight hne from reserve,, pressure (It upstream face to toilsote, pressure OT zero at downstream face,

octina over one-halt the mco of the ho,~zon+ol sectloo““It we;ght of co”crete’t50 pounds per cublctootAll normal stresses are comp,ess,ve except thosepreceded by o negahve slgn,Much ore tensilePosltlve sheor stresses ore caused by sheor forces actmg thus=Qegatlve shear stresses are caused by shear forces octmg IhurL,.Total toad corrled by vertlcot cantlleve,.S,iding Factor= Horizontal F o r c e

Wciqht-Uplift~he,,,-f,,~~,~,, Facto,; (Wemht-Upl,ft)s Coetflclent of Internal Frxtlon+ HWlzontol /Oreo I Umt Sheor Resjstance

Coeff!clent of lnternol f,lCtlon=OG5.Un1t sheor ,es,stonce;4a)pounds per squoreinchWeight of bridge and gates included in onatysisf Figures above elevotlon lmes Include earthquake accele,atlons(vertlcal “prrord and horuontot dornstreom,**Figures obOve elevotlOn lhnes Include earthquake occele,otl~s(ve,tlcal uprard and hotuontot upstream)f** Figures above elevation lines include earthquake eccelerotions(verttcol do*nro,d and horizontal uprtrwm)figures below elevation lines ore for normal condttton&

q t*IDO*. C�O☺EGT - ID.�0

A M E R I C A N F A L L S D A MSRAVITY ANALYSIS -NOttOVERFLOV AR0 SPILLVAY SEtT,O”!

RESERVOIR EMPTY AN0 NORMAL FULL RESERVOtR DPERA,,CINCLUDING COMBINED EARTRPUAKE AGCELERAY,ONS

Figure E-I. American Falls Dan-gravity analyses of nonoverflow and spillway sections including effects of earthquake accelerations

63DOWNST&AM F&E

SECTION(Resulta”!-concrete weight only 4 Resultant-wok, pressure, welqht,and ice 01 elev~t~o” 4354 51 Resultant-water pressu,e,welght,upiift and ice of elevot io” 43545; Resultant-wate,pressure.welght and ICY 01 elevat lo” 4343 2 1 Resultant-water p,essu,e,welght,upllft and ,ce of elew,+w” 4343 2.

UplIft pressure vpr~es OS a straight hne from reservoir pressure 01 upstream face lo to~lwote, pressure o, zero 01 downstream face,acfing over one-hol f the area of Ihe hortzontol sectlo”Unft weioht of concrete= 150 oounds oe, cubic footAll normal stresses ore comb,ess~vk except those preceded by a “egaffve slgn,which ore tenslIePas,tive shear st,esses ~,e caused by rhea, forces actmg thuse,Total load cowed by ve,t,col con,~lever.

neqatlve shear s1,esses are caused by sheor forces actmg thus=

Sl,d,“g Facto,= H$;?;~,‘~~,$$x

Sheo,~f,,c,,o” Foclo,. (WeIghI-Uphft)x Coefflclent of I”ter”0l Frict~o” + Ho,~zo”tal Areo I Unit Shea, Res~sfonce.Horl lontal Force

““ITED ,IADLP.Ir*c*I 0s 7°C

.““I.” or “LCLlYINIPOMA PROJEC’

A M E R I C A N F AGRAVITY ANALYSIS -NONOVERFLOW AND SPILLWAY SECTIONS

NORMAL FULL RESERVOIR OPERATIONWITH I C E L O A D

Figure E-2. American Falls Dam-gravity analyses of’ nonoverflow and spillway sections, normal conditions with ice load.

M A X I M U M A B U T M E N T S E C T I O N

N O R M A L R E S . W.S.EL.

SHEAR MAx++%i2 W A T E R V E R T I C A L F;;;;;; s”:R’,“,“, PRESWRE S T R E S S

U P S T R E A M F A C E MAXIMUM NONOVERFLOW SECTION H O R I Z O N T A L S E C T I O N

/Resu~ont-welght.‘\ResuItont-water pressure and weight. <Resultant-whir pressure,weight and uplift.iResultont-weight and eorthquoke (vertical upward and horizotil downstream).~~ResuItom-water pressure, weight and earthquake (vertical

upward and horizontal UpetreOm). (Resultant-water pressure, weight, uplift and eorthquohe (vertical upward and horizontal upstream).Uplift pressure varies os o straight line from resewoir pressure ot upstream face to tollwater pressure or

zero at downstream face, acting over one-half the oreo of the horizontal section.Unit weight of concrete=l50lbe. per cufr.All norm01 stresses ore compressive except those preceded by o negative sign, which ore tensile.Positive shear stresses ore caused by sheor forces acting thust;Toto load carried by vertical catiilever.

negative shear stresses are caused by sheor forces acting thus=.

Sliding Factor= HOrlz0”to ForceWeight-Up,ift . Shear-Fn’ction Factor= ’Weight-Uplift)xCcefficient of Internal Friciion+Horizontal Area xUnit Shear ResistonceHorizontO Force

Coefficient of internal Friction=O.& Unit Shear Resistonce=4DOlbs. per eq.in.Silt load to elevation ISIS. Unit weight of silt=i201bs. per cu. ft.Figures above elevation lines ore for normal conditions.*Figures below elevation lines include eartbquahe acceleration (vertical upward and horizontal downstream).+t+cFigures below elevation lines include earthquake occelerotion (vertical upword and horizotil upstream).ic+6-*Figures below elevation lines for sliding factor include eoTtllquoke accelertion(vertical dowward and horirotial upstream).

PROPOSED DESIGN GRAVITY ANALYSES OF MAXIMUM ABUTMENT AND

RESERWJIRAND WTHDUT

01.1”,“,,JO

C”ECIED

Figure E-3. Altus Dan-gravity analyses of maximum abutment and nonoverflow sections.

-RES.

RTICAIT R E S S

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ATER3SURE

Sat

MAL RES. W.S. EL.15

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Pour

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6 2 ’ It* ESERVOIR EMPTY’

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W.S. EL.l562**TRESS~RALLEI FACE-

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? Inch

_.MAXIMUM UNCONTROLLEO’=SPILLWAY SECTION

NORMAL RESERWlR

UPSTREAM FACE MAXIMUM CONTROLLED SPILLWAY SECTION HORIZONTAL SECTION DOWNSTREAM FACE

?esul+an+-we~gnt.\. Resulton+ - water pressure ond weight. (Resulton+-water pressure, welght,ond upllft.?esultant-wsight,ond eorthquohe (vert,cal upward and horizontal downstream)7’iReSulfant-water pressure,we~gh+,and

earthqwke (uer+ico\ upword ond horizonto upstream).~Resultont-water pressure,walgh+,upilf+,and mrthquZke(vertn9 upword and horiz~tol upshwm)111ft pressure varies OS o stratght line from reservoir pressure of upstream face to to~lwater pressure or zero ot downstream

fOce,ac+~ng over one-half the area of the horizontal section.,I+ we@,+ of concrete= Mbs. per cu. ftI nmn~l stresses are compressive exceptthose preceded by o negottve sign, which are tensde.tsitlue sheor stresses are caused by sheor forces octlng thus,-; negotlve shear stresses are caused by Shear forces aC+lng tIIuS C.*aI load corned by vertical cantilever. (Weight-Upl~it)xCoeff~c~en+ o f internal Friction+Honron+al AreoxUnlt Shaor ReslstonceHorizontol Forceding Foc+or= Weigh+-Up,,f+ .Shear-friction Foc+or= Horizontal Force)efflcient of Internal Friction=O.& Un<+ shear resls+ance=400 tbs. per sq in.It load to eiwotion 1515. Unit wejght of silt=lZOIbs. per cu.f t.gures above elevation lines are for normoI condlttons.

PROPOSED DESIGN FOR CONCRETE CONSTRUCTlO,

Ffgures below elevation hnes lntlude earthquake occelerotton (verttcol upward and horizontal downstream)..* Figures below .?levOt~on line5 include earthquake acceleration (vertical upward and hor~z~ntol upstream).++Figw?s below elevation lhnes for sliding factor mclude earthquake acceleration (vert~col downward and horizontal upstream).

GRAVITY ANALYSES OF MAXIMUM UNCONTROLLEDSPILLWAY ANOCONTROLLEO SPILLWAY SECTIONS

RESERVOIREMPTY AND NORMAL FULLRESERVOlR CPERATIONW,AND WlTHOUT HORIZONTAL NO YERTlCPlL EARTMUAKE EFFEC,

LIRIWL 1 E e I”l”,TTLD 2-g

Figure E-4. Altus Dam-gravity analyses of spillway sections.

NORMAL RES. W.S. EL.587 R E S E R V O I R E M P T Y

I I P o u n d s p e r Square I n c h

U P S T R E A M F A C E 6 5 F O O T PENSTOCK S E C T I O N H O R I Z O N T A L S E C T I O N O O W N S T R E A H F A C E

k Resultant-Concrete weight and ewthqupke(horiront.I downstream and verticoI upword).~ResuI+on+-Water prers”re,velgh+,ond earth-quake (horizontal upstream and vertical up.grd).~ResuItpnt-Water prcsrurc,rsigh+,upllft,ond earthquake (horIzonto upstream andvertlcol upword).~ResuI+pnt-Water pressure,weight,and ewthq~ofe (horizontal upstream and verticaldawnward)~ Resultant-Waterpressun,welght,uplift,and eorthqupke (horlzontpl upstream and vertical downward).

Sliding Factor= Horizontal ForceWeight-Uplift

Shear-fr,c+ion Factor j (WeIghi-Uplltt)xCoefficien+ of internol fric+~on+Horizontol area li Unitshear resistanceHorlzontol Force

Unit weight of concrete= 150 Ib.per cu ft “n,t sheor res~stpnce = 400 lb. per sq.kn. Coefficient of internal friction = 0.65.Uplift pressure wroes as D straight lane from reservoir water pressure at the upstream face to zero at the downstream foca or tallrater pressure

O+ the downstream face of the power plant, acting over two-thirds the prep of the horizontal section;asrumed to be una/facted by earthquake.Vert~col earthquake acceleration and horizontal eprthqueke pccelero+lon=G.l grpvaty; Period = I second.Total load cawed by vertical cantilever. Analyses mode with gates down and penstocks empty.All normal stresses are compressive except those preceded by 0 negative rlgn which are tenslIe.Positive sheor stresses are caused by shear forces octong thus -. Negative shear stresses ore caused by sheorforcer pctlngthur v,Q All flgurel glvenfor reservoir empty include earthquple eccelemtv3n (horizontal downstream and vertical upward). i All figures given

above hne for reservoir V.S.EI.587 include eorthquoke accelcra+~on(horlzontal upstream and vertical upward).* All figurer glvan below linefor reservoir W.S. El.587 Include eorthquoke occelerption (horizontal upstream and vertical downward).

G R A V I T Y A N A L Y S E S - G A T E S D O W N65 F O O T PENSTOCK S E C T I O N

RESERVOIR EMPTY AND NORMAL FULL RESERVOIR OPERATIONINCLUDING HORIZONTAL ANDVERTICAL EARTHQUAKE

ACCELERATIONS CAUSING THE MOST CRITICAL CONDITIONS

Figure E-5. Keswick Powerplant Dam-gravity analyses of penstock section including effects of earthquake accelerations.

P L A N

NOTESTopography and plan layout token from drawing - 22 * 12, No 119Crown contl lever sec t ion and protcle taken f rom drawcng 2 2 *

P R O F I L E AL O N G A X I S L O O K I N G U P S T REAM (OEVEL~PE~)

Figure E-6. East Park Dam-plan, elevation, and maximum section.

ESERVOIR EN

qf%J

P

56 I 13 I 13 I 1.7UPSTREAM FACE

NORMAL RES. W.S. EL. 185

m

MAX.FLOOD RES.W.S.EL.190

7 2 2 0 . 2

17 2 2 0 . 6

28 7 7 0 . 9

39 9 9 1 . 2

4 8 II II 1 . 5

I

1*

I(E

-A .BSS I 5.7 I 80 I

MAXIMUM NONOVERFLOW SECTION HORIZONTAL SECTION^I Resultant-weight I Resultant-water pressure ond weight irieswrcnr-uorer pressure,we,gnr and up,,,,.

+ Resultant-weight and eorthquake(vertlcal upward ond hwlzontal dornstream).i Resultant-water pressure,welgh+ond eorthquake(vertxal upward

,-2

EL.60 3.*:- : 4 86 82’ A -2 i ‘,90.62’

MAXIMUM NONOVERFLOW SECTION

75hL1 !*

ML

I

RMAL RES. W.S. EL.185u HONL

WATER VERT’CAL;,“,‘,“,“, PRESSURE STRESS

* I 2 **20

ond honzontql upstream) : ReSultqnt-water pressure,we~ght,upllft and earthquake(vert,cal upward and horuonto, upstream).UplIft pressure vor~es 0s q strclght hne from reservou pressure at upstream face to tailwater pressure or zero qt downstream face,

octlng over two-thirds the ore0 of the horizontal sectlonUnit we,ght of concrete = 145 lbs. per cu.ft.All normal stresses ore compressive except those preceded by o negative sign, which ore tenslIe.Posltlve sheor stresses are caused by shear forces actmg thus z== ;Total load carried by vertical cantilever.

negqtlve shear stresses are caused by shear forces acting thus L.

Sledmg Factor = Horlzontol ForceWeaght-Uphft

Sheor-fr,c+,on Factor= (Weught-Upltft)r Coefficient of Internal Fract!ontHorlzontolAreo x Unit ShearResistance,

Coefficient of internal friction = 0 65. Umt Shear resIstonce = 204 Ibs. per sq inHorozontal Force

*c Figures below elevation lines Include earthquake acceleration (vertxal upward and horizontal downstream)+*‘* Figures be low elevation lanes Include earthquake occelerotion (ver t ica l upword ond horirontol upstream).*L t:-+ Fagures below elevation Ilnes forslhdmg factor Include earthquake occelerotion Ivertical downward ond horlzontol upstream).Figures above elevotlon lines do not Include eorthquoke effects.

Figure E-7. East Park Dam-gravity analyses of maximum nonoverflow section.

Irawing No. 2?D 142for p&,profile and

nasonry d abutmentVX!k=2,OOapOOpandsper square inch.russon’s Rotiofcrnwwyordabutmentrock =0.2.rift weight of_^_^^_..per C” it.eservoir w* El. 187.otailwater.empera+“reLiungesin concrete based onnormal wxiation.= Stress at extradm

LOADING CONOITIONS’A(Continued )

187 Earthq&eossm@fa

Camnweupqnd_ _ d.mnheanhximtol-175

&G L--a,Cl..94 j ~:;.@I

ly in tte drectim of/ 166 me he at centers.

;:-‘;“\ 1 1E=-43*.-Pm /

Increasedwuterpesornacts emOllY m a11

All orchesanaly;ad qssymmetrical withsymmet r i ca l loading.

Arch stresses oreactirin hmzmtol directwmrpomlle lathe edgesof me orcles.

Cantileverstressesoeact ing in inc l ineddiracticns~rallelbthedgedmecmk3ws

00+ = Compression= Tensiona~= Crown of archper spare inch:

PROFILE ON AXIS LOOKING UPSTREAM

E ‘. _

Ho+wONTAL LOAO IN T”O”SANOS‘~OF W”NOS PER SO”ARE FOOT- I’

BYRLA” OF “LCLLII.TIO”0 CANTILEVER DEFLECTIONS ORLAND PROJECT-CALIFORNIAX ARCH DEFLECTlOt E A S T P A R K D A M

0 AS CONSTRUCTED -STUDY No 2TRIAL LOAD ANALYSIS - LOADING COND,T,ONS*A’

RAOIAL OEFLECTlON IN FEET

LOAD DISTRIBUTION AND RADIAL ADJUSTMENT D�AW� ac q ,�~�ITTLO

I�AcED I.

Figure E-8. East Park Dam-stresses, load distribution, and radial deflections from trial-load analysis.

P L A N

PROFILE ON AXIS LOOKING UPSTREAM

MAXIMUM NONOVERFLCW S E C T I O N MAXIMUM SPILLWAY SECTION

Figure E-9. Angostura Dam-plan, profile, and maximum section.

how -I/ 3040

P R O F I L E L O O K I N G U P S T R E A M

HORIZONTAL BEAM STRESSES

tt

LOADING CONDITIONSReservoir water surface at elevotlon 3187 2Tatlwoter surface at elevotlon 3040Lht wght of concrete,150 pounds per cube footUnit weight of water,62 5 pounds per cubtc footModulus of elastlclty for concrete: 3,OOOc)OO Ibs

per sq Inch, for rock 600,000 Ibs per sq InchPoisson’s rot10 for con Crete, 0 2Joints assumed grouted so dom can act os o

monohthAll beams analyzed us non-symmetrical wth

non-symmetrical loadmgIce load of 5 tons per linear foot concentrated

at elevation 3186.0.Effect of earth embankment included.

P R O F I L E L O O K I N G U P S T R E A M

CANTILEVER STRESSES

EARTHOUAKE ASSUMPTIONSHonzontol accelerotlon upstream, 0 I gravityVertlcol occeleratlon upward, o I grawtyPertod of vlbrotlon 1 I 0 secondExternal pressure includes earthquake effect

and acts equally on 011 contlleversU = Stress at upstream faceD : Stress ot downstream facet Indlcotes comprewon- Indicates tensjonAll stresses ore I” pounds per square InchCantilever stresses are octlnq ,n lncllned

dlrectlons parallel to the edges of cantileversS+= Mawmum shear stress at rock abutment,

(+I mdlcates downstream shearFor plan proflle and cantilever sectlonr see

D e n v e r OffIce orawmg 45,-o-204 T”.CEO J **

Figure E-IO. Angostura Dam-stresses from trial-load beam and cantilever analysis.

cc

For constants, assumptmns,and loading condlhons see Denver Offlce Drowng 454-D-209.Slldlnq factors ore computed for loodlng candltlons a listed on Denver Offloe Drowng

454-O-209 and ,nclude effects of two- th,rds upl,ft&effluent of Internal Frlctlon ~0 65 Unit Shear Res1slqnCe~200 pounds per square ,nchSlldlng factors ond shear frlctlon factors of safety for grovlty anolys~s are shown on

upstream side Shdlng factors and sheor frlctmn factors of safety for trIoI loadanalysts are shown on downstream side Slldlng foctws are shown above elevation hnesof canl~lever Shear-frtctm factors oe shown below elevation lmes of cani,lever

Factors desranoted bv x ore for inclined abutment olanes

d,,“,IIy ,yI,“I,

Shear frlctlon(Weight -UpI

nOrl2OnfOl kvceShear frlctlon factors of scfety, 0, two-thirds uphft =

tai pIones

(Welght-UpllftlSec+ I Coefflclent of Internal Frichon + Base Area I Un,l Shear Res,stanceHwzontal Force

(for lncllned obufment planes)

Figure E-II. Angostura Dam-stability factors from trial-load beam and cantilever analysis.

JNI

RES. EMPTY

qzgp$j

INCH12

3 3

61

92

107

Bo

85

96

114

0

8

18

IsUPSTREAM FACE


138.00' I If 98.50' -I 136.50'M A X I M U M S P I L L W A Y SECTION

.476HORIZONTAL

SECTIONDOWNSTREAM FACE

i Resultant-concrete weight only.\ Resultant-woter pressure and weight.\Resultont-water pressure, weight, and uplift.Horizontol Force

Sliding Factor= Weight-Uplift

Shear-friction Factor= b’ei@+Uplift) C ff’X oe lclent of Internal Friction +Thickness X Unit Shear ResistanceHorizontal Force

Unit weight of concrete =150 pounds per cubic foot. Unit sheor resistance = 400 pounds per square inch.Coefficient of Internal Friction = 0.65.

Uplift pressure varies OS a straight line from reservoir water pressure at upstream face to toilwoter pressure otdownstreom face, acting over one-half area of horizontal section.

Total load carried by vertical cantilever.All normal stresses ore compressive except those preceded by o negativePositive shear stresses are caused by sheor forces acting thusti;

sign which ore tensile.

sheor forces acting thus-negative shear stresses ore caused by

BLACK CANYON DIVERSION DAMGRAVITY ANALYSES

NON-OVERFLOW AND SPILLWAY SECTIONSRESERVOIR EMPTY AND NORMAL FULL RES. OPERATION

Figure E-12. Black Canyon Diversion Dam-stresses for normal conditions from gravity analyses.

RES. EM

M A X I M U M N O N - O V E R F L O W S E C T I O N

M A X I M U M S P I L L W A Y S E C T I O N

RESERVOII 3 F

H O R I Z O N T A LS E C T I O N

\Resultont-concrete weight and earthquake (horizontol upstream and vertical upword). ’* Resultant-concrete weight,and earthquake (horizontaldornstreom a n d vertical upward) . \ Resu l tant - water pressure, wenght, o n d eorthquoke (ho r i zon ta l ups t ream and vertical upward).~Resultont-water pressure, weight, and earthquake (horizontal downstream and vertical upvord).iResultant-uater pressure weight uplift andearthquake (hOrizonto upetreom and vertical upword).i Res

Sl idang Factor =Horizontal Force, Sheo)r-fric,ion Fac+or =Y’ - .5

Itont-volerpre sure,welght,upllft,ond eorthquoke (horizontaldovnshea;nandJrtical &word).

Weight-UpliftWeight UplIft x Coefficient of Internal Friction +Thickness X Unit Shear Resistance.

Hor izon ta l ForceUnit weight of Concrete = 150 pounds per cubic foot. Unit sheor resistonce =4DD pounds per square inch. Coe f f i c i en t o f i n t e rna l fricticn = 0 .65 .UPlift Pressure varies os o straight line from reservoir water pressure ot upstream face to tai lvoter pressure of downstream foce,octing over

one -ha l f oreo o f ho r i zon ta l sec t ion ; assumed to be una f fec ted by earthquake.Ver t i ca l ea r thquake occelerotion and ho r i zon ta l eorfhquoke occelero+ion -0 .1 g rav i t y , pe r iod = I second.Tota l l o a d corned b y vert,coI cantilever.

BLACK CANYON DIVERSION DAMGRAVITY ANALYSES-NOKOVERFLOW AND SPILLWAY SECTlONS

WITH HORIZONTAL AND VERTICAL EARTHQUAKE EFFECTSV E R T I C A L A C C E L E R A T I O N U P W A R D

RESERVOIR EMPTY AND NORMAL FULL RES. OPERATION

DRAWN T WL-

D O W N S T R E A M F A C E

S T U D Y N O . IDEPARTHENT OF THE INTERlOR

BUREAU OF RECLAYATIONBOISE PROJECT - IDI\”

Al l norm01 StresseS ore ComPreSSive excep t those p receded by o nega t i ve s ign , wh ich a re tens i l e .Positive shear s1resses ore caused by sheor forces acting thus,; n e g a t i v e sheor stresses ore caused by shear forces act ing thus=. CHECKED J.C. c..* lncludlng earthquake Occelemtion(horirontalupsheomondvert~colupvard).~+lnclrding eorthquakeoccelero+ion (horizontal downstream and vertical upword). DENVER, C~LO.

HEET 4 OF sFEB. ‘3,‘93713-D-550

Figwe E-13. Black Canyon Diversion Dam-gravity analyses including effects of earthquake, vertical acceleration upward.

RESERVOIR FULLMOX.

RES. EMPTY

UPSTREAM FACE YAXtdJY SPILLWAY SECTION.s... c-u

HORIZONTPSECTION&Resultant-concrete weightand earthquake (hwizontal upstream and vertlcpt downvord)./Resultant-concrete weight and Bprthg”pke(hprilontol downstream

and vertical downward).~Resut+ant-voter prewywaight, and eorthquoke (horizontal upstream and vertical downward). I, Resultant-voter pressureand earthquake (horizontal downstream and vertical dovnward).~Rewl+ant-wrater pressure, weight uplift and earthquake (horizontal upstream an>

weight,

vertical dovnuard).~ Resultant-rater preSsure.weiah+. uplift. and earthauake (horizonto dovn:+renG and ver+icoI downward).on +Thickness rUnit Shear Resistance .rorce

S,iding F,,c+or= Horizontot ForceWeight-Uplift

. Shear-fric+ion kactbr :(&i&t-UPlift)x Coefi~cien~of Internal FrictiHorizontal I

inch. Coefficient of internal friction =0.65.pressur.? ot downstream face, acting

Unit weight Of concrete =I50 pounds per cubic foot. Unit shear resistance =4OO pounds per squareUplift pressure varies 0s 0 straight tine from reservoir water pressure 01 upstream face to tailwater

Over one-half Oreo of horizontal section; assumed +o be unaffected by Borthquoke.Vertical earthquake accelrrotion and horizontal eorthqwke acceleration = 0. I gravity, period = I second.Total load carried by ver+icaI cantilever.AtI normal stresses ore compressive except those preceded by (1 negative sign, which ore tensile.Khcir:.,^-h”“.-.. ^^^^^ -_- __ __A.. .L..mI. ~~ . . . . ~~.L

..! a* II, 137 41 42 52 2,

IL DOWNSTREAM FACESTUDY NO. t

DEPARTMENT OFTHE INTERlORBUREAU OF RECLAMATIONBOISE PROJECT-IDAHO

BLACK CANYON DIVERSION DAMGRAVITY ANALYSES-NON-OVERFLOW AND SPtLLWAY S E C T I O N S

WITH HORIZONTAL AND VERTICAL EARTHQUAKE EFFECTSVERTtCAL ACCELERATION DOWNWARD

RESERVOIR EMPTY AND NORMAL FULL RES.OPERATION

Figure E-14. Black Canyon Diversion Dam-gravity analyses including effects of earthquake, vertical acceleration downward.

PLAN

TRIALLOADPLAN, ELEVATION AND MAXIMUM SECTION LOCATION

Figure E-15. Kortes Dam-plan, elevation, and maximum section.

ructure deflectmnett,on

wC”rlNGED 0 144 0 1.54,

UK,” STir.TESI -11.4,

“i.0 DEPASTMENT OFTWE ,NTERlOR0’171 6018 BUREAU OF RECLdMITlONMISSOURI BASIN PROJECT

KORTES “NIT- WYOMINGK O R T E S D A M

TRIAL LOAD TWIST ANALYSIS INCLUDING BEAM ACTlON“iJ50:2), 5 9 7 4 MAXIMUM FLOOD CONDITIONS’JOINTS GROUTED

BEAM AND CANTILEVER STRESSES,LOAD DlSTRlBUTlOhAND ADJUSTMENT ATOANTILEVER ELEMENTS

BEAM AND CANTILEVER STRESSESPROFILE LOOKING UPSTREAM

Figure E-I 6. Kortes Dam-stresses and load distribution from trial-load twist analysis.

0

Cantilever restraIned bythrust on od,acen+element

Sl,dlng factors and sheat-friction factors of safety forgrwty onolysis ore shown at upstream sideSliding factors and shear-frlctlon factors of safety for+r,a, load onolys5 ore shown at downstream s,de. STUDY NO I TWlST ISItding factors and sheor-fr,ct\on factors are shown above the eleuatlon l,,,es?$Stob,l,ty factors are for lncllned abutment pIones CHlMCED FROM 144-D-3548 J-3147s,,d,ng factor i Ho”zon’al Force (f h

Weight-Upltfto r Orlzontol planes) S,,d,ng fac,ot Horlzo”+a’ Force (fat abutment pianes,

‘JWTEO STc,TF5OLPARTHENT OF T”E INTEWOR

IWeIght-Upllft)Sec 0 BLJREI” OF RECLAMATlONShear-frlc,,on foc+or_(Welqht-Upllft)xCoefflclent of lnternol frlctlon tBose area xUnit shear resIstonce Lfor hor,zonto, p,anes, UlSSO”Rl BASIN PROJECT

ncmzontol Force ICORTES UNIT-WYOMING

sheor.fr,ction foc+or=(Welght-Upllft)Secmx Coefflctent of rntetnal friction + lncllned base oreo x Unnt shear reslstance(f,, Obu+ment plones) KORTES DAMtior,zontal Force TRIAL LOI\ TWIST .4NALYSIS lNCL”OlNG BEAM ACTlON

Coeft~c,en+ of ,n+erna, fr,ct,on=065.Unlt sheor r.?slstance=400 pounds persquare ,nch U”!tve,gh+ of concrete=150 lb per cu ft MAXIMUM FLOOD CONoITIONS-JOINTS GROUTEDUplIft pressurevornes os o strolght l,ne from reserve,, water pressure at the upstream face to zero or tallwater pressure at the SLIDING FACTORS AND SHEAR FRICTION FACTORS

downstream face, octlng over two-thirds orea of horIzonto se&on OF SAFETY FOR TRIAL LOAD AND GRAVITY ANALYSES

o-.1*1 c G q

Ef TRLDLII q * -r * REr,O*YL�DLD

llPPlO�ED

Y!

0n

Figure E-Z 7. Kortes Dam-stability factors from trial-load twist analysis.

ABUTMENT SECTIONDOWNSTREAM ELEVATION

MAXIMUM SPILLWAY SECTION MAXIMUM ABUTMENT SECTION0 60 120I I

SCALE OF FEET

0 IS0 300III/1I~~,/l I

SCALE OF FEETPLAN AND ELEVATION

T R I A L LOAD T W I S T A N A L Y S I S O F HIS,, C A MMAXIMUM R E S E R V O I R W A T E R S U R F A C E

PLAN,ELEVATION AND MAXIMUM SECTIONS SHOWINGLOCATION OF HORIZONTAL AND VERTICAL ELEMENTS

ORPlWN R L.M.. .S”BMITTED. Q?@?-.,...

Figure E-18. Marshall Ford Dam-plan, elevation, and maximum sections.

15

9ESERVOIR EMPTY NORMAL RES. W. S. EL.

ert,COl S t r e s s Horiz W a t e r V e r t i c a l ,“~‘:,e~~, $Ltr

UPSTR E AM FACE


MAXIMUM SPILLWAY SECTIONHORIZONTAL SECTION

1 Resultant-concrete weight only.‘, Resultant-water pressure and weight ‘k Resultant-water pressure,weight,ond uplift.

Sliding Factor= Horlzontol F o r c e ,Weight- Uplift

Shear-friction Factor= (Weight-Uplift)x Coefficientof Internal Friction + Bose Area x Unit Shear ResistanceHorizontal Force

Unit weight of concrete = 150 pounds per cubicfoot. Unit sheor resistance=300 pounds per square inch.&efficient O f internOl friction = 0 . 6 5 .

Uplift pressure varies as a straight line from reservoir water pressure at upstream face to zero ortoilwoter pressure at downstream foce,acting over two-thirds the Oreo of the horizontal section.

Total load carried by vertical cantileverAll normal stresses ore compressive except those preceded by o negative sign, which are tensile.Positive shear stresses ore caused by shear forces acting thus +,Negotive shear stresses ore caused by shear forces acting thus +==.

NON-OVERFLOW AND SPILLWAY SECTIONSRESERVOIR EMPTY

D R A W N

Figure E-I 9. Marshall Ford Dam-gravity analyses for normal conditions.

RESERVOIR EMPTY NORMAL RES. W.S. EL. RESERVOIR EMPT)

To Face Stress S+resS toFace S+rePounds per square Inch

NORMAL RES. W.S. EL.

w

Pounds Pe ‘r s are inch

+MAXIMUM NON-OVERFLOW SECTION

I

t

MAXIMUM SPILLWAY SECTIONHORIZONTAL SECTIONUPSTREAM FACE

4 Resultant-concrete weightandeorthquake(horlzontal upstream ondvertlcol upward). \ Resultant-concrete werght andearthquake (horizontal downstream and vertical upward) X Resultant - water pressure, werght and earthquoke(horizontal upstream and vertical upward). 1 Resultant-water pressure, weight and earthquake( horizontal downstreamand vertical upward). i Resultant- waterpressure,weight,uplift and earthquake i horizontal upstream and verhcal upward).hResultant-waterpressure,weight,uplift and earthquake

jlidingFactcr= Horizontal Forcedownstream ond vertical upward).

Weight-UpliftShear-fnc+ion Foc+or~(Weiqht-Uplift xcaefficient afIntr-~;;tii~~o;c~se Area x UnitShearResistmce

Jnitweightafconvete=tso pounds perwbicfad. Unitshear resistance=3aapounds persquare inch. Coefficient of Internal Friction: 0.65.@lift pressurevaries as a stmight line from reservoir water pressureat upstream face to zero or toilwaterpressure atdownstream

foce,acting aver two-thirds the area of the horizontal section,assumed to be unaffected by earthquake.Vertical earthquake acceleration and horizontalearthquake acceleratian=o.~g.,periad =ane second.iota1 load carried by vertical cantilever.All normalstresses are compressive except those precededPositive shearstresses are caused by shear farce acting thus=

by a negative sign which are tensile.,negative shearstresses are caused by shearforces acting thus =.

rt Including earthquake acceleratian(harizantal upstream and vertical upward).w&Including earthquake occeleration(harizontal downstream and vertical upward).

DOWNSTREAM FACE

GRAVITY ANALYSES OF HIGH DAMNON-OVERFLOW AND SPILLWAY SECTIONS

RESERVOIR EMPTY AND NORMAL FULL RESERVOlR OPERAT,ONWITH HORIZONTAL AND VERTICAL EARTHQUAKE EFFECTS

VERTICAL ACCELERATION UPWARD

Figure E-20. Marshall Ford Dam-gravity analyses including effects of earthquake, vertical acceleration upward.

rgESEf?VOIR EMPTY NORMAL RES. W. S. EL.

?T+~COI ,“,‘;,‘;z, g;$; water Vertical Stress HorizParallel Shear

‘re== lo FDCX s t r e s s pre==m s+r=== to Face s t r e s s

NORMAL RES. W. S. EL. RESERVOIR EMPTY, S h e a r - M a x Horiz water vertlcaj pso’;Es;, gory;, ver+,cal S t r e s s Horiz

FrictionFactor ,“:r”,z; Pressure s t r e s s ,A Facel S+re*s s t r e s s

Parallel Sheato Face Stres

h P o u n d s per souore InchP o u n d s p e r square i n cI I I


sp+kL

UPSTREAM FACE MAXIMUM SPILLWAY SECTION HORIZONTAL SECTION DOWNSTREAM FACE

j Resultant-concrete weight and earthquake (horizontal upstream and vertrcol downward). ‘\ Resultant-concrete weight and earthquake(horrzontol downstream and vertical downword). \ Resultant-water pressure,weight ond earthquake (horizontal upstream ondvertical downward). -‘x Resultant-water pressure,weight and eorthquoke(horrzontoI downstream ond vertical downward).4Resultont-woter pressure, weight,uplift and earthquake (horrzontol upstream ond vertical downword). i Resultant-water

pressure, weight, uplift and earthquake (horizontal downstream and vertical downward).Sliding Foctor=Homntol Force,

Weight -UpliftSheor.friction Foctor,(Weiqht-Uplrft)xCoefficient of lnt”,‘;P,‘%;iont~;cs~ AreoxUnit Shear Resistance,

tUnrt weight of concrete=150 pounds per cubic foot. Unit Shear Resistance=300 pounds per square inch. Coefficient of Internal Friction=O.65Uplift pressure varies as o strorght line from reservoir water pressure at upstream face to zero or tollwater pressure at downstream face,

acting over two-thirds the Oreo of the horizontol section, assumed to be unaffected by earthquake.Vertical earthquake acceleration ond horizontal earthquake occelerahon = 0 I g , period = one second.Totol lood carried by verhcol cantilever.All normal stresses ore compressive except those preceded by o negative sign which are tensile.Positive shear stresses ore caused by sheor forces acting thus C negative shear stresses ore caused by shear forces acting thus ==G.* lncludrng earthquake occelerotion (horizontol upstream and veriicol downward).** lncludinq eorthquoke accelerotron(horizontol downstream and vertical downward).

Figure E-21. Marshall Ford Dam-gravity analyses including effects of earthquake, vertical acceleration downward.

IORYAL RESERVOIR OPERATION

W A T E R V E R T I C A L STRESS HOMONTAIREWIRE S T R E S S y$;‘ SnEARSTRESS

Pounds per square inch

t

MAXIMUM FLOOD OPERATION

128 112 82 2.9

UPSTREAM FACE

NORMAL RESERVOIR OPERATIONet ,n,uc 1 SHEAR-.I.^-.^.. I .yyI,zoNTALYAXIYUY WATER VERTICAL RLRALLELSTRESS “OR$,~~AL

I

EAR STRESS PRES~RE STRESS To FACE STRESS

1Pounds per s.a”ore mch -I

EL.41M 1ssG+, ! \, I 195.40’ w .me 7.1 143 29 171 314 143211.90’

EL.412Q w..375’- -, 22540’ 769 7.0 145 42 187 33, MS243.70NOVERFLOW SECTION

‘-TOP OF DAY EL.4414MAXIMUM FLOOD OPERATION

Y A X I Y U Y NONOVERFLOW SECTIONHORIZONTAL SECTION D O W N S T R E A M F A C E STUDY No.A

BUREAU\ Resultant -water pressure and uelght. 4 Resultant - water pressure. weloht and uollft. RIO GRAWOE PROJECT-NEW YEXICO-TEXAS

ELEPHANT BUTTE DAMGRAVITY ANALYSES OF YAX,U”M NONOVERFLOW SECTION

NORMAL FULL RESERVOIR OPERATION ANDMAXINUN F L O O D O P E R A T I O N

Horizontal F o r c e .-

Shdmg Factor = Weiaht-Uo,ift , Shear-frlctlon Factor = IWeight-Upllft)x Coefflclent of Internal Frlctlon + Horuontal Area x Umt Shear ResIstonceHnr,,“ntnl Fnrrr

-r_ _ _ _ _ _ _

Unit welght of concrete = 137 pounds per cubic foot. Unit shear resstonce = 400 pounds per square inch. Coefficient of mternal frlctlon =063.Upllft pressure vow% as a straight Ione from reserva~r water pressure at upstream face to zero or tailwater pressure at downstream face,

acting aver two-thirds the area of the horizontal section.Total load carried by vertical cantilever.All normal stresses ore compressive except those preceded by a negative sign, which are tenslIe.Posttwe sheor stresses ore caused by shear forces acting thus wNegatwe shear stresses are caused by shear forces actmg thus +.

Figure E-22. Elephant Butte Dam-gravity analyses for maximum flood condition.

243.78

YAXIYUY NONOVERFLOW S E C T I O N

-‘\ Resultant-water pressure, weight, and earthquake (harlzcntal upstream) $ Resultant-water pressure, weight, uplift and earthquake (hwuontal upstream).. Resultant-water preswre,weqht,and earthquake(vertlcal upward). 1 Resultant-water Pressure,weqht uplift and earthquake (vertical upward).

\\ Resultant-water pressure,weight, and earthquake (horizontal upstream and vertical upward) i Resultant-&oter pressure, wetght, uplift and earthquake(horizontal upstream and vertical uowardl.

S,,d,ng Fottor = Horuontal Force.WebhtUplift

, Shear.tr,& Fictor = (WelgMUplift)lCoefficlent of Internal Frlctlon + Horizontal Area x Umt Shear ResistanceHorizontal Force

Unit weight of COnCrete = 137 pounds per cubic foot. Unit shear reststance = 400 pounds per square Inch. Coefflcent of internal friction : 0.65UPlIft pressure Yarles as a straight line from reservoir water pressure at upstream face to zero or tallwater pressure at downstream face,

acting Over two-thirds the Oreo of the howontal SectIon; assumed to be unaffected by earthquake.Vertical earthquake acceleration and horizontal earthquake acceleration = O.lg, period = one second.Total load carried by vertical cant,lever.All norm stresses are compresswe except those preceded by a negatwe sign, which are tensole.Posltlve shear stresses ore caused by shear forces act,ng thus --. Negotwe shear stresses are caused by shear forces act,ng thus -Earthquake acceleration - +f Horizontal upstream. *Y Vertical upward *+* Horizontal upstream and Vertical upward.* Slldlng factors computed for earthquake acceleration, horlzontol upstream and vertical downward.

GRAVITY ANALYSES OF NORMAL FULL RESERVOIR

AND VERTICAL EARTHQUAKE EFFECTS AS INDICATED

Figure E-23. Elephant Butte Dam-gravity analyses including effects of earthquake accelerations.

COLUMBIA

PLAN

ABUTMENT SECTION SPILLWAY SECTIONDOWNSTREAM ELEVATION

ABUTMENT SECTION

I

,200 PLAN AND ELEVATION

CSTUOY NO.25-TWIST-C)DEPARTMENT OFTHE ,NTER,OR

BUREAU OF REOL4MlTlONCOL”MBlA BASIN PROJECT VASHINOTON

G R A N D COULEE D A MTRIAL LOAD TWIST AND BEAM ANALYSIS---.

346.9’ lRESERVOlR FULL-EARTHQUAKE INCLUDED-JOINTS GROUTEOl

X8.4’\ PLAN ,ELEVATIONAND MAXIMUM SECTIONS

M A X I M U M S P I L L W A Y S E C T I O N ‘-Zoo MAXIMUM ABUTMENT SECTIONSCALE OF FEET

DRAWN, .F.P n: SUBMITTED. eY&?a?IGc/!.T... . .TRACED J. 9.F.. .~~.RECO*.ENoEo.,C H E C K E D 8 . ..APPRO”EO.. . .e. ”

- I K,, _ . ..A.

mlb

Figure E-24. Grand Coulee Dam-plan, elevation, and maximum sections.

PROFILE LOOKING UPSTREAMHORIZONTAL BEAM STRESSES

PROFILE LOOKING UPSTREAMCANTILEVER STRESSES

NOTESU= St ress at upst ream taceD=Stress at downstream face+ lndlcates compresston- lndlcates t e n s i o n

( S T U D Y N O 25.TWIST-C)DEPeiRTMENT OFTHE INTERIOR

BUREAU O F RECL”MAT,ONCOLUMBIA BASIN PROJECT WI?SHlNGTON

G R A N D C O U L E E D A MAl l s t resses are in pounds per square InchCantliever s t resses are act ing in Inclined

direct ions paral le l to the edges of thecanti levers

TRIAL LOAD TWIST AND BEAM ANALYSISRESERVOIR FULL-EARTHQUAKE INCLUDED-JOINTS GROUTE,

STRESSES IN HORIZONTAL BEAM ELEMENTSAND IN CANTILEVER ELEMENTS

DRAWN .F D M SVBMITTED S L Y & -

Figure E-25. Grand Coulee Dam-stresses from t&-load twist and beam analysis.

Cantilever restralned b yo n adjacent e l e m e n t

.688\12.4+.876

* 9.70

thrust

7321 692\6

7321 68h 732%a ’

678\0 116 114 I 1.6 125

x ‘7;‘,’ *‘O& 775 67X 775. 630t9m * 873 ,;,‘“, 9 I3 7.95 978c *955,685, X645D 786 621635 803* 666 * 679? A 749

E* 735

Weight o f concrete=155 p o u n d s p e r cubic f o o tSlldlng f a c t o r s o r e f o r condltlon o f reservoir

water surface at elevation 1288, earthquoheeffect Included, and 4 upllft assumed

JOlnts a s s u m e d groutea s o t h a td a m c o n a c t O S monolith

SlldmgSlldlngSliding

factors and shear friction factors of sofety for grovlty analys is ore shown on upst ream sidefactors ond sheor frlctlon factors of safety for trlol load onalysls ore shown on downst reom s idefactors ore shown obove base line of contllever Sheor frlchon factors ore shown below base hne of conttlever

Factors deslgnoted by++ ore for lncllned abutment p lanes

Slldlng factors, S= H~$$cc~~tce (for horlzontol planes) Slldlng factors, S=~we$$$$~~~~ m (for obutment planes)

Shear frvztlon factors of safety, Q, two-thirds uplift=(Welqht-Upllft)xCoefflcient of Internal Frlchon + Bose Area xUmt Shear Revstance

Horlzontol Force (for horlzontol p lanes)

Shear friction factor of safety, Q,two-thirds upl i f t=( Welqht-UplIft) Set 0 XCoefflclent of Internal Friction + Bose Area x Unit Shear ResIstonce

Horizontal Force(for abutment planes)

Coefflclent o f I n t e r n a l Frlchon =O 6 5 Unit S h e a r Reslstonce=700 p o u n d s p e r square Inch

TRIAL LOAD TWIST AND BEAM ANALYSISRESERVOIR FULL-EARTHQUAKE INCLUDED-JOINTS GROUTE,SLIDING FACTORS AND SHEAR-FRICTION FACTORS

Figure E-26. Grand Coulee Dam-stability factors from trial-load twist and beam analysis.

ESERVOIR E M P T Y NORMAL RES. W.S EL.,rtico, S t r e s s H o r i z

Porol lel Shear Wa+er Verhca’ PSZ;:, :hoe$rtress to Face Strees Pressure S+resS t o F a c e S t r e s s

NORMAL RES. W.S. EL.

Wn+or ,,ar+:m,

4 Resu l tan t - concre te wefght on l y . $ Resul tant -water pressure and weigh? *Resultant-water pressure, weight,and u p l i f t .

Sliding Factor = Hor izon ta l Force ,We igh t -Up l i f t

Shear-friction Foc+or =(Weight- Upllft)x Coefficient of Internal Friction + Horizontal Area X Unit Sheor Reststance.Horizontal Force

Uni t weight of concrete =154 pounds per Cubic foot Unit sheor resistance :6OO pounds persquore inch Coe f f i c i en t o fIn te rna l F r i c t i on = 0 65 .

Upllft pressure vorles 0s o strolght lhne f rom reservoir water pressure at upstream face to zero or tailwater pressure,+ ,in,�nc+ronm lnra �Ai�� *.,a- +.rn-+*:r,tc l *--, -111,“,.““11. ,“~_)“” .,.I ~ “.=, ^ve^ ..� *^l..^^l^l e^^*i^^I”“-II.lll> ,,,= u,su “I l lYl lLVll l ” l DSCII”II.

Total l o a d corrled by vertlcol cantilever.All normoi stresses ore compressive except those preceded by o negative sign, which ore tensilePosltlve sheorstresses ore caused by sheor forces acting thus G== Negative sheor stresses are coused by sheor forces acting thus =Weight of superstrucfure included in analysis of spillway section. a Stablhty factors include effects of splllwoy apron.

Figure E-27. Shasta Dam-gravity analyses for normal conditions.

RESERVOIR EMPTY NORMAL RES. W S. EL,vertico, St ress Horiz

NORMAL RES. W. S. EL. RESERVOIR EMPT’

S+ress Parallel S h e a rto Face s t ress Pressure S+resS

SItding Shear- Vnxti water l~ert~co~ ~~~,~~,! g,“ttr ~ertlca~ Stress Hor’z

to Face St ress RESERVOlR F a c t o r f;;c;;; $+;;3eez: RessureJ S t r e s s +o Face S+ress s t r e s s mra”e’ Shear1

P o u n d s per Square I n c hVI* El ,065 -~-TOP OF DAM El ,077 50 to Face Stress

Pounds per Square Inch

395 425 29

766 ISI 78

DIRECTION OF226 226 0 116 74 74 0 El 850 EARTHQ”AI(E ACCELERATION

281 281 0 89 186 186 0781 83 156 194 319 156 38 62 30345 187 6s 82 135 66 -17 -*a -,4

368 368 0 182 IO8 108 0 Ei 720 796 5.5 254 317 520 254 54 80 43392 III ,,e 147 242 118 -38 --63 -3,

370 607 296 118 194 95db 3k3 160 22 36 ,B

418 685 334 163 268 11,237 389 190 61 101 49

e.71 I 4.8 149 29 45s 744 349 2M 332 162BD.361 94 199 33 283 441 199 93 ,5?, ,*

UPSTREAM FACE MAXIMUM SPILLWAY SECTION HORIZONTAL SECTION DOWNSTREAM FACE

ALL RESULTANT FORCES INCLUDE VERTICAL EARTHQUAKE ACCE LE RATION UPWARD.\ Resultant-concrete weight and earthquake (horizontal upstream).‘r Resultant-concrete weight ond earthquake (horuontol downstream)

S T U D Y NO 4

\Resultont-water pressure, weight.and eorthquake(horizontoI upstream) ‘s Resultant-water pressure weight,and earthquake (horozontal downstream).~Resultont-wter Pressure weight,uploft,and eart~oke(hxuontal upstream). ‘Q Resultant-water pressure ‘wght, uplift, and earJ+hquake (honzpntal downstream).

OLPIRT*L*T OF 7°C INTEIIORB”SEA” or IfCLL*~rIO*

CENTRAL YALLE” PROJECT-CALIFORNIASItding Facto, i f+Xi onf 1 +orcWe~gh+&f+~ Shear-irction Factor =(Weipht-Vollft)x CcefflClenipf lnternpl Fr’C+lpn ;Horlzontql Area x L’ Shear REST. S H A S T A D A MUnit uelghtof concrete ~154 pounds per cubic foot Umt shear resistance =6OD pounds per square inch Coefficient of Internal friction = 0.65.

Horizontal Force G R A V I T Y A N A L Y S E S

Uplift ~(essure vDrleS (IS 0 stra,ight line fropl reservoir water pressare (I+ upstream face lo zero or tailwater pressure (1, downstream face, acting overMAXIMUM NON~OVERFLOW ANDSPILLWAY SECTlONS

two-thIrdsthe area of the horizontal sectlon; assumed to be unaffected by earthquakeRESERVOIR EMPTY AND NORMAL F”LL RESERVOIR OPERAT,~

Vertical earthquake acceleration and horizontal earthquake acceleration = O.lg, period = one second.WITH HORIZONTAL AND VERTICAL EARTHQVAKE EFFEC,

Total load carried by vertical cpnt~leverVERTICAL ACCELERATION “PWARD

All normal stresses are compressive except those preceded by o negative sign, which ore tensalePmtwe sheor stresses are caused b shear forces acting thus ===

OR.*)1 SOL

rNegative shear stresses ore caused by shear forces Octmg thus L,

*IIncludlng earthquake OCCelerOtiOn honzmtal upstream and vertical upvmrdl w4 Including earthquake acceleration (horizontal downstream andverfical upward) C”LCXEO i )(TRACfD -0

Weight of superstructure included I” analysis of spillway section. @ Stability factors include effects of sp~llvoy apron.

Figure E-28. Shasta Dam-gravity analyses including effects of earthquake, vertical acceleration upward.

I NORMAL RES. W.S. EL.

YJg$q$q

I Pounds

s. W.S. EL.

Inch

0’El. 585 & 54’ : ! \ t 4o2’

456!REsERVo’R MAXIMUM NON-OVERFLOW SECTIONv s EL. ,065

t - c

L

+

UPSTREAM FACE

ALL RESULTANT FORCES INCLUDE VERTICAL EARTHWAKE ACCELERATION DOWNWARDi Resultant- concrete weight and earthquake (hor~rontol upstream) ‘~Resultont-concrete uelght and earthquake (horizontal downstream)> Resultant-water pressure, welgh+,and earthquake (horizontal upstream) i Resultan+- water piessure,welght.and eorthquoke (horizontal downstream)* Resultant-water pressure we~ght,upll f+,ond earthquake (horizontal upstream)

HOrizOntol krce4 Resultant-uaier pressure,welgh+,upiif+,ond earthquake (horlzontol dowetream)

Sl ld lng Factor= We,gh+-Up,,f+Sheor-fric+ion Factor= (Welqht-Uplifts * Coefficient of Internal Friction + Horizontal Area X Uni t Shear Resistance

Horlzontol ForceUni t uelght of concrete=l%pounds percublcfoot. Uni t shear resistance:KXJpounds per square Inch Coefficient of internal friction ~0 65Upllff pressure vorles OS o strolght line from resewolr water pressure Ot upstream face to zero or toi lwoter pressure ot downstream face acting

Overfwo-thirds the Oreo of The horizontal sectson; assumed to be unaffected by eorthquokeVe-ttcai eorthquahe occeieration a n d hor~zontol eor thquoke occeierot~on ~0 Ig, perNod= one secondTotol load carried b y vert~coi can+MeverAl l normoi stresses ore com~ress~“e excep t those p receded by o negotlve s,gn, wh ich o re +enz,,eF’Osltive shear s t r e s s e s o r e caused b y sheor f o r c e s octlng thus=== Negative shear stresses are caused by sheor forces oc+,ng thus =‘*Including eor+hquOke occelermlon (hoiizontol upstream and vertical downward) i*?; imluding earthquake o~~e~erntion(horizontol downstream and wrficol downward)Weight of superstructure mcluded 1” analysis of sp~llwoy section. 62 Stabll~ty factors include effects of splilwoy Opron

Figure E-29. Shasta Dam-gravity analyses including effects of earthquake, vertical acceleration downward.

COMPARISON OF GRAVITYAND TRIAL-LOAD METHODS-Sec. E-2

TABLE E-l.-Comparison of stresses and stability factors for 12 dams. -DS2-2(T2)

C A N T I L E V E RPROFILE

‘ C R I T I C A L N O R M A L

ANTILEVERLOdOlNC II 5

S T R E S S ,UPSTREAM

F A C E

MAXI MUMNORMeiLLOKING

#ANTILEVER ~S T R E S S ,

OWNSTREAM MANMUM

F A C ELOIDlNG

M I N I M U M GRA”ITYSHEAR- PiNdLYSlS 16 2 II 0 8 25 4 6 5 07 84 67 5 45 4 8 5 I 5 89 4 8

FRICTIONF A C T O R

TRI*L-LOAO _ _.bNALIS,S _ 543 - ; t77 5 86

I

L O A D I N G N O R M A L;ONOITIONS. L O A D I N G

R,“sTf;” Res f u l l _ _+ slit tTW

Re; f;; ~; R,““T’,“”

SRAV. A N A L . MIY,MUMU . S . F A C E LOllDING

N o r m a l f ’ Norm3 +N;rm$j +N;rma$ CJ;rmt\,E &IV Ice, + E

L O A D I N G N O R M A L Res f u l l 1 R e s f u l l _ _ Res f u l l ~ R e s f u l l 1 ~__ Res full Res full Res full ~~;ONOITIONS, LOAOINB + T W + s,lt tTW w/o T W .+TW 1

;RAV. ANAL. M A X I M U M N o r m a l + N o r m a \_ - - - - - - - -

Normal Normal Normal NOVd Max Normal Normal Normal N o r m a l N o r m a lO.S. FACE LOP.OlNG EJorIcetE f tE 2 tE 2 tE 3,tE +j Flcod+TWtE +j tE +j tE 3 tEw/oTWtt t,

M A X I M U M L O A D I N G N o r m a l + N o r m a l +CONDIT IONS, - _ _ :E + T e m p E tIce + _ M a x F l o o d _ _ ~ __ Normal ~~~

T R I A L - L O A D A N A L Y S I S w/O T W E a r t h + T W tE

R E F E R E N C E S

Unnumber- Unnumber- Unnumber- Unnumber- Unnumber Tecg4y “,“d”u&b;;;Teched Memo’ ed Memo ed Memo ed Memo ed Memo.Oy;,‘,‘, 1 De;:;, Julyg;;,

TTecgh7y ‘u,ndn~;~b;;- Tec\vl;maTec;y;m612 4Aug 25, Feb 28, Apr 8. Sept 3, Sept 21, May 15, June 19, Feb 25, Moy 15,

I1941 1947 1937 1943 I940 1938 1940 1937 1938

’ That s t r e s s which 1s l o w e s t p e r c e n t a g e o f w a t e r pre.sure a t t h e s o m e punt MaxImum compressive a n d tenslie s t r e s s e s parallel t o t h e f a c e o r eshown as well as water preswe at the point, If water pressure exceeds stress at face for ony qlven loadlnq condltlon

‘; Results by TrIoI-Load Arch and Cantilever Analys is S Horizontal S h e a r Stiess

* R e s u l t s b y Trial Load Beam a n d Cantilever Twist Analysis I = I&ados A r c h S t r e s s+ N e a r A b u t m e n t 0 = D o w n s t r e a m F a c eP: Water Pressure U = U p s t r e a m F a c e

E- EarthquakeT w = Tallwaterw/o z WIthout” C = Under ConstructIon


normal loading conditions sliding factors areconsiderably smaller and shear-friction factorslarger (see figs. E-l through E-29, and also figs.A-l 0 through A-14 of app. A). The averagemaximum sliding factor for the gravity analysesfor 12 dams is equal to 0.917 and theminimum shear-friction factor is equal to 7.19.

The maximum effects of twist action inseven gravity dams are shown in table E-2. Themost noteworthy effects of twist action onstresses and stability factors obtained bytrial-load analysis, as compared with thosequantities obtained by gravity analysis, may besummarized briefly as follows:

(1) An increase in sliding factors alongthe steeper inclined rock planes whichform the bases of the cantilevers in theabutment sections.

(2) A decrease in sliding factors in thelonger cantilevers whose bases are locatedin the lower regions of the abutmentslopes.

(3) A decrease in shear-friction factorof safety along the steeper inclined rockplanes at the abutment cantilevers.

(4) An increase in shear-friction factorof safety at the high cantilevers near thelower ends of the abutment slopes.

(5) Relatively small changes in stressesand stability factors in the longercantilevers near the central section of thedam where most of the external load iscarried by the cantilevers.

(6) A decrease in inclined cantilevercompressive stresses along the base of thedam at the downstream edges of theabutment sections and as far toward thecenter of the structure as appreciableportions of external load may be carriedby twist action.

(7) An increase in inclined cantilevercompressive stresses along the base of thed a m a t t h e u p s t r e a m e d g e s o f t h eabutment sections and as far toward thecenter of the structure as appreciableportions of external load may be carriedby twist action.

(8) The development of appreciablehorizontal compressive stresses at andp a r a l l e l t o t h e d o w n s t r e a m f a c e ,

decreasing in magn i tude f rom theabutment slopes toward the center of thedam.

(9) The development of appreciablehorizontal tensile stresses at and parallelto the upstream face of the dam, withpossible resultant cracking, decreasing inmagnitude and effect from the abutmentslopes toward the center of the dam.

(10) Wherever the deflection curves ofthe horizontal elements may indicate thepossible existence of relatively high tensilestresses, diagonal cracking may occur.This condition may exist especially nearthe points of contraflexure of horizontalelements in the upper portions of thedam.

It is seen from the above summary that bothbeneficial and detrimental effects on loads,stresses, and stability factors for straightgravity dams may accrue by twist action. Thelateral transfer of load to the abutments causessome reduction in load on the high cantileversat the lower ends of the abutment slopes.However, the beneficial results of suchreductions are usually of minor importance incomparison with the detrimental effects ofload increases on the shorter end cantilevers. Insome cases, sliding factors at the bases of theseshorter cantilevers are increased to more thanunity; hence the sections theoretically wouldmove downstream if they were not held inplace by the shear resistance and weight of themass of the dam. Fortunately, shear-frictionfactors of safety at’the bases of gravity sectionsincrease as the heights of the sections decrease.Consequently, the shear resistance at the basesof the shorter end cantilevers is usually greatenough to prevent failure even though thesliding factor in these regions may be greaterthan unity.

Theoretically, it may sometimes be possibleto save concrete by reducing slightly thethickness of the cross section at regions wheretwist action is indicated to be beneficial. Inpractice, however, it is usually desirable tokeep the slopes o f t h e f a c e s c o n s t a n tthroughout the length of the dam for economyof construction. Another reason for notmaking reductions in cross section to allow for

TABLE E-2.-Maximum effects of twist action in some gravity damswith principal dimensions of twisted structure. -DS2-2(T3)

G E N E R A L D I M E N S I O N SG E N E R A L D I M E N S I O N S A N D D A T AA N D D A T AI

NAME OF DAM.t- ‘. r ‘- , ’ “arshall Ford] Davis

me?;?.ower-Colo. L o w e r - C o l o .1 Ariij:jgvodal

8 5 0 4118 3 3 9 0 2 7 0 0 4 0 2

Width a t t o p o f dam 2 2 I -20 2 7.5 3 0 2 0 3 0 3 23 0 8 394 720 216 110

17 I I 0

Remarks:Designed OSGrovr ty Dam

Rad ius 700 ft.

Concrete GrovilPenstock Sectic

Notes:

F igures obove Itne-Joints ungrouted. F igures be low l ine- Jo in ts g routed

D i m e n s i o n s i n f e e t , S t r e s s e s i n p.s.i, S t r e s s e s a c t p a r a l l e l t o f a c e .


the effects of beneficial twist action is that overshadow the beneficial effects of twisteffects of nonlinear distribution of stress action.throughout the sections would probably

<<Appendix F

Hydraulic Data and Tables

F-l. Lists of Symbols and ConversionFactors. -The following list includes symbolsused in hydraulic formulas given in chapters IXand X and in this appendix. Standardmathematical notations and symbols havingonly very limited applications have beenomitted.

Symbol

A, a

“A!anbc

‘d

‘i

Co

Cs

D

d

dcdH

di

dL

dl?ld

mcdn

Description

An area; area of a surface; cross-sectional areaof flow in an open channel; cross-sectional areaof a closed conduit

Gross area of a trashrackNet area of a trashrackBottom width of a channelA coefficient; coefficient of dischargeCoefficient of discharge through an orificeCoefficient of discharge for an ogee crest

with inclined upstream faceCoefficient of discharge for a nappe-shaped

ogee crest designed for an Ho headCoefficient of discharge for a partly

submerged crestDiameter; conduit diameter; height of arectangular conduit or passageway; heightof a square or rectangular orifice

Depth of flow in an open channel; height ofan orifice or gate opening

Critical depthDepth for high (subcritical) flow stage

(alternate to dL)Height of a hydraulic jump (difference in

the conjugate depths)Depth for low (supercritical) flow stage

(alternate to dH)Mean depth of flowCritical mean depth

Depth of flow measured normal to channelbot tom

Symbol

ds

dtE

EmF

Ft

f

gH

HA

HI

Hz

h

hahb

hc

HD

hd

HE

HEc

He

Description

Depth of scour below tailwater in a plungepool

Depth of flow in a chute at tailwater levelEnergyEnergy of a particle of massFroude number parameter for defining flow

Vconditions in a channel, F = .-

vsFroude number parameter for flow in a chuteat the tailwater level

Friction loss coefficient in the Darcy-v2

Weisbach formula hf = $- 2g

Acceleration due to the force of gravityHead over a crest; head on center of an orificeopening; head difference at a gate (betweenthe upstream and downstream water surfacelevels)

Absolute head above a datum plane, inchannel flow

Head above a section in the transition of adrop inlet spillway

Head measured to bottom of an orificeopening

Head measured to top of an orifice openingHead; height of baffle block; height of endsill

Approach velocity headHead loss due to bendHead loss due to contractionHead from reservoir water surface to water

surface at a given point in the downstreamchannel

Difference in water surface level, measuredfrom reservoir water surface to thedownstream channel water surface

Specific energy headSpecific energy head at critical flow

Total head on a crest, including velocity ofapproach

415

416

Symbol

hehh;

Ahfh,hL

=hL

AhLUC ( Ah,)

Hoho

Hshs

H T

hthvh

VcK

k

KaKbKcKcKex

KgKL

KPKt

KvL

AL

Description

Head loss due to entranceHead loss due to expansionHead loss due to friction

Incremental head loss due to frictionHead loss due to gates or valvesHead losses from all causes

Sum of head losses upstream from a section

Incremental head loss from all causesSum of incremental head losses from allcauses

Design head over ogee crestHead measured from the crest of an ogee to

the reservoir surface immediately upstream,not including the velocity of approach(crest shaped for design head Ho)

Total head over a sharp-crested weirHead over a sharp-crested weir, not including

velocity of approachTotal head from reservoir water surface to

tailwater, or to center of outlet of a free-discharging pipe

Head loss due to trashrackVelocity head; head loss due to exitCritical velocity head

A constant factor for various equations; a_ coefficientA constantAbutment contraction coefficientBend loss coefficientContraction loss coefficientEntrance loss coefficientExpansion loss coefficientGate or valve loss coefficientA summary loss coefficient for losses due to

all causesPier contraction coefficientTrashrack loss coefficientVelocity head loss coefficientLength; length of a channel or a pipe; effec-

tive length of a crest; length of a hydraulicjump; length of a stilling basin; lengthof a transition

Incremental length; incremental channellength

LI, LII, LIII Stilling basin lengths for different hydraulicjump stilling basins

L’ Net length of a crestM Momentum

*d Momentum in a downstream section

*u Momentum in an upstream section

AM Difference in momentum between successivesections

Symbol

mN

n

P

P

QAQ4

QCqcQiQOR

r

Rb

Rss

A s

S

‘b

swsT

TmaxTmint

AtTsT. W.LJ

b”

yllvcVt

WW


Description

MassNumber of piers on an overflow crest; numberof slots in a slotted grating dissipator

Exponential constant used in equation fordefining crest shapes; coefficient ofroughness in the Manning equation

Approach height of an ogee weir, hydrostaticpressure of a water prism cross section

Unit pressure intensity; unit dynamic pressureon a spillway floor; wetted perimeter of achannel or conduit cross section

Discharge; volume rate of flow

Incremental change in rate of dischargeUnit dischargeCritical dischargeCritical discharge per unit of widthAverage rate of inflowAverage rate of outflowRadius; radius of a cross section; crestprofile radius; vertical radius of curvatureof the channel floor profile; radius of aterminal bucket profile

Hydraulic radius; radius of abutmentrounding

Radius of a bend in a channel or pipeRadius of a circular sharp-crested weirStorage

Incremental storageFriction slope in the Manning equation;

spacingSlope of the channel floor, in profileSlope of the water surfaceTailwater depth; width at the water surfacein a cross section of an open channel

Limiting maximum tailwater depthLimiting minimum tailwater depthTime

Increment of timeTailwater sweep-out depthTailwater; tailwater depthA parameter for defining flow conditions

”in a closed waterway, U = -

@Velocity

Incremental change in velocityVelocity of approachCritical velocityVelocity of flow in a channel or chute, at

tailwater depthWeight of a mass; width of a stilling basinUnit weight of water; width of chute and

baffle blocks in a stilling basin

HYDRAULIC DATA-Sec. F-2 417

and Head.-If it is assumed that streamlines offlow in an open channel are parallel and thatvelocities at all points in a cross section areequal to the mean velocity V, the energypossessed by the water is made up of twoparts: kinetic (or motive) energy and potential(or latent) energy. Referring to figure F-l, if Wis the weight of a mass m, the mass possessesWh, foot-pounds of energy with reference tothe datum. Also, it possesses Wh, foot-poundsof energy because of the pressure exerted bythe water above it. Thus, the potential energyof the mass m is W(h, + h, ). This value is thesame for each particle of mass in the crosssection. Assuming uniform velocity, the kinetic

Symbol

X

A X

Xc

xs

Y

Y

r

AY

YC

YS

ZA Z

2

a

P0

Description

A coordinate for defining a crest profile; acoordinate for defining a channel profile;a coordinate for defining a conduit entrance

Increment of lengthHorizontal distance from the break point, onthe upstream face of an ogee crest, to theapex of the crest

Horizontal distance from the vertical upstreamface of a circular sharp-crested weir to theapex of the undernappe of the overflow sheet

Drop distance measured from the crest of theoverflow to the basin floor, for a free overfallspillway

A coordinate for defining a crest profile; acoordinate for defining a channel profile;a coordinate for defining a conduitentrance

Depth from water surface to the center ofgravity of a water prism cross section

Difference in elevation of the water surfaceprofile between successive sections in aside channel trough

Vertical distance from the break point, onthe upstream face of an ogee crest, tothe apex of the crest

Vertical distance from the crest of a circularsharp-crested weir to the apex of theundernappe of the overflow sheet

Elevation above a datum planeElevation difference of the bottom profile

between successive sections in an openchannel

Ratio, horizontal to vertical, of the slope ofthe sides of a channel cross section

A coefficient; angular variation of the sidewall with respect to the structure centerline

Deflection angle of bend in a conduitAngle from the horizontal; angle fromvertical of the position of an orifice;angle from the horizontal of the edge ofthe lip of a deflector bucket

Table F-l presents conversion factors mostfrequently used by the designer of concretedams to convert from one set of units toanother-for example, to convert from cubicfeet per second to acre-feet. Also included aresome basic conversion formulas such as theones for converting flow for a given time tovolume.

F-2. Flow in Open Channels. -(a) Energy

V2energy of rri is W T( > .

Thus, the total energy of each mass particleis

E, =W(hl+h*+$) (1)

Applying the above relationship to thewhole discharge Q of the cross section in termsof the unit weight of water w,

E=Qw(d+Z+$) (2)

where E is total energy per second at the crosssection.

The portion of equation (2) in theparentheses is termed the absolute head, and iswritten:

(3)

Equation (3) is called the Bernoulli equation.The energy in the cross section, referred to

the bottom of the channel, is termed thespecific energy. The corresponding head isreferred to as the specific energy head and isexpressed as:

V2HE =d+%

Where Q = av, equation (4) can be stated:

(4)


TABLE F-l .-Conversion factors and formulas. -288-D-3199(1/2)

To reduce units in column 1 to units ln column 4, multiply column 1 by column 2To reduce units ln column 4 to units ln column 1, multlply column 4 by column 31

CONVERSION FACTORS CONVERSION FACTORS

Column 1 Column 2 Column 3 Column 4

n o w

Column 1!

Column 2 Column 3I

Column 4

l.ENCTH

I n . . . . . . . . . . . . . . . .I

2.540.0254

0.3937 Cm.39.37 M .

60.086,400.0

31.536x11448.83

M, 317.01.98347

723.88725.7055.5457.5259.5061.49

Jo.0

40.0

38.435.7

0.0283171.6990.99173

--__--7. 4805

( 10,772.O- - - - -

I1.5472

I “j::9- - -

645.33- - - - -I 26.8891 53.33

I

1.04131.07851.1157

I

1.152913.57413.612

- - - - - - -226.24

1 2:;

I 5.3475.128

0.016667.11574X16-~.31709X16-~.2228X16-~15472X16-~

:50417.13813X16-.13778X16--I.018665.017385.016806.016262

,020

,025

.626642

.628011

35.31.5i386

1.0083

0.13368.92834XlW__--0.64632

.1440X16-~

.32585---__0.15496XlW

0.63719.01878

[email protected]

0.442x10-r.0496.05li.~---0.187

,195

Cu. ft./mln.Cu. ft./day.cu. rt./yr.Oal./mln.&I./day.Acre-lt./day.Acre-It./365 days.Acre-ft./366 days.Acre-It./28 days.Acre-ft./29 days.Acre-ft./a days.Acre-It./31 days.

Miner’s Inch in Idaho,Kans., Nebr., N. Men.,N. Dak., 8. Dak., andUtah.

MLner’s I n c h In Ark.,Callf., Mont., Nev., andOreg.

Mlner’a Inch In Cola.Miner’s I n c h in British

Columbia.Cu. m./sec.Cu. m./mln.Acre-ln./hr.

Oal./mln.@J./day.__--------C.f.s.Oal./mln.Acre-ft./day.

C.f.s./sq. mile.____-------C.f.s./sq. mile.Acre-ftJsq. mile._____-------In. depth/28 days.In. depth/29 days.In. depth/36 days.In. depth/31 days.In. depth/365 days.In. depth/366 days.

Oal./min.Miner’s Inch in Calll.Miner’s inch In Cola.

Miner’s inch In Callf.Miner’s Inch in Cola.

I

/

I

I

--

_-

-

sq. in . .._ _ ____.__ 6.4516- - - - - -S q . m. ._.____ 10.764- - - - - - - - - - - - -

Sq. miles.. _____..

/ 640.0 27.8784X101 2.5930.976X101

_----_ -~__43.560.0

Acre. . . . . . . . . . . . . . 4.646.94,840.o

Sq. cm.-_--sq. ft.-____sq. ft.Acres (1 sec-

tion).Sq yd.Sq. km.---__sq. ft.sq. m.Sq. yd.

cu. In.081.Imperial gal.- - -cu. rt.Cu. yd.- - - - -cu. in.Liters.- - - - -cu. ft.Acre-ft- - - - -Oal.- - - -cu. ft.

Cu. m.cu. ft.--__--cu. ft.Acre&- - - - - -cu. ft.Acre-ft.

0. 1556- - - - -

.0929

0.3587x10-’.15625X10-

.3228x16-4,386

- - - - - - -0.22957x16-4.2471X10-3.2066X16-~

cu. ft./SW. (c.f.s.)(second-feet)(sec.-ft.).

“Ol.“HE--

.-

._

.-

._

-

-

-

_

.-

._

.-

.-

.-

.-

-__------Cu. ft./min _..__..._1.728.0

c u . ft. .._..___._ 7.48656.2321

0.5787X10-S.I3368lw46

____-0.028317

.76456

0.4329X36-’.26417

- - - -0.74805~30-1.32585

0.83311-7---

.27548X16-~_--__

0.81071x10-~.22957x10-4

- - - - -0.43044x16-4

.Oll375

0.3587x10+.15625X16-t

l@ gal./day _ ._ _ _CU.~............I

35.31451.3679

Oal... . _. . . . _. .I

231.03.78=“4

Milllon g a l . . 133,681.O3.0689

In. depth/hr.. ____

In. depth/day ______

I m p e r i a l g a l . 1.2003

Acre-in ._. _ _ _ _ _ 3.636.0____-- - -A c r e - f t . ._. 1,233.5

43.560.0

C.f.s./sq. mile----.

Acre-ft./day-.In. on 1 sq. mile..

732.32X10’53.33

Ft. on 1 sq. milr..i

278.584XlOS640.0

oal.lscc . . . . . .._..

-

Bureau o f Reclamation(cu. ft./yr. through 1 sq.ft. under unit gradient).

Melnzcr (gal./daythrough I sq. It.under unit aradl.

48.8 0.02049Milrs/hr... . .._

M./w __....._.._.

Fall in ft./mile...~

1.4667

3.28082.2369

189.39XlO”

0.68182

.304x(44704

5.28XllP

Ft./we.- - - - -

Ft./see.Milrs/hr.

Fall/ft.

HYDRAULIC DATA-Sec. F-2

TABLE F-l .-Conversion factorsand formulas.-Continued.-288-D-3199(2/2)

419

CONVERSION FACTORS

Column 1 Colunln 2 Cdum"3 Column 4

POWER AND ENERnY

0.18182x10-~1.34050.15303x10-3.0236

1.0 1.0

0 . 7 4 6 - - -1.3405Hp.-hr ______._._______._.____

i198.0X10’ 0.505x10+

2. 545.0 .393XlW~--~--- ___~

I

8,760.O 0.11416X10-3

KW.. _ _. _. _ _737.56 .1354x10-211.8 .0346

3,412.0 .29308X10-S

Ft.-lb./see.KW.Kw.-hr./yr.B.t.u./min.

1 C.f.s.‘falling 6.8 ft.

Kw.-hr.Ft.-lb.B.t.“.

- - - - - - - - -Kw.-hr./yr.Ft.-lb./set.C.f.s. falling 1 ft.B.t.u./hr.

Kw.-hr _....._._..._._._____. 0.975 1.025 Acre& falling 1 ft.~___ -----_

778.0 0.1235x10-' Ft.-lb.

B.t.u _...__....... _..____...0.1x10-3 10, CQO Lb. of coal.

LO to.634xict-4 12,ooo

PRESSURE

I 62.4250.4335

Ft. water at max. density.... .02Q5.t?J326

773.3

\

0.016022.3087

33.931.1330.1293X10-~

Lb./w&Lb&q. in.Atm.In. Hg at 30” F.Ft. air at 32” F. and atm.

pressure.

Ft. avg. sea water . . . . . . . .._. 1.026 0.9746 Ft. pure water.

Atm.. sea level, 32’ F _.______-____

14.697

Millibars.. ._. .._..I

295.299x10-475. ax3xlo-~

.068071-----Lb&q. in.

33.663 In. Hg.1.3331 Mm. Hg

Atm ____................._... 29.92 33.48X10-J I”. Hg

0.00136P.p.m~..................-... .0584

8.345

735.29 Tons/acre-ft.17.123 G./gal.0.1198 Lb./lo” gal.

Lb~mm~ __.__........ 1 7.OXlOJ 0.14286X16-J 1 Qr

Om . . . . . . . . . . . . . . . . . .___. 15.432 .0647Q?? Or.~__--__---~---

Kg.~~...................-... 2.2046 .45359 Lb.

I27.6612 0.03612 Cu. in.0.11983 3.345 Gal.

Lh. water at 39.1” F ..__.... .09983 10.016 Imperial gal..453617 2.204 L item..Ol@x? 62.425 Cu. ft. pure water..01560 64.048 Cu. ft. sea water.

Lb. water at 62” F _.......... 0.01604 62.355.01563 63.976

Cu. ft. pure watercu. ft.. sea water.

I

FORMULAS

YOLUME-

Average depth ln inches. or acre-inch per acre

=(C.f.s.) (hr.)acres

=(@4./min.) (hr.)450 (acres)

= (miner’s in.) (hr.)(40’) (acres)

‘Where 1 miner’s in.= l/40 c.f.s.

Use 50 where 1 miner’s in.=l/SO c.f.s.

Conversion of inches depth on area to c.f.s.

c f,s = (645) (sq. miles) (in. on area). .(time in hr.)- -

POWER AND ENERGY-

hp,= (c.f.s.) (head in ft.)8.8

= (c.f.s.) (pressure in Ib./sq. in.)3.3

(gal.imin.) (head in ft.)=-3,960

(gal./min.) (pressure in lb&. in.)=-1,714

b. hp.= water hp.pump efficiency

kw.-hr./l,000 gal. pumped/hr.

(head in ft.) (0.00315)=(pump efficiency) (motor efficiency)

Kw.-hr. = (plant efficiency) (1.025) (head in ft.) (waterin acre-ft.)

-___

Load factor=(kw:hr. in time t)

(kw. peak load) (time t in hr.)

rons/acre-ft.=(unit weight/c”. ft.) (21.78)

rons/day = (c.f.s.) (p.p.m.) (0.0027)

TEMPERATURE

’ C,=; (” F.-32”) a F.=; o C.+32’

420 .DESlGN OF GRAVITY DAMS

-7II

hv2 ;1II-i-I

d2 /19 -

z2 IIIIi

;ection 2 Sectlon I

Her izontot tine I

K m - - - - - - -- - - -

TV-

I ’II I

I ‘,, _ yI 1 “- 29

I I

Datum

Figure F-I. Characteristics of open-channel flow.-288-D-2550

HE =d+E2ga2(5)

For a trapezoidal channel where b is thebottom width and z defines the side slope, if 4

Qis expressed as-& and a is expressed d(b + zd),

equation (5) becomes:

HE = d +q2

2 (6)

Equation (5) is represented in diagrammaticform on figure F-2 to show the relationshipsbetween discharge, energy, and depth of flowin an open channel. The diagram is drawn forseveral values of unit discharge in a rectangularchannel.

It can be seen that there are two values of d,dH, and d, for each value of HE, except at thepoint where HE is minimum, where only a

single value exists. The depth at energy HEm in

is called the critical depth, and the depths forother values of HE are called alternate depths.Those depths lying above the trace through thelocus of minimum depths are in the subcriticalflow range and are termed subcritical depths,while those lying below the trace are in thesupercritical flow range and are termedsupercritical depths.

Figure F-3 plots the relationships of cl to HEas stated in equation (6) for various values ofunit discharge q and side slope z. The curvescan be used to quickly determine alternatedepths of flow in open channel spillways.

(b) Critical Flow. -Critical flow is the termused to describe open channel flow whencertain relationships exist between specificenergy and discharge and between specificenergy and depth. As indicated in sectionF-2(a) and as demonstrated on figure F-2,critical flow terms can be defined as follows:

(1) Critical discharge. -The maximum

HYDRAULIC DATA-Sec. F-2 421

SPECIFIC ENERGY HE, IN FEET

H,=,j+++*zgd*

where 9 =dischorge per unit width

where d,=criticol depth4, =crit~col discharge per unit width

HEmin, -mInimum energy content

Figure F-2. Depth of flow and specific energy for rectangular section in openchannel.-288-D-255 1

discharge for a given specific energy, orthe discharge which will occur withminimum specific energy.

(2) Critical depth. -The depth of flowat which the discharge is maximum for agiven specific energy, or the depth atwhich a given discharge occurs withminimum specific energy.

(3) Crit ical velocity. -The meanvelocity when the discharge is critical.

(4) Critical slope. -That slope whichwill sustain a given discharge at uniformcritical depth in a given channel.

(5) Subcritical flow. -Those conditionsof flow for which the depths are greaterthan critical and the velocities are lessthan critical.

( 6 ) S u p e r c r i t i c a l f l o w . - T h o s econditions of flow for which the depths

are less than critical and the velocities aregreater than critical.

More complete discussions of the criticalflow theory in relationship to specific energyare given in most hydraulic textbooks [ 1, 2, 3,4, 51 .r The relationship between cross sectionand discharge which must exist in order thatflow may occur at the critical stage is:

Q2 -a3g-T-- ( 7 )

where:

a = cross-sectional area in square feet, andT = water surface width in feet.

‘Ntimbers in brackets refer to items in the bibliography, sec.F-5.


Figure F-3. Energydepth curves for rectangular and trapezoidal channels.-288-D-3193


S i n c e Q2 = a2v2, equation (7) can bewritten:

ycy a=-2g 2T (8)

Also, since a = d, T, where d, is the mean

depth of flow at the section, and- =2g hvCyequation (8) can be rewritten:

dh,c =+-

Then equation (4) can be stated

(9)

J-3 4c2dc= g

423

(19)

d, = (201

(23)

qc =dc3J2K (24)

d Q, = 5.67bdc3j2 (25)HE =d, fm,

2 (10)Q, = 3.087bH, 3/2

C(26)

From the foregoing, the following additionalrelations can be stated:

The critical depth for trapezoidal sections isgiven by the equation:

(11) d, =; -;+,/F$ (27)

d QC2=-m~ a2g

v, =K

(12) where z = the ratio, horizontal to vertical, ofthe slope of the sides of the channel.

(13)Similarly, for the trapezoidal section,

(14)vc =/m (28)

andQ, =a-

C(15)

For rectangular sections, if q is the dischargeper foot width of channel, the various criticalflow formulae are:

HE, =73dc (16)

dc =+HE (17)C

vc2d, =-g (18)

Q, = dc3,2J- (2%

The solutions of equations (25) and (29) aresimplified by use of figure F-4.

(c) Manning Formula. -The formuladeveloped by Manning for flow in openchannels is used in most of the hydraulicanalyses discussed in this text. It is a specialform of Chezy’s formula; the completedevelopment is contained in most textbooks onelementary fluid mechanics. The formula iswritten as follows:


10 /i’

II /A

H(A) For channels lessthon 14 feet wide

14 i

12

I3

Top wdth of flow, T

Chart g,ves values of d, for known values of Q, I” the

relatlonshlp Q,=+%i Single solution l\ne qves

relationship between (1,, b, z. and d, (1s shown

PSIDE SLOPES _ r

-

(B) For channels wider than 14 feet

600G,v;en Q and bottom wdth, extend lane across chart ond read

TOO f for vertlcol side slope For sloping s;des, project horlzontal

800 from vert,col slope readmg to obtain f for dewed slope

Example No Icl, = 900 CLS.Bottom w,dth “b”- 12’

Crltlcal depthSide slope “dc ” (feet)

2 I 4 4Vertical 5 6

Example No 2Q = 15.000 CfS.Bottom wdth “b’= 30’

Side slope = 2 IVert,col “d,“= .68b = 20’t

“d,” for 2 , = 10.5) (301= 15’

Figure F-4. Critical depth in trapezoidal section.-288-D-3194


1.486v -y2/3s1/2

n

or

(30)

Q= 1.486ay2/3sl/2

n (31)

where :

Q = discharge in cubic feet per second(c.f.s.),

a = the cross section of flow area in squarefeet,

I, = the velocity in feet per second,n = a roughness coefficient,Y = the hydraulic radius

area (a)= wetted perimeter(p)’ and

s = the slope of the energy gradient,

The value of the roughness coefficient, n,varies according to the physical roughness ofthe sides and bottom of the channel and isi n f l u e n c e d b y s u c h f a c t o r s a s c h a n n e lcurvature, size and shape of cross section,alinement, and type and condition of thematerial forming the wetted perimeter.

Values of n commonly used in the design ofartificial channels are as follows:

Description of channel Values of nMinimum Maximum Average

Earth channels, straightand uniform . . . .

Dredged earthchannels . . . . . . .

Rock channels, straightand uniform . . .

Rock channels, jaggedand irregular . . . .

Concrete lined . . . .Neat cement lined . .Grouted rubblepaving . . . . . . . .

Corrugated metal . .

0 .017 0 .025

.025

.035

.012

.OlO

i! .033

.025 .035

.045

.018

.013 I 0.0225

.0275

.033

.045

.014. . . . . .

.017

.023.030.025 . :024. .

(d) Bernoulli Theorem. -The Bernoullitheorem, which is the principle of conservationof energy applied to open channel flow, maybe stated: The absolute head at any section isequal to the absolute head at a section

425

downstream plus intervening losses of head.Referring to figure F- 1, the energy equation (3)can be written:

Z2 +dz +h,2 =Z1 +d, +h,, +h, (32)

where h, represents all losses in head betweensection 2 (subscript 2) and section 1 (subscript1). Such head losses will consist largely offriction loss, but may include minor otherlosses such as those due to eddy, transition,obstruction, impact, etc.

When the discharge at a given cross sectionof a channel is constant with respect to time,the flow is steady. If steady flow occurs at allsections in a reach, the flow is continuous and

Q=alvl =a2v2 (33)

Equation (33) is termed the equation ofcontinuity. Equations (32) and (33), solvedsimultaneously, are the basic formulas used insolving problems of flow in open channels.

(e) Hydraulic and Energy Gradients. -Thehydraulic gradient in open channel flow is thewater surface. The energy gradient is above thehydraulic gradient a distance equal to thevelocity head. The fall of the energy gradientfor a given length of channel represents the lossof energy, either from friction or from frictionand other influences. The relationship of theenergy gradient to the hydraulic gradientreflects not only the loss of energy, but alsothe conversion between potential and kineticenergy. For uniform flow the gradients areparallel and the slope of the water surfacerepresents the friction loss gradient. Inaccelerated flow the hydraulic gradient issteeper than the energy gradient, indicating aprogressive conversion from potential tokinetic energy. In retarded flow the energygradient is steeper than the hydraulic gradient,indicating a conversion f r o m k i n e t i c t opotential energy. The Bernoulli theoremdefines the progressive relationships of theseenergy gradients.

For a given reach of channel AL, the averageAh,slope of the energy gradient is x, where Ah,

is the cumulative losses through the reach. If

426

these losses are solely from friction, Ah, willbecome nhf and


V2

nhf =

Expressed in terms of the hydraulic propertiesat each end of the reach and of the roughnesscoefficient,

(34)

Ahf=&[(+)2 + (+,qAL (35)If the average friction slope, sf, is equal to

partly full flow in closed conduits is similar tothat in open channels, and open channel flowformulas are applicable. Hydraulic propertiesfor different flow depths in circular andhorseshoe conduits are tabulated in tables F-2t h r o u g h F - 5 t o f a c i l i t a t e h y d r a u l i ccomputations for these sections.

F-3. Flow in Closed Conduits.-(a) PartlyFull Flow in Conduits.-The hydraulics of

s2 + s1 nhf- =z and sb is the slope of the channel2floor, by substituting sbnL for 2, - z,, andHE for (d + h,), equation (32) may be written:

nL =HE1 -HE2

‘b - sf(36)

(f) Chart for Approximating Friction Lossesin Chutes.-Figure 9-26 is a nomograph fromwhich approximate friction losses in a channelcan be evaluated. To generalize the chart sothat it can be applied for differing channelconditions, several approximations are made.First, the depth of flow in the channel isassumed equal to the hydraulic radius; theresults will therefore be most applicable towide, shallow channels. Furthermore, theincrease in velocity head is assumed to varyproportionally along the length of the channel.Thus, the data given in the chart are not exactand are intended to serve only as a guide inestimating channel losses.

The chart plots the solution of the equation

dhfs = z integrated between the limits from

zero to L, or

Tables F-2 and F-4 give data for determiningcritical depths, crit ical velocities, andhydrostatic pressures of the water prism crosssection for various discharges and conduitdiameters. If the area at critical flow, a,, isrepresented as kl D2 and the top width of thewater prism, T, for critical flow is equal tok2 D, equation (7) can be written:

QC' (k, D2 1"-=g k2D ’ or Qc = k3 DSf2 (37)

Values of k3, for various flow depths, aretabulated in column 3. The hydrostaticpressure, P, of the water prism cross section isway, where F is the depth from the watersurface to the center of gravity of the crosssection. If a, = k, D2 and p = k4 D, then

P= k5D3 (38)

Values of k5, for various flow depths, aretabulated in column 4. Column 2 gives thevalues of h,c in relation to the conduitdiameter, for various flow depths.

Tables F-3 and F-5 give areas and hydraulicradii for partly full conduits and coefficientswhich can be applied in the solution of the

nD2Manning equation. If A = kg 4 and r = k, D,

Manning’s equation can be written:

where, from the Manning equation, or

427HYDRAULIC DATA-Sec. F-3

TABLE F-2.- Velocity head and discharge at critical depths and static pressuresin circular conduits partly fill.-288-D-3195

D=Diameter of pipe.d=Depth of flow.

h,e=Velocity head for a critical depth of

Q.=Discharge when the critical depth is d.P=Pressure on cross section of water prism in cubic units of water. To get Pin pounds, when d and D

are in feet, multiply by 62.5. - - -- - - -

d h22 D Q. l)r* P d h.05 P03 d

5 ir 5 iT!yc Q. PD DJi2 03

---P--P-____ ~________

1 2 3 4 1 2 3 4 1 2 3 4-~---- - - ~___~-~_______

0.01 0.0033 0.0006 0.0000 0.34 0.1243 0.6657 0.0332 0. 67 0.29i4 2.4464 0.1644.02 .0067 .om.5 .OOllO .35 1284 .7040 .0356 .68 .3048 2.5182 1700.03 .0101 .@I55 0001 .36 .1326 .7433 .0381 .69 .3125 2.5912 ,175s.04 .0134 .oQ98 .0002 .37 .1368 .7836 .0407 .70 .3204 2.6656 1 8 1 6.05 .01@3 .0153 .ciN3 .38 .1411 .a249 .0434 .71 .3286 2. 7414 1 8 7 5

.06 .0203 .022u .lxQ5 .39 .1454 .8671 .0462 .72 .3371 2.8188 .1935

.07 .0237 .0298 .ooo7 .40 .1497 .9103 .0491 .73 .3459 2.8977 1996

.08 .0271 .0389 0010 .41 .1541 .9545 .0520 .74 .3552 2.9783 .2058

.09 .0306 .0491 .0013 (42 1586 .9996 .0551 .75 3648 3.0607 2121

1 0 .0341 .0605 .0017 .43 .1631 1.0458 .0583 i6 .3749 3. 1450 2185

. l l .0376 .0731 .0021 .44 .1676 1.0929 .0616 .77 .3555 3. 2314 .2249

.12 .0411 .0868 .0026 .4.5 1723 1.1410 .0650 i8 .3967 3.3200 2314

.13 .0446 1 0 1 6 .0032 .46 1769 1.1899 .0684 i9 .4055 3.4112 .2380

.14 .0482 1176 ,003s .47 .1817 1.2399 .0720 .80 .4210 3.5050 2447.15 .0517 .1347 .0045 .48 .1865 1.2908 .0757 .a1 .4343 3.6019 2515

1 6 ,0553 1 5 3 0 .0053 .49 .1914 1.3427 .0795 .82 .4485 3.7021 .2584.17 .0589 1 7 2 4 .0061 .s4 .1964 1.3955 .0833 .83 ,463s 3.8061 .2653.18 .0626 .!928 .0070 .51 .2014 1.4493 .0873 .84 .4803 3.9144 (2723.19 .0662 .2144 .0080 .52 .2065 1.5041 .0914 .85 .4982 4.0276 .2794.2n .06W .2371 .0091 .53 .2117 1.5598 .0956 .86 .5177 4. 1465 .2865

.21 .0736 .2609 .0103 .54 .2170 1.6164 (0998 ,117 .5392 4.2721 .2938

.22 ,0773 .2857 .0115 .55 .2224 1.6735 (1042 .88 .5632 4.4056 .3011

.23 .0811 .3116 .0128 .56 2279 1.7327 1 0 8 7 .89 .5900 4.5486 .3084

2 4 .0848 .3386 .0143 .57 .2335 1.i923 1 1 3 3 .90 .6204 4.7033 .3158

2 5 .0887 .3667 .0157 .58 .2393 1.8530 lli9 .91 6555 4.8725 .3233

.26 .0925 .3957 .Oli3 .59 .2451 1. 9146 122i .92 .6966 5.0603 .3308

.27 .0963 .4259 .0190 .60 .2511 1.9773 1276 .93 .7459 5.2726 .3384

.2a 1002:1042

.4571 .02u7 .61 .2572 2.0409 .1326 .94 .8065 5.5183 ,346O.29 .4893 .0226 .62 .2635 2.1057 .1376 .95 .6841 5.8118 .3537.30 1081 .5225 .0255 .63 .2699 2.1716 .1428 .96 .9885 6.1787 .3615

.31 1121 .5568 .0266 .64 .2765 2.2386 .1481 .9i 1.1410 6.6692 .3692

.32 1161 .5921 .0287 .65 .2333 2.306i .1534 .98 1.3958 7.4063 .3770

.33 .1202 .6284 .0309 .66 .2902 2.3766 .1589 .99 1.9700 8.8263 .38481.00 _...._ . . . . . .3927

Qn 1.4861~ (39) can be written:~8/3~1/2 =k6-4 (k7)2’3 = k, (39)

Values of k,, for various flow depths, are Qn 1.486r1tabulated in column 4. If D = kgd, equation &/3sl/2 = Tk6(k,)2’3(kg)8’3 = klo (40)


TABLE F-3.-Uniform flow in circular sections ji’owing partly full. -288-D-3196

d=Depth of flow.D=Diameter of pipe.A=Area of flow.r=Hydraulic radius.

d5

- -

-

--

--

--d5

ADZ

- -

2

Qn,jPIS$lt

4 1 3_-__

0.01 0.0013 0. co66 o.OwQ7 15.04 0.51 0.4027 0.2531 0.239 1.442.02 .0037 .0132 Oc031 10.57 .52 .4127 .2562 ,247 1.415.03 .fM69 .0197 @x74 8.56 .53 .4227 .2592 .255 1.388.04 .0105 .0262 .00138 7.38 .54 .4327 .2621 .263 1.362.n5 .0147 0325 .00222 6.55 .55 .4426 .2649 ,271 1.336

0 6 .0192 .0389 .@I328 5.95 .56 .4526 .2676 ,279 1.311.07 .0242 .0451 .00455 5. 47 .57 .4625 .2iO3 ,287 1.286.08 .0294 .0513 .00604 5.09 .56 .4724 ,272s ,295 1.262.09 .0350 .0575 .00775 4.76 .59 .4822 .2753 .303 1.2381 0 .0409 .0635 .00967 4. 49 ,643 .4920 .2776 .311 1.215

. l l .0470 .0695 .01181 4.25 .61 .5018 .2799 ,319 1.192

.12 .0534 .0755 .01417 4.04 .62 .5115 .2821 ,327 l.liO

.13 .06@!l .0813 01674 3.86 .63 5212 .2842 .335 1.148

.I4 .0668 .0871 .01952 3.69 .64 .5303 .2862 ,343 1.126

.15 .0739 .n924 .0225 3.54 .65 .5404 .2882 ,350 1.105

1 6 .OSll .0985 .0257 3.41 .66 .5493 .29no.17 .0885 ,1042 .0291 3.28 .67 .5594 .2917.18 .0961 .1097 .0327 3. 17 .68 .5687 .29331 9 .1039 ,1152 .0365 3.06 .69 .5780 .2948.20 .1118 .I206 .0406 2.96 .70 .5672 .2962

,358 1.084366

: 3731.0641.044

,380 1.024,388 1.004

.21 .1199 .I259 (0448 2.87

.n .1281 ,1312 .0492 2. i92 3 1365 .1364 .0537 2.71.24 .1449 .1416 .0585 2.63.25 .1535 .1466 .0%34 2.56

.71 .5964 .2975 .395 0.985

.72 6054:6143

.2987 ,402 ,965.73 .2948 ,409 .947.74 .6231 .3co8 ,416 ,928.75 .6319 .3017 ,422 ,910

.26 .1623 .1516 .0636 2.49 .76 .6405 .3024

.27 .1711 1566 .0739 2.42 .77 .6489 .3031

.28 .1800 1614 .0793 2.36 .78 .6573 .3036

.29 1890 .1662 .0849 2.30 .79 .6655 .3039

.30 .1982 .1709 .0907 2. 25 .80 .6736 .3042

,891,873,856,838,821

.31 .2074 .1756 .0966 2.20

.32 .2167 .1802 .1027 2.14.33 .2260 .1847 .1089 2.09.34 .2355 .1891 .1153 2.05.35 .2450 .1935 .1218 2. on

.81 .6315 .3043

.a2 .a93 .3043

.83 .6969 .3041.84 7043.85 :7115

.3038

.3033

,804,787,770,753,736

.36 .2546 .1978 .1284 1.958

.37 .2642 .2020 .1351 1.915

.38 .2739 .2062 .1420 1.875

.39 .2836 .2102 .14!x 1.835

.40 .2934 .2142 .I561 1.797

86:a7

.7186

.7254.aa .7320.a9 .7384.90 .7445

.3026

.3018

.3007

.2995.2980

,720,703.687,670R,54

4 1 .3032 .2182 .1633 1. 760.42 (3130 .2220 .1705 1.724.43 .3229 .2258 .1779 1.689.44 .3328 (2295 .1854 1.655.45 .3428 .2331 .1929 1.622

.91

.92

.93

.94

.95

.9ti

.97.98,909

1.00

.7504 .2963

.7560 .2944

.7612 .2921

.7662 .2895

.7707 .2865

,429435

,441,447,453

,458,463,468,473,477

.481

.485,488,491,494

,496,497,498,498,498

.4x

.494,489,483,463

,637,621,604,588.571

.46 .3527 .2366 .201 1.590

.47 .3627 .2401 ,208 1.559

.48 .3727 .2435 ,216 1.530

.49 .3827 .2468 ,224 1.500

.50 .3927 .2500 ,232 1.4il

.7749 .2829

.7785 .2787

.7817 .2735

.7841 .2666i854 .25OU

.553,535,517,496,463

Q= Discharge in c.f.s. by Manning’s formula.n= Manning’s coefficient.s=Slope of the channel bottom and of thp water surface.

HY D RAU LI C DATA-Sec. F-3 429

TABLE F-4.- Velocity head and discharge at critical depths andin horseshoe conduits partly full. -288-D-3197

D= Diameter of horseshoe.d=Depth of flow.

h ,~=Velocity head for a critical depth of d.

Q,=Discharge when the critical depth is d.P=Pressure on cross section of water prism in cubic units of water. To get Pin pounds, when d and D

are in feet, multiply by 62.5.

static pressures

I- 0.8230 c]

0.01 0.0033 0. ooog 0. ocal.02 .0667 .0035 .oooo.03 0100 .@I79 .CQOl.04 .0134 .0139 .0002.05 .016a .0217 .lmn

.06 .0201 .0312 .cnlO7

.07 .0235 .0425 0 0 1 0

.08 .0269 .0554 .0014

.09 .0305 .0703 .00181 0 .0351 .0879 .C@24

.ll .0397 .1069 .0030

.12 .0443 1 2 7 2 .0037

.13 .0489 .1487 .0045

.14 .0534 .1714 .0054

.15 .0579 .1953 .0063

.16 .0624 .22u3 .0074.17 .0669 .2465 .c085.18 .0714 .2736 ,009s.19 .0758 .3019 .Olll.20 .0803 .3312 .0125

0.35 0.1472.36 1518.37 :1563.38 .1609.39 .1655

.40 .1702

.41 .1749

.42 .1795,43 .1843.44 .1890

.45 .I938

.46 .1%6

.47 .2035

.48 .2084

.49 .2133

.bo .2133

.51 .2234

.52 .228553

: 54.2337.2191

0.8854 0.0449.9296 .0478.9746 .0508

1.0205 .05401.0673 .0572

1.1148 .06051.1633 .06391.2125 .06751.2626 .07111.3135 IO748

1.3652 .07861.4178 .08251.4712 .08651.5253 .O!nl71.5803 .0949

1.6361 .09921.6928 .10361.7505 .10811.8992 .11271.8686 .1174

0.69 0.3362.70 .3413.‘I1 .352a.72 .3615.73 .3707

.74 .380275

: 76.3w2.4cnl6

.77 .4116

.78 .4232

.79 .4354

.@I .4484

.81 .4623

.a2 .4771

.83 .4930

.84 .5102

.a5 .b289,863 .5494.87 .5719,823 .5%39

2.8922 0. 19992.9702 .2&x43.0499 .21253.1311 .21903.2140 .2255

3.2987 .23213.3853 .23&s3.4740 .24b73.8650 .252b3.6584 .2595

3.7544 .28663.8534 .27373.9557 .2x7094.0616 .2a624.1716 .2956

4.2863 .30304.4063 .31054.5325 .31814.6860 .32-B4. m30 .3335

.21 .0847 .3615 .0140 .55 .2445 1.9294

:23 22 .0891 .0936 .39!28 .4251 .0156 .0173 .56 ,57 .2500 .2557 2.0537 1.9911.24 .0980 .4583 .0191 .58 .2615 2.1174.25 1024 .4926 .0210 ,59 .2674 2.1821

:1223

.1322 1272

.1373

.1425

.89

.90 .91.92.93

.6251 4.9605 .3413

.6570 5. 1256 .3492

.6939 5.3065 .3572

.7371 5.5077 .3653

.7889 5.7354 .3733

.26 .lc69 .5277 .0229 .60 .2735 2.2479 1 4 7 8 .94 .8523 5.9996 .3813

.27 .1113 .5638 .0250 .61 .2797 2.3148 .1532 .95 .9345 6.3157 .3&M

.28 .1158 .6009 0271 .62 .2861 2.3828 .1587 .!?Fl 1.0446 6.7114 .3976

.29 .1202 .6389 .0294 .63 .2926 2.4519 .1643 .97 1. 2053 7.2417 .4058

.30 .1247 .6777 .0317 64 .2994 2.5221 .1700 .98 1.4742 8.0892 4140

.31 .1292 .7175 .0342 .65 .3063 2.5936 .1758 .99 2. o&M 9.5780 .4223

.32 1 3 3 7 .7582 .0367 .66 .3134 2.6663 1 8 1 7 1.00 . . . .._.._... . . ..____._.. .4306

.33 .1382 .7997 .0393 .67 .32G3 2.7402 .1877

.34 .1427 .8421 .0421 .68 .3283 2.8155 .1937

Values of kl ,-,, for various flow depths, are to flow in both closed conduits and opentabulated in column 5. channels, and the formulas for each take the

(b) Pressure Flow in Conduits. -Since same general form. Thus, the equation offactors affecting head losses in conduits are continuity, equation (33), Q = al v1 = a2v2,independent of pressure, the same laws apply also applies to pressure flow in conduits.

4 3 0 DESIGN OF GRAVITY DAMS

TABLE F-5 .-Uniform flow in horseshoe sections flowing partly full. -288-D-3198

d=Depth of flow.D=Diameter.A=Area of flow.r=Hydraulic radius.

Q= Discharge in c.f.s. by Manning’s formula.n=?vfanning’s coeffkient.s=Slope of the channel bottom and of the water surlace.

0.01 0. c019 0.0066 0. OoolO 21.40 0. 51 0.4466 0.2602 0.2705 1.629.02 .0053 .0132 .00044 14.93 .52 .4566 .2636 .2785 1.593.03 .0097 .0198 00105 12.14 .53 .4666 .2657 .2866 1.558.a4 .0150 .0264 Ml198 10.56 .54 .4766 .26f3 .2946 1.524.05 .0209 .0329 CO319 9. 40 .55 .4865 .2707 ,303 1.490

.06 .0275 .0394 w473 8. 58 .56 .4965 .2733 ,311 1.458.07 .0346 .0459 .cM59 7. 92 .57 .5064 .2757 ,319 1.427.08 .0421 0524 Ml876 7.37 .58 .5163 .2781 ,327 1.39i.09 .0502 .05w .01131 6.95 .59 .5261 .2804 ,335 1.368.lO .05a5 .0670 .01434 6.66 .60 .5359 .2824 .343 1.339

. l l .0670 .0748 .01768 6.36 .61 (5457 .2844 ,351 1.310

.12 .0753 .0823 .02117 6.04 .62 .5555 .2864 ,359 1.283

.13 .0839 Ix.95 .02495 5. 75 .63 .5651 .2884 ,367 1.257

.14 .0925 .0964 .02890 5. 47 .64 .5748 .2902 ,374 1.231

.15 .I012 .1031 .0331 5. 21 .65 .5a43 .2920 ,382 1.206

.16 .llcKl .1097 .03i5 4.96 .66 .59% .2937 ,390 1.181

.17 .1188 .1161 .0420 4. 74 .67 .6033 .2953 ,398 1.157

.18 .1277 .1222 (0467 4. 52 .68 .6126 .2967 ,405 1.133

.19 .1367 .1282 .0516 4.33 .69 (6219 .2981 ,412 1.109

.20 .1457 .1341 .0567 4.15 ,420, 7 0 .6312 .2994 1.087

.21 .1549 .1398 .0620 3.98 .il .6403 .3006 ,427 1.064

.22 .I640 .I454 .I%74 3.82 .72 .6493 .3018 ,434 1.042

.23 .1733 .1508 .0730 3.68 .73 .6582 ,302s ,441 1.021

.24 .1825 .1560 .0786 3. 53 .74 .6671 .3036 ,448 1.000

.25 .1919 .1611 .0844 3.40 .75 .6758 .3@44 .454 0.979

.26 .2013 1662 .0904 3. 28 .76 .6a44 .3050 ,461 ,958

.27 .2107 : 1710 .0965 3.17 .77 .6929 .3055 ,467 ,938

.28 .22Q2 .1758 .1027 3.06 .78 .7012 .3060 ,473 ,918

.29 .2297 .1804 .1090 2.96 .79 .7694 .3064 ,479 ,898

.30 .2393 .1850 .1155 2.86 .RO .7175 .3067 ,485 ,879

.31 .2489 .1895 .1220 2. 7: .81 .72.54 .3067 ,490 .86JI

.32 .2586 .1938 .1287 2.69 .82 .7332 .3066 .495 .841

.33 .2683 .19%1 .1355 2.61 .83 .7408 .3064 ,500 ,822

.34 .2780 .2023 1424 2. 53 .84 .7482 .3061 ,505 ,804

.35 .2878 .2%3 .1493 2. 45 .85 .7554 .3056 ,508 ,786

.36 .2975 (2103 .1563 2.38 .86 7625 .3050 ,513 ,768

.37 .3074 .2142 .1635 2.32 .87 .7693 .3042 ,517 ,750

.38 .3172 .2181 .1708 2.25 .88 .7759 .3032 ,520 ,732

.39 .3271 .2217 .1781 2.19 .89 .7823 .3020 ,523 ,714

.40 .3370 .2252 1854 2.13 .w .7884 .3005 ,526 ,696

.41 .3469 .2287 .1928 2.08 (91 .7943 .2988 ,528 ,678(42 .3568 .2322 .21X3 2.02 .92 .7999 .2969 ,529 ,661.43 .3667 .23.x .2079 1.973 (93 .8052 .2947 ,530 ,643.44 .3767 .2396 .21x 1.925 .94 .8101 .2922 ,530 ,625.45 .3867 .2422 .2233 1.878 .95 .8146 (2893 ,529 ,607

.46 .3966 .2454 .2310 1.832 .96 .8188 .2858 ,528 ,589

.47 .4066 (2484 .2388 1.788 .97 .8224 .2816 ,525 .569.48 .4166 .2514 .2466 1.746 .98 82% (2766 ,521 ,550.49 (4266 2544 (2545 1.705 .99 .x280 .26s6 ,513 ,527.50 .4366 .2574 .2625 1.667 1.00 .8293 ,253s ,494 ,494


A mass of water, as such, does not havepressure energy. Pressure energy is acquired bycontact with other masses and is, therefore,transmitted to or through the mass under

consideration. The pressure head-$ (where p is

the pressure intensity in pounds per squarefoot and w is unit weight in pounds per cubicfoot), like velocity and elevation heads, alsoexpresses energy. Thus, to be applicable topressure flow in a conduit, the Bernoulliequation for flow in open channels, equation(3), can be rewritten:

431

of energy, either from friction or from frictionand other influences. The relationship of theenergy gradient to the pressure gradient reflectsthe variations between kinetic energy andpressure head.

( d ) Friction Losses. - M a n y e m p i r i c a lformulas have been developed for evaluatingthe flow of fluids in conduits. Those in mostcommon use are the Manning equation and theDarcy-Weisbach equation, previously given inthis appendix and further discussed inchapter X.

The Manning equation assumes that theenergy loss depends only on the velocity, thedimensions of the conduit, and the magnitudeof wall roughness as defined by the frictioncoefficient ~1. The y1 value is related to thephysical roughness of the conduit wall and isindependent of the size of the conduit or ofthe density and viscosity of the water.

The Darcy-Weisbach equation assumes theloss to be related to the velocity, thedimensions of the conduit, and the frictionfactor f. The factor fis a dimensionless variablebased on the viscosity and density of the fluidand on the roughness of the conduit walls as itrelates to the size of the conduit.

Data and criteria for determining J‘values forlarge pipe are given in a Bureau of Reclamationengineering monograph [ 61.

F-4. Hydraulic Jump. -The hydraulic jumpis an abrupt rise in water surface which mayoccur in an open channel when water flowingat high velocity is retarded. The formula forthe hydraulic jump is obtained by equating theunbalanced forces acting to retard the mass offlow to the rate of change of the momentum offlow. The general formula for this relationshipis:

The Bernoulli theorem for flow in a reach ofpressure conduit (as shown on fig. F-5) is:

-$+Z1 +hvl =e +z, +hV2 +Ah, (42)

where Ah, represents the head losses withinthe reach from all causes. If HT is the totalhead and v is the velocity at the outlet ,Bernoulli’s equation for the entire length is:

HT = C(Ah,) +h,

As in open channel flow, the Bernoulli theoremand the continuity equation are the basicformulas used in solving problems of pressureconduit flow.

( c ) Energy and Pressure Gradients. - I fpiezometer standpipes were to be inserted atvarious points along the length of a conduitflowing under pressure, as illustrated on figureF-5, water would rise in each standpipe to alevel equal to the pressure head in the conduitat those points. The pressure at any point maybe equal to, greater than, or less than the localatmospheric pressure. The height to which thewater would rise in a piezometer is termed thepressure gradient. The energy gradient is abovethe pressure gradient a distance equal to thevelocity head. The fall of the energy gradientfor a given length of conduit represents the loss

2- a2F2 -alTl

Vl -g

a, l-2( )

(44)

a2

where:

Vl = the velocity before the jump,a, and a, = the areas before and after the

jump, respectively, and


A-lead loss due to entrance conditions,Jieod l o s s d u e t o s u d d e n expansion

F i g u r e F - S . C h a r a c t e r i s t i c s o f p r e s s u r e f l o w i nconduits,-288-D-2555

y1 and yz = the corresponding depths fromthe water surface to thecenter of gravity of thecross section.

The general formula expressed in terms ofdischarge is:

a2fi -a171

Q’=g 1 1---al a2

(45)

or:

e” +a y1 = Q2gal ’ sa,+a2Y2 (46)

For a rectangular channel, equation (44) can&

be reduced to v1 2 = -2d Cd, + dl 1, where dl

and d2 are the flow depths before and after thejump, respectively. Solving for dz :

I2v12dl d12-+-

4 (47)g

Similarly, expressing dl in terms of d2 and v2 :

dl z-$+/m. (48)

A graphic solution of equation (47) is shownon figure F-8.

VlI f t h e F r o u d e n u m b e r F1 = - i s

disc-

substituted in the equation (47):

+=&m-l) (49)

Figure F-6 shows a graphical representationof the characteristics of the hydraulic jump.Figure F-7 shows the hydraulic properties ofthe jump in relation to the Froude number, asdetermined from experimental data [7]. Andfigure F-8 is a nomograph showing the relationbetween variables in the hydraulic jump.

Data are for jumps on a flat floor with nochute blocks, baffle piers, or end sil ls .Ordinarily, the jump length can be shortenedby incorporation of such devices in the designsof a specific stilling basin.

F-5. Bibliography.111

PI

131

141

[51

Lb1

[71

King, H. W., revised by E. F. Brater, “Handbook ofHydraulics,” fourth edition, McGraw-Hill Book Co., Inc.,New York, N.Y., 1954.Woodward, S. B., and Posey, C. J., “Steady Flow in OpenChannels,” John Wiley & Sons, Inc., fourth printing,September 1949.Bakhmeteff , B. A., “Hydraulics of Open Channels,”McGraw-Hill Book Co., Inc., New York, N.Y., 1932.Binder, R. C., “Fluid Mechanics,” Prentice-Hall, Inc.,Englewood Cliffs, N.J., third edition, 1955.Rouse, Hunter, “Engineering Hydraulics,” John Wiley &Sons, Inc., New York, N.Y., 1950.Bradley, J. N., and Thompson, L. R., “Friction Factorsf o r L a r g e C o n d u i t s F l o w i n g F u l l , ” E n g i n e e r i n gMonograph No. 7 , U.S. Depar tment of the Inter ior ,Bureau of Reclamation, March 1951.Bradley, .I. N., and Peterka, A. J., “The Hydraulic Designof Stilling Basins,” ASCE Proceedings, vol. 83, October1957, Journal of Hydraulics Division, No. HY5, PapersNo. 1401 to 1404, inclusive.

HY D RAU LI C DATA-Sec. F-5 433

------$------

k . . ~. . . . ~.~~.. L -..m----------+(8) RELATION OF SPECIFIC ENERGY

(Ai HYDRAULIC JUMP - ON HORIZONTAL FLOOR TO DEPTH OF FLOW

F i g u r e F - 6 . H y d r a u l i c j u m p s y m b o l s a n dcharacteristics.-288-D-3190

LOSS OF ENERGY IN JUMP

LENGTH OF JUMP

Figure F-7. Hydraulic jump properties in relation toFroude number.-288-D-2558

434 DESIGN OF GRAVITY DAMSI IO-

IOO-

- sII

go- Ls_ 0- Y- 0-l

-E_ CL- I-- w

60- f- z-

- k- 3_ -J

- ?- 070- m- Q

- c

- 0”

- Ii60- Z

d,K E Y

EQUATION: d,= -F4+.,/e

-I

Figure F-8. Relation between variables in the hydraulic jump.-288-D-2559

<<Appendix G

I n f l o w D e s i g n F l o o d S t u d i e s

G-1. Introduction. -A 1970 report of theUnited States Committee on Large Dams(USCOLD) [ I] * gives a definition of an inflowdesign flood (IDF) as:

‘ ‘ T h e r e s e r v o i r i n f l o w - d i s c h a r g ehydrograph used in estimating the maximumspillway discharge capacity and maximumsurcharge elevation finally adopted as a basisfor project design . . . .”

An inflow design flood selected for design ofa dam impounding considerable storage locatedwhere partial or total failure would causesudden release of water and create majorhazards to life or property downstream shouldbe equal to a probable maximum flood (PMF).The USCOLD. report defines a probablemaximum flood as:

“ E s t i m a t e s o f h y p o t h e t i c a l f l o o dcharacteristics (peak discharge, volume andhydrograph shape) that are considered to bethe most severe reasonably possible at aparticular location, based on relativelycomprehensive hydrometeorological analysesof critical runoff producing precipitation(and snowmelt, if pertinent) and hydrologicfactors favorable for maximum floodrunoff.”

This appendix discusses flood hydrologystudies relating to estimates of an inflow designflood equal to a probable maximum flood, asdefined in the USCOLD report. The phrase“relatively comprehensive hydrometeorologicalanalyses” in the preceding definition refers tostudies by hydrometeorologists directed

‘Numbers in brackets refer to items in the bibliography, sec.G-32.

towards estimation of the physical upper limitso f s t o r m rainfall and maximum snowaccumulation and melt rates. The resultingestimates of the physical upper limits to stormrainfall in a basin or region are usually calledthe “probable maximum storm” or “probablemaximum precipitation” [ 21. Both of theseterms are used in this text but with moreprecise meanings attached to each term asdiscussed in sections G- 14 through G 17 ondesign storm studies.

Bureau of Reclamation policy in design ofdams located where failure might create majorhazards requires an inflow design floodestimated by evaluating the runoff from themost critical of the following situations:

(1) A probable maximum storm inc o n j u n c t i o n with severe, b u t n o tuncommon, antecedent conditions.

(2) A probable maximum storm fort h e s e a s o n o f h e a v y s n o w m e l t , i nconjunction with a major snowmelt floodsomewhat smaller than the probablemaximum.

(3) A probable maximum snowmeltf l ood i n con junc t i on w i th a ma jo rrainstorm less severe than the probablemaximum storm for that season.

(a) Items to be Evaluated. -Depending onmeteorological conditions for the basin above adamsite, on the size of the drainage area and,to a lesser extent, on the proposed size ofreservoir and type of dam, it may be necessaryto evaluate:

(1) Each of the above assumptions.(2) Each of the two assumptions in

which snowmelt is a factor.(3) Where snowmelt is not a factor,

435


dumsite, not on generalized probable maximumprecipitation values for a region. The methodsof preparing a study which yields generalizedestimates of probable maximum precipitationinherently result in values that are somewhatgreater than values obtained from an individualbasin study.

Sections G-14 through G-17 present ageneral discussion of methods and assumptionsthat a hydrometeorologist may use in thepreparation of hydrometeorological studies forindividual basins. The physical characteristicsof a basin may vary as to: drainage area size,relatively small to extremely large; runoffcharacteristics, similar throughout the basin orincluding tributary areas with markedlydissimilar runoff producing conditions;contribution from snowmelt; etc. SectionsG-23 through G-26 describe some methods ofestimating the contribution of snowmelt runoffto inflow design floods.

The final IDF study converting probablemaximum precipitation values to an IDFhydrograph should be prepared by experiencedf l o o d h y d r o l o g i s t s . R e m a r k s r e g a r d i n gconsiderations for development of a final IDFstudy are included throughout the text and abrief summary of these considerations is givenin sections G-30 and G-3 1.

Computational procedures given in this textare oriented toward step by step “long-hand”solutions, recognizing that the ever-increasingadvances in computer technology providegreatly expanded capability in all phases offlood hydrology studies. One should bemindfu l , t hough , a s stated in WorldMeterological Organization (WMO) TechnicalNote No. 98 [2] that: “While the computer isa powerful tool, it must be recognized that it issimply that, and results are no better than thebasic logic and methods of application.”

The bibliography, section G-32, includesselected references to hydrometeorologicalstudies in addition to those specifically referredto in the text.

two probable maximum storms-a stormcausing the maximum peak inflow, and astorm causing the maximum volume ofinflow.

It is beyond the scope of this text to presenta complete manual of all procedures used forestimating inflow design floods, becauseselection of procedures is dependent onavailable hydrological data and individualwatershed characteristics.

(b) Discussions in This Text. -Discussions inthis text will provide design engineersinformation about the problems encounteredand some methods for their solution. Broaddiscussions accompany presentation of theinformation which concerns:

(1) Hydrologic data for estimatingfloodflows and data sources in the UnitedStates.

(2) Analyses of basic data.(3) Unit hydrograph procedures for

synthesizing the distribution of runoff ofa basin above a damsite.

(4) Sources of generalized probablemaximum precipitation values.

(5) An example of computation of ap r e l i m i n a r y i n f l o w d e s i g n f l o o dhydrograph and establishment of reservoirrouting criteria for the flood.

Designers also need estimates of floodflowsthat may occur at the damsite during theconstruction period in order to estimaterequirements for streamflow diversion. Suchestimates are usually included in an inflowdesign flood study. Sections G-28 and G-29discuss selected methods of estimating floodmagnitudes and frequency of occurrence at thedamsite.

Every damsite presents one or more uniquep r o b l e m s t o p r o b a b l e m a x i m u m f l o o destimates. An inflow design flood (IDF) usedfor final designs of a dam should be based one s t i m a t e s b y a n e x p e r i e n c e dhydrometeorologist of probable maximumprecipitation values for the basin above the

I DF STUD I ES-Sec. G-2

A. COLLECTION OF HYDROLOGIC DATA FOR

USE IN ESTIMATING FLOODFLOWS

437

G-2. General.-For all flood studies,compilation and judgment as to quality of allavailable s t reamflow, precipitation, andw a t e r s h e d d a t a a r e most important.Mathematical procedures cannot improve thequality of input data, and analyses proceduresmust be compatible with the data available.

C-3. Streamflow Data. -The hydrologic datamost directly useful in determining floodflowsare actual streamflow records of considerablelength at the location of the dam. Such recordsare rarely available. The engineer should obtainthe streamflow records available for the generalregion in which the dam is to be situated.Locations of stream gaging stations andprecipitation stations in the United States areshown on a series of maps entitled “River BasinMaps Showing Hydrologic Stations,” edition1961,* prepared under the supervision of theNational Weather Service. Such data collectingstations are subject to change in location,discontinuation, or initiation of new stations.These maps cannot be kept current, andinformation thereon must be supplemented byadditional investigations in order to be sure ofthe location and operation of stations in agiven area. The engineer should consult thewater supply papers, catalogs, maps, andindexes of the U.S. Geological Survey’ and, ifpossible, confer with the Survey’s districtengineer. He should also make a search of therecords of other Federal agencies which mayhave collected information in the region, andthe records of State water conservationagencies or State geological surveys; and heshould determine whether any informationmay be available from other State departments,f rom coun ty eng inee r o f f i c e s , f r ommunicipalities in the vicinity, or from utilitycompanies. Where streamflow records are notavailable, some agencies or inhabitants of thevicinity may have information about

*Published by the Government Printing Office and availablein l ibraries designated as depositories of Governmentpublications; most important libraries in the United States areso designated.

high-water marks caused by specific historicfloods.

With respect to the character of thestreamflow data available, floodflows at thedamsite may be determined under one of thefollowing conditions:

(1) Streamflow record at or near thedamsite. -If such a record is available andcovers a period of 20 years or more, thefloodflows shown by the record may beanalyzed to provide flood frequencyvalues. Hydrographs of outstanding floodevents can be analyzed to provide runofffactors for use in determining themaximum probable flood.

If such a record is available but coversonly a few years, it may not include anyflood of great magnitude within its limitsand, if used alone, it would give falseindication of flood potential. Analysismay, however, give some or all of therunoff factors needed to compute theprobable maximum flood. Frequencyvalues obtained from a short recordshould not be used without analysis ofd a t a f r o m n e a r b y w a t e r s h e d s o fcomparable runoff characteristics.

(2) Streamflow record available on thestream itself, but at a considerabledistance from the damsite. -Such a recordmay be analyzed to provide unitgraphcharacteristics and frequency data whichmay be transferred to the damsite byappropriate area and basin-characteristiccoefficients. This transfer can be madedirectly from one drainage area to anotheri f t h e a r e a s h a v e c o m p a r a b l echaracteristics. Often damsites are locatedwi th in t he t r ans i t i on zone f rommountains to plains and the stream gagingstations are located well out on the plains;in such instances, special care must beexercised when using the plains record fordetermination of floodflows at thedamsite.

( 3 ) No adequate streamflow d a t a


nonrecording or recording gages, is included inthe following publications: “Equipment forC u r r e n t - M e t e r G a g i n g S t a t i o n s , ” U . S .Geological Survey Water Supply Paper 371;“Stream-Gaging Procedure,” U.S. GeologicalSurvey Water Supply Paper 888; and “StreamFlow,” by Grover and Harrington, John Wiley& Sons, Inc., New York, 1943. The advice ofGeological Survey engineers will be helpful inthe site selection and installation, operation,and interpretation of records obtained.

A series of manuals “Techniques ofWater-Resources Investigations of the UnitedS t a t e s G e o l o g i c a l S u r v e y , ” d e s c r i b e sp r o c e d u r e s f o r p l a n n i n g a n d e x e c u t i n gspecialized w o r k i n water-resourcesinvestigations. The material is grouped undermajor subject headings called books andfurther subdivided into sections and chapters;section A of book 3 is on surface water. Theunit of publication, the chapter, is limited to anarrow field of subject matter. This formatpermits flexibility in revision and publicationas the need arises.

Provisional drafts of chapters are distributedto field offices of the U.S. Geological Surveyfor their use. These drafts are subject torevision because of experience in use orbecause of advancement in knowledge,techniques, or equipment. After the techniquedescribed in a chapter is sufficiently developed,the chapter is published and is for sale by theSuperintendent of Documents.2

The importance of utilizing records ofrunoff originating from the watershed abovethe damsite cannot be overemphasized. In thecase of a damsite located on an ungagedstream, the establishment of measuringfacilities as discussed above may produce basicdata which would justify “eleventh hour”revision of the plans, thus improving the designof the dam.

G-4. Precipitation Data.-In each of thesituations outlined in the preceding section,precipitation data are needed to evaluatefactors for use in computing the probablemaximum flood. The engineer should assemblethe information with respect to precipitation

available on the specific stream, but asatisfactory record for a drainage basin ofsimilar characteristics in the sameregion. -Such a record may be analyzedf o r u n i t g r a p h c h a r a c t e r i s t i c s a n dfrequency data, and these data transferredto the damsite by appropriate area andbasin-characteristic coefficients.

(4) Streamflow records in the region,but not satisfactorily useful forapplication and analysis under one of theabove methods.-These records may beassembled and analyzed as referencei n f o r m a t i o n o n g e n e r a l r u n o f fcharacteristics.

(5) U s e o f h i g h - w a t e rmarks. -High-water marks pointed out byinhabitants of the valley should be usedw i t h c a u t i o n i n estimating floodmagnitudes. However, where there are anumber of high-water marks in thevicinity of the project, and particularly ifsuch marks are obtained from the recordsof public offices (such as State highwaydepartments or county engineers), theymay be used as the basis of a separatesupplemental study. These records may beu s e d t o d e t e r m i n e t h e w a t e rcross-sectional area and the water surfaceslope for the flood to which they refer,and from these data an estimate of thatparticular flood peak may be preparedusing the slope-area method described inappendix B of the Bureau of Reclamationpublication “Design of Small Dams”[311.

Whenever it appears that there will be one ormore flood seasons between the selection ofthe damsite and construction of the dam,facilities for securing a streamflow record forthe project should be set up as promptly aspossible. This is of particular importance inorder to obtain watershed data directlyapplicable to the computation of the inflowdesign flood for the dam, although a recordusable for frequency computations cannot besecured. The, facilities for obtaining such arecord should be the best possible dependingon the circumstances. A detailed discussion ofthese facilities, which may consist of either ‘In lot. cit. p. 431

IDF STUDIES-Sec. G-5

during the greater storms in the region, andparticularly for those storms for which runoffrecords are available. Such information can beobtained from publications of the NationalWeather Service3 and Environmental DataService. At present (1974), daily precipitationdata for each month for each State arecontained in the publication “ClimatologicalData. ” Hourly data for each month for eachState obtained by recording precipitation gagesare contained in the publication “HourlyPrecipitation Data.“4 In areas where largestorms have occurred, often precipitation dataobtained by the National Weather Serviceprecipitation stations have been supplementedby “bucket survey” data, i.e., information onrainfall amounts of unusual storms obtainedfrom residents within the storm area bypersonnel of the National Weather Service andother Government agencies.

Locations of precipitation stations as of1961 are shown on the series of maps “RiverBasin Maps showing Hydrologic Stations,”previously referred to.

If plans are made to install streamflowmeasuring facili t ies as discussed in thepreceding section, provision should also bemade for obtaining precipitation records. Animportant item to consider is the selection ofthe location (or locations) of the precipitationgage, so that the catch will be a representativesample of average precipitation over thewatershed. A comprehensive discussion oftypes of precipitation gages and observational

439

procedures is contained in the NationalWeather Service publication “Instructions forClimatological Observers,” Circular B, eleventhedition, January 1962.

G-5. Watershed Data. -All availablei n f o r m a t i o n c 0 n c erning w a t e r s h e dcharacteristics should be assembled. A map ofthe area above the damsite should be preparedshowing the drainage system, contours ifavailable, drainage boundaries, and locations ofany precipitation stations and streamflowgaging stations. Available data on soil types,cover, and land usage provide valuable guidesto judgment of runoff potential. Soil mapsp r e p a r e d b y t h e U . S . D e p a r t m e n t o fAgriculture will prove helpful when thewatershed lies within areas so mapped. Thesesurveys (if in print) are available for purchasefrom the Superintendent of Documents,Washington, D.C. Out-of-print maps and otherunpublished surveys may be available forexamination from the U.S. Department ofAgriculture, county extension agents, colleges,universities, and libraries.

The hydrologist preparing the flood studyshould make an inspection trip over thewatershed to verify drainage area boundariesand soil and cover information, and todetermine if any noncontributing areas areincluded within the drainage boundaries. Thetrip should also include visits to nearbywatersheds if it is anticipated that records fromnearby watersheds will be used in the study.

B. ANALYSES OF BASIC HYDROLOGIC DATA

G-6. General. -A flood hydrologist firstdirects attention to individual large floodevents, seeking procedures whereby a goodestimate may be made of the hydrograph thatwill r e s u l t f r o m a given amount of

3 Official designation: U.S. Department of Commerce,National Oceanic and Atmospheric Administration, NationalWeather Service.

4Subscription to these publications may be made throughthe Superintendent of Documents, U.S. Government PrintingOffice, Washington, D.C. 20402.

precipitation. As floods which consist ofcombined snowmelt and rainfall runoff ared i f f i c u l t t o s e p a r a t e i n t o t h e i r t w ocomponents, usually snowmelt floods and rainfloods are analyzed separately. Analyses of rainfloods only are discussed in these sections G-6through G-8 with inclusion of examples ofs o m e m a t h e m a t i c a l c o m p u t a t i o n s .Considerations for runoff contribution fromsnowmelt are discussed separately in sectionsG-22 through G-26. Flood analyses of rainfall


data are interrelated to analyses of respectiverunoff data, so that discussions of proceduresfor one must include some references to theother. In the discussion that follows, analysisof storm rainfall is described first and isfollowed by a description of the analysis of theresulting flood runoff. Procedures used toanalyze streamflow data for estimating thefrequency of occurrence of flood magnitudesare discussed in sections G-28 and G-29.

G-7. Estimating Runoff From Rainfall. -( a ) G e n e r a / . - T h e h y d r o m e t e o r o l o g i c a lapproach to analyzing flood events and usingthe information obtained to estimate themagnitude of hypothetical floods requires afirm estimate of the difference betweenprecipitation and the resulting runoff. From aflood determination point of view, thisdifference is considered loss, that is, loss fromprecipitation in the form of water over a givenwatershed. A simple solution to derive this lossvalue appears to be in finding the rate at whichwater will infiltrate the soil. If this infiltrationrate is known, along with the amount ofprecipitation, a simple subtraction should givethe amount of runoff. However, there are otherprecipitation losses in addition to infiltration,such as interception by vegetative cover,surface storage, and evaporation, that may havematerial effect on runoff amounts.

Various types of apparatus have beendevised to test the infiltration rates of soils,and studies have been made of interception andevaporation losses. Although maps to anextremely large scale could define most of thesurface storage area, it is apparent that anaccurate volumetric evaluation of all the lossf a c t o r s c a n b e m a d e o n l y f o r a h i g h l yinstrumented, small plot of ground and thatsuch an evaluation is not practical for a naturalwatershed composed of many square miles ofvarying type soils, vegetative cover, and terrainfeatures. For this reason, hydrologic literaturecontains arguments against the “infiltrationrate approach” to determination of runoffamounts. However, the infiltration rateapproach is applied on an empirical basis toobtain a practical solution to the problem ofdetermining amounts of runoff, recognizingthat the values used are of the nature of index

values rather than true values.Natural events are studied and the difference

between rainfall and runoff determined. Sincethis difference includes all the losses describedabove, it is usually called a retention loss or aretention rate. Such retention rates derivedfrom available records may be adjusted toungaged watersheds by analogy of soil type andcover.

The characteristics of a hydrograph must beunderstood so that respective amounts ofrunoff and precipitation are compared forestimating retention rates (and for othercomparisons described later). A hydrograph ofstorm runoff obtained at a streamflow gagingstation represents one or more of the followingtypes of runoff from the watershed: channelrunoff, surface runoff, interflow, and baseflow. Brief definitions of these types are:

Channel runoff. -Caused by rain fallingon the water surface of the stream. Itbegins with the start of precipitation andmay be discernible from a slight rise ofthe hydrograph just after rainfall begins,but the quantity of channel runoff is sosmall that it is ignored in hydrographanalyses.

Surface runoff-Occurs only when therainfall rate is greater than the retentionloss rate. This type of runoff causes mostfloods and the computational proceduresin this text consider this type of runoffdominant.

In terflo w. -Occurs when rainfallinfiltrating the soil surface encounters anunderground zone of lower permeability,travels above the zone to the surfacedownhill, and reappears to becomesurface runoff. This type of flow may alsobe called subsurface flow or quick returnj70 w.

Base flow.-The fairly steady flow of astream from natural storage as shown byh y d r o g r a p h s d u r i n g nonstorm ( o rnonactive snowmelt) periods.

In flood hydrology it is customary to dealseparately with base flow and to combine allother types of flow into direct runoff inunknown proportions as assumed in this text.

Making studies to compare rainfall with

IDF STUDIES-Sec. G-7 441

runoff requires a knowledge of the units ofm e a s u r e m e n t u s e d a n d t h e f a c t o r s f o rconversion to common units. These conversionfactors are given in appendix F. In the UnitedStates, precipitation is measured in inches andrunoff is measured in cubic feet per second(abbreviated c.f.s.).

It is necessary to know the watershed areacontributing the runoff at a given measuringpoint, in order to express the runoff volume ofinches of depth over the watershed forcomparison with precipitation amounts. Whenmaking such comparisons, the amount ofrunoff, expressed as inches, is termed rainfallexcess, and the difference between the rainfallexcess and the total precipitation is consideredretention loss as just discussed.

The fo l lowing me thod o f mak ing arainfall-runoff analysis has been selected fordescription in this text. The objectives of suchanalyses are: (1) the determination of aretention rate, and (2) the determination of theduration time interval of rainfall excess. Acomparison of retention rates derived fromseveral analyses leads to adoption of a rate fordesign flood computations. The determinationof the duration of excess rainfall is necessaryfor the hydrograph analyses computationsinvolving determinations of unitgraphs andlag-times, which are discussed later in thissection and in sections beginning with G-9. Inall such analyses, the runoff volume which iscompared with precipitation amounts is thatwhich relates directly to the rainfall understudy. Therefore, the base flow of thestreamflow hydrograph must be subtracted outbefore comparisons are made (see sec. G-~(C)).

(b) Analysis of Observed Rainfall Data.-(1) Mass curves of rainfall. -Mass curves of

cumulative rainfall during the storm periodshould be plotted for all precipitation stationsin and near the basin as shown on figureG-l(A). To show clearly the relation of rainfallto runoff, it is sometimes desirable to plot themass curves to the same time scale as thedischarge hydrograph of storm runoff. Usually,however, the curves should be given a moreexpanded time scale than it is desirable to usefor the hydrograph analysis. When only onerecording station is located nearby, and in the

absence of better information, the mass curveof precipitation at a nonrecording station isusually considered to be proportional in shapeto that of the recording station, except asotherwise defined by the observer’s readingsand notes (fig. G-l(A)). The speed anddirection of travel of the rainburst should betaken into account. Many rainfall observersenter the times of beginning and ending on thesame line as the current daily reading. Thenotes may therefore refer to the previous day,especially when the gage is regularly read in themorning.

(2) Isohyetal maps.-The total amounts ofrainfall occurring during the portion of thestorm that produced the flood hydrographunder study should be determined from themass curves for each station in and near thedrainage area. F o r a f l o o d h y d r o g r a p hconsisting of a single event, this will be thetotal depth of precipitation occurring duringthe storm period. For a compound hydrograph,in which individual portions of the hydrographare studied separately, temporary cessations ofrainfall will usually be indicated in the masscurves, and from inspection it usually will beapparent which of the increments of rainfallcaused the runoff event under study. Theappropriate depths of rainfall are then used tod r a w a n i s o h y e t a l m a p , u s i n g s t a n d a r dprocedures. A typical isohyetal map forplains-type terrain is shown on figure G-l(B).Isohyets are generally drawn smoothly,interpolating between precipitation stations.The interpolation should not be excessivelymechanical.

Extreme caution should be used in drawingthe isohyetal pattern in mountainous areaswhere the orographic effect is an importantfactor in the area1 distribution of rainfall. Forexample, if there is a precipitation station in avalley on one side of a mountain range andanother station in a valley on the opposite sideof the range with no intervening station, itcannot be assumed that the rainfall during astorm would vary linearly between the twostations. It is likely that the rainfall wouldincrease with increases in elevation on thewindward side of the divide, whereas on theleeward side, precipitation would decrease

4 4 2 D E S I G N O F G R A V I T Y D A M SA , recordin rain 909~8, C, 0, nonrocording loges measured deify 01 6 p.m.

Observer’s notes:

B. Apr. 16. began 9 p . m .Ii! e n d e d 9.‘30 o.m.

began I I o.m.ended I p. mm e a s u r e d 6 5 . 5 6 i n c h e sp.m.,

0. Apr. 16. begon f0p.m.I?. meosured 8 3 . 4 0 i n c h e so.m.,

e n d e d I:30 p.m.meowred 6 4 . 0 6 i n c h e s (doi& tot00p.m.,

C . A p r . lb. began I I p . m .17, meowred 6 2 . 0 6 i n c h e sp.m.,

9p.m. Mdnt.

APRIL 16

30.m. 60.m. 90.m. l2n. 3p.m.

APRIL 17

(A) M A S S C U R V E S O F R A I N F A L L

LEGEND

(B) ISOHYETS A N D THIESSEN P O L Y G O N SFigure G-l. Analysis of observed rainfall data.-288-D-3158


rapidly with distance from the divide. Thistype of distribution can usually be verified inmountainous areas where there are sufficientprecipitation stations to define the isohyetalpattern accurately.

A storm isohyetal pattern for mountainousterrain may be constructed by the isopercentaltechnique, discussed in WMO Technical NoteNo. 98 [ 21 as follows:

“In mountainous regions the simplei n t e r p o l a t i o n technique would yieldunsatisfactory isohyets. Yet to prepare avalid isohyetal pattern in a mountainousregion is not easy. One commonly usedprocedure is the isopercental technique,excellent under certain limited conditionsstated in the next paragraph. This methodrequires a base chart of either mean annualp r e c i p i t a t i o n , o r p r e f e r a b l y m e a nprecipitation for the season of the storm,such as winter, summer, or monsoonmonths. In this method the ratio of thestorm precipitation to the mean annual orm e a n s e a s o n a l p r e c i p i t a t i o n ( b a s eprecipitation) is plotted at each station.Isolines are drawn smoothly to thesenumbers. The ratios on the lines are thenmultiplied by the original base chart valuesat a large number of points to yield thestorm isohyetal chart. Thus the stormisohyetal gradients and locations of centerstend to resemble the features of the basechart, which in turn is influenced by terrain.

“The first requirement for success of theisopercental technique is that a reasonablyaccurate mean annual or mean seasonalprecipitation chart be available as a base.The base chart is of more value if it containsprecipitation stations in addition to thosereporting in the storm than if both charts aredrawn exclusively from data observed at thesame stations. The value of the base chart isalso enhanced, in regions where the runoffof streams is a large percentage of theprecipitation, if the precipitation shown onthe chart has been adjusted not only fortopographic factors, but also adjusted toagree with seasonal streamflow. In regionswhere a large percentage of the precipitationevaporates, adjustment to runoff volumes

would be of dubious value.“An additional requirement for success of

the isopercental technique is that most ofthe annual or seasonal precipitation in theregion result from storms with relatively thesame wind direction, and from storms withminimal convective activity. Under thesecircumstances an individual storm will have astrong resemblance to the mean chart, as thelatter is an average of kindred storms.

“In the Tropics with the dominance ofconvective activity and with lighter winds,the isopercental technique is of less value inanalysis of an individual storm than inmiddle latitude locations that meet the otherrequirements.”After the preliminary hydrographs and the

isohyetal maps have been drawn, the atypicalf l o o d e v e n t s f o r u n i t h y d r o g r a p h sdetermination may readily be eliminated.Those floods having a combination of largevolume, uniform intensities, isolated periods ofrainfall, and uniform area1 distribution ojrainfall, should be chosen for further study.

( 3 ) A v e r a g e r a i n f a l l b y T h i e s s e npolygons.-The average rainfall on a drainagearea can be determined from precipitationstation records by the Thiessen polygonmethod. A sample computation of averagehourly rainfall from the mass curves on figureG-l(A), using Thiessen polygons indicated onfigure G-l(B), is given in table G-l.

The first step is to construct the Thiessenpolygons, which are the areas bounded by theperpendicular bisectors of lines joining adjacentprecipitation stations. The percentage of thedrainage area controlled by each station’spolygon is planimetered and entered in tableG-l. Next, the average depth of rainfall overeach station’s polygon is determined byplanimetering areas between isohyets on figureG-l(B). A factor to be used in weighing stationrainfall values is obtained by multiplying thepercentage of the drainage area controlled byeach station’s polygon by the ratio of theaverage depth of rainfall over each station’spolygon to the observed rainfall at the station,and dividing by 100.

Hourly incremental rainfall values aredetermined for each precipitation station from


Table G-l .-Computation of rainfall incrementsCOMPUTATION OF STATION WEIGHTS

Percent of bsslnarea

(3)

Station

(1)

Averagerainfall over

Thiessen polygon

(2)

Rainfall at statlon Weight. col. (2) x col. (3)100 x col. (4)

(5)(4)

4. 735. 562.064.06

38. 937.021. 13.0

0.35.31.29.04

COMPUTATION OF WEIOHTED AVERAQE HOURLY RAINFALL OVER BASIN

T TStatlon A T IStatlon B Statlon C Statlon D

Mass rf. A rf.

T-

).35xArf.

(2) (3)

0.20 0.070.20 ,070.33 1lG.47 ,164

0 0.85 ,298.75 ,262.35 .122.75 ,262.30 .105.20 ,070

0 0.19 .066.ll ,038.03 ,010

-Mass rf. A rf.

(1) (2)--

017

:3352

:f!Ql.M1.411.852.913.494. 194. 795.085. 185. 185.495. 565. 56

-__

4. 73 1.653 .._.____..

0.17.16.19.28.40.21.44

1.06.58.70.60.2910

0.31.07

0--

5. 56

-

1.31xArf. Mass rf.

(3) 0)

0.053,050,059,087,124,065136,329,180,217,186,090,031

0,096,022

0

_ _ _ _ . _.0

.M1

.17

.32

.52

.52

.891.221.371. 701.831.921.922. cm2.042.06

-~

1.725

J.29xArf.

-A rf. ,

(2) _-(3)

_.

_0.09 0.026.08 ,023.15 ,044.2u ,058

0 0.37 ,107.33 .o%.15 ,044.33 ,096

13:09

,038,026

0 0.08 ,023.04 ,012.02 ,006

2.06

-.599

Mass rf.

(1)

. _ _ _ _ _ _0.15.29.52.84

1.011.342.052.473.003. 403. 633. 733.833. 074.044.06

).04xArf

-_-

A rf. (

(2)_-

(3)

0. 15.14.23.32.17.33.71.42.53.40.231010.14.07.02

_ _ _0.006,006,009,013,007,013.028,017,021,016,009.004,004.oG6,003,001

4.06 163

-

Welghtedaverage,sum of

COlS. (3)

0.053,056,161189.207.294,149,762,555,404,560,242.131.004,191.075,017

~-

4.140

Time, hours-

1

-

-

-a

- -

_.

- -

-

-

--

_.- _.

-

_-

--

_

-

-

--

.

-

(1)

0.20.40.73

1.201.202.052. 803. 153.904. M4.404.404. 594. 704. 73

_- --

.

-

0 . . . . . . . . . . . . . . . . .l..........._ .....2~. ...............3~. . .._...........4 ......-..........5 .......-.........6m ._ ..............7~. ..............8. .............._9~. ............_ ..10~. _ ....._...._..11 ...............12 .............-..13~ ...............14.. ............_.15 .. _ __. _. _ .......16 ................17 ................

Total.......

the mass curves of figure G-l(A) and aremultiplied by the appropriate weight factors asshown in table G-l, to obtain the total for thedrainage area.

Additional information on determiningaverage rainfall is given in “Cooperative StudiesTechnical Paper No. 1,” published by theNational Weather Service, and in references [ 21and [ 171.

(4) Determination of rainfall excess. -Twomethods may be used to determine rainfallexcess: by assuming a constant averageretention rate throughout the storm period,and by assuming a retention rate varying withtime. The capacity rate of retention decreasesprogressively throughout the storm period untila constant minimum rate is reached if the rainis sufficiently prolonged. With dry antecedentconditions, the initial capacity rate will be

greater and will decline faster. Because the useo f a v a r y i n g r e t e n t i o n rate requires acomplicated method of computation, it isoften preferable to assume an average retentionrate (sometimes referred to as infiltrationindex) with an estimate of initial loss beingmade if antecedent conditions are relativelydry.

The method of determining the period ofrainfall excess, when an average retention rateis used, is a trial-and-error process in which aretention rate is assumed and subtracted fromhourly rainfall increments determined as theaverage over the basin. Various retention ratesare assumed until the total of the computedrainfall excess equals the measured stormrunoff. An example of this procedure is givenin table G-2. If the correct retention rate hasnot been assumed after two trials, a rainfall


Table G2.-Computation of rainfall excess

Time, hours

-

-

2 First trial Second trial Third trial0

0.05 0.25 . .._ ~... 0. 15.ffi ---- . . . . . .._ . . . .._...16 . . . .._.. .~ _.... ~...I9 -------- . . . . . . . . _........30 . ..~ 0.05 . . . . . . . ..29 .._.... .04 . . . . . . . ..15 ---- .-.. 0 . . . . . . ~~.76 . . . . . . . 5 1.56 ..~ :31 .._......40 -...._.. .15 __.......56 . ..__.. .31 ._._.....24 . . . . . . 0 ~..13 ._...... . .._ ~~..

0 ..~~.. ~...~... ~.~.I9 ~. . . . . . . ~. _.._.....03 ~~ . . . . . . ..02 .25 ~~.. .15

___-

4.14 ~.~....~ 1.37

I

.

_.

-

-

-I-I--

.17 . . . . . . . .--____-

2.15 . . .._.. 1.96

Total rainfall, 4.14 inches; observed runoff, 2.0 inches; totalretention in 17 hours, 2.1 inches. The average retention rate of0.17 inch per hour assumed in the third trial gives the bestagreement of computed rainfall excess with measured runoff.

excess-retention curve will facilitate thesolution. In the example of table G-2, the curvecould be drawn through the two pointsrepresented by the coordinates 0.25, 1.37, and0 . 1 5 , 2 . 1 5 . T h e c o r r e c t r e t e n t i o n r a t ecorresponding to a rainfall excess of 2.0 incheswould then be taken from this curve.

The duration time of excess rainfall is thattime during which rainfall increments exceedthe average retention rate. In the third trial,table G-2, the duration time may be taken aseither 8 or 9 hours, or as two periods, one of 2or 3 hours, and the other of 5 hours (the final0.02 inch of precipitation being disregarded),a c c o r d i n g t o t h e c h a r a c t e r i s t i c s o f t h ehydrograph. A small amount of excess rain in amarginal period is frequently assumed to haveoccurred within only a small part of thatperiod and may be neglected.

(5) Discussion of observed rainfall analysesprocedures. -The above classic procedure ofr a i n f a l l - r u n o f f a n a l y s i s i s simple and

445

satisfactory, given rainfall data such as used inthe illustration and a relatively homogeneouswatershed not exceeding a few hundred squaremiles in area. As stated earlier in sectionG-7(a): “A comparison of retention ratesderived from several analyses leads to adoptionof a rate for design flood computations.”Experienced judgment is needed for suchcomparison with due reconsideration given tothe characteristics of the data for each analysisand of the watershed. The selected rate is notnecessarily the minimum rate computed. Masscurves of rainfall and isohyetal patterns shouldalways be constructed as described in sectionsG-7(b)(2) and (3) to obtain good results fromany rainfall-runoff analysis.

The importance in flood computations ofgood estimates of retention losses is evident. Asthe ratio of retention loss to flood causativeprecipitation increases, the relative effect ofretention loss estimates on resulting floodmagnitudes increases. Research studies directedt o w a r d s i m p r o v e d understanding andevaluation of all processes contributing toretention losses are increasing yearly. Manycomplex functions a r e b e i n g t e s t e d b yelectronic computer programs to model suchprocesses. However, the most practicalapproach for estimating natural watershedretention losses continues to be use ofempirically derived relationships, preferablyfrom records within the watershed.

Often, relationships as percentages of runoffto rainfall, runoff coefficients, are obtained byanalyses and judicially used in flood studies.This approach may be practical in cases wherebasic data are meager.

The following extract from WMO TechnicalNote No. 98 121 gives information of a methodthat may be used.

“ . . . For a particular river basin withrecords of streamflow and precipitation, acommon procedure is to develop multiplevariable rainfall-runoff correlations. Suchc o r r e l a t i o n s m a y b e d e r i v e d e i t h e rgraphically or analytically. They usuallyinvolve at least four variables, (i) depth ofstorm rainfall over the basin, (ii) surfacerunoff volume from the storm event, (iii) anindex of moisture conditions in the basin


identification for entering tables fromwhich respective runoff curve numbers,CN, may be obtained.

(IV). Runoff values are obtained froma family of curves on a plot of rainfallversus runoff or by solution of theequation used to define the curves.

( V ) . T h r e e a n t e c e d e n t m o i s t u r econditions, AMC, of a watershed areconsidered in relation to curve numbers;namely, AMC-I, AMC-II, AMC-III.

The mathematical procedure is given in thistext with minimum definitions of the termsused in the procedure and without inclusion ofa list of about 4,000 soil-type names andrespective hydrologic group classificationscompiled by the Soil Conservation Service. Afull discussion of the procedure including thelist of soil-type names is given in “Design ofSmall Dams” [31]. In format ion on thedevelopment of the runoff curves may befound in the SCS National EngineeringHandbook [ 31.

Further explanation of each of the abovesteps follows.

(I) Hydrologic soil groups. -Four major soilgroups are used. The soils are classified on thebasis of intake of water at the end oflong-duration storms occurring after priorwetting and opportunity for swelling, andwithout the protective effects of vegetation.

I n t h e d e f i n i t i o n s t h a t f o l l o w , t h einfiltration rate is the rate at which waterenters the soil at the surface and which iscontrolled by surface condition, and thetransmission rate is the rate at which the watermoves in the soil and which is controlled bythe soil horizons. The hydrologic soil groups, asdefined by SCS soil scientists, are as follows:

Group A (low runoff potential).-Soilshaving high infiltration rates even whenthoroughly wetted and consisting chiefly ofdeep, well to excessively drained sands orgravels. These soils have a high rate of watertransmission.

G r o u p B . - S o i l s h a v i n g m o d e r a t einfiltration rates when thoroughly wettedand consisting chiefly of moderately deep todeep, moderately well to well drained soils

prior to the storm, and (iv) a seasonal factor.In some cases storm duration is included as afifth variable. The methods of determiningthese factors from the observational recordsin a basin or a region and graphical andanalytic procedures for multiple-variablecorrelation analyses are outlined in the WMOGuide to Hydrometeorological Practices,Annex A, WMO 168.TP.82.”A hydrologist making an inflow design flood

study seldom finds rainfall-runoff records forthe watershed above a particular damsiteadequate to establish a good estimate ofretention loss for the watershed. Recourse isthen made to information of analyses for otherw a t e r s h e d s h a v i n g s i m i l a r r u n o f fcharacteristics. For example, hydrologists ofthe Soil Conservation Service, U.S. Departmentof Agriculture, have made extensive analyses ofrunoff from small experimental watershedshaving individually homogeneous soil and covercharacteristics but such characteristics differingb e t w e e n watersheds. A procedure wasdeveloped from these studies for estimatingrunoff from precipitation for any watershedfor which certain soil and cover data areknown; such soil and cover data are usuallyo b t a i n a b l e o r s u b j e c t t o r e a s o n a b l eapproximations [ 31.

The SCS procedure with modifications to fitspecific purposes is described in appendix A ofthe Bureau of Reclamation publication “Designof Small Dams,” second edition [3 11. Anabridgement of that description is given in thefollowing subsection. (The descriptive itemshave been renumbered for convenience.)

(6) Method of estimating retentionlosses.-This method consists of the followingsteps:

(I). Classification of watershed soilsinto hydrologic groups A, B, C, or D, andestimation of percent of area1 extent ofeach in the watershed.

( I I ) . I d e n t i f i c a t i o n o f l a n d u s ec h a r a c t e r i s t i c s d o m i n a n t f o r e a c hhydrologic group.

(III). The combination of a hydrologicgroup and its land use characteristics togive a hydrologic soil-cover complex


with moderately fine to moderately coarsetextures. These soils have a moderate rate ofwater transmission.

Group C.-Soils having slow infiltrationrates when thoroughly wetted and consistingchiefly of soils with a layer that impedesdownward movement of water, or soils withmoderately fine to fine texture. These soilshave a slow rate of water transmission.

Group D (high runoff potential). -Soilshaving very slow infiltration rates whenthoroughly wetted and consisting chiefly ofclay soils with a high swelling potential, soilswith a permanent high water table, soils witha claypan or clay layer at or near the surface,and shallow soils over nearly imperviousmaterial. These soils have a very slow rate ofwater transmission.(II). Land use and treatment classes. -These

c l a s s e s a r e u s e d i n t h e p r e p a r a t i o n o fhydrologic soil-cover complexes (identifiedherein as item III), which in turn are used inestimating direct runoff. Types of land use andt r e a t m e n t a r e c l a s s i f i e d o n a f l o o drunoff-producing basis. The greater the abilityof a given land use or treatment to increasetotal retention, the lower it is on a floodrunoff-production scale. Land use or treatmenttypes not described here may be classified byinterpolation.

Crop rotations.-The sequence ofcrops on a watershed must be evaluatedon the basis of its hydrologic effects.Rotations range from poor (or weak) togood (or strong) largely in proportion tothe amount of dense vegetation in therotation. Poor rotations are those inwhich a row crop or small grain is plantedin the same field year after year. A poorrotation may combine row crops, smallgrains, or fallow, in various ways. Goodrotations will contain alfalfa or otherclose-seeded legumes or grasses, toimprove tilth and increase infiltration. Forexample, a 2-year rotation of wheat andfallow may be a good rotation for cropproduction where low annual rainfall is alimiting factor, but hydrologically it is apoor rotation.

Native pasture and range.-Three

conditions are used, based on hydrologicconsiderations, not on forage production.Poor pasture or range is heavily grazed,has no mulch, or has plant cover on lessthan about 50 percent of the area. Fairpasture or range has between about 50and 75 percent of the area with plantcover and is not heavily grazed. Goodpasture or range has more than about 75percent of the area with plant cover, andis lightly grazed.

Farm woodlots.-The classes are basedon hydrologic factors, not on timberproduction. Poor woodlots are heavilygrazed and regularly burned in a mannerthat destroys litter, small trees, and brush.Fair woodlots are grazed but not burned.These woodlots may have some litter, butusually these woods are not protected.G o o d woodlots a r e p r o t e c t e d f r o mgrazing so that litter and shrubs cover thesoil.

Forests. -See hydrologic soil-covercomplex, item III following.

Straight-row farming.-This classincludes up-and-down and cross-slopefarming in straight rows. In areas of 1 or 2percent slope, cross-slope farming instraight rows is almost the same ascontour farming. Where the proportion ofcross-slope farming is believed to besignificant, it may be classed halfwaybetween straight-row and contour farmingin the table G-3(A).

Co ntouring. -Contour furrows usedwith small grains and legumes are madewhile planting, are generally small, andtend to disappear due to climatic action.Contour furrows, and beds on thecontour, as used with row crops aregenerally large. They may be made inplanting and later reduced in size bycultivation, or they may be insignificantafter planting and become large fromcultivation. Average conditions are used intable G-3(A).

Surface runoff reductions due tocontour farming are greater as land slopesdecrease. T h e c u r v e numbers forcontouring shown in table G-3(A) were


obtained using data from experimentalwatersheds having slopes of 3 to 8percent.

Contour furrows in pasture or rangeland are usually of the permanent type,Their dimensions and spacing generallyvary with climate and topography. TableG-3(A) considers average conditions in theGreat Plains.

Terracing. -Terraces may be graded,open-end level, or closed-end level. Theeffects of graded and open-end levelterraces are considered in table G-3(A),and the effects of both contouring andthe grass waterway outlets are included.

When considering land use and treatmentclasses for hydrologic soil groups within a largewatershed, the above definitions should beapplied broadly, estimating percentage of landuse in each group, assigning proper CN andcomputing a weighed CN for each particularsoil group.

( I I I ) H y d r o l o g i c s o i l - c o v e rcomplexes. -Combinations of hydrologic soilgroups and land use and treatment classes intohydrologic soil-cover complexes with respectivecurve numbers are given in table G-3(A), (B),(C). The numbers show the relative value of thecomplexes as direct runoff-producers. Thehigher the number, the greater the amount ofdirect runoff to be expected from a storm.Table G-3(A) is applicable to farm lands andrelated areas, and table G-3(B) is applicable toforested watersheds. A more detailed methodof estimating curve numbers for heavy forestedland in humid regions is given in appendix A of“Design of Small Dams,” second edition [31].

Table G-3(C) is applicable for forest-rangeareas in the Western United States. Descriptionsof the types of cover listed are as follows:

H e r b a c e o u s . - G r a s s - w e e d - b r u s hmixtures with brush the minor element.

Oak-Aspen. -Mountain brush mixturesof oak, aspen, mountain mahogany, bitterbrush, maple, and other brush.

Juniper-Grass. -Juniper or pinon withan understory of grass.

Sage-Grass. -Sage with an understory ofgrass.

(IV) Rainfall-runoff curves for estimating

direct runoff amounts.-The curves of figureG-2 are obtained using the equation:

e = (P - o.2S)2P+O.8S (1)

where :

Q = direct runoff, in inchesP = storm rainfall, in inches, andS= maximum potential difference between

P and Q, in inches, at time of storm’sbeginning.

There is some loss of rainfall before runoffb e g i n s d u e p r i n c i p a l l y t o i n t e r c e p t i o n ,infiltration, and surface storage, so provisionfor an initial abstraction I, is included in therunoff equation (see diagram on figure G-2).With the condition that 1, cannot be greaterthan P, an empirical relationship of I, = 0.2swas adopted in developing the equation,obtaining the empirical relationship of I, and Sfrom data from watersheds in various parts ofthe country.

For convenience in interpolation, the curvesof figure G-2 are numbered from 100 to zero.The numbers are related to S as follows:

1,000Curve number, CN = -

1o+s (2)

The procedure recommended in this text forestimating incremental rainfall excesses fromdesign storm rainfall using appropriate CN andfigure G-2 or the runoff equation is given insection G-l 9. In the process of hydrographanalyses, preliminary estimates of curvenumbers for a watershed can be quicklyobtained from figure G-2 by using total stormrainfall and runoff amounts. However, suchpreliminary estimates have to be revised bytrial computations of rainfall excesses using theprocedure given later in section G-l 9.

(V) Antecedent moisture conditions. -Thefollowing generalized criteria define threeantecedent moisture conditions of watershedsused in the development of the runoff curvenumbers.

AMC-I. -A condition of watershed soilswhere the soils are dry but not to the


Table G-3.-Hydrologic soil-cover complexes and respective curve numbers (CN)

(A) RUNOFF CURVE NUMBERS (CN) FOR (B) RUNOFF CURVE NUMBERS (CN) FORFARMLANDS AND RELATED AREAS FORESTED WATERSHEDS

[FOR WATERSHED CONDITION AMC-II] COMMERCIAL OR NATIONAL FOREST, FOR WATERSHED

CONDITION AMC-II

Land “se or cover

Fallow.. _ _ _ _ _ ._

Row crops . . .._.__...

Small grain ._.._._...

Close-seededlegumes ’ orrotation meadow.

Pasture or rsnge.....

Meadow(permanent).

woods (farmwoodlots).

Roads (dirt)* (hardsurface) .*

T rent.merit 0prsctio

- -

SR

SRS RCC

C & TC & T

S RS RCC

C & TC & T

SRS RCC

C & TC & T

CCC

. _ _

1 Close-drilled or broadcast.* Including right-of-way.

SR=Straight row.C-Contoured.T=Terraced.

c&T = Contoured and terraced.

-

re

,

1

,

,

11(

-

Hydrologiccondition 101

infiltrating

Hydrologic soil group-.A-

B D

. . . . . . . . . .._.

-.

. .

.

.

.

.

C-

7: 8l 9 1 94

Poor. . . _. ._ _Good _._ . . _.Poor .-......Good.. .._. -_Poor .-......oood.. .._. . .

72 81 8.F 9161 71 8.5 897c 7f 84 88a 7! 82 866f 7’ 80 8262 71 78 81

PoOr __. _.Good ___ .._ _._Poor.. .._. . .Good... . . . . . .P00r . . . . . . . . .Good.. . . . . . . .

65 7f 84 8863 7l 83 8763 74 82 8561 7 3 8 1 846 1 7 2 79 8259 7 0 78 8 1

Poor... . . . . .Good. .._. . . . .Poor.. . . . . . .Oood ._...._ . .POOK. . . . . ._.oooa ._ . . . . . . .

66 77 85 8958 72 81 8564 75 83 8555 69 78 8363 73 80 8351 67 76 80

POOI. . . . . . . . . 68 79 86 89Fair. .._.. . . . . 49 69 79 840ood.. . . . . . . . 39 6 1 74 80Poor~. .._ . .._ 47 67 8 1 88Fair.. . . . . . _. 25 59 75 833ood __ . . . . . . . 6 35 70 79

.--do.. .._._. 30 58 7 1 78

Poor . . . . . . . . .Fair ._ . . . . . . . .3ood... . . . . . _

45 66 77 8336 60 73 7925 55 70 77

59 74 82 86

_......._. . . . 72 82 87 8974 84 90 92

-

- - -

(U.S. Soil Conservation Service.)

wilting point, and when satisfactoryplowing or cultivation takes place. (Thiscondition is not considered applicable tothe design flood computation methodspresented in this text.)

AMC-II. -The average case for annualjloods, that is, an average of theconditions which have preceded the

Hydrologic condition classHydrologic soil group

I B C D

I . Poorest..........~..~. . . . . . . . . . . . . . . . 56I I . Poorest-. . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

I I I . Medium...-...........~~.........~. 36IV. Good .._. . . . . . . . . . . . . . . . . . . . . . . . .._ . . 26

V . Best--.. . . . . . . . . . . . . . . . . . . . ..-...- . . 15

75 86 9168 78 8460 70 7652 62 6944 54 6 1

(C) RUNOFF CURVE NUMBERS (CN) FOR FORESTRANGE AREAS IN WESTERN UNITED STATES

(AMC-II)

CoverSoil groups

Condition A B C D

Herbaceous P o o r - - - - - - - - - - 78 85 92F& -______ _ _ _ 68 81 88G o o d - - - - - - - - - 59 7 1 84

Sage-Grass Poor ---_ ___ __- 64 78 ___F& _______ __ _ 46 67 _ _ _Good _____ _ _ _- 35 46 ___

Oak-Aspen

Juniper-Grass

Poor- _ _ _ _ _ _ _ _ - 63 71 _ _ _F& _______ _ _ _ 40 54 _ _ _Good _____ _ __ - 30 40 _ _ _

poor--- - - - - __- 73 84 __ _Fair _______ _ _ _ 54 70 _ _ _Good ______ _ _ _ 40 59 _ _ _

occurrence of the maximum annual floodon numerous watersheds.

AMC-III. -Heavy rainfall has occurredduring the 5 days previous to the givenstorm and the soil is nearly saturated.

Curve numbers in table G-3(A), (B), (C) forhydrologic soil-cover complexes all relate toAMC-II. Table G-4(A) lists curve numbers forAMC-II with respective S values (column (4))and 0.2s values (column (5)) which may beused to solve the runoff equation on figure


G-2. Curve numbers for AMC-I and AMC-IIIrespective to the CN for AMC-II in column (1)are listed in columns (2) and (3). Thisinformation is useful for estimating retentionlosses. If data are available for analyzingobserved storms and resulting runoff, anestimate of antecedent moisture condition of awatershed may be made from table G-4(B).

G - 8 . A n a l y s e s o f S t r e a m f l o wData. Streamflow data at a given location mayconsist of: (1) a continuous hydrograph ofdischarges obtained from waterstage recordingm e c h a n i s m s ; ( 2 ) m e a n ( a v e r a g e ) d a i l ydischarges computed from waterstage recordersor from once or twice daily observed waterstages; or, in some instances (3) peak dischargescomputed from flood marks or crest stagegages. U.S. Geological Survey publicationsshould be consulted for information about

collection and processing these data forpublication. However, one should be awarethat U.S.G.S. publications give for eachpublished station record an estimate of thedegree of accuracy of field data and computedresults for that record as follows:

“Excellent means that about 95 percentof the daily discharges are within 5 percent;good, within 10 percent; and fair, within 15percent. Poor means that daily dischargeshave less than fair accuracy.”Objectives of streamflow data analyses for

inflow design flood computations are:( 1 ) D e t e r m i n a t i o n s o f w a t e r s h e d

retention losses (previously discussed).(2) Determination of characteristic

watershed response to precipitation; thisis usually accomplished by deriving a unithydrograph for the watershed. (Complex

Q-O t o 8 i n c h e s

Figure G-2. Rainfall-runoff curves-solution of runoff equation, Q = “,~~~‘* (sheet 1 of 2) (U.S. Soil

Conservation Service).-288-D-3178(1/2) ’

3 6

3 2

2 8

w”2 6

2 2 4Z-

2 2Z-

8

6

2

00 2 4 6 8 IO 12 14 16 18 2 0 22 2 4 2 6 28 3 0 32 3 4 3 6 38 4 0

R A I N F A L L (PI I N I N C H E S[-I

Figure G-2. Rainfall-runoff curves-solution of runoff equation, Q =(P - o.2S)2

p+ o ~ (sheet 2 of 2) (U.S. Soil

Conservation Service).-288-D-3178(2/2) (Note: Curve designated by number is Mow number.)

computer-programed watershed runoff provide ratio estimates of total retention lossmodels may use other means of estimating to total storm precipitation.time distribution of runoff.) Continuous hydrographs are essential to unit

Continuous hydrographs can provide for h y d r o g r a p h d e r i v a t i o n s f r o m r e c o r d e destimates of retention loss variations with time, streamflow data. When mean daily dischargeswith accumulative loss, or with accumulative only are available, a continuous hydrograph isprecipitation. Mean daily discharges can s k e t c h e d f o r m a k i n g u n i t h y d r o g r a p h


1

CN forcondition

I I

1 0 0 1 0 0 1 0 0 0 0 6 0 4 0 18 6.679 9 9 7

1.331 0 0 .lOl .02 5 9 3 9 7 7 6.95

9 81.39

9 4 9 9 ,204 .04 5 8 3 8 76 7.24 1.4591 9 1 9 9 .309 .06 5 7 3 7 7 5 7.54 1.519 6 8 9 9 9 .417 .08 5 6 3 6 7 5 7.86 1.57

9 5 8 7 9 8 .526 .ll 5 5 3 5 7 4 8.18 1.649 4 8 5 9 8 .638 .13 5 4 3 4 7 3 8.52 1.709 3 8 3 9 8 .753 .15 5 3 3 3 7 2 8.87 1.779 2 8 1 9 7 .870 .17 5 2 3 2 7 1 9.23 1.859 1 8 0 91 .989 .20 5 1 3 1 7 0 9.61 1.92

9 0 7 8 9 6 1.11 .22 5 08 9 7 6 9 6 1.24 .25 4 98 8 75 9 5 1.36 .27 4 88 7 7 3 9 5 1.49 .30 4 78 6 7 2 9 4 1.63 .33 4 6

ZJ2 92 82 7

7 06 96 8

2:

10.0 2.0010.4 2.0810.8 2.1611.3 2.2611.7 2.34

8 5 7 0 9 4 1.76 .35 4 5 2 6 6 5 12.2 2.448 4 6 8 9 3 1.90 .38 4 4 2 5 6 4 12.7 2.548 3 6 7 9 3 2.05 .41 4 3 2 5 6 3 13.2 2.648 2 6 6 9 2 2.20 .44 4 2 2 4 6 2 13.8 2.168 1 6 4 9 2 2.34 .47 4 1 2 3 6 1 14.4 2.88

8 0 6 3 9 1 2.50 .50 4 0 2 2 6 0 15.0 3.007 9 6 2 9 1 2.66 .53 3 9 2 1 5 9 15.6 3.127 8 6 0 9 0 2.82 .56 3 8 2 1 5 8 16.3 3.267 7 5 9 8 9 2.99 .60 3 7 2 0 5 7 17.0 3.407 6 5 8 8 9 3.16 .63 3 6 1 9 5 6 17.8 3.56

15 5 7 8 8 3.33 .677 4 5 5 8 8 3.51 .707 3 5 4 8 7 3.70 .747 2 5 3 8 6 3.89 .787 1 5 2 8 6 4.08 .82

3 53 4

;;3 1

1 8 5 5 18.6 3.121 8 5 4 19.4 3.881 7 5 3 20.3 4.061 6 5 2 21.2 4.241 6 5 1 22.2 4.44

:tl i:4 8 8 44 7 8 34 6 8 2

4.28 .864.49 .904.70 .944.92 .985.15 1.03

3 0 1 5 5 0

4 33 73 0

2 21 3

0

23.3 4.66

2 5 1 22 0 91 5 6

30.0 6.0040.0 8.0056.7 11.34

6 5 4 5 8 2 5.38 1.086 4 44 8 1 5.62 1.126 3 4 3 8 0 5.87 1.176 2 4 2 7 9 6.13 1.236 1 4 1 7 8 6.39 1.28

1 050

420

90.0 18.00190.0 38.00infinity infinity

t

Table G-4.-Curve numbers, constants, and seasonal rainfall limits

(A) CURVE NUMBERS (CN) AND CONSTANTS FOR THE CASE Ia = 0.2s

5CP

coneI

3r

OllS

I I I

*For CN in column 1 (value = 0.2s)

4

svalues*

inches

5

Curve *startswhereP =

inches

1

CN forcondition

I I

i

213CN for

cornI

litionsI I I

(B) SEASONAL RAINFALL LIMITS FOR AMC

AMC groupTotal 5day antecedent rainfall, inches

Dormant season I Growing season

I Less than 0.5 Less than 1.4I I 0.5 to 1.1 1.4 to 2.1

I I I Over 1.1 Over 2.1

4

svalues*

inches

5

Curve*startswhereP =

inches

I D F STUD I ES-Sec. G-8

estimates; the chance of introducingconsiderable error is obvious. Discussionswhich follow assume continuous hydrographsobtained from continuous recording waterstagerecords converted to discharges expressed ascubic feet per second (c.f.s.), the degree ofaccuracy of the records being excellent orgood.

( a ) U n i t H y d r o g r a p h ( U n i t g r a p h )Principles. -The 1970 USCOLD report [ 11states: “In general the unit hydrographmethod, in conjunction with the estimatedprobable maximum precipitation, is used inestimating probable maximum floods . . . .”The unit hydrograph principle was originallydeveloped by Sherman [4] in 1932. Althoughnumerous refinements have been added byother investigators, the basic principles aspresented by Sherman remain the same. Theseprinciples as now applied are given andillustrated on figure G-3.

Sherman’s definition of unit hydrograph didnot imply a specific volume of runoff, and theterm was applied to the observed hydrographas well as to a hydrograph of l-inch volumecomputed from the observed graph. In presentpractice, observed hydrographs are usuallyidentified as such, and the term unitgraphrefers either to the l-inch volume unitgraphderived from a specific observed hydrograph orto a l-inch volume unitgraph representative ofthe watershed and used to compute syntheticfloods from rainfall excess over the watershed.Random variations in rainfall rate in respect totime and area have a great effect on the shapeof the runoff hydrograph. To minimize theeffect of the time variations in rainfall rate, ithas been found that the rainfall excess durationtime of a basin unitgraph should not exceedone-fourth the basin lag-time as defined insection G-8(e), and the shorter the rainfallexcess period with respect to lag-time, thebetter the unitgraph results are likely to be.

The term unit hydrograph, or unitgraph, asused in this text always means l-inch volumeof runoff; the volume notation is seldomincluded. The rainfall excess unit duration timeis always given for a watershed representativeunitgraph.

Natural flood hydrographs at a given stream

453

gage are assumed to give integrated results ofall interdependent effects on runoff such aswatershed precipitation, retention losses, androuting effects of watershed vegetative coverand channel systems. A unit hydrograph whichhas been derived from recorded floods at agiven stream location, and which will give closereconstruction of recorded flood hydrographsfrom recorded respective precipitation eventsas affected by retention losses, is consideredrepresentative of that particular watershed andalso considered representative of otherw a t e r s h e d s h a v i n g s i m i l a r r u n o f fcharacteristics.

On this basis, synthetic unit hydrographs forungaged basins are derived by judgingcomparative watershed characteristics andadjusting “representative” unit hydrographs totit the size and lag-time of the ungagedwatershed. Mathematical watershed runoffmodels are currently being developed bycomputer integration of meteorological,hydrological, and physiographical factors.Some hydrologists prefer to use these modelsrather than a unitgraph. However, each modelincludes constants related to watershedcharacteristics that must be empiricallydetermined by trial analyses of recorded flows.As in the application of synthetic unitgraphs,transference of a mathematical model from agaged to an ungaged watershed also requiresexperienced judgment of the effect fromvariations in watershed characteristics.

The use of the unit hydrograph is limited inthe following ways:

(1 ) The p r inc ip l e o f t he un i thydrograph is applicable to basins of anysize. However, it is desirable in thederivation of unitgraphs to use stormsthat are well distributed over the entirebas in and p roduce runo f f nea r lyconcurrently from all parts of it. Suchstorms rarely occur over large areas. Theextent of the basin for which a unitgraphmay be derived from observed data istherefore limited in each case to the area1extent of rainfalls that have beenobserved.

(2) Hydrographs containing more thansmall amounts of snowmelt runoff are

454 DESIGN OF GRAVITY DAMS10 I I I

- - -Pe r i od qf ra in fa l l exck

I I 1 II I I 1

a--(i-ho& z-inch un i tg raph) 1

I I I I

Runoff:from i.o-inch’ excesd

.50coIic ; 40

/ kq-,, $;hour ;-inch ynitgrayhl- 1

6 12 I6 24 30 36 42t

%F ,n

T I M E - H O U R S

(A)

[ ‘,:IEch re,spec+itiy ‘*I- --Rainfall excess 0.4’0 7 1.61 o 3

ti sol I II I I ! ! J

’ ‘PI \1 <o!Finch !unoff ’ - 1

6 I2 I6 24 30 36 42T I M E - H O U R S

(61

Figure G-3. Unit hydrograph principles (sheet 1of 2).-288-D-3179(1/2)

usually unsuitable sources of unitgraphs.(3) The observed hydrograph of storm

discharge is a smooth curve, because it isactually made up of unitgraphs producedby infinitely short increments of excessrain. It cannot be reproduced perfectly by

Def in i t i ons :Unttgraph- A h y d r o g r o p h o f d i r e c t runoff a t o gtven point tho t

WIII r e s u l t f r o m o n I s o l a t e d e v e n t o f raInfoIl e x c e s soccurrrng wrthrn o unrt of ttme a n d s p r e a d I” o n a v e r a g epa t t e rn ove r t he contrlbutlng d r a i n a g e area. ldentlfred byby the unrt trme and volume of the excess roinfoll,that ISI - h o u r I-Inch unrtgroph

Rolnfoll e x c e s s - T h a t portron of ralnfoll t ha t en te rs o s t r e a mchannel OS direct runoff and produces the runoff hydrogropha t t h e m e a s u r i n g pornt, b a s e f l o w i n c l u d e d

B a s i c A s s u m p t i o n s :(I) T h e e f f e c t s o f 011 ohvsrcal choracterlstrcs o f o orven

dramoge bosrn o r e r e f l e c t e d In t he shape o f the direct r u n -o f f hvdroaraoh f o r t h a t bastn.

(2) A t ‘ a grien’ pornt o n o s t r e a m , drschorge ordrnates o fdtfferent undgraphs o f t h e s o m e umt time o f rornfollexcess ore mutually proportlonal to respective volumes.See (A)at left.

(3) A hydrograph of storm drscharge that would result froma serves of bursts of excess ram or from continuous excessram of vorroble intenstty m a y b e c o n s t r u c t e d f r o m o serieso f over-lopplng unitgraphs e a c h resulttng f r o m o srngleIncrement of excess rotn of unrt durotton. See (B) at left.

P r a c t i c a l A p p l i c a t i o n :F o r o given runo f f contrtbuttng a r e a , a unltgraph r e p r e s e n t -ing exactly one inch of runoff (ratnfall excess) for o selecteduntt trme Interval IS computed. Increments of rainfall excessf o r t h e s o m e untt time I n t e r v a l o r e determrned fo r o s t o r m .A t o t a l h y d r o g r a p h o f d i r e c t r u n o f f f r o m t h e s t o r m i s t h e ncomputed usrng assumptrons(2)ondW)obove. See graph (8)ot lef t .

*Nofe: Direct runoff is defined in section G-8.

Figure G-3. Unit hydrograph principles (sheet 2 of2).-288-D-3179(2/2)

t h e u s e o f r a i n f a l l i n c r e m e n t s o fmeasurable duration. When unitgraphs arec o m b i n e d t h e y p r o d u c e a r e g u l a rundulation similar to a harmonic with aperiod equal to that of the rainfallincrements, superimposed upon thef u n d a m e n t a l h y d r o g r a p h . A n o t h e robstacle to exact reproduction is the factthat the successive rainfall increments donot have the same isohyetal pattern and asingle form of unitgraph is not strictlya p p l i c a b l e t o a l l o f t h e m . T h e s ephenomena contradict, to a certainextent, the third basic assumption of theunit hydrograph (fig. G-3). They can bed i s r e g a r d e d i n t h e s y n t h e s i s o fh y d r o g r a p h s , but frequently causedifficulty in the use of arithmeticalprocedures for analyzing them.

An engineer attempting unitgraph analysesor researching literature regarding unitgraphssoon becomes aware that the three basic


assumptions listed on figure G-3 are nottheoretically supportable. However, experiencehas shown that this does not negate use of themethod as a practical tool.

( b ) Selection o f H y d r o g r a p h s t oAnalyze. -The statement made in sectionG-7(b)(2) bears enough importance to unithydrograph studies to be repeated: “Thosefloods having a combination of large volume,uniform intensity, isolated periods of rainfall,and uniform area1 distribution of rainfall,should be chosen for further study.”

Streamflow discharge records and basinprecipitation records must be examined jointlyfor selection of hydrographs to analyze for unithydrograph derivation. Isolated floods likely tomerit investigation are easily identified by arapid rise to a single peak and a smooth curverecession to low flow. Preferably, volumes ofselected hydrographs should be equivalent toabout one-half inch or more of runoff from thewatershed. P r e l i m i n a r y e s t i m a t e s o fhydrograph volumes can be made by summingthe daily mean daily discharges in c.f.s.-daysfor the flood period. A sum of c.f.s.-days equalin number to 15 times the drainage area size insquare miles is equivalent to 0.56 inch ofrunoff from- the area. A useful equation forconverting discharge volume to equivalentinches of rainfall is:

P,= v26.89 A

(3)

where :

P, = rainfall excesses, inches, averagedepth over basin,

V = volume of runoff, c.f.s.-days, andA = drainage area in square miles.

Hydrographs with volume sum of c.f.s.-daysless than five times the drainage area size, 0.19inch runoff, are almost always unsuitable forunit hydrograph analyses.

After noting dates of all flood hydrographsthat satisfy preliminary volume criteria, rainfallrecords for respective flood events areexamined for conformance with the idealcorn bination of short duration, uniform

intensity, and uniform area1 distribution ofrainfall over the entire watershed. Those stormsapproaching nearest to the ideal criteria areanalyzed as previously described in section G-7.If enough rainfall data are not available to do agood storm analysis for some of the isolatedflood events having satisfactory volumes, theflood hydrographs may be analyzed forunitgraph comparisons as discussed in sectionG-8(e) by assuming that the beginning ofrainfall excess coincides with the beginning of asharp rise of the hydrograph, provided there isenough information available to reasonablyassume the rainfall covered the total watershed.

Unit hydrograph derivations are difficult inregions where isolated flood events are rareand, instead, flood hydrographs commonlyhave two or more peaks caused by stormswhich usually persist for several days.Procedures for analyzing multipeaked floodhydrographs cannot be included in this textbut can be found in publications listed in thebibliography, section G-32.

(c) Hydrograph Analyses-Base FlowSeparation. -The purpose of flood hydrographanalyses is to determine for a watershed thetime-distribution of the runoff which quicklyreaches a particular point on a stream whenrain falls on the watershed. The portion of therainfall that infiltrates through the soil mantleinto the ground-water supply will not reach thestream until days or months after the storm.Ground-water supply to a stream, base flow,may be a large proportion of that stream’s totalyearly discharge, but the base flow volumeduring an isolated flood is small in ratio to thetotal flood volume. However, base flow mustbe estimated and subtracted from the totaldischarge hydrograph in order to determine thedirect runoff hydrograph. The schematicgraphs on figure G-4 show three commonapproaches for estimating base flow discharges[6]. Base flow estimates are usually madegraphically after plotting total flood dischargeson linear or semilogarithmic graph paper.

(d) Hydrograph Analysis of DirectR u n o f f - N e e d f o r S y n t h e t i c U n i tHydrographs.-It is often necessary to usesynthetic unit hydrographs for inflow designflood estimates and for obtaining indices for


I I IType A - Straight line base flow between

beglnning and end of direct runoff.Type 8. - Base flow peaked at some

pu;mf;,hortly after peok directType C - Base flow depletes for some

time after beginning of directrunoff. then straight lme to endof direct runoff.

Figure G-4. Three common approaches for estimating base flow discharges.-288-D-3180

synthetic unitgraph estimates. Suitable recordsof observed discharge are seldom available atthe exact stream point for which a unitgraph isneeded; in this discussion, at a proposeddamsite. Even if such records are available,often the proposed reservoir will be largeenough to inundate several miles of streamchannels above the damsite, thus causingwatershed runoff to enter a full reservoir morequickly than the respective runoff would arriveat the damsite through natural channels.Therefore, a unitgraph usable for estimatingfloods at the damsite under natural conditionsmust be properly adjusted to be usable toestimate inflow to a full reservoir.

The shape of a representative watershedunitgraph can be obtained by a proper averageof several unitgraphs computed from observeddischarge records at a gage, or occasionally bya single unitgraph from an intense rainburst,well centered and distributed. If there areavailable several isolated direct runoffhydrographs suitable for simple conversion tol-inch volume unitgraphs by multiplying thehydrograph discharge ordinates by the ratio of1 inch to the direct runoff volume in inches,only those unitgraphs having equal durationtimes of rainfall excess can be directlyaveraged. Most likely, rainfall excess durationtime will be different for each l-inchunitgraph. A general similarity in shape of theunitgraphs will be recognized, but they mayshow pronounced differences in their relativesteepness and time of peak discharge.

It is possible to eliminate these differencesto a large degree by adjusting the ordinates andabscissae of each unitgraph in proportion to

some index related to both the duration ofrainfall excess and to the average time intervalb e t w e e n t h e r a i n f a l l e x c e s s a n d s o m erepresentative point near the center of therespective runoff unitgraph. The index used forthis purpose is known as lag-time which, forprocedures to be described in this text isdefined as: The time interval between themid-time of rainfall excess duration and thetime of occurrence of one-half the volume ofthe hydrograph.

Lag-time may be used as later described toc o n v e r t e a c h u n i t g r a p h into ad i m e n s i o n l e s s - g r a p h f o r m a n d t h edimensionless-graphs can then be averaged.(Note: In this text, the hyphenated termdimensionless-graph refers to the particularform used within the Bureau of Reclamation.The two words, dimensionless graph(s) refer ingeneral to graphs expressing time versusdischarge as ratios.) Lag-time is also an index oftime-of-concentration (time interval betweenend of rainfall excess and point of inflection onrecession limb of direct runoff hydrograph) ofrunoff for a watershed, and can be correlatedwith certain measurable physical featurescommon to all watersheds such as area, streamc h a n n e l l e n g t h , a n d s l o p e . Correlationsbetween lag-times derived from recorded floodsand respective watershed features, in the formof lag-time curves, provide means forestimating lag-time at any desired ungagedstream point on the basis of watershed featuresabove that point.

A synthetic unitgraph may be estimated fora watershed area, given a representativelag-time curve and dimensionless graph based


on the same lag-time definition. Hydrologytextbooks and published professional papersgive many different definitions of lag-time,several different dimensionless graph forms,and many variations in correlations of basinfeatures with lag-times.

Investigators are continually striving toimprove estimates of time-distribution ofrunoff from rainfall. Only the lag-time versusbasin f a c t o r r e l a t i o n s h i p s a n d r e l a t e ddimensionless-graph form used most often inBureau of Reclamation inflow design floodstudies will be described in detail in this text.

(e) Hydrograp h Analysis of DirectRunoff-Dimensionless-Graph Computationsand Lag-Time Estimates.-A direct runoffh y d r o g r a p h m a y b e c o n v e r t e d t odimensionless-graph form using a function oflag-time. A lag-time for the flood event mayalso be computed if sufficient rainfall data areavailable to define the duration time of rainfallexcess.

All hydrographs may be converted todimensionless-graph form by the mathematicalprocedure to be described, but experiencedjudgment must be employed to select thosethat are suitable for further considerations.Lag-time is the basic index; however, a relatedvalue known as lag-plus-semiduration is theactual index used for dimensionless-graphc o m p u t a t i o n s . Lag-plus-semiduration isobtained by adding one-half of the durationtime of rainfall excess to the lag-time. Thisaddition provides a means of obtainingc o m p a r a b l e d i m e n s i o n l e s s - g r a p h s f o run i tg raphs of different rainfall excessdurations, as, by definition, a unitgraph startsat the beginning of rainfall excess and themeasurement of lag-time starts at the mid-timeo f r a i n f a l l e x c e s s d u r a t i o n .Lag-plus-semiduration is the elapsed timebetween the beginning of the major rise of thehydrograph and the point of 50 percent ofrunoff volume. Thus, in the analysis of anobserved direct runoff hydrograph for whichrainfall excess can be established and beginsconcurrently with the start of the major rise ofthe hydrograph, lag-time is computed aslag-plus-semiduration minus one-half of therainfall excess duration.

457

When analyzing direct runoff hydrographsby the dimensionless-graph method, it is notnecessary to first convert each hydrograph to avolume equivalent to 1 inch of runoff. Inpractice, selected observed direct runoffh y d r o g r a p h s a r e c o n v e r t e d t odimensionless-graph form as follows. Thee l apsed t ime f rom the beg inn ing o f ahydrograph to the point of 50 percent volumeis computed; this is the lag-plus-semidurationvalue for the hydrograph. The abscissae of thehydrograph is converted from actual hours intopercent of the lag-plus-semiduration value.Each ordinate of the hydrograph, cubic feetper second (or c.f.s.), is multiplied by thelag-plus-semiduration value, and the product isdivided by the total direct runoff hydrographvolume expressed as c.f.s.-days. The convertedordinates and abscissae are dimensionless andmay be plotted for comparisons and averagingwith other dimensionless-graphs similarlyobtained.

The above method of eliminating the effectof rainfall excess duration time by lag-timerelations is considered satisfactory in thecomparison and averaging of a group ofdimensionless-graphs when the maximum valueof the rainfall excess duration, expressed inpercent of lag-time, does not exceed about fourtimes the minimum value found in the samegroup, expressed in the same way. When thed u r a t i o n o f r a i n f a l l e x c e s s c a n n o t b ed e t e r m i n e d with reasonable accuracy,lag-plus-semiduration can frequently bemeasured directly from the start of rise of thed i r e c t r u n o f f h y d r o g r a p h . T h u s ,dimensionless-graphs may be obtained fromrecorded floods from watersheds wherestreamflows are gaged but precipitation dataare meager or not collected. Use of thisprocedure increases the data available forsynthetic unitgraph derivations.

To determine the average shape of a groupof dimensionless-graphs, first determine theaverage of the peak ordinates and the averageof the corresponding abscissae. These twovalues become the coordinates of the peak ofthe average graph. Points on the lower portionsof the accession and recession are averaged onthe horizontal, that is, an ordinate is assumed

458

and the average of the abscissae correspondingto that ordinate is determined. If the plotting ison semilog paper and the recessions end intangents, only two averages are needed todefine the mean tangent. The shoulder portionsof the mean graph are best sketched in byvisual inspection. Arithmetical averages shouldnot be used near the peak unless the ordinatesof the points averaged are taken at a fixedpercentage of the respective peak ordinates, orunless the individual peaks as plotted are atvirtually the same height.

(1) Procedures.-A method of completeh y d r o g r a p h a n a l y s e s f o r o b t a i n i n g adimensionless-graph and lag-time estimate froma selected isolated flood event is given as astep-by-step outline with pertinent comments,graphically illustrated on figure G-5, andsupplemented by a table of computation, tableG-5. For illustrative purposes, computationsincluded in table G-5 are more detailed than


necessary in practice. An outline of proceduresfollows:

(a) Plot recorded hydrograph on Cartesiancoordinate paper and on semilog paper:

01 on figure G-5(A), and

01 on figure G-5(B)Hypothetical total flood discharges arelisted in table G-5. A hyetograph ofaverage hourly basin rainfall, ifobtainable, plotted as shown on thesame coordinate paper with the totalf l o o d h y d r o g r a p h , i s h e l p f u l f o rde te rmin ing t h e c o i n c i d e n c e o fbeginning time of rainfall excess anddirect runoff. The plot on semilogpaper helps in making base flowestimates.

( b ) E s t i m a t e b a s e f l o w , 2 o n f i g u r e0G-5(A) and (B), by trial and error.Subtract base flow from recorded

Figure G-S. Hydrograph analysis.-288-D-2457.


hydrograph and plot net hydrograph,

03 on figure G-5(B). If the base flowhas been estimated correctly, thedescending limb of hydrograph @ onfigure G-5(B) will be a straight line( e x p o n e n t i a l r e c e s s i o n ) [ 71,(0 = @minus@on figure G-5(B).)

Large base flow discharges were used in thise x a m p l e t o i m p r o v e g r a p h i c a lillustration.

( c ) C o m p u t e v o l u m e o f n e thydrograph @ as follows (method 1,table G-5):

1. Add average hourly discharges (inc.f.s.-hours) to a point such as y onthe exponential recession, 3 onfigure G-5(B). 0

2. Compute hourly recession constant,k,,, from two points on exponentialrecession line by use of followingequation:

where :

40 =4t =t=

discharge at first point,discharge at second point, andtime interval, in hours, betweenpoints 1 and 2.

(4)

3. Storage, or volume after point y (inc.f.s.-hours) equals:

-qY

lo& kh r(5)

where:

qy = discharge in c.f.s. atpointy, and

lO&kh, = 2.3026 (log, ok/&

4. Total volume is sum of volume to yplus volume after y .

(d) For comparison with rainfall data,

459

convert volume of @ to inches ofrunoff:

Inches of runoff =volume in c.f.s.-hours

(area in sq. mi.) X 645.3” (6)

*( 1 inch P, 1 /sq. mi. = 26.888 c.f.s.-days:(26.888)(24) = 645.3 c.f.s.-hrs.)

(e) Analyze rainfall data, if available;determine period D of rainfall excess.

(f) Compute time of occurrence of one-halfvolume of hydrograph @ , figureG-5(C). The time to center of volume,Tc “, equals time from beginning of riseof net hydrograph to time one-halfvolume has passed measuring point.

(g) Find lag, Lg, time in hours frommidpoint of excess rainfall period totime of occurrence of one-half volume.

(h) Compute dimensionless graph as followsand plot on semilog paper, @ onfigure G-5(B).

1. Abscissa-hours from beginning ofexcess rain expressed as percent ofvg + ~/a.

2. Ordinates-discharge in c.f.s. of @) (atrespective abscissa) multiplied by (Lg+ D/J), all divided by nethydrograph volume expressed as\

c.f.s.-days = (c.f.s-.-urs) .

(2) Lag-time curves.‘-Lagtime is a keyfunction for estimating synthetic unitgraphs.An average lag-time value for a watershed isobtained by averaging the results of severalgood analyses of stream gage records. Suchaverage values for different gages on a streamand/or different streams of similar runoffcharacteristics can be correlated empiricallywith certain measurable watershed features.The correlation equation most often used inthe Bureau of Reclamation is of the form:

-%l xLag-time, hours = C

[ Ia (7)

where: C and x are constants,


Table G5 .-Hydrograph analysis computations

BASIC DATA:Name of streamgage = (Hypothetical for this table) A, drainage area, sq. mi. = 319Date of flood = (Assume May l-3,1970) Volume, c.f.s.days, net = 26,150Time, beginning of direct runoff-net hydrograph = 12:OO p.m., 30 AprilTime, point of 50 percent volume of net hydrograph, Tc, = 9:30 a.m., 1 May

Lag-plus-semiduration, hrs.;( >Lg+f = 9.5

Duration of rainfall excess, D, hrs. = 4 (obtained by storm analysis)

Lag-time, hrs. = (Lg +%) - (%) = 7.5

Q = instantaneous discharge, c.f.s.

THourandday

l- Iydrograph! Net v

Netc hr.

Totalflood,

eBase flow Net Increm.2

Q Q c.f.s.-hrs.

rmeAccum.1,000

c.f.s.-hrs.

12P30 0 2,000 2,000 0 0 0IA1 1 2,250 2,000 250 125 .122Al 2 3,560 2,000 1,560 905 1.033Al 3 8,120 2,000 6,120 4.874Al

3,8404 18,640 2,000 16,640 11,380 16.25

5Al 5 36,040 2,000 34,040 25,340 41.596Al 6 56,290 2,000 54,290 44,165 85.76

7Al8Al9AllOAllA112Nl

7

9”101 112

70,510 2,000 68,510 61,400 147.1673,000 2,000 71,000 69,755 216.9166,330 2,000 64,330 67,665 284.5855,360 2,000 53,360 58,845 343.4243,250 2,000 41,250 47,305 390.7233,520 2,000 31,520 36,385 427.11

1Pl 1 3 26,900 2,020 24,880 28,200 455.312Pl 14 22,830 2,050 20,780 22,830 478.143 P l 1 5 19,810 2,080 17,730 19,255 497.404Pl 16 17,230 2,100 15,310 16,520 513.925Pl 1 7 15,390 2,120 13,270 14,290 528.206Pl 1 8 13,780 2,150 11,630 12,450 540.66

8Pl ‘20 11,090 2,200 8,890 (20,520) (561.18)12Pl 24 7,460 2,300 5,160 (28,100) (589.28)6A2 30 4,840 2,500 2,340 (22,500)12N2

(611.78)36 3,700 2,650 1,050 (10,170) (621.94)

6P2 42 3,305 2,830 475 ( 4,575) (626.52)12P2 48 3,215 3,000 215 ( 2,070) (628.59)

6A312N36P312P36A4

54 3,100 3,000 10060 3,045 3,000 4566 3,020 3,000 2072 3,010 3,000 1078 3,000 3,000 0

( 960)( 420)( 180)

90)30)

(629.55)(629.97)(630.15)(630.24)(630.27)

‘Note variations in time intervals for listing discharges (optional).

2 c.f.s-hrs. = x (time interval, hrs.).3

010.521.131.642.152.663.2

73.784.294.8

105.8115.8126.4

136.9147.4158.0168.5179.0189.5

210.6

3315.9

3442.3

rless-graphOrdinates,

D

net Q x[ 1Lg+?--

vol.

00.090.572.226.0

12.419.7

24.925.823.419.415.011.4

9.07.56.45.64.84.2

3.23

3.85

3.17

‘For plot on semilog paper, only enough points to define a straight Iine need be computed.


Table G-S.-Continued

461

Equations for dimensionless-graph: Net volume computations:

Abscissae =net ?? hr.- x 1 0 0

DLq-

Method 1, by equations.

Ordinates = net Q xLg+P

vol., c.f.s.-days

qo: Q at net x hr. 20 = 8,890 c.f.s.qr: Q at net z hr. 30 = 2,340 c.f.s.

t: time interval, q. to qt = 10 hrs.

[ c.f.s.-days = ( “fs$urs)]

Lag-plus-semiduration:

l/2 volume is between net x hrs. 9 and 10By linear interpolation:

Volume, method 1,

Lg+$= 9.50 hrs.

Volume, method 2,

Lg +f= 9.52 hrs.

Except for very small watersheds, lag-plus-semidurationvalues are rounded to nearest l/10 hr.

For dimensionless-graph equations:

Use: Lg+T = 9.5

Volume = 26,150 c.f.s.days

Lag estimate:

D=4hrs.

kh, -: I;-= 0.875

-40Volume after net z hr. 20 = log, khr

-8,890_-0.1336

= 66,540 c.f.s.-hrs.

xnet volume, hrs. O-20 = 561,180 c.f.s.-hrs.Total net volume = 627,720 c.f.s.-hrs.

= 26,150 c.f.s.-days% total net volume = 313,860 c.f.s.-hrs.

Method 2.Ordinates of total net hydrograph used as shown

in table at left,Discharges of recession limb read at time intervals

for which recession curve can be approximatedas a straight line.

Total volume = 630,270 c.f.s.-hrs.= 26,260 c.f.s.days

r/z volume = 315,140 c.f.s.-hrs.

Lag = 9.5 -$= 7.5 hrs.

L = length of longest watercourse frompoint of interest to watersheddivide, measured in miles,

cu = centroid of basin-usually found byvertically suspending a cardboardcutout of basin shape successivelyfrom two or more points and findingintersection of plumb lines fromeach point,

Lca = length of watercourse from point ofinterest to intersection of perpen-dicular from ca to streamalinement, and

S = overall slope in feet per mile of

longest watercourse from point ofinterest to divide.

Values for the constants C and x areobtained empirically from plots on log-log

4,paper of a values versus lag-time, hours,

and fitting a straight line, either “by eye” or byleas t-squares computations. The lag-time

-%clindicated by the curve for an-a-

value of 1 .O

is the constant C, and the “slope” of the lineon log-log paper is the constant x.


A lag-time curve for a watershed should bebased on as many hydrograph analyses as canbe obtained from the data available within thewatershed and for other watersheds withsimilar runoff characteristics. When developinga lag-time curve, a consistent method ofhydrograph analyses should be used andmeasurements of watercourse lengths should bemade on maps of the same scale. If suitabledata are limited to only one stream gagelocation, a lag-time curve can be constructedby drawing a line with slope of 0.33 throughthe point plotted on log-log paper of average

Lag-time, hours = 1.6

L&llag-time versus-G

value.

In the absence of any runoff data suitablefor hydrograph analyses, preliminary estimatesof lag-times for direct runoff for watershedshaving rapid runoff characteristics can be madeby the following generalized equation:

The above equation gives values acceptableas preliminary estimates of direct runofflag-times for many streams in the plains andsouthwestern regions of the United States andfor foothill streams of the Rocky Mountains.Certain types of watersheds have largevariations in lag-times that are not adequatelyreflected by the generalized C value given.These include watersheds which have physicalfeatures tending to retard surface runoff suchas near level terrain, dense vegetative cover,etc.; and those in which the streams extendinto high, well-forested mountains or whosestreamflow records show pronounced interflowcontribution. Lag-time estimates for suchwatersheds should be made by an experiencedhydrologist.

C. SYNTHETIC UNIT HYDROGRAPH

G-9. Synthetic Unitgraphs by Lag-TimeDimensionless-Graph Method.-Computationof a unitgraph for a watershed above a specificlocation by this method is done by reversingthe mathematical process used to derive adimensionless-graph. The important factors forobtaining a representative unitgraph for a givenwatershed are the selections of a properlag-time curve and proper dimensionless-graph.An example of a unitgraph derivation for anungaged watershed follows, given as astep-by-step outline with pertinent commentsand graphically illustrated on figure G-6.

(1) Outline drainage boundary, determinearea (fig. G-6(A)).

(2) Find basin center of area, cu and projectto the nearest point on the longestwatercourse. Measure L (to divide at head oflongest watercourse) and L,, miles. (Refer tosec. G-8(e)(2).) Determine S (for upperelevation, estimate average elevations alongdivide in vicinity o f h e a d o f l o n g e s twatercourse, not the specific elevation at the

point of extention of longest watercourse todivide).

LLl(3) Compute -

AD-’(4) Enter graph, lag-time curve (fig. G-6(B)),

L&lwith -a

value and read the corresponding

lag-time. (Lag-time curve (B) represents meanc u r v e d r a w n “ b y e y e ” t h r o u g h p l o t t e dlag-times obtained from hydrograph analyses

L&lversus respective -

G--for basins of similar

runoff characteristics.)(5) Select a dimensionless-graph (fig. G-6(C))

(usually an average dimensionless-graph of anumber of dimensionless-graphs derived for thesame stream or for streams of similarcharacteristics).

(6) Select a unit rainfall duration time; thisshould be one-fourth or less of lag-time forb a s i n . ( U n i t t i m e s are selected for

Figure G-6. Unitgraph derivation for ungaged area.-288-D-3182

computational convenience, usually l-, 2-, 3-, e n t e r e d wi th successive 1 ag-plus-4-, or 6-hour units for lag-times of 4 hours or semiduration values, and respectivegreater. Unit times larger than 6 hours are ordinates read from the graph. Ordinatesseldom used. Units of one-half or one-quarter are substituted in the ordinate equationhour are used for lag-times less than 4 hours.) for solution of discharge values. When

(7) Compute unitgraph (fig. G-6(D)) using: done by desk calculator, discharges are(a) Basin area, square miles. rounded.(b) Lag-time plus one-half selected unit (Note: Dimensionless-graph ordinates

rainfall duration time. listed in the table of sample computations(c) Dimensionless-graph. (fig. G-6) do not agree numerically at( d ) N o t e s r e g a r d i n g c o m p u t a t i o n a l respective accumulative time values with

procedure. dimensionless-graph ordinates in table1. E q u a t i o n s f o r d e r i v i n g a G-5, because the dimensionless-graph

dimensionless-graph are given in table G-5. ordinates in the table were derived atUnitgraph computation requires solving i n t e r v a l s o f 1 0 . 5 p e r c e n t o ffor instantaneous discharges at end of lag-plus-semiduration but the ordinatessuccessive unit time intervals. for 2-hour unitgraph derivation in figure

2. Time, hours, accumulative by unit G-6 were read at intervals of 20 percent oftime intervals are l isted, and each a different lag-plus-semiduration value.)accumulative value expressed as percent 4. Caution. -The volume of a syntheticof lag-plus-semiduration. unitgraph should always be checked

3. Dimensionless-graph (fig. G-6(C)) is before being used, to be sure it has a


volume within 1 percent of l-inch runoffvolume for the watershed area. All of theordinates of a unitgraph ((D) of fig. G-6)may be computed by reading the entiredimensionless-graph (C) and summing theordinates to check the volume.

Another procedure may be used if theselected dimensionless-graph has anexponential recession limb such as onfigure G-6(C). Unitgraph ordinates areobtained by reading the dimensionless-graph forward to an ordinate that is onthe beginning portion of the exponentiallimb of the dimensionless-graph (see sec.G - 8 ( e ) ( l ) ( b ) ) . T h e v o l u m e o f t h eunitgraph thus far obtained is computedand subtracted from the volume of 1 inchof runoff for the watershed area, givingthe remaining volume, V, . A recessionconstant, k, for the selected unit timeinterval can be computed by the equation,

dimensionless-graph. This procedureassures correct unitgraph volume.

G-10. Trial Reconstruction of Past

log, k= -+x

(8)

where :

Floods. -Final decisions regarding appropriatelag-time, dimensionless-graph, and retentionlosses for a gaged watershed are madeempirically by computing hydrographs of pastrecorded floods. Retention losses believedappropriate are applied to the observed stormprecipitation data for each flood to ber e c o n s t r u c t e d t o d e t e r m i n e un i t t imeincrements of rainfall excess equivalent to ther e s p e c t i v e h y d r o g r a p h v o l u m e . T h e s eincrements are applied to a representativeunitgraph according to basic assumption (3),figure G-3. The hydrograph thus computed iscompared with the recorded hydrograph forgoodness of fit; preliminary conclusionsregarding appropriate factors are revised, ifnecessary, until an acceptable fit is obtained.These test trial reconstructions should be madefor the large floods. Preferably, the largestflood of record should be excluded from theset of hydrographs selected for analyses andthe parameters resulting from analyses testedby the fit achieved using them to reconstructthe largest flood.

q = the discharge ordinate, c.f.s., onthe exponential limb, and

I’, = the remaining volume expressed inunit time (c.f.s.-hours).

The factor k is used to compute theordinates of the unitgraph following thelast ordinate obtained by reading the

G-l 1. Synthetic Unitgraphs by OtherMethods. -Descriptions of several differentmethods of estimating synthetic unitgraphsmay be found in technical publications. Amongthose often used are the S-curve hydrograph[8], Snyder’s method [ 91, and basin routingm e t h o d s b a s e d o n t h e C l a r k a p p r o a c h[51,[101,[111,[121.

D. STREAMFLOW ROUTING

G-12. General. -Computation of an inflowdesign flood (IDF) hydrograph often requiresthat floodflows from several subareas withinthe drainage area be computed separately.Beginning with the farthest upstream subarea,hydrographs are transferred downstream bysome method of streamflow routing, the flowsbeing consecutively combined with other floodhydrographs, and the total inflow design flood

h y d r o g r a p h o b t a i n e d f o r t h e p r o p o s e dreservoir. Watershed features above a damsitewhich indicate the need to subdivide the basininto subareas include:

( 1) Large tributary areas which haved i f f e r e n t s i z e s , s h a p e s , a n d c o v e rcharacteristics.

(2) Existing reservoirs or natural lakeswhich control runoff from significant portions


of the drainage area above a proposed damsite.The flood runoff from the portion of thedesign storm for the total drainage area thatoccurs above such an existing feature should bereservoir-routed through the feature to obtainan outflow hydrograph before routing ondownstream. If an existing dam impounds alarge-capacity reservoir, the capability of theexisting dam to safely withstand the computedinflow flood must be determined. Should theupstream dam be found to have an inadequatespillway capacity (or structural weakness),steps should be taken to get the owners of theupstream dam to make modifications asnecessary to safely pass the inflow designflood. Or as an alternative, failure of thestructure should be assumed and provisionmade at the proposed downstream dam andreservoir to safely handle the flood wave surgethat might be expected with failure and anadditional inflow volume equivalent to thecapacity of the upstream reservoir.

(3) Drainage areas in which storm potentialvaries to an extent that an assumption ofaverage precipitation over the total area duringa design storm is unreasonable.

(4) Drainage areas in which during designstorm conditions some streams will havesnowmelt runoff in addition to rainfall runoffand other streams have only rainfall runoff.

G-13. Practical Methods of StreamflowRouting Computations. -Streamflow routing,the determination of a flood dischargehydrograph at any point on a stream from adischarge hydrograph at some point upstream,requires solution of the movement of floodwaves in natural open channels which areextremely complex. A discussion of thetheoretical and mathematical bases of floodrouting methods is beyond the scope of thistext. Many different methods and procedureshave been described in engineering literature. Ifstreamflow routing is necessary in thederivation of an inflow design floodhydrograph and the damsite is located on astream that has discharge records at two ormore locations, an applicable routing methodmay be selected from descriptions inpublications, for example, “Hydrology forEngineers” [ 131.

Usually, inflow design flood derivations thatinclude streamflow routing computationsinvolve ungaged streams. Description of twopractical methods of mathematical streamflowrouting which can be used on the basis of anestimate of peak discharge travel time betweentwo points on a reach of natural streamchannel follows. These methods have beenfound to give acceptable results when tested byusing recorded discharge hydrographs.

(a) Tatum’s Method [ 141 .-This method isalso known as the Method of SuccessiveAverages. Factors used when applying thismethod are travel time of peak dischargethrough the channel reach, Tin hours; selectedrouting interval between discharges of theupstream hydrograph to be routed, t in hours;and routing constants listed in table G-6 forrespective number of routing steps. Definiterules for selecting lengths of stream channelreaches for each routing computation cannotbe set, but use of extremely long reaches maygive very poor results. When computing aninflow design flood hydrograph, channelreaches are those on the main stream betweenpoints of inflow from subareas. Thus, inflowfrom a subarea can be added to the routed flowat the subarea inflow point to obtain acombined floodflow for routing through thenext reach. After estimating travel time Tbelieved applicable for a reach, a routinginterval t is selected choosing an interval smallenough to define well the hydrograph, and thenumber of routing steps for that reachcomputed by the equation:

Number of routing steps = 2T/t (9)

Computed fractional steps are rounded tothe nearest whole number. The computationalprocedure is illustrated in table G-7. In actualpractice when using a desk calculator, therouting constants are copied in a column on aseparate sheet of paper and used as a slidebeside the column of discharges to be routed.Products of the multiplications of constantsand respective discharges are accumulated inthe machine and only the total of each set ofmultiplications recorded. Constants for largernumbers of routing steps than given in table


Table G-&-Coefficients for jloodrouting by Taturn’s method

Routingconstants

Clc2c3c4c5

c6Gc8c9Cl0Cl1

0.2500.5000.2500

3

0.1250.3750.3750.1250

Number of

G-6 may be computed from the expression (Yz+ ?!2)” by the general equation for each term ofa binomial expansion, IZ as the number of steps.Streamflow routing by Tatum’s method using adesk calculator becomes tedious and timeconsuming when more than eight routing stepsare used. The procedure may be easilyprogramed for computer use.

(b) Translation and Storage Method.-In apaper describing a graphical reservoir-routingmethod, Wilson [ 151 also discusses streamflowrouting, pointing out that it is partly analogousto reservoir routing but that natural channelstorage produces less “flattening” effect on aninflow hydrograph than does reservoir storage.He suggested that in streamflow routing, theout flow (routed) hydrograph would liebetween a hydrograph obtained by applyingthe graphical reservoir-routing method and theinflow hydrograph translated downstream atime interval equivalent to the reach traveltime, and presented an example in which therouted hydrograph showed half translatoryeffect and half storage effect.

A report of the California Division of WaterResources [ 161 presented a streamflow routingmethod based on an adaptation of Wilson’sg raph ica l rou t ing me thod showing tha ttranslation effect (travel time) and channelstorage effect (attenuation) on the shape of aflood hydrograph moving downstream can betreated separately. In their studies, each effectwas found to have approximately equal weight.

The translation and storage method of

uting stl6

0.0156 0.0078.0937 .0547.2344 .1641.3126 .2734.2344 .2734

.0937.0156

.1641

.0547

.0078

8

0.0039.0313.1094.2187.2734

.2187

.1094

.0313

.0039

streamflow routing was devised5 on the basisof evaluating separately the effects of traveltime and channel storage and assuming equalweight for each effect in natural streamchannels having “usual” storage characteristics.An equation for mathematical application ofWilson’s graphical routing method was given inthe U.S. Department of Agriculture, SoilC o n s e r v a t i o n E n g i n e e r i n g H a n d b o o k ,Supplement A, 1956. The given equation isused in the translation and storage method ofstreamflow routing as follows:

0, =01 +K(I, +I2 -201) (10)

where:

I,, I2 = inflow, consecutive incrementalinstantaneous discharges at thehead of a stream reach, and

01, O2 = outflow, successive incrementalinstantaneous discharges at theend of a stream reach; O2 is theoutflow resulting from I, and 1,and the preceding outflow O1.

The routing constant, K, in the above equation,is obtained as follows:

T = travel time, hours, of peak flow throughthe reach consisting of:

5 Described in unpublished memoranda, Flood HydrologySection, Engineering and Research Center , Bureau ofReclamation, Denver, Colo.


Table G-I.-Illustrative example of streamflow routing by Tatum’s method

HYPOTHETICAL PROBLEM: Streamflow-route total flood hydrograph, table G-5, through channel reach having travel time of4 hours.

(2x4)If selected 1= 1 hr., routing steps = T= 8

GV(4)If selected t = 2 hrs., routing steps = 7 = 4

---Hour Upstreamand Qdate 1,000 c.f.s

-___

-..-

t = 1 hr., 8 routing stepsIllustrative positioning

of routing constants’

Routed3Q

1,000 c.f.s.-4P30 ‘2.05 P 2.0 0.00396 P 2 . 0 .0313

7 P 2.0 .10948 P 2.0 .2184YP 2.0 .27341OP 2 . 0 .218711P 2.0 .109412P30 2.0 .0313 l1Al 2.3 .00392A 3.63A 8.1 0.00394A 18.6 .0313 3.00395A 36.1) .1094 .0313 I.00396A 5 6 . 3 .2187 .1094 .0313

7A 70.5 .2734 .2187 .10948A 73.0 .2187 .2734 .2187YA 6 6 . 3 .1094 .2187 .27341OA 5 5 . 4 .0313 .1094 .218711A 4 3 . 2 .0039 .0313 .109412Nl 33.5 .0039 .0313

lP1 26.9 .00392 P 22.8

- -:Constant base flow of 2,000 c.f.s. assumed to precede flood event.

61.3‘64.8

42.0

61.7

i

t = 2 hrs., 4 routing stepsIllustrative positioningof routing constants’

0 .0625

.2500

.3750

.2500

.0625

.--

0.0625

.2500

.3750

.2500

.0625

I.0625

.2500 3.0625

.3750 .2500

.2500 .3750

.0625 .2500

.0625

Routed3Q

1,000 c.f.s.

4 7 . 7

658.6

37.8

IAll routing constants are placed opposite respective Q’s at t intervals.3Discharge at bottom of reach; each Q is instantaneous discharge at time given in column 1.4Sum of products of each constant times respective Q.‘Peak discharge of routed hydrograph, occurs 4 hours later than upstream peak.6Peak discharge of routed hydrograph, agrees in time with routing t = 1 hr., but differs in magnitude because of longer routinginterval.

T, = translation time component, hours(when assuming equal weight tostorage effect, T, = OST)

Then for stream routing evaluation of storagetime effect,

T, = storage time component, hours(when assuming equal weight totranslation effect, T, = OST)

andwhere:

tK=2Ts+t

T = T, + T,t = routing time interval, hours,

with t <_ O.ST,.

468

Solving the equation for O2 gives aninstantaneous discharge value at the end of theincremental time interval designated by 1,. IfI,, I,, etc., are designated by time at the headof a reach, the time of occurrence of O2 at thebottom of the reach is obtained by adding thetranslation time component, T, to the time ofrespective 1, .

Use of the above equation with anassumption that the travel time for the reach isdivided equally into translation time, T,., andstorage time, T,, gives as acceptable results asthose obtained by using Tatum’s Method butrequires less computational time when doingm a n u a l r o u t i n g . A d e t a i l e d e x a m p l e o fapplication of the translation and storagemethod is shown in table G-8. Of course, inpractice, such a detailed table is not necessary.

The translation and storage method, inaddition to being easy to apply to streamreaches for which Tatum’s method might beused, is also versatile enough to be applied tostream reaches having more or less storageeffect than “usual.” The relationship of storagetime and translation time is not rigid, but mayb e v a r i e d d e p e n d i n g o n c h a n n e l r e a c hcharacteristics. If hydrographs are available atthe head and bottom of a stream reach, a few


trial routings will give an acceptable value foreach component. Characteristics of ungagedstream channels are judged by comparison withcharacteristics of gaged streams when necessaryto use streamflow routing methods.

(c) Comparison of Methods. -An illustrationof results of applying the above two methodsof streamflow routing is shown on figure G-7on which the hypothetical flood hydrograph,with discharges listed in table G-5, is plotted.This hydrograph was routed downstreamassuming a reach travel time of 4 hours: first,by Tatum’s method assuming routing intervalsof 1 hour and 2 hours; and secondly, by thetranslation and storage method using a routinginterval of 1 hour. Routed (downstream)hydrographs are also plotted on figure G-7(computations are not included). The tworouted hydrographs obtained by Tatum’smethod differ because of different routingintervals; the routing by l-hour intervals is themore representative because the upstreamhydrograph is best defined in l-hour intervals.The routed hydrograph obtained by thetranslation and storage method is acceptablysimilar to the hydrographs obtained byTatum’s method.

E. DESIGN STORM STUDIES

G-14. General.-Major floods, except thoseassociated with dam failure, earthquakes, orlandslides, result from a combination of severemeteorological and hydrological conditions. Itfollows that estimates of meteorologicalconditions which may approach the physicalupper limits of rainfall or snow accumulationand melt rates must be considered where aninflow design flood (IDF) is required. Thissection is concerned only with rainfall studies.For the purpose of this text, the followingterminology is used in regard to estimates ofthe physical upper limits of storm rainfall in abasin or region.

(a) Probable Maximum Precipitation(PMP). -Probable maximum precipitationvalues represent an envelopment of maximized

intensity-duration values obtained from alltypes of storms. It is recognized that probablemaximum precipitation values for all durationsand all areas may not occur from only one typeo f s to rm. For example , a max imizedthunderstorm is very likely to provide probablemaximum precipitation over an area of 50square miles for a duration of 6 hours or less,but the controlling values for longer durationsor for larger areas generally will be obtainedfrom general-type storms.

(b) Probable Maximum Storm (PMS).-Theprobable maximum storm values represent anenvelopment of maximized intensity-durationvalues obtained from storms of a single type.Consideration is given to storm type andvariations of precipitation with respect to


Table G-&-Translation and storage method of streamflow routing

(1) (2) (3)Time, Inflow, I1 +z2,

hours’ c.f.s. c.f.s.

600600646

1,196

3,5428,346

15,67223,200

0 3003 300 6006 415 7159 1,604 2,019

12 5,458 7,062

1 5 10,093 1555118 16,567 26,6602 1 17,924 34,49124 18,608 26,532

21 19,244 37,85230 19,772 39,01633 25,913 45,68536 23,499 49,412

39 20,552 44,05142 17,377 31,92945 14,703 32,08048 12,054 26,757

‘Time of instantaneous discharge at head of reach.:Discharge at end of reach; (6) + preceding value in (7).

28,53232,26034,96239,252

43,31643,61041,33837,634

Equation: 02 = 01 + K(Ii +I2 - 2 01)

T = 12 hours

T, = 6 hours

T, = 6 hours

t = 3 hours

(For definitions of symbols, see sec. G-13 (b).)

(4) (5) (6)

201 (3) - (4) (K)(5)

0 0115 23

1,373 2755,866 1,173

12,009 2,402 4,173 2 118,314 3,663 7,836 2418,819 3,764 11,600 2113,332 2,666 14,266 30

9,320 1,864 16,130 336,756 1,351 17,481 36

10,723 2,145 19,626 3 910,160 2,032 21,658 42

735-5,681- 9 , 2 5 8

-10,877

147- 1 , 1 3 6- 1 , 8 5 2-2,175 -

K=L2T,+t

3K=-12+ 3

K = 0.20

(7) (8)Outflow,2 Time,

c.f.s. hours4

3300 6300 9323 1 2598 1 5

1,771 1 8

21,805 4520,669 4818,817 5116,642 54

“Constant flow in reach assumed.4Time of instantaneous discharge at end of reach. Translation time, T,, added to time at head of reach.

location, area1 coverage of a watershed, andstorm duration.

(c) Design Storm. -The precipitation valuesselected for computing an inflow design floodare usually referred to as a design storm. Thesedesign storm values may or may not be equalto the PMP. The hydrometeorological reportwhich describes the considerations andcomputations leading to the recommendationof a design storm for a particular watershed isusually called a “Design Storm Study.”

(d) Additional References. -It is beyond thescope of this text to discuss in detail themeteorological considerations and computa-tions involved in obtaining the “maximized

intensity-duration values” cited in the abovedefinitions. A comprehensive discussion of thissubject is given in chapter 2, “MaximumRainfall,” of WMO Technical Note No. 98 [ 21.A brief discussion on estimation of probablemaximum storms is given in subsequentparagraphs. Also included in this section aregeneralized precipitation charts for estimatingprobable maximum precipitation values east ofthe 105’ meridian and general-type designstorm values west of the 105’ meridian forwatersheds in the 48 conterminous UnitedStates. These charts also are presented inchapter III of “Design of Small Dams,” secondedition [ 3 11, associated with procedures for


E X P L A N A T I O NUpstreom Hydrogroph

Travel time for channel reach - 4 hours

II i x-x-x--x By Tatum’s method, t = 2 hrs . 4 s teps

o o o o By t rons lo t ion and s toroge method

n\\ t = I hr

St reamf low Routed Hydrogrophs- - B Y Totum’s m e t h o d . t = I hr: 8 steos

8400- -

Tr = 2 hr:Ts = 2 hr:

g 3 55 I \

\

5 3 0 If

\

\\.v)0 0 :

,I25

I 1 1 I 1 I I I

3P 6P SPI

3A 6A 9A 12N 3P 6P SPI

3A 6A 9A 12N 3P 6P 9P30 I 2

DATE AND TIME

Figure G-7. Comparison of results of streamflow routings.-288-D-3183

estimating inflow design floods for small dams.Discussion of design thunderstorm rainfall

has been omitted in this text, anticipating thatreaders will be concerned generally withdamsites controlling drainage areas largeenough to preclude the use of thunderstormrainfall. However, thunderstorm rainfall shouldnever be ignored completely, as it may provecritical under some circumstances.

G - 1 5 . P r o b a b l e M a x i m u m S t o r mConsiderations. -Estimates of probablemaximum storms (PMS) are based on analyseswhich c o n s i s t o f three steps: (1)determination of the area1 and temporaldistribution of the larger storms of record inthe general area; (2) augmentation of these

observed storms through moisture adjustment;and (3) consideration of storm transposition.

One objective of the first step cited above isthe determination of maximum values of stormrainfall for selected durations and area.Depth-area-duration (DAD) values of eachtotal storm are analyzed without regard towatershed boundaries [ 171. Comparison ofDAD values will indicate which storms are bestsuited for further analysis. If hydrographs offloods for specific watersheds associated witht h e s t o r m s a r e available for analyses,determination of rainfall data for these specific


watersheds can be included as a part of theanalyses.

Technical literature [ 21 should be consultedfor a detailed discussion of the theoreticalassumptions included in the computationalprocedures for storm maximization, step (2),and storm transposition, step (3). An abridgeddiscussion of a procedure often used formaximization and transposition of storms inplains-type terrain follows. Discussion ofprocedures for storm maximization and limitedtransposition in mountainous terrain is beyondthe scope of this text.

G-16. Procedure for Storm Maximization,Plains- Type Terrain. -This procedure is basedon assuming a saturated air-mass with apseudoadiabatic lapse rate. Moisture contentunder these circumstances is a unique functionof surface dewpoint temperature, so thatdewpoint t e m p e r a t u r e s m a y b e u s e d t oquantitatively estimate total atmospheric watervapor or precipitable water values. Tables [ 181have been published which list ambienttemperatures for various elevations or pressuresabove a 1 ,OOO-mb. ( 1 ,OOO-millibar) surface,approximately equivalent to mean sea level, fors e l e c t e d t e m p e r a t u r e s i n a saturatedatmosphere with a pseudoadiabatic lapse rate.

Tables [ 181 also list, for each 1 ,OOO-mb.dewpoint temperature, values of precipitablewater in inches for layers between the1,000-mb. surface and various elevations toextreme heights in a saturated, pseudoadiabaticatmosphere. These precipitable water valuesmay be used as an index to the moisturecontent of a unit column of air between sealevel and the top of a moisture-bearing air-mass.Maps with isotherms of maximum 12-hourpersisting 1 ,OOO-mb. dewpoint temperatures(O F.) of record for each month for the 48conterminous states are available in the“Climatic Atlas of the United States” [ 1.91 .

C o m p u t a t i o n a l p r o c e d u r e s f o r s t o r mmaximization and transposition, plains-typeterrain, follow:

(a) Muximization of u Storm in Place ofOccurrence.

( 1) Observed storm dewpoint. -Arepresentative 12-hour persisting surface

471

dewpoint temperature is obtained for thestorm period under study from temperaturestations in the path of the inflowing moist air.If the rainfall is of a frontal type, the surfacedewpoints within the rainfall area will be lowerthan those of the inflowing moist air, thusgiving a low estimate of storm moisturecontent. Distance and direction from the stormcenter to the representative dewpoint stationor stations should be recorded.

( 2 ) A d j u s t m e n t t o 1,000-mb.surface. -Since during major storms the airmasswill be saturated, the dewpoint temperature atthe representative station can be adjusted to a1,000mb. surface temperature assuming asaturated, pseudoadiabatic lapse rate oftemperature.

(3) Precipitable water values. -From the1 ,OOO-mb. dewpoint temperature determinedin (2) above, obtain two precipitable watervalues, Wp , for the observed storm:

(a) Wpvl is the precipitable waterbetween 1,000 mb. and the top of themoist layer for the storm system; anelevation of 40,000 feet, or pressure of200 mb., is usually assumed.

(b) Wp-z is the precipitable waterbetween 1,000 mb. and the mean surfaceelevation of the central portion of theobserved storm. If the inflowing moist airhas passed over a topographical barrierwith a higher elevation than at the centralportion of the storm, Wpm2 is obtainedusing the inflow barrier elevation.

(4) Observed storm’s precipitable water,W,.-Compute the observed storm’s moisturecontent or available precipitable water, W,, asWP-1 minus Wp.2.

(5) Probuble maximum precipitable waterfor the storm, W,. -An estimate of theprobable maximum moisture content indicatedfor the storm is obtained as follows:

(a) From the “Climatic Atlas of theUnited States” [ 191, the max imum12-hour persisting dewpoint temperatureof record can be determined for the dateof storm occurrence and the location oft h e r e p r e s e n t a t i v e dewpoint fo r theobserved s to rm. F requen t ly , t he

472

maximum recorded dewpoint temperaturewithin a period of plus or minus 15 daysis used.

(b) From the maximum dewpoint ofrecord, precipitable water is obtained forthe same layers as used in VP- 1 and WPm2above. These precipitable water values aredesignated Wr- 1 and Wr-, .

(c) The estimated probable maximumprecipitable water, W, , will be Wr-, minus

(6)w&%sture maximization factor, Mf. -Themoisture maximization factor, Mf, is computeda s t h e r a t i o o f t h e p r o b a b l e m a x i m u mprecipitable water to the precipitable waterobserved during the storm, or Mf = W, /W,.

(7) Maximized storm values. -Maximizedstorm values are computed by multiplyingdepth-area-duration (DAD) values of theobserved storm by the maximization factor,

Mf.Note: This procedure assumes that the

magnitude of rainfall in a storm is a functiononly of the inflow moisture charge. It alsoassumes that the most effective combination ofstorm efficiency and inflow wind has occurredor has been closely approached in the majorstorms of record. The procedure may notalways prove adequate, particularly for regionswhere rainfall is strongly influenced byorographic effects [ 21.

( 8 ) E x a m p l e o f computations-maximization in place.

( a ) Dewpoint observation station:elevation 1000 feet.

Location: 100 miles southeast of stormcenter.

Representative 12-hour storm dewpoint:69O F.

Sea level, 1,000 mb., dewpoint: 7 1 O F.

(b) Surface elevation, storm center: 1500feet.

WP-1 = 2.38 inches (at 40,000 feet)WP-Z = 0.32 inch (at 1500 feet)

W, = 2.06 inches


( c ) Maximum dewpoint o f r e c o r d ,observed 100 miles southeast of stormcenter: 78O F. 1191.

Wr- 1 = 3.35 inches (at 40,000 feet)Wr-2 = 0.41 inch (at 1500 feet)

W, = 2.94 inches

(d) Moisture maximization factor:

Mf = 2.9412.06Mf = 1.43

( b ) M a x i m i z a t i o n o f T r a n s p o s e dStorm.-When a storm is transposed andm a x i m i z e d f o r m o i s t u r e c o n t e n t , t h emaximization factor is usually computed forthe storm only at its transposed location.Computation of available precipitable water forthe observed storm, W,, remains the same asdescribed above.

T h e m o i s t u r e m a x i m i z a t i o n f a c t o r i scomputed by determining the surface elevationat the center of the storm at its transposedposition or the height of the mean inflowb a r r i e r t o t h a t l o c a t i o n . T h e m a x i m u mdewpoint of record is obtained from the chartsof dewpoints [ 191 at the same distance fromthe transposed center and in the same directionas the observed storm dewpoint was obtained.

( 1) Example of computations-moisturemaximization of transposed storm,

(a) Assume that the storm used in theprevious example is transposed to alocation where the elevation of the stormcenter is 2500 feet and that there is not ah ighe r inflow barrier between thetransposed c e n t e r a n d t h e m o i s t u r esource.

( b ) M a r k t h e l o c a t i o n of thetransposed center on the charts ofm a x i m u m r e c o r d e d dewpointtemperatures and measure 100 milessoutheast to determine the maximumdewpoint of record; for example 77’ F.

(c) Observed storm precipitable waterremains the same; W, = 2.06 inches.

(d) Maximum precipitable water for adewpoint of 77’ F:


W =r- 1 3.19 inches (at 40,000 feet)Wr-2 = 0.64 inch (at 2500 feet)

W, = 2.55 inches

(e) Moisture maximization factor forthe transposed storm:

Mf = 2.5512.06Mf= 1.24

Note: If an Mf factor greater than 2.0is computed, reexamine the computationsand all meteorological aspects of thetransposed storm. An Mf factor greaterthan 2.0 has not been used in Bureau ofReclamation design storm studies.

( 2 ) M a x i m i z e d transposed stormvalues. -The maximized values for thetransposed storm are computed by multiplyingthe DAD values of the observed storm by them a x i m i z a t i o n f a c t o r f o r t h e t r a n s p o s e dlocation.

G-17. Design Storm-Probable MaximumPrecipitation (PMP) or Probable MaximumS t o r m ( P M S ) E s t i m a t e s f o r aWatershed. -Estimates of PMP or PMS, whethermade by storm transposition and procedure ofdewpoint adjustment described above or bymore detailed theoretical computations [ 201 6,are based generally on the results of analyses ofobserved storms. In the United States, passageof the Flood Control Act of 1936 led to thedevelopment of a National Storm StudyProgram under the primary sponsorship of theU.S. Army Corps of Engineers. Under thisprogram more than 600 storms throughout theUnited States have been analyzed in a uniformmanner and summary sheets distributed toGovernment agencies and the engineeringprofession [ 2 1 I . An example of a stormanalysis summary sheet from the publication“Storm Rainfall in the United States” [ 21 I isshown on figure G-8. Each storm analyzed hasbeen assigned a designation such as MR 4-24 onthe figure. Unfortunately, not all of thesummary sheets have a reference to theobserved storm dewpoint, such as shown onfigure G-8(A). Depth-area-duration (DAD) datafor each storm analyzed are given in a table,

61ncludes 23 separate reports.

such as the one at the bottom of figure G-8(A).A storm location map and a few selected

mass rainfall curves are given on figure G-8(B).Summaries of observed storm data such aspresented in “Storm Rainfall in the UnitedStates,” provide broad outlines of stormmagnitudes and their seasonal and geographicalvariations.

A simplified example of the derivation ofdesign storm values for a particular watershedfollows. Sources of numerical values used arereferenced when possible. The isohyetalpatterns and watershed map are not presented.This example may provide the reader withinformation that will be useful in a betterunderstanding of how preliminary design stormestimates are obtained from the generalizedPMP charts given later.

( a ) Example o f a D e s i g n S t o r mStudy. -(Final-type design storm studies shouldbe prepared by experienced hydrometeorolo-gists.) Let us assume that design storm valuesrepresenting PMS estimates are required for awatershed with a 200-square-mile area atlongitude 99’30’ west, latitude 41’00’ north, ar e g i o n where storm transposition andmaximization by dewpoint adjustment is anacceptable approach. Procedural steps aredescribed first, then numerical computationsare given.

( 1) Transposition limits of majorstorms. -The broad limits within which majorobserved storms can be transposed should beestablished first. This will require consultationwith an experienced hydrometeorologist.However, for the United States east of the105O mer id i an , guidelines have beenestablished in Hydrometeorological Report 33[201.

( 2 ) I n v e n t o r y o f d a t a o f m a j o rstorms. -Referring to “Storm Rainfall in theUnited States” [ 211, rainfall depth-durationvalues can be obtained for an area of 200square miles for all major storms that havebeen analyzed in the r eg ion fo r wh ichtransposition is applicable. Analysis may berequired for recent major storms in the regionin order to complete the inventory.

(3) Selection of storms for furtherstudy.-Several of the larger storms are

4 7 4 D E S I G N O F G R A V I T Y D A M S

:PARTMENT OF THE ARMY CORPS OF ENGINEE

S T O R M S T U D I E S - P E R T I N E N T D A T A S H E E TStorm of 17-19 September 1926Assignment kx? 4-24Loca:ionIa,blinn,Ne$-3.3. & WisStudy Prepared by:Blissouri River DivisionCknaha District Office

Part I Reviewed by H. M. Sec. ofWeather Bureau, 0/s/47

Part II Approved by Off ice, Chiefof Engineers for Distributionof Factual Data, 12/23/47

Remarks: Centers nearELzyden & Maurice, Ia.hwpt. 700 - Hef. Pt. 175 SSE

Grid C-15

DATA AND COMPUTATIONS COMPILEDPART I

Preliminary isohyetal map, in 2 sheets, scale 1: SOO,WOPrecipitation data and mass curves: (Number of Sheets)

Form 5001-C (Hourly precip. data)- _ _ - _ _ _ - _ _ - - _ - _ _ _ _ _ _ _ _ 8Form 5001-B (24-hour * 1 ~~------ ---_--- -__---- -F o r m 5 0 0 1 - D ( I8 ” ” ___------_----------- 11Miscl. precip. records, meteorological data, etc.- _ _ _ __ _ __ __- -_ 29Form 5002 (Mass rainfall curves)- _ ___ _______ _ __- - - -- ___ 27

PART IIFinal isohyetal maps, in 1 sheet , scale i:1,oc)o,oooData and computation sheets:

Form S-IO (Data from mass rainfall curves)----- ___-__ ___ 3Form S-II (Depth-area data from isohyetal map)----------- 2Form S-12 (Maximum depth- duration data)- _ ___-_ _________ 17Maximum duration - depth- area curves--- _ _ -_ _ __ _ _ _ _ _ __ __ 1Data relating to periods of maximum rainfall _____________ 7

MAXlkrIrea i n Sq. ML

IM AVERAGE”0lEPT 01

ratio o fx-Tiz

3024.0

21.7 21.717.8 17.814.4 16.613.3 13.310.6 10.58.4 8.56.6 6.65.5 5.54.4 4.43.0 3.22.7 2.9

PAm

36G21.717.816.413.3N.68.6

;::1: .33.63.3

INi i

f

I

IFALci - x -- rz;21.717.Y1~5.613.310.68.66.45.5

:I:;3.5

IN INCHESH o u r s

Max.Station10

100200500

1,0002,0005,000

30,00023,50050,00063,:~o

618.415.112.811.7

;:;5.94.13.02.11.41.2

1

1223.929.717.115.812.410.16.06.35.24.12.72 .4

L1821r.c)21.717..8lb.613.3lO.!J

::25.44.32.92.4

5

.rn S-2 (A)Figure G-8. Example of summary sheet , “Storm Rainfa l l in the U.S .” ( sheet 1

of 2).-288-D-3184(1/2)


EPARTMENT O F T H E A R M Y

S T O R M S T U D I E S - ISOHYETAL M A PC O R P S O F ENGINEE,

Storm of 1 X 9 SeDtember 1 9 2 6Study &pored by: o,-,

Assignment MR 4-24ah. Nebr, Uistrict

Missour i River Mvishn

S C A L EI

19.000,000Pdyconlc Rojnctio”

Figure G-8. Example of summary sheet, “ S t o r m R a i n f a l l i n t h e U . S . ” ( s h e e t 2of 2).-288-D-3184(2/2)


assumed transposed and the depth-durationvalues for 200 square miles maximized formaximum moisture charge to identify thosestorms that give the greatest values. Anyindividual storm may not yield maximumvalues for all durations. It may be necessary,therefore, to consider a number of storms inthe final analysis.

( 4 ) T r a n s p o s i t i o n o f i s o h y e t a lpatterns. -The isohyetal patterns of the stormswhich yield large values should be obtained,and these patterns then overlaid individually ona map of the subject watershed. The position,within limits, that gives the greatest total basinaverage rainfall depth should be used. Inpositioning a transposed storm isohyetalpattern, the orientation of the observed stormpattern is maintained generally within limits ofplus or minus 20’.

(5) Average watershed precipitation oftransposed storm. -The average storm rainfallwithin the watershed boundaries of eachtransposed storm isohyetal pattern is obtainedby planimetry. The depth of precipitation for agiven area for the total storm was obtainedfrom a DAD tabulation similar to that shownon figure G-8(A). These values were, of course,measured from the isohyetal pattern in theoriginal storm without regard to any watershedboundaries. Obviously, only an assumption of aperfect fit of the transposed isohyetal patternto the basin configuration would give the sametotal basin rainfall for the transposed storm asthat listed in the DAD tables.

(6) Fit-factor. -A fit-factor, Ff, that is, theratio of the watershed average rainfall depth tothe storm pattern rainfall depth, for equalareas, is computed for each transposed storm.The importance of the fit-factor to PMSestimates varies depending on the size, shape,and orientation with respect to major stormpatterns of each individual watershed. In theexample region, watersheds are typically longand narrow with their major axis orientedgenerally east-west, so that a fit-factor in thisregion is quite important, except for extremelylarge gainage basins.

If PO represents the average rainfall depthfor the total observed storm for a given areaand c,. represents the average rainfall depth

measured from the isohyetal pattern of theobserved storm, as transposed, then

ptrFf =p (11)

0

It should be obvious that Ff 51.(7) Total maximization adjustment fat tor,

A df -The total maximization adjustmentfactor, Adf, for a storm, as transposed to awatershed, i s t h e p r o d u c t o f t h e s t o r mmoisture maximization factor, Mf, and thefit-factor, Ff, or,

Adf = (Mf) (Ff) (12)

(8) Design storm values, depth-durationcurve. -The maximized depth-duration valuesfor each storm, as transposed to a watershed,are computed by multiplying the observedstorm depth-duration values by the respectivemaximization adjustment factor, Adf. Thecomputed values for each storm should beplotted with accumulative time in hours as theabscissa versus the accumulative rainfall depthsin inches as the ordinate.

A design storm depth-duration curve isobtained by drawing a smooth curve. Anenveloping curve will give design storm valuesapproaching PMP for a watershed. A curvedrawn through the data for one storm only willgive selected PMS values.

Since the depth-duration curve is ordered insuch a manner as to show only the maximumvalues of rainfall for various durations, thecurve does not indicate a realistic sequence ofrainfall increments which might occur duringthe actual design storm. Incremental designstorm values obtained from the smoothdepth-duration curve should be arranged inrealistic sequence for flood computation.

For storms of long duration (several days),the design storm depth-duration curve may notbe smooth throughout but have two or moreperiods of intense rainfall separated by periodsof little or no rainfall. Such storms arefrequently critical for very large basins orbasins in tropical regions. In these instances,incremental design storm values may be


arranged in any realistic sequence, within thelimitation that the separate periods will not beso combined as to produce a rainfall sequencethat would have exceeded the recommendeddesign storm depth-duration curve at anypoint.

(9) Numerical computations. -Table G-9presents numerical values for proceduresdescribed in the subsections above. Mapsshowing the transposed storm isohyetalpatterns as fitted to the watershed and theplanimetry notes for determination of averagebasin rainfall for each transposed storm are notincluded. A plot of depth-duration values ofthe transposed storms, as maximized, and therecommended depth-duration curve of thedesign storm are shown on figure G-9. In thisinstance, the design storm duration is 17 hoursand rainfall values approach PMP. Theenveloping curve on figure G-9 was drawn“by eye” as adequate for a preliminary PMSestimate. Design storm values read from thecurve at l-hour intervals are listed in table G-10because a flood hydrologist may wish to use al-hour unitgraph to compute an inflow designflood hydrograph for this size watershed.

Service in collaboration with the U.S. ArmyCorps of Engineers [ 201. These 6-hour valuesfor IO-square-mile areas can be modified fordurations in excess of 6 hours and for largerareas up to 1,000 square miles by use of figureG-l 1. No variation is assumed between pointand 1 O-square-mile precipitation. For durationsshorter than 6 hours, the time distribution ofprecipitation can be obtained from curve C,figure G-12. Subsequent to the publication ofHydrometeorological Report No. 33, the Corpsof Engineers have recommended7 that thefollowing adjustment percentages be applied tothe depth-duration values obtained from figureG-l 0 in order to provide for the imperfect fitof the isohyetal patterns of observed storms tothe shape of a particular basin.

Drainage area,square miles

Adjustment factor applicableto H.R. 33 rainfall values,

percent

(b) Generalized Precipitation Charts. -Mapsshowing smoothed isohyets of PMP for theUnited States east of the 10.5’ meridian andPMS values for the United States west of the105O meridian are presented here to provide ameans of quickly obtaining preliminary designstorm values for selected watersheds aboveproposed damsites. It is impossible to show onthe generalized charts all of the refinementsand variations that can influence the magnitudeo f d e s i g n storm values for individualwatersheds. Design storm values obtained fromthe generalized charts represent a reasonableupper limit and, in most instances, will exceedthe values obtained for a specific watershed bya detailed hydrometeorological study, aspreviously discussed.

(2) Generalized chart for the United Stateswest of the 105’ meridian. -Figure G- 13 showsprobable maximum 6-hour point general-typestorm values for areas of the United States westof the 10.5O meridian. This chart is based onthe results of approximately 330 design storma n a l y s e s p r e p a r e d by the Bureau ofReclamation for specific drainage basins westof the lOSo meridian, as well as considerationof numerous design storm analyses made bythe Special Studies and HydrometeorologicalBranches of the National Weather Service.

( 1) Generalized chart for the United Stateseast of the 105O meridian. -Figure G-10 showsprobable maximum 6-hour precipitation valuesfor any area of 10 square miles for the UnitedStates east of the 105’ meridian. This chart isbased on one presented in Hydrometeorologi-cal Report No. 33, prepared by the Hydro-meteorological Section of the National Weather

The variable topography of this part of theUnited, States greatly influences the stormp o t e n t i a l a n d p e r m i t s o n l y l i m i t e dtransposition of storms. These point stormvalues can be applied to areas up to 1,000square miles by use of the curves presented onfigure G-14. The 6-hour general-type stormvalues can be extended for longer durationperiods by multiplying the 6-hour value by the

‘Engineer Circular No. 1110-z-27, dated August 1, 1966,“Policies and Procedures Pertaining to Determination ofSpillway Capacities and Freeboard Allowances for Dams.”


Table G-9.-Example of design storm derivation for area east of 10.5’ meridian

BASIC DATA:Watershed location: 99’3O’W, 41’00’ N

Drainage area: 200 sq. mi.Inflow barrier: 2,500 feet

(A) MAJOR STORMS SELECTED FOR TRANSPOSITION

TApproximate InflowDesignation geographic Date of barrier, stor

No. location-name storm feet OF.’

MR4-24 Boyden, Iowa g/17-19126 1,200 7 0MR4-5 Grant Township, 6/3-4/40 1,200 663

Nebr.MR6-15Rl&l-l4

Stanton, Nebr. 6/10-13/44 1,500 70Greeley, Nebr. 8/12-13/66 2,000 71

’ 1,000 millibars, or mean sea level.‘Average rainfall depth, 200 sq. mi.3Revised value in lieu of 63’F. [21]4Recent storm analysis, preliminary, Bureau of Reclamation, Engineering and Research Center, Denver, Colo.

(B) STORM TRANSPOSITION AND MAXIMIZATION

(Column heading symbols as previously defined in text.)

Reference

Fig. G-8A[211

y1

Observed storm _- Transuosed storms Maximizing factorsStorm Dwpt.,

No. ’ F.Barrier, w

feet p-l I$-2 wsDwpt.,’ Barrier,

5 OF. feetw

r-l wr-3 wx 7;;1 Mf Ff Adf

MR4-24 70 1,200 2.21 0.25 2.02 16.6 76 2,500 3.04 0.62 2.42 12.3 1.20 0.74 0 .89MR4-5 66 1,200 1.86 .22 1.64 11.2 76 2,500 3.04 .62 2.42 9 . 6 1.48 .86 1.27MR6-15 70 1,500 2.27 .31 1.96 14.4 7 6 2,500 3.04 .62 2.42 13.0 1.23 .90 1.11RlO-l-l 71 2,000 2.38 .42 1.96 13.4 77 2,500 3.19 .64 2.55 12.4 1.30 .93 1.21

‘From Climatic Atlas of United States [ 191

(C) MAXIMUM OBSERVED DEPTHS, INCHES

Storm 3 6 9 12

MR4-24 11.7 15.8MR4-5 5.5 9 . 6 11.1 11.2MR6-15 11.1 12.9RlO-l-l 6.7 9.4 12.5 13.1-

‘Storm ended at 54 hrs.*Storm ended at 20 hrs.3Storm ended at 78 hrs., depth = 14.4 in.4Storm ended at 17 hrs.

Duration in hours15 18 24 30 36 48 60 72

16.6 16.6 16.6 16.6 16.6 ll6.611.2 11.2 *Il.2

12.9 12.9 12.9 13.1 14.1 14.3 314.413.2 413.4

(D) MAXIMUM TRANSPOSED DEPTHS, INCHES

‘At 5 4 hrs.*At 2 0 hrs.3Also at 78 hrs.4At 1 7 hrs.

IDF STUDIES-Sec. G-17 4 7 9

4

f

‘2-

4

1

i

T R A N S P O S E D A N D A D J U S T E D S T O R M

W a t e r s h e d D r a i n a g e A r e a : 2 0 0 S q . M i .L o c a t i o n : A p p r a x . L a n g . 99O 3O’W

L a t . 41’ 0 0 ’ N

I . September 17-18, 1926 centered near Bayden, lawa2 . J u n e 3-4,194O c e n t e r e d a t G r a n t T o w n s h i p , Nebr:3 . June 10-13, 1940 centered near Stanton, Nebr:4 . A u g u s t IZ-13,1966 c e n t e r e d n e a r G r e e l e y , Nebr

6 12 I8 24 30 36 42 48T I M E - H O U R S

54 60 66 72 78

Figure G-9. Design storm-depth-duration values.-288-D-3185

480

Table G-lO.-Design storm depth-durationvalues, inches

BASIC DATA: Hypothetical example.Watershed area = 200 sq. mi.Location = approximately 99”30’ W,

41’00’ N

Time, Accumulated Incrementalending at hour depth, inches depth, inches

0 0 04.20 4.206.40 2 .208 .10 1.709 .70 1.60

11.10 1.40

89

10

1 1121 3141 5

16 .0016.1016.15

16 16.201 7 16 .2018 16.20

12.3013.3014.3015.1015.45

15.7015.90

1 .201.001.00

.80

.35

.25

.20.lO.lO.05

.05

8

appropriate factor shown in table G-l 1. Valuesfor duration of less than 6 hours can beobtained from the appropriate curve of figureG-12.

(3) Use of generalized charts. -Design stormvalues for any watershed of a l,OOO-square-milearea or less in the conterminous 48 UnitedStates may be obtained from the generalizedcharts, but it must be noted that such designstorm values should be considered as onlypreliminary estimates for watersheds controlledby large dams. Design storm values obtained


from figures G-l 0 and G-13 show considerabledifference at their common boundary along the105’ meridian. This is due to the techniquesused in determining the values shown on thecharts.

Preliminary design storm values for aparticular watershed obtained from eithergeneralized c h a r t s h o u l d b e p l o t t e d o nc o o r d i n a t e p a p e r a n d a n e n v e l o p i n gdepth-duration curve drawn. Plotting offers amethod of checking the computations, as asmooth curve should be indicated, and alsoprovides the means of obtaining hourly designstorm values for the total storm period ifneeded. Inc remen ta l va lues f rom thedepth-duration curve may be arranged in anysequence desired by a flood hydrologist forcomputation of a preliminary inflow designflood.

The generalization charts for estimatingpreliminary design storm values have beenlimited to an area of 1,000 square milesbecause generalizations of criteria becomemore difficult as the size of the area increases.Preliminary design storm estimates can bemade for areas greater than 1,000 square milesin regions of nonorographic rainfall by theprocedure described in section G-l 7. The stepof determining a fit-factor is omitted. Adepth-duration curve is drawn on the basis ofinformation compiled in a tabulation such astable G-9(D), using the moisture maximizationfactor, Mf, instead of the total adjustmentfactor, Adf, to compute values for the table.Preliminary design storm estimates for largemountainous basins (with predominatelyorographic rainfall) should be obtained from ahydrometeorologist.

F. PRELIMINARY INFLOW DESIGN FLOOD, RAINFALL ONLY

G- 18. General.-This subchapter outlines from runoff curves, section G-7(b)(6); and (3)procedures for estimating preliminary inflow the lag-time dimensionless-graph method ofdesign flood (IDF) hydrographs using: (1) obtaining unitgraphs, section G-9. An exampledesign storm values from the generalized is given of computation of preliminary inflowprecipitation charts, figures G-10 and G-13; (2) design flood hydrographs for a watershed eastan estimation of incremental rainfall excesses of the 10.5’ meridian, with accompanying


Figure G-IO. Probable maximum precipitation (inches) east of the 105’ meridian for an area of 10 squaremiles and 6 hours’ duration.-288-D-3191

discussions directed toward considerationsapplicable to all inflow design flood studies.Procedures applicable to watersheds west oft h e 105’ are outl ined. A discussion ofp r epa r ing recommendations for routingpreliminary inflow design flood hydrographsthrough proposed reservoirs concludes thispresentation.

G 19. Example-Preliminary Inflow DesignFlood Hydrographs, Watersheds East of 105’Meridian. -A hypothetical watershed in a

general location east of the 105’ meridian hasbeen assumed in order to illustrate several oft h e p r o b l e m s e n c o u n t e r e d i n I D Fcomputations, all of which would not likely bepresented by a specifically located watershed.

( a ) B a s i n D e s c r i p t i o n . - A map o f theassumed watershed above a proposed damsite isshown on figure G-15. The center of the basinis assumed to be located in zone 4 somewherea l o n g t h e 30-inch, 6 -hou r PMP fo r1 O-square-mile isohyet, figure G- 10. An outline

482

P E R C E N T 0 ‘ 10 SOUARE M I L E S - 6 - H O U R V A L U E S

P E R C E N T O F 10 S Q U A R E M I L E S - 6 - H O U R V A L U E S

P E R C E N T O F 10 SQUARE M I L E S - 6 - H O U R VA&ES

Figure G-11. Depth-area-duration relationships-percentage to be applied to 10 square miles, 6-hour probablemaximum precipitation values.-288-D-2450

IDF STUDIES-Sec. G-19 4 8 3

.80

.60

0 I 2 3 4 5 6

T I M E I N H O U R S

Figure G-12. Distribution of 6-hour rainfall for area west of 105’ meridian (see fig. G-13 for area included ineach zone).-288-D-2758

of the proposed reservoir surface at normalwater storage capacity is shown, because thelength of natural stream channels to besubmerged influences lag-time calculations. It isassumed that runoff characteristics of the areasdrained by the two main tributaries differenough to warrant consideration of dividingthe watershed into two subareas, A and B, asthere is information available indicating thatsubarea A d e f i n i t e l y h a s r a p i d runoffcharacteristics. All of the area enclosed by thenatural divides contributes runoff.

( 1) Drainage areas are:

Total basin 800 square milesSubarea A 240 square milesSubarea B 560 square milesReservoir surface 26 square miles

As the reservoir surface area is about 3percent of the total basin area in this example,reservoir surface may be considered as landarea, except for lag-time computations.Whenever there is found a reservoir surface areaof about 10 percent or more of totalcontributing drainage area, computationsshould be made separately of the runofforiginating from the land area, to which


Figure G-13. Probable maximum 6-hour point precipitation values in inches for general-type storms west ofthe 105O meridian.-288-D-3192

IDF STUDIES-Sec. G-191.00

485

.96

.60

56

0 100 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 6 0 0 9 0 0 1 0 0 0

A R E A I N S O U A R E M I L E S

Figure G-14. General-type storm-conversion ratio from 6-hour point rainfall to area rainfall for area west of105’meridian.-288-D-2759

Table G-11 .-Constants for extending 6-hourgeneral-type design-storm values west

of 105’ meridian to longer duration periods’

Duration,hours2 Zone A

ConstantsZone B

tZone C

8 1.20 1.18 1.1410 1.39 1.36 1.2612 1.58 1.53 1.3614 1.76 1.66 1.4316 1.93 1.77 1.50

18 2.10 1.87 1.5720 2.26 1.95 1.6422 2.42 2.03 1.7124 2.57 2.10 1.7830 2.95 2.28 1.97

36 3.2642 3.5548 3.7960 4.1472 4.34

2.38 2.152.40 2.252.41 2.28

L

‘Multiply 6-hour point rainfall from figure G-13 by indicatedconstant.2For durations shorter than 6 hours, the time distribution ofstorm values can be obtained from the appropriate curve. ^. -._presented on figure ti-12.

retention losses are applicable to design stormrainfall, and the increased inflow to thereservoir due to design rainfall on the reservoirsurface area where retention losses are zero.There are instances where rain falling onreservoir surfaces supplies the major portion ofinflow. When rain falling on a reservoir surfacemust be considered, rainfall increments ininches are converted to equivalent incrementalflow in cubic feet per second and combinedwith respectively timed increments of inflowfrom the land area. Watersheds in which areservoir will submerge miles of mainstreamchannel, and numerous side tributaries flowdirectly into the reservoir, the watershedshould be divided into at least two subareas,the subarea above the head of the reservoir andthe area directly tributary to the reservoir.Subarea B, figure G 15, approaches thissituation. If a final-type IDF study were madefor the example watershed, a better evaluationof a final-type IDF would be obtained bydividing subarea B into two subbasins and


I. Measure stream length E, to EP; L , miles2. Measure stream length E, to w; Lc,, miles

Note: Do not include “a’; stream lengththat will be submerged.

3. s= Elevation EZ minus elevation EI.L , miles

In the above, x =center of area projected.

Damsites with 2(or more)morkedly differenttributaries require 2(or more) unitgraphs.

F i g u r e G-15. Basin map-example of prel iminary inf low design f loodcomputation.-288-D-3186

deriving a unitgraph for each; the subbasinswould be above and below the head of thereservoir, point E, , figure G- 15.

(2) Streamflow records.-Two assumptionsare made for lag-time illustrating purposes:first, that there are no streamflow recordsavailable for analysis; second, that tributary Bhas been gaged at the mouth near the damsite,and hydrograph analyses have indicated alag-time of 22 hours for subarea B.

(3) Soils and cover.-Use of runoff curvesrequires hydrologic classification of watershedsoils and cover, discussed in section G-7(b)(6),for selection of applicable runoff curvenumber, These classifications are made by fieldinspections, examination of soils maps, etc. Fort h i s e x a m p l e , i t i s a s s u m e d a v a i l a b l einformation indicates:

Subarea A:

Soils, hydrologic group CLand use, mostly poor pastureRunoff curve, AMC-II CN86 (table

G-W))

Subarea B:

Soils, hydrologic group BLand use, mostly small grain, contour

terracedRunoff curve, AMC-II CN70 (table

G-3(A))

(b) Dimensionless-Graph Selection.-Ashydrograph analyses cannot be made in thefirst instance because of lack of streamflowrecords, a dimensionless-graph must be selectedfrom other sources. The dimensionless-graphshown as (C), figure G-6, which was derivedfrom a flood hydrograph in the general regionof the assumed location of the watershed, hasbeen selected as applicable to both subareas ofthe watershed. It is also used in the secondexample, where streamflow records areavailable.

(c) Lug-Times.-A cutout of each subarea,including the respective reservoir portion ineach, was made, the center of area of eachdetermined and projected to the main streamsat the points marked x on the stream channelsas shown on figure G-1 5 (see sec. G-9(2)).Longest watercourse lengths listed below weremeasured from the map. Slope values for thisexample, S in feet per mile, were selected fromgeneral data. In the usual study, elevations forcomputing slope values for a given watershedare obtained from topographic maps.

Subarea A:

L = 29.0 miles from head of reservoirto divide, E, to E, , figure G- 15.

Lc a = 12.7 miles from head of reservoirto center of area projected,

E, to x, figure G 15.S = 23.2 feet per mile (assumed in

this example).


Subarea B: (Assumption of no streamflowrecords.)

487

L = 48.9 miles from head of reservoirto divide, El to E2, figure G-l 5.

L ca = 15.4 miles from head of reservoirto center of area (projected),El to x, figure G-15.

S = 12.6 feet per mile (assumed forthis example).

For use in assumption that streamflowrecords have indicated a lag-time of 22 hoursfor tributary B:

L = 59.8 miles from mouth (gage) todivide.

L,, = 26.3 miles from mouth (gage) tocenter of area, x.

S = 16.5 feet per mile (assumed forthis example).

Two sets of lag-times are estimated for thisexample on the basis of the two assumptionsregarding available streamflow records. Underthe assumption that no streamflow records areavailable, the generalized lag-time equation isconsidered applicable.

LL,, Q.33Lag-time hours = 1.6 __[ 1fl ( S e c . G-8(e)(2).)

Estimated lag-times are:

Subarea A:

LLca-= (29.4X12.7) = 77 5

G- d23.2 ’

Lag-time = 6.7 hours.

Subarea B:

LLca-=(48.9)( 15.4) = 2 1 2 2

a- -,/12.6 *

Under the assumption that hydrographanalyses for streamflow gaged near the mouthof tributary B indicates a lag-time of 22 hoursfor subarea B, the following lag-times areestimated:

Subarea A:

No change, lag-time = 6.7 hours.

Subarea B:

Referring to section G-8(e)(2), if a reliablelag-time for a basin is found by hydrographanalyses at a gaging station, a lag-time for anungaged portion of the basin may beobtained by passing a curve with slope 0.33through the point plotted on log-log paper,LLca -4,

Gversus lag hours. An-value for

csubarea B above the assumed gaging stationis:

(59.W26.3) = 386.7JizF

If the generalized lag-time curve has beenplotted on log-log paper, plot 387 versus thelag-time of 22 hours and draw a line throughthe plotted point parallel to the generalizedlag-time curve. Read a lag-time of 18 hours for

L-hat h e - value of 212 from the constructedn

curve. In this example, the proposed reservoirhas the effect of reducing the lag-time forsubarea B from 22 hours for natural conditionsto 18 hours after the dam is built. The effect ofa proposed reservoir on natural lag-timesshould not be overlooked in the preparation ofinflow design flood hydrographs.

Of course, the lag-time of 18.0 hours canalso be obtained without plotting the curves,by solving the equation,

LL,, o*33Lag-time = C ~[ 3Lag-time = 9.4 hours,


for C, substituting 22 hours for lag-time and-4,

386.7 for -.fi’

this gives C = 3.08. Then, using

LLthis computed value for C, and 2 12.2 for -z,

lag-time in hours equals 18.0.(d) Preliminary Design Storm Values.-A

specific watershed location is identified on thegeneralized charts, figures G-1 0 and G-1 3, bycounty boundaries within the States andreading the zone and 6-hour PMP valuesapplicable to the watershed. A specific locationfor the watershed for this example has notbeen designated other than it is assumed to bein zone 4 where 6-hour probable maximumprecipitation (PMP) for 10 square miles is 30i n c h e s ( f i g u r e G 10). Computation ofpreliminary design storm values are shown intable G-1 2. The design storm is assumed tocover the entire watershed area of 800 squaremiles. Percentages of the 6-hour PMP for 10square miles applicable to 800 square mileswere read from the depth-area-durationrelationships on the chart for zone 4, figureG-1 1, and PMP values for 6, 12, 24, and 48hours for 800 square miles computed. Thesevalues were adjusted to 90 percent of thecomputed values in accordance with the fitadjustment factors given in section G-1 7(b)( 1).Hourly depth-duration values for the maximum6-hour period of the storm were computed bypercentages read from curve C on figure G-1 2.Depth-duration values, line 5 of table G-12,were plotted and a preliminary design stormdepth-duration curve drawn as shown on figureG-16.

(e) Arrangement of Design Storm RainfallIncrements and Computation of Increments ofRainfall Excess. -Arrangement of incrementsof rainfall of a preliminary design stormestimated from figure G-10 is illustrated intable G-1 3, along with the computation ofrespective increments of excess rainfall.Computation of table G-1 3 is explained in thefollowing paragraphs. General comments ondesign storm arrangements are included.

(1) Selection of design storm unit timeinterval . -Design storm increments andrespective rainfall excesses obtained therefrommust be for the same unit time interval as theunitgraph to which the excesses will be appliedto compute an inflow design flood (IDF)hydrograph. Unit time of a unitgraph is relatedto the lag-time of a basin, being one-fourth orless of the lag-time (sec. G-9(6)). In thisexample, a l-hour unitgraph is required forsubarea A because a lag-time of 6.7 hours hasbeen estimated for that subarea. A 2-hourunitgraph could be used for subarea B, lag-time9 . 4 h o u r s . H o w e v e r , t h e c o m p u t e dhydrographs for the two subareas must becombined to give the preliminary inflow designflood hydrograph. A better definition of theIDF hydrograph will be obtained if theunitgraphs for the two subareas have the sameunit time interval. A l-hour unitgraph for eachsubarea was used in this example. Hourlyvalues of preliminary design storm rainfall wereread to the nearest tenth inch from thedepth-duration curve, figure G-16, from 1 to24 hours and tabulated in column 2 of tableG 13. Hourly increments of rainfall are listed incolumn 3 of table G- 13.

Table G-12.-Preliminary design storm estimate for hypothetical watershed, east of IO5O meridian

BASIC DATA:Location: HypotheticalReference: Figure G-10, zone 4, 6-hr. PMP’, 10 sq. mi.: 30 inchesAreas: Total basin, 800 sq. mi.; subarea A, 240 sq. mi.; subarea B, 560 sq. mi.

--.-Time in hours

I tem 1 2 3 4 5 6 1 2 24 48 Text reference____-

1 . Percent of 6-hr. PMP’ for 800 mi.sq. 62 70 77 87 Fig. G-l 12 . Computed PMP, 800 mi., inchessq. 18.6 21.0 23.1 26.13 . PMP, adjusted to 90 percent 16.7 18.9 20.8 23.5 Sec.G-17(b)(l)4. Ratios to 6-hr. rainfall 0.49 0.64 0.75 0.85 0.93 1.00 Fig. G-12, zone C5. Design PMP, 800 mi., inchessq. 8.2 I 10.7 12.5 14.2 15.5 16.7 18.9 20.8 23.5 Fig.G-16

‘PMP = probable maximum precipitation.


HYPOTHETICAL WATE A S T O F 105’= MEI8 0 0 SQ. M I L E S

.ERSHED?IDIAN

3 6 9 12 I5 I8 21 2 4 2 7 3 0 3 3 3 6 3 9 4 2T I M E - H O U R S

Figure G-16. Preliminary design storm-depth-duration curve.-288-D-3187

5 i n c h e d

( 2 ) A r r a n g e m e n t o f d e s i g n s t o r mi n c r e m e n t a l r a i n f a l l . -Norma l ly , t hearrangement with respect to time of incrementsof design storm rainfall is not established in adesign storm study (sec. G-1 7(a)(8)). Floodhydrologists arrange design storm incrementsto give rainfall excesses that produce the mostcritical inflow design flood hydrograph. Exceptfor basins having several thousands of squaremiles of drainage area, design storm rainfall isassumed to occur with the same time sequenceover the total watershed area. If a constantretention loss rate is used to compute rainfallexcesses, a critical arrangement may be easilyfound by arranging design storm incrementsopposite the ordinates of the unitgraph for thebasin, so that the largest rainfall increment(which would give the largest excess increment)

is opposite the largest ordinate; and thesecond largest rainfall increment is opposite thesecond largest ordinate, etc.

This arrangement is then reversed to give thedesign storm arrangement in correct timesequence, because rainfall excesses are reversedin sequence of natural occurrence when beingapplied to unitgraph ordinates by calculators.Otherwise, much additional work must bedone: (1) computing discharges for eachordinate of the unitgraph for each excessincrement; (2) tabulating the individualdischarges in correct time sequence; and (3)add ing respectively timed incrementaldischarges to get the total flood hydrograph. Ifa retention loss rate which varies with time isused, a critical design storm arrangement isfound by trial.

4 9 0 D E S I G N O F G R A V I T Y D A M S

Table G-13.-Preliminary design storm east of 105’ meridian-arrangement of incremental rainfall;computation of incremental excesses, AP,, for subareas A and B

BASIC DATA:Total area (for design storm estimate)-800 sq. mi.

Subarea size and retention data:

1Time,ending

Subarea A: 240 sq. mi.; CN 86, selected minimum loss rate, 0.12 in./hr.Subarea B: 560 sq. mi.; CN 70, selected minimum loss rate, 0.24 in./hr.

I- - ---.

6 7 8 9 10 1 1T__2_I1_Design rainrrdepthdu.ration=, AP,

inches inches

i4 I5

Arrangement ofdesignAP,

ra

inches

infallx:p,

Inches

Rainfall e:xc’ esses, P,

LlY p,,inches

.rbareaApe,

inchesA loss,inches

3X p,,inches

A loss,inches

1 8.2 8.2 1.2 1.22 10.7 2.5 1.7 2.93 12.5 1.8 1.8 4 . 74 14.2 1.7 8 . 2 12.95 15.5 1.3 2.5 15.46 16.7 1.2 1.3 16.7

I 17.48 17.99 18.2

10 18.51 1 18.71 2 18.9

17.4 15.27 .5817.9 15.65 .3818.2 15.83 .1818.5 16.01 .I818.7 16.09 .0818.9 16.17 .08

1 3 19.11 4 19.31 5 19.51 6 19.61 7 19.81 8 2 0 . 0

.I

.5

.3.3.2.2

.2

.2

.2

.1

.2

.2

.l

.l

.2

.2

.l

.l

.7

.5

.3.3.2.2

.2

.2.2.l.2.2

.I

.l

.2

.2

.l

.l- -

19.1 16.25 .0819.3 16.33 .0819.5 16.41 .0819.6 16.41 019.8 16.49 .082 0 . 0 16.57 .08

19 20.120 20.22 1 2 0 . 422 20.623 20.724 ’ 20.8

20.12 0 . 220.420.620.72 0 . 8

0 .30 0 .30 0 .90 0 .02 0 .02 1.181.57 1.27 .43 .66 .64 1.063.18 1.61 .19 1.82 1.16 .64

11.13 7.95 .25 8 .884.12

1 .06 1.1413.51 2.38 11.14 2 .26 ‘.2414.69 1.18 .12 12.20 1.06 .24

.12

.12

.12

.12

.12

.12

.12

.12JO.12.12.12

12.66 .46 .2412.92 .26 .2412.98 .06 .2413.04 .06 .2413.04 0 .24

6 6

‘Balance of design rainfall considered lost to retention.

2By equation x Pe = $T I$;’ for CN 86, S = 1.63; 0.2s = 0.33,0.8S = 1.30 (table G-4).

3By above equation, for CN 70, S = 4.28; 0.2s = 0.86,0.8S = 3.42 (table G-4).4APe by CN 86 indicates A loss = 0.03 in., which is less than 0.12 in. Use 0.12 in. loss/hr.‘AP, by CN 70 indicates A loss = 0.15 in., which is less than 0.24 in. Use 0.24 in. loss/hr.6Total of remaining excess not significant for preliminary IDF.

A definite arrangement of design storm of rainfall increments in column 4, table G-1 3.increments has been specified for preliminary The maximum 6-hour period of design rainfalldesign storm values obtained from each is assumed to occur during the first 6-hourgeneralized precipitation chart, figures G-l 0 p e r i o d o f t h e d e s i g n s t o r m . H o u r l yand G-13, because the selected general method precipitation amounts within the maximumof computing rainfall excesses using rainfall 6-hour period are arranged in the followingrunoff curves has “built-in” varying retention order of magnitude: 6, 4, 3, 1, 2, 5. Incrementsloss rates. The arrangement specified for of design storm rainfall after the sixth hourpreliminary design storm values east of the105O meridian is illustrated by the arrangement

decrease and are taken directly from the designstorm depth-duration curve.


(3) Computation of increments of rainfallexcess. -The method of estimating excessrainfall increments given in section G-7(b)(6)h a s b e e n t a k e n f r o m t h e S C S N a t i o n a lEngineering Handbook [3] with the followingmodifications introduced to give a procedureapplicable to preliminary design storm rainfallobtained from generalized precipitation charts.

The rainfall-runoff relationships shown bythe curves of figure G-2 were developed by SoilConservation Service hydrologists fromanalyses of rainfall and respective runoffrecords at numerous small area experimentalwatersheds. The relationships were developedfor use with daily nonrecording rainfall data,which are more plentiful in the United Statesthan are recording rainfall data. Data used inthe development are totals for one or morestorms occurring in a calendar day and nothingis known about their time distributions. Therelationships developed, therefore, excludetime as an explicit variable which means thatrainfall intensity is ignored.

Strict adherence to use of the runoff curveson f igu re G-2 r e s u l t s i n h o u r l y r u n o f finc remen t s a l m o s t e q u a l t o h o u r l yprecipitation increments after a few hours formany of the design storm values obtained fromgeneralized precipitation charts. Infiltrometerstudies indicate that all but impervious claysoils have minimum constant infiltration ratesafter saturation that may range from 0.05 inchper hour to greater than 1.00 inch per hour,depending on the type of soil. Therefore, toutilize the rainfall-runoff relationships in thecomputational procedures given in this text,time-sequences of incremental rainfall for adesign storm are specified and precipitationexcesses are then computed using the runoffcurve relationships, with the provision thathourly retention rates indicated by use of therunoff curves be tabulated for each hourlyrainfall increment. Progressively through thearranged precipitation sequence, these hourlyretention rates are compared wi th thetabulated minimum retention rates assigned tothe four hydrologic soil groups (see tableG-1 4). When the retention rate given by use ofa runoff curve becomes less than an assignedminimum retention rate, the minimum rate is

491

used to’ compute excesses thereafter for theremainder of the storm.

F o r t h i s e x a m p l e , d e t e r m i n a t i o n o fapplicable runoff curve numbers, AMC-II, forsubareas A and B has been assumed asdescribed earlier in section G-1 9(a)(3) on soilsand cover. East of the 105’ meridian, soilmoisture within a watershed which has similart o a v e r a g e c o n d i t i o n s p r e s e n t b e f o r eoccurrence of the maximum annual flood(AMC-II) is considered a reasonable assumptionfor occurrence of a design storm. Therefore,the curve numbers referred to above wereobtained from table G-3(A), which lists curvenumbers for AMC-II; CN 86 was selected forsubarea A and CN 70 for subarea B, tocompute rainfall excesses. Minimum retentionrates selected are those for general cases, tableG-14: 0.12 inch per hour for subarea A,hydrologic soil group C; and 0.24 inch per hourfor subarea B, hydrologic soil group B.

Computations of rainfall excesses are made tohundredths of an inch, as shown in table G- 13.Runoff curves, figure G-2, cannot be accuratelyread to hundredths unless plotted to a largescale, so it is recommended that rainfallexcesses be computed by the equation shownon figure G-2. The symbol P, is used in thistext to designate direct runoff values, rainfallexcesses, in lieu of Q shown on figure G-2.Values of S and 0.2s in inches for each curvenumber are listed in table G-4. Referring totable G-13, computations of hourly rainfallexcesses for subarea A are described. Thisprocedure applies to all such computations.

(1) Obtain S and 0.2s values fromtable G-4 for CN 86. Compute O.&S value.

(2) Fill in column 5, CP, by summingthe arranged design storm increments.

Table G-14.-Minimum retention rates forhydrologic soil groups

RecommendedHydrologic Range of minimum rate for use insoil group retention rates, general case,

inches per hour inches per hour

A 0.30-0.45 0.40B 0.15-0.30 0.24C 0.08-0.15 0.12D 0.02-0.08 0.04


unitgraph for a watershed have been given insection G-9(7). The principle of obtaining at o t a l f 1 o o d hydrograph resulting fromsuccessive increments of excess rainfall isillustrated on figure G-3. Therefore, detailedtables showing computation of unitgraphs forsubareas A and B and the application ofrespective sets of rainfall excesses to respectiveunitgraphs are omitted. In lieu thereof, copiesof the printouts from the Bureau’s AutomaticData Processing (ADP) program for applicationof the dimensionless-graph lag-time method ofcomputing flood hydrographs are included astables G 1.5 and G- 16. Table G-l 5 is as i m u l a t e d p r i n t o u t o f t h e c o m p u t e dpreliminary design flood contribution fromsubarea A resulting from the incrementalrainfall excesses listed in column 7 of tableG-13. The program is designed to computedischarges to the nearest cubic foot per second(c.f.s.) so the ordinates of the l-hour unitgraphfor a lag-time of 6.7 hours, listed in the thirdcolumn of table G-1 5, are more exact thanwarranted by the basic data. (The samecomment applies also to the computed floodhydrograph discharges.) Table G- 16 is a similarprintout for subarea B.

( 1) Preliminary inflow design floodhydrograph using generalized lag-time curve forboth subareas. -Design flood contributions foreach subarea are tabulated, combined, andtotal preliminary IDF discharges listed in tableG-1 7. Subarea hydrographs and the totalhydrograph are shown on figure G- 17. (In usualpractice, only the total flood hydrograph isplotted.) A base flow has not been added tocomputed flood discharges, because base flowdischarges are insignificant in relation to thecomputed flood discharges in this example. Amethod of obtaining the volume of the IDFhydrograph is detailed in table G- 17.

(2) Preliminary inflow design floodh ydrograph, watershed not divided intosubareas. -Under the assumption t h a t n ostreamflow records are available within thewatershed and that the same dimensionless-graph, lag-time curve, and preliminary designstorm values are to be used for both subareas, apreliminary inflow design flood hydrographmay be computed using one unitgraph for the

(3) To obtain column 6, begin with thefirst CP value that exceeds the applicable0.2s value and, successively by hours,compute I;P, by the equation:

xp = cp - o.w2e (P+O.8S)

(13)

Each successive CP value in column 5 oftable G-1 3 becomes the P for theequation, and the values of 0.2s and 0.8sare those obtained as in (1) above.

(4) Determine increment of excessrain, AP, for each hour, and tabulate inc o l u m n 7 , t h e n s u b s t r a c t AP, f r o mrespective AP, column 4, and enter a lossvalue thus obtained in column 8.

(5) As successively computed, comparen loss value with assigned minimumretention rate: 0.12 inch per hour forsubarea A. If loss is greater than 0.12 inchper hour, proceed to next hour and repeatprocedure; if loss is less than 0.12 inch, donot use the computed AP, value. Drop useof runoff equation and use the constanthourly loss rate of 0.12 inch per hour tocompute that hour’s excess and the rest ofthe hourly increments of excess rainfall.This change occurred at hour 5 in theexample in table G 13.

The hourly increments of excess rainfalllisted in column 7 will be applied to a l-hourunitgraph for subarea A.

I n a l l c a s e s w h e n t h e g e n e r a l i z e dprecipitation charts are used to estimatep r e l i m i n a r y d e s i g n s t o r m v a l u e s f o r awatershed, hourly increments of excess rainfallshould be obtained by the above procedure. Ifa 2-, 3-, or 4-hour unitgraph is to be used forthe watershed, the computed hourly rainfallexcesses are grouped into respective 2-, 3-, or4-hour s u m s a n d a p p l i e d t o t h e c h o s e nunitgraph.

(f) Computation of Preliminary InflowDesign Flood Hydrographs. -Computation ofan inflow design flood (IDF) hydrograph is aroutine mathematical process after decisionsa r e m a d e r e g a r d i n g s e l e c t i o n o fdimensionless-graph, lag-time, retention rate,and design storm values and arrangement.Procedural steps for obtaining a synthetic


Table G-l 5 .-Simulated automatic data processing Table G- 16. -Simulated automatic data processingprintout-pre l iminary inf low design f lood (IDF) pr intout-pre l iminary inflow design flood (IDF)

contribution, subarea A contribution, subarea B

,000,300

1.270I.6107.9502.380

1.100,580.Bo,180,180

,080,080.oao,080,080

,000,080.o@l,000,000

,000,000,000,000,000

,000,000,000,000,000

,000,000,000,000,000

,000,000.OOO,000,000

,000,000.ooo.ooo,000

,000,000,000,000.ooo.ooo

17i,2474988

1288720571

0

5::336,

1359140900

.oo1.002.003.004.005.00

2313,2043,15042107877795

96644l&151826858510668829163,

6.007.000.009.00

10.00

6238 242607 11.005107 192229 12.004217 150359 13.003575 121417 14.002980 99867 15.00

2502 83365 16.002140 70906 17.001900 60650 18.001575 52146 19.00,305 45261 20.00

,082897743616510

21.0022.0023.0024.0025.00

423 16123 26.0035, 13290 27.0029, 11018 28.0024, 9144 29.00200 7602 3l.00

1651371149 47 8

655 44 43 73,

2 521171 412

IO

Y6

:

63245255436336313020

25012074,719,425118,

979811672557462

3833172632,s181150

31.0032.0033.0034.0035.00

X.0037.0038.0039.0040.00

4, .oo42.0043.0044.0045.00

46.0047.0048.0049.0050.00

5, .oo52.0053.OQ54.0055.00

56.0057.0058.0059.0060.00

61 .oo62.0063.0064.0065.00

66.0067.00

H"0R0w.AP"CFS

HOURS EXCESSESI N C H E S

:E 14:,640 842

1.160 28247.060 75582.260 16840

1.060,460,260,060,060

,000,000,000,000,000

.ooo,000,000,000.ooo

,000,000.ooo,000,000

.ooo,000,000,000.ooo

.ooo,000,000.ooo.ooo

.ooo,000,000,000,000

,000,000,000,000.ooo

,000,000,000

2:

,000,000,000,000,000

,000,000,000,000,000

,000,000,000,000,000

,000,000

268303561838938

:z

25421 45944219932 46768715560 42402012603 35643710754 2903409518 2328738093 1887506930 1572756232 1346145464 114743

4806 9M794229 865983721 759603558 667503103 5889,2707 521222362 478102060 424851797 374201568 32799

,368 28697,193 25054,041 21874908 ,908,792 16645

69, 14520603 12667526 11050459 9639400 8408

349 7335304 b399266 5582232 4869202 4247

176154134117102

89:::;46‘3ii2 32 0

;:1 3

;:,

HYoROGRnPHCFS

0

IO,'757392,

14710

4207298,X19414,304039404552

37053232282024602146

,872,633,424,242,084

945825719628547

478417363317277

24,210

494

Time,endingat hour


Table G-l I.-Preliminary inflow design flood hydrograph, east of 109meridian-same lag-time curve for both subareas

--I- -T- TDis larges, 1,000 c.fSubarea Subarea

A B

2.

Prelim .I D F

Time,endingat hour

DiSubarea

A

SC1 :.f.iarges, 1,000 (Subarea

B

s .Prelim.

I D F

0.00.05.6

3.413.64 0 . 9

0.0. O.l.8

3.914.7

0 . 0.l.I

4.217.555.6

23336394245

4.42.51.4.8.5

21.914.5

9 . 66.44.2

9 6 . 6184.5268.6306.7291 .6

138.7282.6462.7610.7696 .2

4851545160

.3

.23.1

<.l

2.81.91.2.8.5

242.6192.2150.4121.4

9 9 . 9

702.0659 .9574.4477.8390 .2

6366

.4

.2

0 26.31 17.02 11.03 1.24 4.75

3.16 42.1 2.17 98.1 1.38 194.1 .89 304.0 .5

10 404.6.4

1 1 459.4 .212 467.713 424.014 356.4 Computation of IDF volume:1 5 290 .3 Sum, discharges, O-29 hrs. 6,977,200

% discharge, hr. 30 20,2001 6 232 .9 Volume. O-30 hrs. 6,997,400 c.f.s.-hrs.17 188.81 8 157.3 % discharge, hr. 30 20,20019 134.6 Sum, discharges, 33-63 hrs. 74.40020 114.7 % discharge, hr. 66 ‘100

Sum 94,70021 9 8 . 5 Volume, 30-66 hrs.,22 86.6 (3 times 94,700) 284,100 c.f.s.-hrs.23 76.024 66.8 Total IDF volume25 5 8 . 9 Equivalent to

Equivalent to26 52.1 For a check, compare with the sum of volumes in27 47.8 tables G-15 and G-16, or 601,600 ac.-ft.28 42.529 31.430 32.8

‘Instantaneous at designated hour.2Larger time intervals may be used for lower portions of hydrograph recessions.31f needed, discharges “cut off’ to shorten computations (see table G-15) may be extended using the hydrograph’s recessioncoefficient.

83.41 0 . 960.752.145.3

316.3259 .7218.0186.7160.0

39.934.429.124.019.7

138.4121.0105.1

9 0 . 878.6

7,281,500 c.f.s.-hrs.303,400 c.f.s.-24 hrs.600,800 ac.-ft.

16.113.311.0

9.17.6

68.261.153.546.540.4

total watershed area. Estimating a total basinlag-time by weighting subarea lag-timeproportional to the areas of 240 and 560square miles gives a lag-time of 8.6 hours. Aweighted runoff curve number, CN 7.5, andweighted minimum retention rate, 0.20 inchper hour, are obtained as shown in table G-l 8.The calculations are shown because thismethod of weighting curve numbers is used toobtain a weighted CN for a basin (or subbasin)which contains various areas of different soiland cover complexes. Table G-l 8 shows thecomputation of incremental rainfall excesses

which were applied to a l-hour unitgraph forthe watershed, lag-time 8.6 hours, area 800square miles. Ordinates of the computedpreliminary IDF hydrograph, peak discharge768,600 c.f.s., volume 597,700 acre-feet, areplotted on figure G-17.

Either of the preliminary IDF hydrographsshown on figure G-1 7 could be recommendedfor use for preliminary designs. Under theassumptions m a d e f o r c o m p u t i n g t h e s ehydrographs, an acceptable result is obtainedby considering the basin as a whole or bydividing the basin into two subareas.


7 5 0

700

6 5 0

6 0 0

@ I D F C o n t r i b u t i o n f r o m suboreo A 2 4 0 s q . m i . P e o k 3 0 6 , 7 0 0 c . f . s .

0 2 I O F C o n t r i b u t i o n f r o m s u b a r e a B 5 6 0 sq. mi. P e o k 4 6 7 , 7 0 0 c . f . s .

Inflow d e s i g n f l o o d , 8 0 0 s q . m i . P e o k 7 0 2 , 0 0 0 c . f . s .

V o l u m e 6 0 0 , 0 0 0 ac,-ft.

i n f l o w d e s i g n f l o o d o r d i n a t e s , 8 0 0 s q . m i . , w a t e r s h e dn o t d i v i d e d i n t o s u b a r e a s P e a k 7 6 8 , 6 0 0 c.f.s.

V o l u m e 5 9 7 , 7 0 0 0c:ft

5 5 0

5 0 0 I

5 0 1. I I,

0 ’0 3 6 9

E A S T O F 105’ M E R I D I A NS A M E L A G - T I M E C U R V EF O R A L L U N I T G R A P H S

t

s4s 51 5 4 57 (

T I M E - H O U R S

Figure G-l 7. Example of preliminary inflow design flood hydrographs-same lag-time curve for allunitgraphs.-288-D-3188

(3) Preliminary inflow design floodhydrograph using a different lag-time curve foreach subarea. -As lag-time differences betweensubarea drainage sys terns within a basinincrease, added consideration needs to be givento dividing the basin into subareas andobtaining the design flood contribution fromeach subarea for combination to form theinflow design flood. This is demonstrated bythe hydrographs shown on figure G-l 8. Usingthe assumption given in section G-19(a)(2) thattributary B had streamflow records giving alag-time of 22.0 hours from which a lag-time of18.0 hours is obtained for subarea B for inflowto the proposed reservoir (sec. G-19(c)), a

l-hour unitgraph for subarea B was computed.The design flood contribution from subarea Ashown on figure G-l 7 @ is not changed and isreplotted on figure G-l 8 0 .

The increment of rainfall excesses forsubarea B, table G-1 3, column 10, applied tothe new unitgraph for subarea B gives the floodc o n t r i b u t i o n s h o w n o n f i g u r eG-18 @ . Combining the hydrographs fromthe two subareas, table G- 19, gives apreliminary inflow design flood hydrograph,figure G-18 @ ) having two peaks, themaximum of which is a peak discharge of332,500 c.f.s. (as estimated when plotting thegraphs) and a 72-hour volume of 597,000

0


Table G-M-Preliminary inflow design flood, east of 105’ meridian-computation ofincremental excesses, n P,, considering basin as a whole, and

using an areal weighted CN and minimum loss rate.

BASIC DATA:Subarea A: AMC-II CN 86; min. loss, 0.12 in./hr.; area, 240 sq. mi.Subarea B: AMC-II CN 70; min. loss. 0.24 in./hr.: area. 560 sa. mi.

WEIGHTED VALUES FOR USE: ’ ’ ’(86)(240) + (70)(560) = 74 8. use AMC-II CN 75

800 . ,

(0.12)(240) + (0.24)(560) = o,204. use o 2. in.,hr800 , .

Time,endingat hour

1.2 1.2 0 .07 0 .071.7 2.9 .89 .821.8 4.7 2.21 1.328.2 12.9 9.61 7.40

5 2.5 15.4 11.91 2 .306 1.3 16.7 13.01 1.107 .7 17.4 13.51 .508 .5 17.9 13.81 .30

910

.3 18.2

.3 18.5

.2 18.7

.2 18.9

13.9114.0114.01

.lO

.lO01 1

12

AP,’ CP, EP,Y3 apet -inches inches inches inches

T-

Rainfall excesses, 1

n loss,inches

1.13.88.48.80

4.20.20.20.20

.20.?O.20

‘Arranged design rainfall, see column 4, table G-l 3.2Balance of rainfall less than retention loss in this approach.

3By equation, P, = (i: ~$2, for CN 75,s = 3.33, 0.2s = 0.67,0.8S = 2.66 (table G-4).

4aPe by equation indicates n loss of 0.10 in., less than 0.20 in.; use 0.20 in./hr.

acre-feet. Ordinates of a flood hydrographcomputed using a l-hour unitgraph having abasin weighted lag-time of 14.6 hours andincremental rainfall excesses listed in tableG-1 8 are shown as @ on figure G-l 8. Thisflood hydrograph has a peak of 492,000 c.f.s.,excessively high in comparison with the floodhydrograph obtained by combining the twosubarea flood hydrographs. The procedure ofconsidering the watershed as a whole does notgive an acceptable preliminary IDF hydrographin this instance.

G-20. Preliminary Inflow Design FloodEst imates , Watersheds West of IO5OMeridian. -It is very likely that runoff fromsnowmelt will contribute a portion of thedischarges of an inflow design flood (IDF)hydrograph for large dams at sites west of the105’ meridian. In many instances though,

design rainstorm potential is so great thatrunoff from a design rainstorm gives the majorportion of an inflow design flood. Preliminaryinflow design flood estimates for many areaswest of the 105O meridian can be made usingpreliminary design storm values obtained fromfigure G-1 3 and associated procedures, themethods of arranging design storm incrementalrainfall and computing rainfall excesses given inthis section, and adding appropriate base flowsto the computed rain flood hydrograph. Ingeneral, for western mountainous watershedshaving seasonal snowmelt runoff which reachesa maximum after mid-May, base flows foraddition to the hydrograph computed from apreliminary design rainstorm may be estimatedas those discharges likely to occur during thelast 5 days of the maximum 15-day period of a1 percent chance maximum annual 15-day

IDF STUDI ES-Sec. G-20500

..

497

IEXPLANATION

I D F Contrlbutmn f r o m suboreo A, 240 sq ml P e a k 306,700 c f s

IDF Contrlbutlon f rom subarea B. 560 sq mi . Peak 266.800 cf.s

Prellmlnary Inflow design f l o o d 8 0 0 sq m i P e a k 332.500 c.f.s.( f rom plottlnq)Volume 0-n hrs ,5 9 7 . 0 0 0 ac.-ft.

Ordinates, f lood computed by not divldlng8 0 0 sq. ml. Into subareas.Hydrograph not acceptable 05

Peak 49z.oooc f sVolume o-72 hrs

a prelimanary IDF. 5 9 5 . 0 0 0 ac-ft

0

t+ I t

i’+L i i i i i i / / / i I ) / I

0

Figure G-18. Example of preliminary inflow design flood hydrograph-different lag-time curve for eachsubarea.-288-D-3189

seasonal snowmelt runoff flood. (See sets.G-28 and G-29 for a discussion of statisticalanalyses-frequency studies.) However, thisgeneral approach cannot be used formountainous watersheds where maximumstorm potential occurs during the wintermonths October through April. Examples are:Sierra Nevada Mountains in California andNevada, Cascade Range in Oregon andWashington, and Mogollon Rim in Arizona.Extreme floods on streams in these regionsresult from rain falling on snow-coveredwatersheds. Estimation of rain-on-snow floodsrequires special procedures as discussed insections G-22 through G-26. Exception also

must include those watersheds having a largepercentage of total basin drainage area atrelatively low elevations where the ground maybe frozen and winter rain falling on a lightsnow cover can cause large floods.

Procedures for estimating the rain-floodportion of a preliminary inflow design floodhydrograph from preliminary general-typedesign storm values for a watershed west of the105O meridian differ in two respects from theprocedures wh ich have been g iven fo rwatersheds east of the 105O meridian; namely,a r rangement o f d e s i g n storm rainfallincrements, and assignment of appropriaterunoff curve number, CN.


T Discharaes. .ooo c.f.s.’ Tending Subareaat hour 2A

0 0.001 .052 .63 3.44 13.65 4 0 . 9

0.02:

:1.5

1.3

0.0.l.6

3.514.14 2 . 2

6 9 6 . 6 3.2I 184.5 6 . 98 268 .6 13.19 306.7 23.5

1 0 291.6 39.5

1 1 242 .6 6 2 . 812 192 .2 94.113 150.4 129.114 121 .4 165.31 5 9 9 . 9 200 .7

9 9 . 8191.4281 .1330 .2331 1L

305.4286 .3279.5286 .7300.6

16 8 3 . 4 231 .0 314.41 7 7 0 . 9 252 .5 323 .41 8 60.7 263 .5 324 .219 52.1 266 .8 318.92 0 4 5 . 3 260.5 305.8

2 1 39.9 244 .4 284 .322 34.4 224 .4 258 .823 29.1 200 .8 229 .924 2 4 . 0 177.5 201.525 19.7 156.4 176.1

26 16.1 137.6 153.721 13.3 120.8 134.128 11.0 105.9 116.92 9 9.1 9 4 . 9 104.03 0 7.6 8 6 . 0 9 3 . 6

.

Table G-19.~Preliminary inflow design flood hydrograph, east of IO.?meridian-different lag-time curve for each subarea

Prelim.I D F

TTime,endingat hour

D :harges 1,000 c s.Subarea Subarea Prelim.

A B I D F

33 4 . 4 6 7 . 6 7 2 . 036 2.5 5 3 . 2 55.139 1.4 4 3 . 2 4 4 . 64 2 .8 35.2 36.045 .5 28.7 29.2

4 85 15 4576 0

.3

.2

<::

24.820.316.413.210.6

25.120.516.513.210.6

8.563666972

8.56 . 85.54 . 4

*

6.85.54 . 4

*Continuing discharges may be computed at 3-hour intervalsusing recession coefficient of 0.8031. Volume after hour 72:

Vol. = -4loge k3

-4 400vo’. = -0.21928

Vol. = 20,060 c.f.s.-3 hrs.2,508 c.f.s.-24 hrs.4,970 ac.-ft.

Vol. (O-72 hrs.), 301,050 c.f.s.-hrs.597,100 ac.-ft.

‘Instantaneous at designated hour.2Same discharges as for subarea A, table G-17.31-hr. unitgraph, lag-time 18.0 hrs., used to compute discharges. Excesses column 10, table G-13.

(a) Preliminary Design Storm Values,Watersheds West of lOSo Meridian. -Bygeographical location (county) obtain probablemaximum 6-hour point rainfall value fromfigure G- 13. Note zone designation, A, B, or C,in which watershed is located.

( 1) Compute 6-hour basin rainfall bymultiplying 6-hour point rainfall by ratioobtained from applicable zone curve, figureG 14, for watershed drainage area, squaremiles.

(2) Make a tabulation of design stormdepth-duration values at l-hour intervals for adesign storm duration extending to the hour

beyond which hourly rainfall increments areequal to or less than the minimum hourlyretention loss rate for the watershed. Hourlydistribution of maximum 6-hour rainfall isobtained from the applicable curve of figureG-1 2. Design storm values beyond 6 hours arecomputed at 2-hour intervals by appropriateconstants listed in table G-l 1. From 6 to 24hours, use average of even-numbered 2-houraccumulative rainfall for the interveningo d d - n u m b e r e d h o u r . If hourly rainfallincrements are needed after 24 hours, drawdepth-duration curve for rainfall amountscomputed by constants in table G-l 1 and read


hourly values. Compute depth-duration rainfallvalues to nearest hundredth of inch.

(b ) Ar rangement o f D e s i g n S t o r mIncrements of Rainfall. -Beginning with thesecond largest 6-hour design storm rainfallamount, hours 6-12 of depth-duration values,arrange hourly increments of design rainfall inascending order of magnitude for the first 6hours of arranged design storm values. Forhours 7 through 12, arrange hourly incrementsof maximum 6-hour rainfall in the followingorder of magnitude: 6, 4, 3, 1, 2, 5. Hourlyrainfall amounts after the 12th hour arearranged in descending order of magnitude.

(c) Assignment of Runoff Curve Number,CN, and Computation of Increments of ExcessRainfall. -Watershed soils, cover and land usedata are used to estimate an applicable runoffcurve number from the information given insect ion G-7(b)(6). T h e e s t i m a t e d c u r v enumber, CN, is for antecedent moisturecondition II, AMC-II. This number is thencoverted to the respective AMC-III CN listed intable G-4 and the AMC-III CN used tocompute hourly rainfall excesses by themethod illustrated in table G-13. Antecedentmoisture cond i t i on I I I i s a s sumed fo rwatersheds west of the 105O meridian, becauselate May and June design storm potential islikely to be concurrent with, or immediatelyafter, snowmelt runoff while watershed soilmoisture is high.

If a unit time period longer than 1 hour isused for obtaining a unitgraph, the two largestincrements of rainfall excesses should begrouped together. If such grouping of hourlyexcesses results in only 1 hourly excessinc r emen t i n a un i t t ime pe r iod a t t hebeginning and/or end of excess rainfall period,the l-hour increment of excess is assumed astotal excess for the unit time period.

499

(d) Floods From Design ThunderstormR a i n f a l l . - D a t a f o r e s t i m a t i n g d e s i g nthunderstorm rainfall have not been includedin this text. If an estimate of a preliminaryinflow design flood (IDF) caused by designthunderstorm rainfall is required, preliminarydesign thunderstorm rainfall estimates forwatersheds west of the 105O meridian may beo b t a i n e d f r o m g e n e r a l i z e d d a t a i n t h epublication “Design of Small Dams,” secondedition, [ 311 along with data for estimatingincrements of excess rainfall to be applied to aunitgraph. The procedures which have beendescribed in this text for developing aunitgraph can be used to obtain a unitgraph forthat portion of a watershed over which a designthunderstorm might occur. In the event thatthis type of preliminary IDF estimate provescritical for design, a hydrometeorologist shouldbe consulted for an estimate of designt h u n d e r s t o r m rainfall for the specificwatershed.

G-21. Recommendations for RoutingPreliminary Inflow Design Floods Through aProposed Reservoir. -It is necessary fordesigners to assume an elevation of thereservoir pool at the start of an inflow designflood for reservoir routing studies to determinerequired spillway capacity. Normally, thereservoir pool is assumed to be full to the topof planned conservation storage capacity or,when either inviolate or joint use flood controlcapacity is proposed, full to the top of eithertype of flood control capacity at the beginningof a preliminary inflow design flood. If largecapacities of flood control space are beingconsidered in preliminary planning, criteria forrouting a final-type IDF as discussed in sectionsG-30 and G-31 should be established to theextent possible with information available.

G. SNOWMELT RUNOFF CONTRIBUTIONS TO INFLOW DESIGN FLOODS

G-22. General . -“Hydraulic engineers hydrologic and an economic viewpoint, in there sp on si ble for planning and designing planning and design of multipurpose storagemultiple-purpose storage reservoirs recognize reservoirs. In northern latitudes and at highsnow as a form of precipitation possessing elevations, snow falls and accumulates on thecertain characteristics which can be evaluated earth’s surface in frozen crystalline form anda n d a p p l i e d t o a d v a n t a g e , b o t h f r o m a usually remains until a proper sequence of

500

m e t e o r o l o g i c e v e n t s p r o v i d e s t h ethermodynamic conditions essential for eitherevaporation or melting. Periodic snow surveysprovide a reliable index of the relative snowaccumulation. With knowledge of the processesof storage, evaporation, and melting, theengineer can predict, with reasonable accuracy(for normal climatic conditions and for knownsnowpack) the characteristics and amount ofstreamflow to be expected * * * In the WesternUnited -States, the economy of the arid andsemiarid lands lying between the mountainr a n g e s i s increasingly d e p e n d e n t o ndevelopment of multiple-purpose storagereservoirs to utilize the streamflow originatingin the high mountain snow packs. Engineers ofthe Western States accept as a blessing the factthat the predictable characteristics (italicsadded) of this streamflow enable economies inp l a n n i n g a n d designing multiple-purposereservoirs by the joint use of space allocated tothe various functions and by reduction ofspillway capacities.”

The above extract from Mr. H. S. Riesbol’spaper “Snow Hydrology for Multiple-PurposeReservoirs” [22] is quoted to point out theimportance of snow in hydrologic studies andthe predictable characteristics of streamfloworiginating from snowpacks. These predictablec h a r a c t e r i s t i c s o f t e n m a k e p o s s i b l eemployment of simple empirical correlationswhich give acceptable estimates of snowmeltrunoff, although this runoff results from acomplex thermodynamic process. Discussion ofempirical methods of estimating snowmeltrunoff as related to inflow design floodestimates is the main objective in theses e c t i o n s . R e a d e r s i n t e r e s t e d i n m o r ein fo rma t ion a b o u t t h e p h y s i c a l a n dthermodynamic characteristics of snow andsnowmelt processes may consult “SnowHydrology” [ 23 1 and “Handbook of AppliedHydrology” [241.

As previously stated in section G-l, Bureauof Reclamation policy does not provide forcombining probable maximum snowmeltrunoff with probable maximum rainfall runofffor estimation of an inflow design flood. It isb e l i e v e d t h a t s u c h c o m b i n a t i o n s a r eunreasonably severe. It is considered more

DESIGN OF GRAVITY DAMSreasonable to combine runoff from a probablemaximum rainstorm that could occur duringthe snowmelt season with a major snowmeltflood, or to combine runoff from a majorr a i n s t o r m t h a t c o u l d o c c u r d u r i n g t h esnowmelt season with probable maximumsnowmelt runoff. In regions where maximumprobable rainstorms can occur during wintermonths when watersheds may have a largeamount of snow on the ground, the amount ofsnow melted during the design rainstorm mustbe estimated and runoff calculated from thetotal combined rain and melted snow wateravailable on the ground surface. Procedureshave been developed for computing this typeof rain-on-snow floods, utilizing data andanalyses described in detail in the report“Snow Hydrology” (231. One should bem i n d f u l t h a t e a c h i n d i v i d u a l 1DF s t u d yrequires some variations within the frameworkof a general approach, depending uponwatershed characteristics, location, basic dataavailable, and proposed operational capacity ofthe future reservoir.

G- 23. Major Snowmelt Runoff DuringSeasonal Melt Period for Combination WithProbable Maximum Storm Runoff. -A methodof estimating snowmelt runoff contribution forthis type of combination has been describedbriefly in connection with preliminary IDFestimates for watersheds west of the 105’meridian. Additional items need be consideredwhen making “best possible” preliminary IDFor final-type IDF estimates. Inclusion of floodcontrol capacity and its amount in a proposedreservoir may have a direct bearing on the timeduration of flow required in estimation of aninflow design flood hydrograph.

(a) Damsites for Reservoirs With no FloodControl Capacity Proposed. -These projects areintended to store seasonal snowmelt runoff asrapidly as possible, allowing only minimumrequired releases until reservoir capacitybecomes full to top of conservation storage. Aduration time of 15 days is usually adequatefor an inflow design flood hydrograph for thistype of structure, as a reservoir may beassumed full to top of conservation capacity atthe beginning of the 15-day period. A 1percent chance (100 year) 15-day volume of

I D F STUD I ES-Sec. G-23 501

snowmelt runoff is usually considered as amajor snowmelt flood. It is obtained from afrequency study of maximum annual 15-daysnowmelt runoff volumes using runoff recordsfor the contributing watershed, if available, orrecords for similar nearby watersheds. The15-day volume indicated by the frequencycomputations (sets. G-28 and G-29) is adjustedto the specific watershed above a damsite byarea relationships.

Caution : Occasionally there will be foundreferences or data of an extremely largesnowmelt flood exceeding all recently recordedfloods and, perhaps, exceeding the 1 percentchance value indicated by frequency analysesof more recent records. These data should notbe ignored without making full effort toincorporate the data into the snowmelt floodestimate.

(1) Assembly of basic stream-flow data forfrequency analyses. -Concurrently withtabulation of maximum annual 15-day seasonalsnowmelt runoff values from streamflowrecords, climatological data should beexamined to determine if each year’s 15-dayrunoff volume was snowmelt runoff or wasincreased by rainfall amounts large enough tocause runoff during that period (small rainfallevents may be ignored). If a large snowmeltvolume is indicated, an estimate of therain-flood portion can be made and subtractedby plotting the daily discharge values onsemilogarithmic paper and sketching anestimated snowmelt recession (due to lowertemperatures accompanying rainfall) under theobvious rain-flood portion. This procedure mayhave to be used in a few regions where almostevery year some rainfall runoff is concurrentwith snowmelt runoff.

(2) Daily distribution of 1 percent chance15day snowmelt runoff volume. -Springtimesnowmelt runoff coordinates closely withtemperature fluctuations. Large areas usuallyhave about the same daily temperaturesequence. Usually snow-fed streams in a givenvicinity have similar daily distribution patternsof runoff, magnitudes of discharges reflectingindividual watershed snowmelt contributingareas. These distribution patterns will also besimilar year to year. Therefore, a distribution

pattern for one of the larger 15-day volumesrecorded for the stream where a damsite islocated, or for a nearby similar watershed, canbe selected and the 1 percent chance 15-daysnowmelt r uno f f vo lume fo r t he damsitedistributed into daily discharges proportionalt o t h e s e l e c t e d r e c o r d e d f l o o d . A napproximately symmetrical 15-day patternwith the maximum daily discharge occurringwithin the 7th to 10th day of the 15-dayperiod is usually selected. An addit ionalrefinement may be included in selecting thed i s t r i b u t i o n p a t t e r n , i f b y c h a n c eclimatological records show that a small raine v e n t o c c u r r e d a d a y o r t w o a f t e r t h emaximum daily discharge of a large recorded15-day volume and discharges decreased due tolowered temperatures associated with the rainevent. This sequence of events agrees with thepattern of natural conditions assumed by theoccurrence of a probable maximum rainstorm ad a y o r t w o a f t e r t h e m a x i m u m d a y o fsnowmelt runoff.

(3) Combination of probable maximum rainflood with 1 percent chance 1Pday snowmeltflood. -Selection of an appropriate day withina 15-day p e r i o d o f snowmelt r u n o f f a s abeginning time of design rain-flood runoff is am a t t e r o f eng inee r ing judgment . Onereasonable assumption is a 2-day intervalbetween the day of maximum temperature andthe beginning of runoff caused by a designstorm. Under this assumption, the apparentl a g - t i m e i n d a y s b e t w e e n m a x i m u mtemperature and maximum daily snowmeltd i s c h a r g e f r o m a w a t e r s h e d s h o u l d b econsidered. The lag-time may be quicklydetermined by plotting a few of the largerannual maximum 15-day mean daily dischargesand respective daily maximum temperaturesfrom an *index temperature record. Dependingon size and runoff characteristics of awatershed, the time interval between maximumtemperature and resulting daily maximumsnowmelt discharges at a damsite may varyfrom zero to 3 or more days. If the timeinterval is zero days, design rain-flood runoff isadded to the snowmelt runoff, beginning onthe third day after the peak of the snowmeltflood. As the lag-time interval between

502

maximum temperature and peak of snowmeltrunoff increases, the beginning time for adesign rain-flood hydrograph is advanced closerto the peak of the snowmelt flood by l-dayintervals. Thus, for large watersheds, it may bereasonable to combine a design rain flood withthe maximum daily discharges of a snowmeltflood.

(b) Damsites for Reservoirs With ProposedJoint Use Flood Control Capacity, -A reservoirwhich has a joint use flood control capacityallocation is intended to control seasonalsnowmelt discharges downstream from the damto a limit of safe channel capacity throughoutthe entire snowmelt season, and also to storeenough water to assure that the reservoir is fullto the top of the joint use capacity at the endof each snowmelt season. Forecasts of seasonalsnowmelt runoff volumes are a necessary partof this kind of operation.

A seasonal major snowmelt flood as a part ofan inflow design flood (IDF) hydrographusually is required when joint use flood controlcapacity is proposed. However, if planned jointuse capacity is small and there is a likelihoodtha t snowmelt d i s c h a r g e s p r e c e d i n g t h emaximum 15day period of a 1 percent chancesnowmelt flood may fill the joint use pool, a15day IDF hydrograph will be adequate. Whena seasonal major snowmelt flood hydrographfor combination with a probable maximumr a i n - f l o o d h y d r o g r a p h i s n e e d e d , firstconsideration is given to the use of streamflowdata.

The duration period of a seasonal IDFcorresponds with the seasonal duration of thelargest snowmelt floods which have occurred inthe vicinity. Frequency analyses include annualmaximum 30-day, 6(lday, a n d i f n e e d e d90-day p e r i o d s o f snowmelt v o l u m e s i naddition to analysis of the annual maximum15-day discharge period. A recorded seasonalsnowmelt flood is selected as a pattern forrunoff distribution. The design rain flood iscombined with the estimated snowmelt runoffhydrograph according to the criteria previouslydiscussed.

If available streamflow data are not suitablefor satisfactory results using the abovea p p r o a c h , one o f t h e m e t h o d s o f


temperature-runoff correlations described inthe referenced publications may be foundadaptable to the situation.

G-24. Probable Maximum Snowmelt Floodst o b e C o m b i n e d W i t h M a j o r R a i nFloods. -(a) General. -An estimate of probablemaximum snowmelt runoff may be necessarywhen making an inflow design flood (IDF)study for a watershed where snowmelt runoffcauses the major portion of yearly flow. Thedegree of refinement needed in making thistype of estimate may vary from preliminarycomparisons to computation by detailedprocedures depending on factors such as thefollowing: storage capacity, space allocations,a n d o p e r a t i o n a l p l a n s o f t h e p r o p o s e dreservoir; snowmelt runoff characteristics ofthe watershed; and difference in magnitudes ofprobable maximum rainstorm and majorrainstorm potentials for the watershed. Forsome watersheds, a f e w p r e l i m i n a r ycomputations may show an IDF combinationo f m a j o r snowmelt r u n o f f a n d p r o b a b l emaximum rain runoff to be definitely criticalfor design. In other instances detailedcomputations of each type IDF consisting ofcombined snowmelt and rain runoff have to bemade and both types of IDF hydrographsprepared for use in design of a dam.

S t u d i e s p r e p a r e d b y t h e B u r e a u o fReclamation show that usually a critical inflowdesign flood results from a combination ofrunoff of a major snowmelt flood and ap robab l e max imum ra in s to rm . In mos tinstances, an approximation of probablemaximum snowmelt f l o o d m a g n i t u d e b ysimple correlations shows that it will not becritical for design. Development of a bestestimate of probable maximum snowmeltrunoff is a complex procedure and requiresspecial treatment for each site. Therefore, thisdiscussion is limited to general aspects of theproblem, with references to publicationscontaining more detailed information.

(b) Considerations for Estimates ofP r o b a b l e M a x i m u m SnowmeltFloods. -Estimating probable maximumsnowmelt contribution to an inflow designflood can be thought of as requiring threesteps: ( 1) estimating probable maximum

IDF STUDI ES-Sec. G-24 503

seasonal accumulation of snow on a watershed,(2) estimating critical melt rates of the snowpack and (3) estimating the amount ofsnowmelt runoff and its timing at the reservoir.The probable maximum seasonal accumulationof snow on a mountainous watershed drainedby one main stream can be adequatelye s t i m a t e d b y a s t u d y o f w i n t e r s e a s o np r e c i p i t a t i o n r e c o r d s i n a n d n e a r t h ewatershed, supplemented by snow survey data,Special studies are required for probablemaximum s e a s o n a l s n o w accumulationestimates for large multitributary river systemssuch as the Colorado River above Glen CanyonDam. One of two basic approaches can betaken to estimate crit ical snowmelt ra tes ;namely, calculation of snowmelt runoff bym e a n s o f a n a i r t e m p e r a t u r e i n d e x , o rcalculation of melt using generalized snowmelte q u a t i o n s b a s e d o n e n e r g y b a l a n c econsiderations. Methods using some form of anair temperature index have given good resultsfor many watersheds. There is some physicalbasis for using a snowmelt air temperatureindex. Air temperature is reasonably wellcorrelated, at a particular time and place, withthe atmospheric factors which affect meltrates, such as solar radiation and vaporpressure, although it is by no means a perfectindex of these factors.

Snowmelt equations which consider energybalance are used to evaluate short-waveradiation melt, long-wave radiation melt, meltdue to convective heat transfer from theatmosphere and to latent heat of water vaporcondensing into the snow surface, melt due toheat of rain drops, and melt by heatconduction from the ground. The Corps ofEngineers report “Snow Hydrology” 123 1presents detailed information regarding bothapproaches. A Corps manual, “Runoff fromSnowmelt,” EM 1110-2-1406 [ 251, presentssynopses of investigations of meltingrelationships, generalized basin snowmeltequations and their application in methods ofcomput ing m ax imum snowmelt f loods.Selection of an approach to be used dependson the basic data available and the importanceof snowmelt runoff contribution to an inflowdesign flood. Whichever approach is taken, it is

necessary to test the snowmelt computationprocedures for the basin in question in order todetermine basin values of the coefficientsinvolved.

Approximation of a maximum probablesnowmelt flood for a period of 10 to 20 daysusually is directed toward determination ofvolume. This volume is then distributed in timeby using a large recorded snowmelt runoffhydrograph as a pattern, as previouslyd e s c r i b e d i n s e c t i o n G-23(a)(2). I f atemperature index has been used directly in thecomputations, the volume may be distributedby a synthetic temperature sequence.

(c) Springtime Seasonal Probable MaximumSnowmelt F l o o d E s t i m a t e s . - G e n e r a lprocedures for estimating total seasonalprobable maximum snowmelt runoff are notoutlined in detail in this text. Brief statementsabout some approaches w h i c h m a y b econsidered for use, and reference to respectivespecific descriptions, are given below.

(1) Hydrothermogram approach.-Thepaw-, “Snow Hydrology for Multiple-PurposeReservoirs” [ 221, includes a description of anapproach in which during the melting seasondaily temperatures above a base temperatureare directly related to resulting direct runoff bya device referred to as a hydrothermogram. Ahydrothermogram is a hypothetical dischargehydrograph computed on the assumption thateach effective degree of temperature above abase temperature will generate the sameamount of runoff volume. This procedure,adjusted to fit individual basin problems, hasbeen found useful in several Bureau ofReclamation IDF studies (unpublished) whereprobable maximum snowmelt flood estimateswere important.

(2) Generalized melt equations forspringtime snowmelt floods. -The Corps ofEngineers Manual, “Runoff from Snowmelt”[25], includes a chapter describing probablemaximum snowmelt flood derivation usinggeneralized melt equations. The Salmon RiverBasin which drains 14,100 square miles ofrugged, mountainous regions of central Idaho iscited as an example in the discussion.

(3) Correlations. -Correlations betweentemperature and runoff, snowcover and runoff,


while the watersheds are partially orcompletely covered with snow. In many areas,storm systems may consist of precipitationbeginning as snow then changing to rain orclosely spaced successive storm systems, thefirst system occurring as snow, the second asrain accompanied by warm temperatures.Devastating floods have resulted from certainrain-on-snow combinations; in other instances,apparently similar conditions have producedonly high flows causing little damage. Detailedinvestigations of differences betweenrain-on-snow flood magnitudes point towardthe following two items as the maincontributors to these differences: densityconditions of the snowpack at the time of rainoccurrence, and convective condensation meltrelated to wind velocities during the rainstorm.Generalized equations for estimating snowmeltduring rainfall, developed as described in“Snow Hydrology” [ 231, have proved veryuseful in procedures for estimating runoff dueto rainfall on snow.

In addition to estimates of snowpackmelting rates, procedures for estimating runoffcaused by rain-on-snow conditions includeevaluations of snowpack release of free waterto the ground surface, retention losses, anddistribution in time of the runoff at the pointof interest. A procedure used by the Corps ofEngineers is given in the manual, “Runoff fromSnowmelt” [25]. The procedure used inBureau of Reclamation studies is described inEngineering Monograph No. 35, “Effect ofSnow Compaction on Runoff from Rain onSnow” [ 261. In both procedures snow meltingrates during rainfall are computed by the samemelting equations and water released at groundsurface is determined. Excesses are computedby subtracting retention losses, and aredistributed in time by a basin unitgraph.Differences between the procedures lie inestimations of snowpack free-water holdingcapacities.

The Corps procedure establishes a limit ofliquid water holding capacity of a snowpack asa percentage of snowpack water content.Nearly all data considered when developing thelimit of water holding capacity were obtainedfrom spring snowpack of densities above 35

etc., are usually evidenced because of thepredictable nature o f snowmelt r u n o f f .Hydrologists knowledgeable in the use ofcorrelation studies may find this type ofapproach useful.

(d) Major Rain-Flood Estimates forCombination With Probable MaximumSnowmelt Runoff. -

( 1) Major rainstorm and runoff. -Designstorm studies for watersheds where snowmeltrunoff contributes to inflow design floodsshould also include a hydrometeorologicalestimate of a major rainstorm that could occurduring the snowmelt season. For areas wheremajor rainstorms have often occurred in thevicinity of the watershed during the snowmeltseason, the largest rainstorm of record withinthe area of transposability is fitted to the basin.In areas where major rainstorm occurrencesduring the spring snowmelt season areinfrequent, watershed design storm valueswithout maximization for moisture adjustmentmay be considered. A hydrograph of runofffrom the major rainstorm is computed by thedimensionless-graph lag-time procedurespreviously discussed, but special attention isgiven to effects of snowmelt on retention lossesapplicable to the major rainstorm. The portionof the watershed covered by a meltingsnowpack will have little or no retentioncapacity for rainfall, and the portion recentlydenuded of snow will have high moisturecontent, hence low retention capacity duringrainfall. Guide criteria for combining rain-floodhydrographs and snowmelt flood hydrographshave been discussed in section G-23(a)(3).

( 2) Observed rain floods. -Occasionally,streamflow data used for snowmelt runoffanalyses will include a major rain flood duringa snowmelt season. In these instances, specialstudies are made to separate the rain-floodhydrograph from the snowmelt runoff, and theseparated rain-flood hydrograph is used forcombination with the estimated probablemaximum snowmelt flood hydrograph.

G-25. Probable Maximum Rain-On-SnowIDF Estimates. -There are many watershedsalong or near the coasts of the United Stateswhere major rainstorms or probable maximumrainstorms can occur during the winter months

IDF STUDI ES-Sec. G-26

percent. The procedure in EngineeringMonograph No. 35 relates snowpack liquidwater holding capacity to snowpack densitiesjust preceding the start of rainfall, and toincreases in snowpack density due to meltingand added rainfall until the pack attains adensity of 40 or 45 percent when release ofliquid water to the ground surface is assumedto begin. Development of the procedure wasdirected primarily for use for evaluatingwintertime conditions where a rainstormsystem closely follows a snowstorm and thenewly deposited snowpack has had little timeto change in structure. Topics of discussion inEngineering Monograph No. 35 are adevelopment o f t h e p r o c e d u r e andreconstitution of the December 1955 flood onSouth Yuba River near Cisco, Calif. Estimationof a probable maximum rain-on-snow flood isnot discussed in the monograph. Data requiredfor use of the procedure for IDF computationsare: (1) estimates of watershed snowcoverdepth and water content antecedent to a designstorm occurrence; and (2) hydrometeorologicaldata of temperatures and wind velocitiesconcurrent with design storm rainfallincrements.

505

G-26. Special Situations.--(a) FrozenGround.-Frozen ground conditions seldomoccur in well-forested areas or under deepsnowpacks. On the other hand, open areaswhere periods of subfreezing temperatures andlight snowfall are normal can develop frozensoil conditions such that retention losses arepractically nil. These areas may experiencesevere winter floods due to combinations ofshallow snowcover, rising temperature, andrelatively minor rainfall. Frozen groundconditions may also reduce lag-time. Analysesfor this type of condition require individualwatershed study.

(b) Snowmelt in the Great Plains Region ofthe United States.-Probable maximumprecipitation potential is so great in the GreatPlains region that snowmelt runoff is notusually considered in inflow design floodstudies except for large drainage areas withheadwaters in the Rocky Mountains. In thenorthern Great Plains, major floods haveresulted from rapid spring snowmelt and frozenground conditions. Consideration of this typeof flood may be necessary for large drainageareas near the northern border of the UnitedStates.

H. ENVELOPE CURVES

G-27. General. -Peak discharge envelopecurves and flood volume envelope curves canbe prepared by drawing curves envelopingplotted points representing maximum recordedvalues for various drainage areas. The valuesplotted should represent similar type floods(rain floods or snowmelt floods) that haveoccurred within the broad geographicalsubdivision within which the subject watershedlies, and should not be limited to events of asingle small river system. Preparation ofenvelope curves for a general area provides anengineer with valuable information on pastflood history and an indication of the flood ofrecord comparable to the subject area.However, they should not be relied upon as ameans of estimating probable maximum floodvalues. Design flood values purporting to be theprobable maximum should be higher than

those obtained from envelope curves. Only inspecific instances where a watershed hasdefinitely lower flood potential thanneighboring watersheds due to soil type,surface storage, etc., would it be goodjudgment to adopt an inflow design flood ofsmaller magnitude than that of a flood whichhas occurred nearby.

A simple method of preparation of envelopecurves is to tabulate maximum peak discharges(or volumes of a selected duration) andrespective drainage areas prior to plottingpoints. In most instances, the drainage areaabove a stream gaging station or the point of alarge flood discharge measurement is given inthe U.S. Geological Survey water supply paperlisting the flood. When it is known that only aportion of the drainage area above a point ofmeasurement contributed to a flood, the size


of that contributing portion should be used in straight line for small ranges in areas. Highthe envelope curve analysis. Discharges or discharges from local thunderstorms mayvolumes are plotted versus respective drainage suggest consideration of two curves-one forareas using log-log paper. Data thus plotted smaller areas subject to such occurrences andusually indicate a curved line envelopment on another for larger areas where maximumlog-log paper which may be approximated by a discharges originate from general storms.

I. STATISTICAL ANALYSES-ESTIMATES OF

FREQUENCY OF OCCURRENCE OF FLOODS

G-28. General. -Estimates of the magnitudeof floods which have frequencies of 1 in 5, 1 in10, or 1 in 25 years are helpful in estimatingrequirements for stream diversion duringconstruction. These floods are often termedthe “5, 1 O-, or 25-year flood.” The magnitudeof more rare events such as the SO- or lOO-yearflood may be required for reasons such as toestablish sill location of emergency spillways,etc. The usual term of expression, “x-yearflood,” should not lead to the wrongconclusion that the event indicated can happenonly once in x years, and having occurred, willnot happen again for another period of x years.It does mean that over a long span of years wecan expect as many x-year floods (or larger) asthere are x-year-long periods within that span.Floods occur randomly and may be bunched orspread out unevenly with respect to time. Nopredictions are possible for determining theirdistribution; the probable maximum flood cayloccur the first year after the project is built,though of course, the odds are heavily againstit.

The frequency of a flood should beconsidered as the chances of occurrence of aflood of that size (or one larger) in any oneyear. Stated another way, the chances of theflood in any one year being equaled orexceeded by floods of the magnitudesindicated as the 5-, 1 Ck, 25-, or lOO-year floodshave ratios of 20: 100, 10: 100, 4: 100, and1: 100, respectively.

Many methods of flood frequencydeterminations based on streamflow data havebeen published. Excellent summaries of thesemethods, along with comments on factorsaffecting their accuracy and limitations, are

contained in the papers entitled “Review ofF l o o d F r e q u e n c y M e t h o d s ” [27] a n d“Methods of Flow Frequency Analysis” [ 281.While the many methods of flood frequencydeterminations made from streamflow data areall based on acceptable statistical procedures,the difference in methodology can giveappreciably different results when extensionsare made beyond the range of adequate data.To provide for a uniformity in Federal waterresources planning, the Water ResourcesCouncil has recommended that all Governmentagencies use the Log-Pearson type IIIdistribution as a base method. The method isdescribed in the publication “A UniformTechnique for Determining Flood FlowFrequencies” [ 291. Hazen’s method [ 301 givesresults that are comparable to those obtainedwith the Log-Pearson type III method and iseasier to use when computations are made byhand with or without the aid of mechanicalcalculating machines. A procedural outline forHazen computations is presented in section 59of “Design of Small Dams,” second edition1311.

If streamflow data for a period of 20 yearsor more are available for the subject watershedor comparable watersheds, frequency curvecomputations yield acceptable results forestimates up to the 25-year flood and may beextrapolated to indicate the lOGyear floodwith a fair assurance of obtaining acceptablevalues.

G-29. Hydrographs for Estimating DiversionRequirements During Construction. -Usually,inflow design flood (IDF) studies includehydrographs of floods for different frequenciesof occurrence to be used for estimation


diversion requirements during construction of a computed frequency curves. In some instances,dam. a peak discharge and associated volume of a

The hydrograph of a particular frequency recorded flood will correspond closely with aflood is usually sketched to conventional shape particular frequency value, in which case theusing t h e p e a k d i s c h a r g e v a l u e a n d recorded flood hydrograph is used.corresponding volume value obtained from

J. FINAL-TYPE INFLOW DESIGN FLOOD STUDIES

G-30. General. -Preparations of final-typeinflow design flood (IDF) studies differ frompreliminary studies only in the degree ofrefinement used to estimate each variablecausing flood runoff. For example, a basinunitgraph may be derived from a single largeflood hydrograph in a preliminary study,whereas in a final-type study several floodhydrographs are analyzed and a selected basinunitgraph tested by reproduction of recordedflood hydrographs. Perhaps the most importantconsideration in the preparation of final-typestudies is making certain that all availablehydrological and meteorological data available,including historical and recent events, haveb e e n c o n s i d e r e d p r o p e r l y . Ahydrometeorologist prepares the design stormstudy for the basin, including therein designtempera tu re s and wind ve loc i t i e s i frain-on-snow floods are to be considered.Preliminary estimates of each flood-producingvariable are reviewed and revised if additionaldata so indicate, Preliminary dam and reservoiroperation plans are examined for certainty thatthe critical IDF situation for the chosen typeof design and operation has been used.

Hydrologists and hydrometeorologists mustestimate effects of ever-varying naturalphenomena. Studies of these phenomena asrelated to a particular watershed begin with theinception of a project and continue thereafter,unless the project is determined infeasible andnot built.

G-3 1. Flood Routing Criteria. -Normally,the reservoir pool is assumed to be full to thetop of conservation storage at the start of therouting of the inflow design flood (IDF).However, when either inviolate or joint useflood control space is provided, thedetermination of space available at the

beginning of the inflow design flood willdepend upon the spacing of preceding storms,t h e r e l a t i v e m a g n i t u d e o f snowmeltcontribution to the design flood, and theoperational criteria proposed for the reservoir.

(a) Preceding Storms.-In some areas of thewest, for example areas for which the Gulf ofMexico i s t h e m o i s t u r e s o u r c e , t h emeteorological situation is such that a majorstorm could occur a few days prior to themaximum possible storm. In these areas, theflood control pool is assumed to be partially orcompletely occupied at the start of the inflowdesign flood. The determination of the portionof flood control pool that is occupied dependsupon the distance of the area from themoisture source and a study of historical floodevents in the area.

(b) Seasonal Flood Hydrograph. -For thoseareas in which floods occur on a fixed seasonalbasis, largely as the result of snowmelt, it isfrequently desirable to prepare a flood-seasonhydrograph including the inflow design floodand maximum antecedent and superveningflows that could reasonably be expected tooccur with the inflow design flood. Thishydrograph is then routed through thereservoir with the conservation pool full at thebeginning of the season inflow, if thatassumption can be justified on the basis ofcarryover storage. Otherwise, the minimumdrawdown for the beginning date of seasonalinflow is selected from project operationstudies.

(c) Operational Criteria. -The assumedreservoir elevation at the start of the inflowdesign flood will also be dependent upon thetype of flood control space, which may be afixed inviolate amount or a varying amount,normally referred to as joint use storage space.


Report No. 28, “Generalized Estimate of MaximumPossible Precipitation Over New England and NewYork,” 1952. -

Report No. 33, “Seasonal Variation of the ProbableMaximum Precinitation East of the 105th Meridianfor Areas from 10 to 1,000 Square Miles andDurations of 6, 12, 24, and 48 Hours,” 1956.

Report No. 36, “Interim Report-Probable MaximumPrecipitation in California,” Washington, D.C., 1961.

Report No. 39, “Probable Maximum Precipitation in theHawaiian Islands,” Washington, D.C., 1963.

Report No. 40, “Probable Maximum Precipitation,Susquehanna River Drainage above Harrisburg,Pennsylvania,” Washington, D.C., 1965.

Report No. 41, “Probable Maximum and TVA Precipitationover the Tennessee River Basin above Chattanooga,”Washington, D.C., 1965.

Report No. 42, “Meteorological Conditions for theProbable Maximum Flood on the Yukon River aboveRampart, Alaska,” Washington, D.C., 1966.

Report No. ‘43, “Probable - Maximum Precipitation,Northwest States.” Washington. D.C.. 1966.

Report No. 44, “Probable Maximum’Precipitation over theSouth Platte River, Colorado, and Minnesota River,Minnesota,” Washington, D.C., 1969.

Cooperative Studies Reports, Cooperative StudiesSection, Division o f Climatological a n dHydrologic Services, National Weather Service, incooperation with the Bureau of Reclamation:

Report No. 9, “Maximum Possible Flood-ProducingMeteorological Conditions.” (1) Colorado River Basinabove Glen Canyon Damsite, (2) Colorado RiverBasin above Bridge Canyon Damsite, (3) San JuanRiver Basin above Bluff Damsite, (4) Little ColoradoRiver Basin above Coconino Damsite. June 1949.

Report No. 11, “Critical Meteorological Conditions forDesign Floods in the Snake River Basin,” February1953.

Report NO. 12, “Probable Maximum Precipitation on SierraSlopes of the Central Valley of California,”Washington, D.C., March 1954.

1211 “ S t o r m R a i n f a l l i n t h e U n i t e d S t a t e s ,Depth-Area-Duration Data,” Department of the Army,Office of the Chief of Engineers. Washineton. DC.. 1945.

WI

1231

~241

PI

1261

~271

WI

1291

I301

[311

Riesbol, H. S., “Snow Hydrology for Multiple-PurposeReservoirs,” Trans. ASCE, VOL 119, 1954, pp. 595-627.“Snow Hydrology,” Summary Report of SnowInvestigations, U.S. Corps of Engineers, June 1956.“Handbook of Applied Hydrology,” A Compendium ofWater -Resources Technology , Ven Te Chow(Editor&Chief), McGraw-Hill Book Co.. Inc.. NewYork, N.Y., 1964.

, I

“Runoff from Snowmelt,” EM 1110-2-1406. U.S. Corm~, ---Lo

of Engineers, 1960.Bertle, F. A., “Effect of Snow Compaction on RunoffFrom Rain on Snow,” Engineering Monograph No. 35,Bureau of Reclamation, 1966.“Review of Flood Frequency Methods,” Final Report ofthe Subcommittee of the Joint Division Committee onFloods, Trans. ASCE, vol. 118, 1953, pp. 1220-1231.“Methods of Flow Frequency Analysis,” Bulletin No.13, Subcommittee on Hydrology, Inter-AgencyCommittee on Water Resources (now the HvdroloavCommittee, Water Resources Council), Washington,D.C., April 1966.“A Uniform Technique for Determining Flood FlowFrequencies,” Bulletin No. 15, Hydrology Committee,Water Resources Council, Washington, D.C., December1967.Hazen, A., “Flood Flows,” John Wiley & Sons, Inc.,New York, N.Y., 1930.“Design of Small Dams,” second edition, Bureau ofReclamation, 197 3.

<<Appendix H

Sample Spec i f icat ions for Concrete

H-l. Introduction. -Designs of any structureare based on assumptions regarding the qualityof work which will be obtained duringconstruction. I t i s t h rough the means o fspecifications that the assumed quality isd e s c r i b e d , a n d i t i s i m p o r t a n t t h a tconformance to the specifications be obtainedfor all work.

This appendix includes sample specificationsfor concrete in the dam and its appurtenances.For the construction of a particular dam, thesespecifications will be supplemented by localconditions, selected provisions, and specialmeasures required for the construction of thestrut ture.

The sample specifications are written on thebasis that the concrete mixes to be used in thework will be designed and controlled by thepurchaser (referred to in the specifications asthe Contracting Authority or simply as theAuthority) within the maximum water tocement or water to cement plus pozzolan ratioand slump limitations specified, the limitationsfor quality and grading of aggregates, and thelimitations for the other materials as specified.Also, the specifications are written on the basisthat the quantity of sand and each size ofcoarse aggregate to be used in the concretemixes will be determined by the purchaser. Thequality limitations shown in the specificationsfor sand and coarse aggregate are considered asstandard limits. These limits may be reducedwhen only substandard materials are availablewithin economical hauling distance, andprovided it has been determined by tests ofconcrete made with such aggregates thatdurable concrete meeting the design strengthcriteria can be produced.

Under these specifications the purchaser’sown engineering force or an engineeringorganization retained by the purchaser wouldaccomplish testing of proposed aggregates andother materials, perform the design of mixes,and handle the inspection and quality testingthroughout the contract. If the purchaser willrequire the contractor to provide such mixdesign, i n s p e c t i o n and control, thespecifications should so provide and shouldinclude specific design compressive strength(s)at designated age(s) for the concrete. Theconcrete mixes should be designed to providecompressive strengths of test cylinders suchthat 80 percent of the cylinders will havecompressive strength(s) at the specified age(s)greater than the design compressive strength[Il.’

References to “designations” in the samplespecifications refer to designations in theappendix of the Bureau of ReclamationConcrete Manual, eighth edition [ 1 I. Wherematerials or other requirements are to conformto Federal specifications, or other standardspecifications such as ASTM, the constructionspecifications for specific work should providethat the specifications for the materials orr e q u i r e m e n t s concerned should be incompliance with the latest editions or revisionsthereof in effect on the date bids are receivedor award of contract is made, whichever isappropriate.

H-2. Contractor’s Plants, Equipment, andConstruction Procedures. -Prior to theinstallation of the contractor’s plants and

’ Numbers in brackets refer to items in the bibliography,sec. H-25.

511


e q u i p m e n t f o r p r o c e s s i n g , h a n d l i n g ,transporting, storing, and proportioningc o n c r e t e ingredients, and fo r mix ing ,t r an sp orting, and placing concrete, thecontractor shall submit drawings covering hisplans for approval b y t h e C o n t r a c t i n gA u t h o r i t y , s h o w i n g p r o p o s e d p l a n tarrangement, including plans of locations anddescription of facilit ies for sampling ofconcrete and concrete materials as hereinafterprovided. Included with the plans shall be adescription of the equipment the contractorproposes to use in sufficient detail that anadequate review can be accomplished. Thedrawings and description of plant, equipment,and sampling and testing facilities shall besubmitted at least 60 days prior to planterection.

A f t e r c o m p l e t i o n o f i n s t a l l a t i o n , t h eoperation of the plant and equipment shall besubject to the approval of the ContractingAuthority.

Sampling and testing facilities for use by theAuthority shall be provided by the contractorand shall include power-driven mechanicalsampling devices, satisfactory to the Authority,as may be necessary for procuring and handlingrepresentative test samples of aggregates andother concrete materials during batching; andfor obtaining samples of concrete as dischargedfrom the mixers, for mixer efficiency, slump,and other tests, except that power-drivenmechanical sampling devices will not berequired for sampling concrete from truckmixers if and when the use of truck mixers ispermitted by these specifications. The concretesampling device shall be capable of procuringsamples of concrete from any point in thedischarge stream as the concrete is beingdischarged from the mixer.

After completion of the plant installation,the operation of the sample taking facilitiesshall be demonstrated to the satisfaction of theAuthority that they are suitable for thepurpose intended. If truck mixers are usedwhere permitted by these specifications, thecontractor shall provide a stable, level platformwith adequate shelter, satisfactory to theAuthority, for concrete tests at the point ofd i s c h a r g e f r o m t h e t r u c k m i x e r s . T h e

contractor shall also provide ample andprotected working space adjacent to thebatching and mixing plants, free from plantvibration; and shall furnish necessary utilitiessuch as compressed air, water, heat, ande l e c t r i c a l p o w e r f o r o p e r a t i o n o f t h eA u t h o r i t y ’ s t e s t i n g e q u i p m e n t a n d f o rexecution of tests by Authority personnel ofconcrete and concrete materials at the batchingand mixing plants.

Where these specifications require specifictypes of equipment to be used or specificprocedures to be followed, such requirementsare not to be construed as prohibiting use byt h e c o n t r a c t o r o f a l t e r n a t i v e t y p e s o fequipment or procedures if it can bedemonstrated to the satisfaction of theAuthority that equal results will be obtainedby the use of such alternatives. Approval ofplants and equipment or their operation, or ofany construction procedure, shall not operateto waive or modify any provisions orrequirement contained in these specificationsgoverning the quality of the materials or of thefinished work.

The cost of providing facilities and workingspace for procuring and handling representativetest samples of concrete and concrete materialsat the batching and mixing plants shall beincluded in the prices bid in the schedule forconcrete.

The contractor shall keep the Authorityadvised as to when batching and mixing ofconcrete, installation of reinforcement andforming, preparations for placing and placingof concrete, finishing, and repair of concretewill be performed. Unless inspection is waivedin each specific case, these constructionactivities shall be performed only in thepresence of a duly authorized Authorityinspector.H-3. Composition. -(a) General. -Concrete

shall be composed of cement, pozzolan, sand,coarse aggregate, water, and admixtures asspecified, all well mixed and brought to theproper consistency. It is contemplated thatpozzolan will be used in all concrete except formiscellaneous items of concrete whereelimination of pozzolan is directed by theContracting Authority.

CONCRETE SPECIFICATIONS-Sec. H-3 513

(b ) Maximum Size of Aggregate. -Themaximum size of coarse aggregate in concretefor any part of the work shall be the largest ofthe specified sizes, the use of which ispracticable from the standpoint of satisfactoryconsolidation of the concrete by vibration.

Except where it is determined by theAuthority that, owing to closely spacedreinforcement or other reasons, the use of asmaller maximum size of aggregate is necessaryto obtain satisfactory placement of theconcrete, the maximum size of aggregate shallbe as follows:

( 1) Six-inch maximum-size aggregate shall,in general, be used in concrete for the dam,stilling basins, gravity walls, and elsewhere inother equally massive portions of structureswhere c o n c r e t e con ta in ing the 6-inchmaximum-size aggregate can be properlyplaced.

(2) Three-inch maximum-size aggregate shallbe used in concrete for walls that are 15 inchesor more in thickness and in slabs that are 8inches or more in thickness, such as in massivefloors and walls, and elsewhere where concretecontaining 6-inch maximum-size aggregatecannot be placed, except that the requirementsof subsection (3) below shall apply for tunnels,and for structures under conditions indicated.

(3) Three-inch maximum-size aggregate shallbe used in concrete in tunnels where theconcrete is 12 inches or more in thickness andthe reinforcement, if any, consists of only onerow or will not otherwise prevent satisfactoryplacement of the concrete, as determined bythe Authority: Provided, that the contractormay use 2%inch maximum-size aggregate tofacilitate pumping: Provided further, that thecontractor may use 2X-inch maximum-sizeaggregate in concrete that would otherwisecontain 3-inch maximum-size aggregatew h e n e v e r c o n c r e t e con ta in ing 2%-inchmaximum-size aggregate is being used at thattime in work requiring pumping. One andone-half-inch maximum-size aggregate shall beused in concrete in tunnels where the concreteis less than 12 inches in thickness and forgreater thicknesses when it is determined bythe Authority that concrete containing a larger

maximum size of aggregate cannot be properlyplaced.

(4) One and one-half-inch maximum-sizeaggregate shall be used in concrete for walls(except tunnel walls) that are less than 15inches in thickness and in slabs that are lessthan 8 inches in thickness. However, where thewalls or slabs are so heavily reinforced that1%inch size aggregate cannot be properlyplaced, as determined by the Authority, %-inchmaximum-size aggregate may be permitted.

(5) In locations where concrete is to beplaced against excavated surfaces and thethickness of concrete to be placed is greatert h a n t h a t s h o w n o n the d r awings ,correspondingly larger maximum size aggregatefrom that specified for the thickness ofconcrete shown on the drawings shall be used:Provided, that aggregate with a maximum sizegreater than that indicated above will not berequired.

(c) Mix Proportions. -The proportions inwhich the various ingredients are to be used fordifferent parts of the work and the appropriatewater to portland cement plus pozzolan ratiow i l l b e d e t e r m i n e d b y t h e A u t h o r i t y .Adjustments in the mix proportions and waterto portland cement plus pozzolan ratio will bemade by the Authority from time to timeduring the progress of the work, as tests aremade of samples of the aggregates and theresulting concrete. These adjustments will havethe objective of procuring concrete havingsuitable workability, density, impermeability,durability, and required strength, without theuse of an excessive amount of cement.

It is contemplated that the composition ofthe concrete will be within the ranges given inthe accompanying tabulation.

The proportions shown in the referencedtabulation may be modified by the Authorityto suit the work or the nature of the materials,or to comply with limitations on the water toportland cement plus pozzolan ratio, and thecontractor shall be entitled to no extracompensation by reason of such modification.

The net water to portland cement pluspozzolan ratio of the concrete (exclusive ofwater absorbed by the aggregates) shall not


Maximum sizeof aggregate

(inches)

Cementing materials, portlandcement plus pozzolan (approximate) Coarse aggregate, percent of total

Percent pozzolan Sand, percent coarse aggregate only, by weightTotal pounds (by weight of of total aggre- 3% to 1 % 3

per cubic yard portland cement gate, by weight 3116 to 1 % to toof concrete plus pozzolan) 3% inch inches 3 inches 6 inches

63

1 %Y4

(Values to be determined by laboratory tests and inserted here for specifications.)

exceed 0.47, by weight, for concrete in thinsections of structures which will be exposed tofrequent alternations of freezing and thawing,such as curbs, gutters, sills, the top 2 feet ofwalls, piers, and parapets; and walls ofstructures in the range of fluctuating waterlevels or subject to spray. The net water toportland cement plus pozzolan ratio shall notexceed 0.53, by weight, for other concrete instructures which will be exposed to freezingand thawing. The net water to portland cementplus pozzolan ratio shall not exceed 0.60, byweight, for mass concrete in the dam, stillingbasin, gravity walls, and elsewhere in otherequally massive portions of structures; and forconcrete in structures that will be covered withfill material or be continually submerged orotherwise protected from freezing and thawing.

(d) Consistency. -The amount of water usedin the concrete shall be regulated as required tosecure concrete of the proper consistency andto adjust for any variation in the moisturecontent or grading of the aggregates as theye n t e r t h e m i x e r . A d d i t i o n o f w a t e r t ocompensate for stiffening of the concreteb e f o r e p l a c i n g w i l l n o t b e p e r m i t t e d .Uniformity in concrete consistency from batchto batch will be required.

The slump of the concrete, after theconcrete has been deposited but before it hasbeen consolidated, shall not exceed 2 inchesfor mass concrete; for concrete in the tops ofwalls, piers, parapets, and curbs; and forconcrete in slabs that are horizontal or nearlyhorizontal. Similarly, the slump shall notexceed 4 inches for concrete in sidewalls andarch of tunnel lining; and 3 inches for all otherconcrete. The Authority reserves the right torequire a lesser slump whenever concrete ofsuch lesser slump can be consolidated readily

into place by means of the vibration specifiedin section H-18(c) (Consolidation). The use ofbuckets, chutes, hoppers, or other equipmentwhich will not readily handle and placeconcrete of such lesser slump will not bepermitted.

(e) Tests. -The compressive strength of theconcrete will be determined by the Authoritythrough the medium of tests of 6- by 12-inchcylinders made and tested in accordance withdesignations 29 to 33, inclusive, of the eighthedition of the Bureau of Reclamation ConcreteManual [ 11, except that, for all concretesamples from which cylinders are to be cast,the pieces of coarse aggregate larger than 1%inches will be removed by screening or handpicking. Slump tests will be made by theAuthority in accordance with designation 22.

H-4. Cement. -(a) General. -Cement forconcrete, mortar, and grout shall be furnishedby the contractor. The cement shall be freefrom lumps, unground clinker, tramp metal,and other foreign material, and shall beotherwise undamaged when used in concrete. Ifthe cement is delivered in paper bags, emptypaper bags shall be disposed of as directed. Thecontractor shall inform the ContractingAuthority in writing, at least 60 days beforefirst shipments are required, concerning themill or mills from which the cement is to beshipped; whether cement will be ordered inbulk or in bags; and the purchase ordernumber, contract number, or other designationthat will identify the cement to be used by thecontractor.

When bulk cement is not unloaded from theprimary carriers directly into weathertighthoppers at the batching plant, transportationfrom the mill, railhead, or intermediate storageto the batching plant shall be accomplished in


adequately weathertight trucks, conveyors, orother means which will protect the cementcompletely from exposure to moisture.Separate facilities, other than those providedfor pozzolan, shall be provided for unloading,transporting, storing, and handling bulkcement. Locked unloading facilities shall beprovided, and unloading of cement shall beperformed only i n t h e p r e s e n c e o f t h eAuthority or his representative. Immediatelyupon receipt at the jobsite, bulk cement shallbe stored in dry, weathertight, and properlyventilated bins which shall be constructed sothat there will be no dead storage. All storagefacilities shall be subject to approval and shallbe such as to permit easy access for inspectionand identification.

The bins shall be emptied and cleaned by thecontractor when so directed; however, theintervals between required cleanings willnormally be not less than 4 months. If cementis obtained from more than one cement plant,shipments from each plant shall be blendedwith those from the other plant or plants byplacing the cement from the different plants inalternate layers when unloading into silos atthe railhead or at the jobsite, or by any othermethod satisfactory to the Authority. Toprevent undue aging of cement furnished inbags, after delivery, the contractor shall use thebagged cement in the chronological order inwhich it was delivered to the jobsite. Eachshipment of cement in bags shall be stored sothat it may readily be distinguished from othershipments.

The cement shall meet the requirements ofFederal Specification SS-C- 192G [ 91, includingAmendment 3 for type II, low-alkali cement,and shall meet the false-set limitation specifiedtherein. In addition, cement for contractionjoint grouting shall be air separated, and 100percent o f t h e f i n i s h e d p r o d u c t , afterprocessing at the cement plant, shall pass a No.30 United States standard sieve and 97.7percent shall pass a No. 100 United Statesstandard sieve. Cement for contraction jointgrouting shall also be screened at the jobsitethrough a No. 16 crimped screen which shall beinstalled by the contractor between the mixerand agitator in the grout plant. The cement for

contraction joint grouting shall be furnished inwaterproof bags which will prevent hydrationof the cement from exposure and also preventlumping of the cement due to warehouse setfor a minimum of 90 days. Cement forfoundation grouting shall be furnished in bags:Provided, that bulk cement may be used forsuch grouting if a suitable method, satisfactoryto the Authority, is used for weighing andaccounting for the cement used.

(b) Inspection. -Except for sieve fineness ofcement for contraction joint grouting, thecement will be sampled and tested by theAuthority in accordance with Federal TestMethod Standard No. 158A [ 1 I], includingChange Notice 1 thereto, except that for initialpenetration under method 2501.1 the rod shallbe released 20 seconds after completion ofmixing, and except that the note at the end ofmethod 2501.1 concerning variations in initialpenetration will be disregarded.

Fineness tests of the cement for contractionjoint grouting will be made by the Authority inaccordance with ASTM Designation C 184 [ 51,except that the tests will be performed on No.30 and No. 100 sieves.

Acceptance tests, except for false set butincluding fineness tests, will be made onsamples taken as bins of cement are filled andr e s e r v e d f o r e x c l u s i v e A u t h o r i t y u s e .Acceptance tests for false set will be made onsamples taken from the cement at the latesttime, prior to shipment in cars or trucks, thatthe cement is still in possession of the cementc o m p a n y . C e m e n t n o t m e e t i n g t e s trequirements will be rejected, a n d t h econtractor shall be entitled to no adjustmentsin price or completion time by reason of anydelays occasioned thereby.

The contractor will be charged the cost oftesting of all Authority-tested cement whichhas been ordered in excess of the amount ofc e m e n t u s e d f o r t h e w o r k u n d e r t h e s especifications. The charges to be made for thecost of testing excess cement will be at the rateof 3.5 cents per hundredweight (cwt.), whichcharge includes the Authority overhead, andwill be deducted from payments due thecontractor.

( c ) M e a s u r e m e n t a n d Pay men t.-


accomplished in adequately designed trucks,conveyors, or other means which will protectthe pozzolan completely from exposure tomoisture. Separate facilities, other than thosefor cement, shall be provided for unloading,transporting, storing, and handling bulkpozzolan. Locked unloading facilities shall beprovided and unloading of pozzolan shall beperformed only in the presence of theContracting Authority or his representative.

Immediately upon receipt at the jobsite,bulk pozzolan shall be stored in dry,weathertight, and properly ventilated bins. Allstorage facilities shall be subject to approvaland shall be such as to permit easy access fori n s p e c t i o n and identification. Sufficientpozzolan shall be in storage at all times tocomplete any concrete lift or placementstarted. The bins shall be emptied and cleanedby the contractor when so directed; however,the intervals between required cleanings willnormally be not less than 4 months. Thepozzolan shall be free from lumps and shall beotherwise undamaged when used in concrete.

The contractor shall inform the Authority inwriting, within 60 days after date of notice toproceed, concerning the source or sources fromwhich he proposes to obtain the pozzolan;together with information as to location,shipping point or points, purchase ordernumber, contract number, or other designationand information that will identify the pozzolanto be used by the contractor.

(b) Inspection. -The pozzolan will besampled and tested by the Authority ina c c o r d a n c e with Federal SpecificationSS-P-570B [ 101. Acceptance tests will be madeon a lot or lots of pozzolan, which lot or lotsshall be reserved in bulk storage in sealed binsat the source for exclusive Authority use.Untested lots shall not be intermingled orcombined with tested and approved lots untilsuch lots have been tested and approved.Pozzolan will also be sampled at the jobsitewhen determined necessary. Release forshipment and approval for use will be based oncompliance with 7-day lime-pozzolan strengthrequirements and other physical and chemicaland uniformity requirements for which testscan be completed by the time the 7-day

Measu remen t , f o r paymen t , o f c emen tfurnished in bags will be on the basis of thenumber of bags of cement used at the mixer.Measurement, for payment, of bulk cementwill be on the basis of batch weights at thebatching plant. Any cement, either bulk or inbags, used for grouting, finishing, or othermiscellaneous work will be measured forpayment in the most practicable manner. Onebag of cement shall be considered as 0.94hundredweight.

Payment will be made for cement used inconcrete placed within the. pay lines forconcrete; and for cement used in concreteplaced outside the concrete pay lines, unlessthe r equ i r emen t f o r s u c h c o n c r e t e i sdetermined by the Authority to be the resulto f c a r e l e s s e x c a v a t i o n , o r excavationintentionally performed by the contractor tofacilitate his operations. No payment will bemade for cement used as follows: cement usedin wasted concrete, mortar, or grout; cementused in the replacement of damaged ordefective concrete; cement used in extraconcrete required as a result of carelessexcavation; and cement used in concrete placedby the contractor in excavation intentionallyperformed by the contractor to facilitate hisoperations. As determined by the Authority,payment will be made for a reasonable amountof cement used in grout required to keep thepipelines full during the grouting operations.

Payment for furnishing and handling cementwill be made at the applicable unit prices perhundredweight or bag bid therefor in theschedule, which unit prices shall include thecost of rail and truck transportation of thecement from the mill to the jobsite and thecost of storing the cement.

H-5. Pozzolan. -(a) General. -Pozzolan forconcrete shall be furnished by the contractor.The contractor shall use pozzolan concrete asprovided in section H-3 (Composition). Thepozzolan shall be in accordance with FederalSpecification SSP-570B [ 101.

When bulk pozzolan is not unloaded fromprimary carriers directly into weathertighthoppers at the batching plant, transportationfrom the source railhead or intermediates t o r a g e t o t h e b a t c h i n g p l a n t s h a l l b e


lime-pozzolan strength test is completed.Release for shipment and approval for use ont h e a b o v e b a s i s w i l l b e c o n t i n g e n t o ncon t inu ing compliance w i t h t h e o t h e rrequirements of the specifications. Nopozzolan shall be shipped until notice has beengiven that the test results are satisfactory andall shipments will be made under supervision ofthe Authority. Any lot or lots of pozzolan notmeeting test requirements will be rejected.Rejected pozzolan shall be replaced withacceptable pozzolan, and the contractor shallbe entitled to no adjustments in price orcompletion time by reason of any delaysoccasioned thereby.

The contractor will be charged the cost oftesting of all Authority-tested pozzolan whichhas been ordered in excess of the amount ofpozzolan used for the work under thesespecifications. The charges to be made for thecost of testing excess pozzolan will be at thetesting rate per ton plus overhead cost to theAuthority and will be deducted from paymentsdue the contractor.

( c ) M e a s u r e m e n t a n d Payment.-Measurement, for payment, of pozzolan will bemade on the basis of batch weights at thebatching plant with deductions made for thepercentage of moisture in the pozzolan. Themoisture content will be determined by heatinga 500-gram sample to constant weight in anoven at 105’ C. The percentage of moisturewill be 100 times the quantity obtained bydividing the loss in weight, in grams, by theweight in grams of the moist sample. Anypozzolan used for miscellaneous work will bemeasured in the most practicable manner.

Pozzolan will be paid for on the basis of thenumber of tons (2,000 pounds net dry weight)used in the work covered by thesespecifications. No payment will be made forpozzolan used as follows: pozzolan used inwasted concrete; pozzolan used in thereplacement of damaged or defective concrete;pozzolan used in extra concrete required as aresult of careless excavation; and pozzolan usedin concrete placed by the contractor inexcavation intentionally performed by thecontractor to facilitate his operations.

Payment fo r fu rn i sh ing and hand l ing

pozzolan will be made at the unit price per tonbid therefor in the schedule, which unit priceshall include the cost of rail and trucktransportation of the pozzolan from the mill tothe jobsite a n d t h e c o s t o f s t o r i n g t h epozzolan.

H-6. Admixtures. -(a) Accelerator.-Calcium chloride shall not be used in concretein which aluminum or galvanized metalwork isto be embedded or in concrete where it maycome in contact with prestressed steel. Thecontractor shall use 1 percent of calciumchloride, by weight of the cement, in all otherconcrete p l a c e d w h e n t h e m e a n d a i l ytemperature in the vicinity of the worksite islower than 40’ F. Calcium chloride shall notbe used otherwise, except upon writtenapproval o f t he Con t r ac t i ng Authority.Request for such approval shall state the reasonfor using calcium chloride and the percentageof calcium chloride to be used and the locationof the concrete in which the contractor desiresto use the calcium chloride. Calcium chlorideshall not be used in excess of 2 percent, byweight of the cement. Calcium chloride shall bemeasured accurately and shall be added to thebatch in solution in a portion of the mixingwater. Use of calcium chloride in the concreteshall in no way relieve the contractor ofr e s p o n s i b i l i t y f o r c o m p l i a n c e w i t h t h erequirements of these specifications governingprotection and curing of the concrete.

(b) Air-En training Agen ts .-An air-entraining agent shall be used in all concrete.The agent used shall conform to ASTMD e s i g n a t i o n C 2 6 0 161, excep t t ha t t helimitation and test on bleeding by concretecontaining the agent and the requirementrelating to time of setting shall not apply. Theagent shall be of uniform consistency andquality within each container and fromshipment to shipment. Agents will be acceptedon manufacturer’s certification of compliancewi th specifications: Provided, t ha t theAuthority reserves the right to requiresubmission of and to perform tests on samplesof the agent prior to shipment and use in thework and to sample and test the agent afterdelivery at the jobsite.

The amount of air-entraining agent used in


each concrete mix shall be such as will effectthe entrainment of the percentage of air shownin the following tabulation in the concrete asdischarged from the mixer:

Maximum size ofcoarse aggregate

in inches

Total air, percentby volume of

concrete

=/4 6.0 plus or minus 11 % 4.5 plus or minus 13 3.5 plus or minus 16 3.0 plus or minus 1

The agent in solution shall be maintained atuniform strength and shall be added to thebatch in a portion of the mixing water. Thissolution shall be accurately batched by meansof a reliable mechanical hatcher which shall beso constructed that the full measure of solutionadded to each batch of concrete can beobserved in a sight gage by the plant operatorprior to discharge of the solution into themixer. When calcium chloride is being used inthe concrete, the portion of the mixing watercontaining the air-entraining agent shall beintroduced separately into the mixer.

(c) Water-Reducing, Set-ControllingAdmixture. -The contractor shall, except ashereinafter provided, use a water-reducing,set-controlling admixture, referred to herein asWRA, in all concrete. The WRA used shall bee i t h e r a suitable lignosulfonic-acid orhydroxylated-carboxylic-acid type.

The WRA shall be of uniform consistencyand quality within each container and fromshipment to shipment. WRA will be acceptedon manufacturer’s certification of conformanceto Bureau of Reclamation “Specifications andM e t h o d o f T e s t f o r W a t e r - R e d u c i n g ,Set-Controlling Admixtures for Concrete,”dated August 1, 1971: Provided, that theAuthority reserves the r i gh t t o r equ i r esubmission of and to perform tests on samplesof the agent prior to shipment and use in thework and to sample and test the agent afterdelivery at the jobsite.

If Authority testing of the WRA is required,the contractor shall submit a sample of theWRA and five bags (94 pounds each) of thecement proposed for use in the work at least

90 days before use is expected. The size of thesample of WRA to be submitted shall be 1liquid gallon.

The quantity of WRA to be used in eachconcrete batch shall be determined by theAuthority and for the lignosulfonic-acid typeshall not exceed 0.40 percent, by weight ofcement plus pozzolan, of solid crystallinelignin, and for the hydroxylated-carboxylic-acid type shall not exceed 0.50 percent, byweight of cement plus pozzolan, of liquid.

Since the quantity of WRA required willvary with changing atmospheric conditions, thequantity used shall be commensurate with theprevailing conditions. The Authority reservesthe right to use lesser quantities or no WRA inconcrete for any part of the work, dependingon climatic or other job conditions, and thecontractor shall be entitled to no additionalcompensation by reason of reduction in orelimination of WRA in any concrete to beplaced under these specifications.

The WRA solution shall be measured foreach batch by means of a reliable visualmechanical dispenser. The WRA, in a suitablydilute form, may be added to water containingair-entraining agent for the batch if thematerials are compatible with each other, orshall be introduced separately to the batch in aportion of the mixing water if the two areincompatible.

When requested, the contractor shall submittest data by the manufacturer showing effectsof the WRA on mixing water requirements,setting time of concrete, and compressivestrength at various ages up to 1 year.

The contractor shall be responsible for anydifficulties arising or damages occurring as aresult of the selection and use of WRA, such asdelay or difficulty in concrete placing ordamage to the concrete during form removal.T h e c o n t r a c t o r s h a l l b e e n t i t l e d t o n oadditional compensation above the unit pricesbid in the schedule for concrete by reason ofsuch difficulties.

(d) Furnishing Admixtures. -Air-entrainingagent, accelerator, and WRA, as required, shallbe furnished by the contractor, and the cost ofthe materials and all costs incidental to their


use shall be included in the applicable pricesbid in the schedule for concrete in which thematerials are used.

H-7. Water.-The water used in concrete,mortar, and g rou t shall be free fromobjectionable quantities of silt, organic matter,alkali, salts, and other impurities.

H-8. Sand. -(a) General. -The term “sand”is used to designate aggregate in which themaximum size of particles is 3/l 6 of an inch.Sand for concrete, mortar, and grout shall befurnished by the contractor and shall benatural sand, except that crushed sand may beused to make up deficiencies in the naturalsand grading. The contractor shall maintain atleast three separate stockpiles of processedsand; one to receive wet sand, one in theprocess of draining, and one that is drained andready for use. Sand to be used in concrete shallbe drawn from the stockpile of drained sandwhich shall have been allowed to drain for aminimum of 48 hours. Sand, as delivered to thebatching plant, shall have a uniform and stablemoisture content, which shall be less than 6percent free moisture.

(b) Quality. -The sand shall consist of clean,hard, dense, durable, uncoated rock fragments.The maximum percentages of deleterioussubstances in the sand, as delivered to themixer, shall not exceed the following values:

Deleterious substancePercent,by weight

Material passing No. 200 screen(designation 16) . . . . . . . . . . . .

Lightweight material (designation 17) .Clay lumps (designation 13) . . . . . .Total of other deleterious substances

(such as alkali, mica, coated grains,soft flaky particles, and loam) . . , .

. 3

. . . 2

. . . 1

. . . 2

The sum of the percentages of all deleterioussubstances shall not exceed 5 percent, byweight. Sand producing a color darker than thestandard in the calorimetric test for organicimpurities (designation 14) may be rejected.Sand having a specific gravity (designation 9)saturated surface-dry basis, of less than 2.60may be rejected. The sand may be rejected ifthe portion retained on a No. 50 screen, whensubjected to 5 cycles of the sodium sulfate testfor soundness (designation 19), shows a

weighted average loss of more than 8 percent,by weight. The designations in parenthesesrefer to methods of tests described in theeighth edition of the Bureau of ReclamationConcrete Manual [ 11 .

(c) Grading. -The sand as batched shall bewell graded, and when tested by means ofstandard screens (designation 4) shall conformto the following limits:

Screen No.

Individual percent,by weight,

retained on screen

4 0 to 58 * 5to15

16 *lO to 2530 10to3050 15 to 35

100 12to20Pan 3 to 7

*If the individual percent retained on the No. 16screen is 20 percent or less, the maximum limit for theindividual percent retained on the No. 8 screen may beincreased to 20 percent.

The grading of the sand shall be controlledso that at any time the fineness moduli(designation 4) of at least 9 out of 10consecutive test samples of finished sand willnot vary more than 0.20 from the averagefineness modulus of the 10 test samples.

H-9. Coarse Aggregate. -(a) General. -Theterm “coarse aggregate,” for the purpose ofthese specifications, designates aggregate ofsizes within the range of 3/16 of an inch to 6inches or any size or range of sizes within suchlimits. The coarse aggregate shall be reasonablywell graded within the nominal size rangeshereinafter specified. Coarse aggregate forconcrete shall be furnished by the contractorand shall consist of natural gravel or crushedrock or a mixture of natural gravel and crushedrock.

Coarse aggregate, a s d e l i v e r e d t o t h ebatching plant, shall have a uniform and stablemoisture content.

(b) Quality. -The coarse aggregate shallconsist of clean, hard, dense, durable, uncoatedrock fragments. The percentages of deleterioussubstances in any size of coarse aggregate, asdelivered to the mixer, shall not exceed thefollowing values:


Percent,by weight

Material passing No. 200 screen(designation 16) . . . . . . . . . . . . . . . %

Lightweight material (designation 18) . . . . . 2Clay lumps (designation 13) . . . . . . . . . . . %Other deleterious substances . . . . . . . . . . . 1

The sum of the percentages of all deleterioussubstances in any size, as delivered to themixer, shall not exceed 3 percent, by weight.Coarse aggregate may be rejected if it fails tomeet the following test requirements:

( 1 ) L o s A n g e l e s r a t t l e r t e s t(designation 21 ).-If the loss, usinggrading A, exceeds 10 percent, by weight,at 100 revolutions or 40 percent, byweight, at 500 revolutions.

(2) Sodium sulfate test for soundness(designation 19).-If the weighted averageloss after 5 cycles is more than 10 percentby weight.

(3) Specific gravity (designationlo).-If the specific gravity (saturatedsurface-dry basis) is less than 2.60.

The designations in parentheses refer tomethods of test described in the eighthedition of the Bureau of Reclamation ConcreteManual [ 11.

(c) Separation. -The coarse aggregate shallbe separated into nominal sizes and shall begraded as follows:

Designationoi: size(inches)

%1 %36

Nominalsize range(inches)

3/16 to %$4 to 1%

11/2to 33 to 6

Minimum percentretained on

screens indicatedSize of screen

Percent (inches)

50 31825 1%2 0 2%2 0 5

Coarse aggregate shall be finished screenedon vibrating screens mounted over the batchingplant, or at the option of the contractor, thescreens may be mounted on the groundadjacent to the batching plant. The finishscreens, if installed over the batching plant,shall be so mounted that the vibration of thescreens will not be transmitted to, or affect theaccuracy of the batching scales. The sequenceof coarse aggregate handling and plant

management shall be such that, if final and/orsubmerged cooling are used, excessive freemoisture shall be removed and diverted outsideof the plant by dewatering screens prior tofinish screening so that a uniform and stablemoisture content is maintained in the plantstorage and batching bins. The method and rateof feed shall be such that the screens will notbe overloaded and will operate properly in amanner that will result in a finished productwh ich cons i s t en t l y mee t s t he g r ad ingrequirements of these specifications. Thefinished products shall pass directly to theindividual batching bins. Material passing the3/16-inch screen that is removed from thecoarse aggregate as a result of the finishedscreening operation shall be wasted.

Separation of the coarse aggregate into thespecified sizes, after finish screening, shall besuch that, when the aggregate, as batched, istested by screening on the screens designated inthe following tabulation, the material passingthe undersize test screen (significant undersize)shall not exceed 2 percent, by weight, and allmaterial shall pass the oversize test screen:

Aeereeate sizedesignation

(inches)Size of square opening in screen (inches)

For undersize test 1 For oversize test

Screens used in making the tests forundersize and oversize will conform to ASTMDesignation E 11 [7] , with respect to permis-sible variations in average openings.

H-10. Production of Sand and CoarseAggregate. -(a) Source of Aggregate.-Sand andcoarse aggregate for concrete, and sand formortar and grout may be obtained by thecontractor from any approved source ashereinafter provided.

If sand and coarse aggregate are to beobtained from a deposit not previously testedand approved by the Contracting Authority,the contractor shall submit representativesamples for preconstruction test and approvalat least 60 days after date of notice to proceed.The samples shall consist of approximately 200

CONCRETE SPECIFICATIONS-Sec. H-10

pounds each of sand and 3/l 6- to 3/4-inch sizeof coarse aggregate, and 100 pounds of each ofthe other sizes of coarse aggregate.

The approval of deposits by the Authorityshall not be construed as constituting theapproval of all or any specific materials takenfrom the deposits, and the contractor will beheld responsible for the specified quality of allsuch materials used in the work.

In addition to preconstruction test andapproval of the deposit, the Authority will testthe sand and coarse aggregate during theprogress of the work and the contractor shallprovide such facilities as may be necessary forprocuring representative samples.

If any deposit used by the contractor islocated within an approved area owned orcontrolled by the Authority, no charge will bemade to the contractor for materials takenfrom such deposit and used in the workcovered by these specifications. Any royaltiesor other charges required to be paid formaterials taken from deposits not owned orcontrolled by the Authority shall be paid bythe contractor.

(b) Developing Aggregate Deposit. -Thecontractor shall carefully clear the area of thedeposit, from which aggregates are to beproduced, of trees, roots, brush, sod, soil,unsuitable sand and gravel, and otherobjectionable matter. If the deposit is ownedor controlled by the Authority, the portion ofthe deposit used shall be located and operatedso as not to detract from the usefulness of thedeposit or of any other property of theAuthority and so as to preserve, insofar aspracticable, the future usefulness or value ofthe deposit. Materials, including stripping,removed from deposits owned or controlled bythe Authority and not used in the workcovered by these specifications shall bedisposed of as directed.

The contractor’s operations in and aroundaggregate deposits shall be in accordance withthe provisions of the specifications sections onenvironmental protection.

(c) Processing Raw Materials. -Processing ofthe raw materials shall include screening, andwashing as necessary, to produce sand andcoarse aggregate c o n f o r m i n g t o t h e

521

requirements of sections H-8 (Sand) and H-9(Coarse Aggregate). Processing of aggregatesproduced from any source owned or controlledby the Authority shall be done at an approvedsite. Water used for washing aggregates shall befree from objectionable quantities of silt,0 rganic matter, alkali, salts, and otherimpurities. To utilize the greatest practicableyield of suitable materials in the portion of thedeposit being worked, the contractor maycrush oversize material and any excess materialof the sizes of coarse aggregate to be furnished,until the required quantity of each size hasbeen secured: Provided, that crusher finesproduced in manufacturing coarse aggregatethat will pass a screen having 3/16-inch squareopenings shall be wasted or rerouted throughthe sand manufacturing plant. Crushed sand, ifused to make up deficiencies in the naturalsand grading, shall be produced by a suitableball or rod mill, disk or cone crusher, or otherapproved equipment so that the sand particlesshall be predominately cubical in shape andfree from objectionable quantities of flat orelongated particles.

The crushed sand and coarse aggregate shallbe blended uniformly with the uncrushed sandand coarse aggregate, respectively. Crushingand blending operations shall at all times besubject to approval by the Authority. Thehandling, transporting, and stockpiling ofaggregates shall be such that there will be aminimum amount of fines resulting frombreakage and abrasion of material caused byfree fall and improper handling. Where excessesin any of the sand and coarse aggregate sizesoccur, the contractor shall dispose of theexcess material as directed by the Authority.

(d) Furnishing Aggregates. -The cost ofproducing aggregates required for work underthese specifications and the cost of aggregatesn o t o b t a i n e d f r o m a s o u r c e owned o rcontrolled by the Authority shall be includedin the unit prices bid in the schedule forconcrete in which the aggregates are used,which unit prices shall also include all expensesof the contractor in stripping, transporting, andstoring the materials. The contractor shall beentitled to no additional compensation formaterials wasted from a deposit, including

522

crusher fines, excess material of any of thesizes into which the aggregates are required tobe separated by the contractor, and materialswhich have been discarded by reason of beingabove the maximum sizes specified for use.

H-l 1. Batching. -(a) General. -Thecontractor shall provide equipment and shallmaintain and operate the equipment asrequired to accurately determine and controlt h e p r e s c r i b e d a m o u n t s o f t h e v a r i o u smaterials, including water, cement, pozzolan,admixtures, sand, and each individual size ofcoarse aggregate entering the concrete. Theamounts of bulk cement, pozzolan, sand, andeach size of coarse aggregate entering eachbatch of concrete shall be determined byseparate weighing, and the amounts of waterand each admixture shall be determined byseparate weighing or volumetric measurement.Where bagged cement is used, the concreteshall be porportioned on the basis of integralbags of cement unless the cement is weighed.

When bulk cement, pozzolan, and aggregatesare hauled from a central batching plant to themixers, the cement and pozzolan for eachbatch shall either be placed in an individualcompartment which during transit will preventthe cement and pozzolan from interminglingwith each other and with the aggregates andwill prevent loss of cement and pozzolan; orthe cement and pozzolan shall be completelyenfolded in and covered by the aggregates byloading the cement, pozzolan, and aggregatesfor each batch simultaneously into the batchcompartment. The bins of batch trucks shall beprovided with suitable covers to protect thematerials therein from wind or wet weather.Each batch compartment shall be of sufficientcapacity to prevent loss in transit and toprevent spilling and intermingling of batches ascompartments are being emptied. If the cementand pozzolan are enfolded in aggregatescontaining moisture, and delays occur betweenfilling and emptying the compartments thecontractor shall, at his own expense, add extracement to each batch in accordance with thefollowing schedule:

DESIGN

*Hours of contact betweencement and wet aggregate

oto 22 to 33 to 44 to 55 to 6Over 6

OF GRAVITY DAMS

Additionalcement required

0 percent5 percent

10 percent1.5 percent20 percentBatch will be

rejected.

*The Contracting Authority reserves the right to requirethe addit ion of cement for shorter periods of contactduring periods of hot weather and the contractor shall beentitled to no additional compensation by reason of theshortened period of contact.

Batch bins shall be constructed so as to beself-cleaning during drawdown and the binsshall be drawn down until they are practicallyempty at least three times per week. Materialsshall be deposited in the batch bins directlyover the discharge gates. The 1%, 3-, and&inch coarse aggregates shall be deposited inthe hatcher bins through effective rock ladders,or other approved means. To minimizebreakage, the method used in transporting theaggregates from one elevation to a lowerelevation shall be such that the aggregates willroll and slide with a minimum amount of freefall.

Equipment for conveying batched materialsffom the batch hopper or hoppers to and intothe mixer shall be so constructed, maintained,and operated that there will be no spillage ofthe batched materials or overlap of batches.Equipment for handling portland cement andpozzolan in the batching plant shall beconstructed and operated so as to preventnoticeable increase of dust in the plant duringthe measuring and discharging of each batch ofmaterial. If the batching and mixing plant isenclosed, the contractor shall install exhaustfans or other suitable equipment for removingdust.

( b ) E y u i p m e n t . -The weigh ing andmeasuring equipment shall conform to thefollowing requirements:

( 1) The construction and accuracy ofthe equipment shall conform to theapplicable requirements of Federal

CONCRETE SPECIFICATIONS-Sec. H- l 1

Specification AAA-S-121d [ 81 for suchequipment, except that an accuracy of 0.4percent over the entire range of theequipment will be required.

The contractor shall provide standardtest weights and any other equipmentrequired for checking the operatingperformance o f e a c h s c a l e o r o t h e rmeasuring device and shall make periodictests over the ranges of measurementsinvolved in the batching operations. Thetests shall be made in the presence of anA u t h o r i t y i n s p e c t o r , a n d s h a l l b eadequate to prove the accuracy of themeasuring devices. Unless otherwisedirected, tests of weighing equipment inoperation shall be made at least onceevery month. The contractor shall makesuch adjustments, repairs, or replacementsas may be necessary to meet the specifiedr e q u i r e m e n t s f o r a c c u r a c y o fmeasurement.

(2) Each weighing unit shall include avisible springless dial which will registerthe scale load at any stage of the weighingoperation from zero to full capacity. Theminimum clear interval for dial scalegraduations shall be not less than 0.03inch. The scales shall be direct reading towithin 5 pounds for cement and 20pounds for aggregate. The weighinghoppers shall be constructed so as top e r m i t t h e c o n v e n i e n t r e m o v a l o foverweight materials in excess of theprescribed tolerances. The scales shall beinterlocked so that a new batch cannot bestarted until the weighing hoppers havebeen completely emptied of the last batchand the scales are in balance. Each scaledial shall be in full view of the operator.

(3) The equipment shall be capable ofready adjustment for compensating forthe varying weight of any moisturecontained in the aggregates and forchanging the mix proportions.

(4) The equipment shall be capable ofcontrolling the delivery of material forweighing or volumetric measurement sothat the combined inaccuracies in feedingand measuring during normal operation

523

will not exceed 1 percent for water; 1%percent for cement and pozzolan; 3percent for admixtures; 2 percent forsand, 3/4-inch aggregate, a n d lx-inchaggregate; and 3 percent for 3- and 6-inchcoarse aggregate.

(5) Convenient facili t ies shall bep r o v i d e d f o r r e a d i l y o b t a i n i n gr e p r e s e n t a t i v e samples o f c e m e n t ,pozzolan, admixtures, sand, and each sizeof coarse aggregate from the dischargestreams between bins and the batchhoppers or between the batch hoppersand the mixers.

(6) The operating mechanism in thewater-measuring device shall be such thatleakage will not occur when the valves areclosed. The water-measuring device shallbe constructed so that the water will bedischarged quickly and freely into themixer without objectionable dribble fromthe end of the discharge pipe. In additionto the water-measuring device, there shallbe supplemental means for measuring andintroducing small increments of waterinto each mixer when required for finalt e m p e r i n g o f t h e c o n c r e t e . T h i sequipment shall introduce the addedw a t e r w e l l i n t o t h e b a t c h . Eachwater-measuring device shall be in fullview of the operator.

(7) Dispensers for air-entraining agents,calcium chloride solutions, and WRA shallhave sufficient capacity to measure at onetime the full quantity of the properlydiluted solution required for each batch,and shall be maintained in a clean andfreely operating condition. Equipment formeasu r ing s h a l l b e d e s i g n e d forconvenient confirmation by the planto p e r a t o r o f t h e a c c u r a c y of themeasurement for each batch and shall beso constructed that the required quantitycan be added only once to each batch.

(8) The mixing plant shall be arrangedso that the mixing action in at least one ofthe mixers can be conveniently observedfrom its control station. Provisions shallbe made so that the mixing action of eachof the other mixers can be observed from


a safe location which can be easilyr e a c h e d f r o m t h e c o n t r o l s t a t i o n .Provisions shall also be made so that theoperator can observe the concrete in thereceiving hopper or buckets after beingdumped from the mixers.

(9) Equipment that fails to conform tothe requirements of this section shall beeffectively repaired or satisfactorilyreplaced.

H-12. Mixing. -(a) General. -The concreteingredients shall be mixed thoroughly in batchmixers of approved type and size and designedso as to positively ensure uniform distributionof all of the component materials throughoutthe mass at the end of the mixing period. Theadequacy of mixing will be determined by themethod of “Variability of Constituents inConcrete” in accordance with the provisions ofdesignation 26 of the eighth edition of theBureau of Reclamation Concrete Manual [ 11.Mixers when tested shall meet the followingcriteria:

(1) The unit weight of air-free mortarin samples taken from the first and lastportions of the batch as discharged fromthe mixer shall not vary more than 0.8percent from the average of the twomortar weights.

(2) For any one mix, the averagevariability for more than one batch shallnot exceed the following limits:

Average variability(percent based on average

Number of tests mortar weight of all tests)

3 0.66 .5

20 .49 0 .3

(3) The weight of coarse aggregate percubic foot in samples taken from the firstand last portions of the batch asdischarged from the mixer shall not varymore than 5.0 percent from the average ofthe two weights of coarse aggregate.

The Contracting Authority reserves the rightto either reduce the size of batch to be mixedor to increase the mixing time when thecharging and mixing operations fail to producea concrete batch which conforms throughout

to the above-numbered criteria and in whichthe ingredients are uniformly distributed andthe consistency is uniform. Water shall beadded prior to, during, and following themixer -charg ing operations. Overmixing,requiring addition of water to preserve therequired consistency, will not be permitted.Any concrete retained in mixers so long as torequire additional water in excess of 3 percentof the design mix water (net water-cement pluspozzolan ratio water, not including waterabsorbed by aggregates) to permit satisfactoryplacing shall be wasted. Any mixer that at anytime produces unsatisfactory results shall berepaired promptly and effectively or shall be:-eplaced.

Use of truck mixers in accordance withsubsection (c) below will be permitted only formiscellaneous items of concrete work whereand as approved by the Authority.

(b) Central Mixers. -Mixers shall not beloaded in excess of their rated capacity unlesss p e c i f i c a l l y a u t h o r i z e d . The concreteingredients shall be mixed in a batch mixer fornot less than the period of time indicated inthe following tabulation for various mixercapacities after all of the ingredients except thefull amount of water are in the mixer, exceptthat the mixing time may be reduced if, asdetermined by the Authority, thorough mixingconforming to subsections (a) (1) and (2)above can be obtained in less time.

Capacity of mixer

2 cubic yards or less3 cubic yards4 cubic yardsLarger than 4 cubic

yards

Time of mixing

1% minutes2 minutes2% minutesTo be determined by

tests performed bythe Authority

(c) Truck Mixers.-Use of truck mixers willbe permitted only when the mixers and theiro p e r a t i o n are s u c h t h a t t h e c o n c r e t ethroughout the mixed batch and from batch tobatch is uniform with respect to consistencyand grading. Any concrete retained in truckmixers sufficiently long as to require additionalwater to permit placing shall be wasted.

Each truck mixer shall be equipped with (1)an accurate watermeter between supply tankand mixer, the meter to have indicating dials


and totalizer, and (2) a reliable revolutioncounter, which can be readily reset to zero forindicating the total number of revolutions ofthe drum for each batch. Each mixer shall haveaffixed thereto a metal plate on which thedrum capacities for both mixing and agitatingare plainly marked in terms of volume ofconcrete in cubic yards and the maximum andminimum speeds of rotation of the drum inrevolutions per minute.

Mixing shall be continued for not less than50 nor more than 100 revolutions of the drumat the manufacturer’s rated mixing speed afterall the ingredients, except approximately 5percent of the water which may be withheld,are in the drum. The mixing speed shall be notless than 5 nor more than 20 revolutions perminute. Thereafter, additional mixing, if any,shall be at the speed designated by themanufacturer of the equipment as agitatingspeed; except that after the addition ofwithheld water, mixing shall be continued atthe specified mixing speed until the water isdispersed throughout the mix. After a periodof agitation a few revolutions of the drum atmixing speed will be required just prior todischarging. In no case shall the specifiedmaximum net water-cement plus pozzolanratio be exceeded.

When a truck mixer or agitator is used fortransporting concrete, the concrete shall bedelivered to the site and the dischargec o m p l e t e d w i t h i n 1 % h o u r s a f t e r t h eintroduction of the cement into the mixer.Each batch of concrete, when delivered at thejobsite from commercial ready-mix plants, shallbe accompanied by a written certificate ofbatch weights and time of batching.

Mixers shall be examined daily for changesin condition due to accumulation of hardconcrete or mortar or to wear of blades. Nomixer shall be charged in excess of its ratedcapacity for mixing or agitating; however, ifany mixer cannot produce concrete meetingthe requirements heretofore specified whenmixing at rated capacity, within the specifiedlimitation on the number of revolutions of themixing drum at mixing speed, the size of batchmixed in that mixer may be reduced until,upon testing, a uniformly mixed batch,

525

conforming to the mixer performance tests asprovided in subsection (a) above, is obtained.

H- 13. Temperature of Concrete. -Thetemperature of mass concrete for the damshall, when concrete is being placed, be notmore than 50’ F. and not less than 40’ F. Forall other concrete, the temperature of concretewhen it is being placed shall be not more than90’ F. and not less than 40° F. in moderateweather or not less than 50° F. in weatherduring which the mean daily temperature dropsbelow 40’ F. Concrete ingredients shall not beheated to a temperature higher than thatnecessary to keep the temperature of themixed concrete, as placed, from falling belowthe specified minimum temperature. Methodsof heating concrete ingredients shall be subjectto approval by the Contracting Authority.

If concrete is placed when the weather issuch that the temperature of the concretew o u l d e x c e e d t h e m a x i m u m p l a c i n gtemperatures specified, as determined by theAuthority, the contractor shall employeffective means as necessary to maintain thetemperature of the concrete, as it is placed,below the maximum temperatures specified.These means may include placing at night;precooling the aggregates by cool airblast,immersion in cold water, vacuum processing, orother suitable method; refrigerating the mixingwater; adding chip or flake ice to the mixingwater; or a combination of these or otherapproved means. The contractor shall beentitled to no additional compensation onaccount of the foregoing requirements.

H-14. Forms. -(a) General. -Forms shall beused, wherever necessary, to confine theconcrete and shape it to the required lines.Forms shall have sufficient strength tow i t h s t a n d t h e p r e s s u r e r e s u l t i n g f r o mplacement and vibration of the concrete, andshall be maintained rigidly in position. Formsshall be sufficiently tight to prevent loss ofmortar from the concrete. Chamfer strips shallbe placed in the corners of forms so as toproduce beveled edges on permanently exposedconcrete surfaces. Interior angles on suchsurfaces and edges at formed joints will notrequire beveling unless requirement forbeveling is indicated on the drawings. Inside

526

forms for nearly horizontal circular tunnelshaving an inside diameter of 12 feet or moreshall be constructed to cover only the arch andsides. The bottom 60’ of the insidecircumference shall be placed without forming:Provided, that the contractor may increase theangle of the inside circumference to be placedwithout forming on written approval of theContracting Authority. Request for approvalshall be accompanied by complete plans anddescription of the placing methods proposed tobe used.

Forms for tunnel lining shall be providedwith openings along each sidewall and in eacharch, each opening to be not less than 2 by 2feet. The openings shall be located in thecrown and along each sidewall, as follows:

(1) Openings in the crown shall bespaced at not more than 8 feet on centersand shall be located alternately on eachside of the tunnel centerline.

(2) Openings in sidewall forms fortunnels having an inside diameter less than12 feet shall be located at midheight ofthe tunnel in each sidewall and shall bespaced at not more than 8 feet on centersalong each sidewall.

(3) Openings in sidewall forms fortunnels having an inside diameter of 12feet or more shall be located along twolongitudinal lines in each sidewall, thelocations of which are satisfactory to theAuthority. The openings along the twoselected longitudinal lines in each sidewallshall be staggered and shall be spaced atnot more than 8 feet on centers alongeach longitudinal line.

The cost of all labor and materials for formsand for any necessary treatment or coating offorms shall be included in the unit prices bid inthe schedule for the concrete for which theforms are used.

(b) Form Sheathing and Lining.-Woodsheathing or lining shall be of such kind andquality or shall be so treated or coated thatthere will be no chemical deterioration ordiscoloration of the formed concrete surfaces.The type and condition of form sheathing andlining, and the fabrication of forms for finishesF2, F3, and F4 shall be such that the form


surfaces will be even and uniform. The abilityof forms to withstand distortion caused byplacement and vibration of concrete shall besuch that formed surfaces will conform withapplicable requirements of these specificationspertaining to finish of formed surfaces. Wherefinish F3 is specified, the sheathing or liningshall be placed so that the joint marks on theconcrete surfaces will be in general alinementboth horizontally and vertically. Where pine isused for form sheathing, the lumber shall bepinus ponderosa in accordance with theStandard Grading Rules of the Western WoodProducts Association or shall be other lumberof a grading equivalent to that specified forpine. Plywood used for form sheathing orlining shall be concrete form, class I, grade B-Bexterior, mill oiled and edge sealed, inaccordance with Product Standard PS l-66 ofthe Bureau of Standards [ 121. Materials usedfor form sheathing or lining shall conform withthe following requirements, or may be othermaterials producing equivalent results:Requiredfinish of Wood sheathing Steel sheathing

formed or lining or lining *surface

Fl

F 2

F 3

Any grade-S2E Steel sheathing per-mitted.

Steel lining permitted.No. 2 common or Steel sheathing per-

better, pine shiplap, mitted.or plywood sheathing Steel lining permittedor lining. if approved.

No. 2 common or Steel sheathing notbetter pine tongue-and- permitted.groove or plywood Steel lining notsheathing or lining, permitted.except where specialform material is

F 4prescribed.

For plane surfaces, S t e e l s h e - p e r -No. 1 common or betterpine tongue-and-groove or shiplap orplywood. For warpedsurfaces, lumberwhich is free fromknots and other imper-fections and whichcan be cut and bentaccurately to therequired curvatureswithout splinteringor splitting.

mitted.Steel lining not

permitted.

*Steel “sheathing” denotes steel sheets not supported by abacking of wood boards. Steel “lining” denotes thin steelsheets supported by a backing of wood boards.


(c) Form Ties. -Embedded ties for holdingforms shall remain embedded and, exceptwhere Fl finish is permitted, shall terminatenot less than two diameters or twice theminimum dimension of the tie in the clear ofthe formed faces of the concrete. Where Flfinish is permitted, ties may be cut off flushwith the formed surfaces. The ties shall beconstructed so that removal of the ends or endfasteners can be accomplished without causingappreciable spalling at the faces of theconcrete. Recesses resulting from removal ofthe ends of form ties shall be filled inaccordance with section H-19 (Repair ofConcrete).

(d) Cleaning and Oiling of Forms.-At thetime the concrete is placed in the forms, thesurfaces of the forms shall be free fromencrustations of mortar, grout, or other foreignmaterial. Before concrete is placed, the surfacesof the forms shall be oiled with a commercial-form oil that will effectively prevent stickingand will not soften or stain the concretesurfaces, or cause the surfaces to becomechalky or dust producing. For wood forms,form oil shall consist of straight, refined, pale,paraffin base mineral oil. For steel forms, formoil shall consist of refined mineral oil suitablycompounded with one or more ingredientswhich are appropriate for the purpose. Thecontractor shall furnish certification ofcompliance with these specifications for formoil.

(e) Removal of Forms.-To facilitatesatisfactory progress with the specified curingand enable earliest practicable repair of surfaceimperfections, forms shall be removed as soonas the concrete has hardened sufficiently toprevent damage by careful form removal.Forms on upper sloping faces of concrete, sucha s f o r m s o n t h e w a t e r s i d e s o f w a r p e dtransitions, shall be removed as soon as theconcrete has attained sufficient stiffness toprevent sagging. Any needed repairs ortreatment required on such sloping surfacesshall be performed at once and be followedimmediately by the specified curing.

To avoid excessive stresses in the concretethat might result from swelling of the forms,wood forms for wall openings shall be loosenedas soon as this can be accomplished without

527

d a m a g e t o t h e c o n c r e t e . F o r m s f o r t h eopenings shall be constructed so as to facilitatesuch loosening. Forms for conduits and tunnellining shall not be removed until the strengthof the concrete is such that form removal willnot result in perceptible cracking, spalling, orbreaking of edges or surfaces, or other damageto the concrete. Forms shall be removed withcare so as to avoid injury to the concrete andany concrete so damaged shall be repaired inaccordance with section H-19 (Repair ofConcrete).

H - 1 5 . T o l e r a n c e s f 0 r ConcreteConstruction. -(a) General. -Permissiblesurface irregularities for the various classes ofconcrete surface finish as specified in sectionH-20 (Finishes) are defined as “finishes,” andare to be distinguished from tolerances asdescribed herein. The intent of this section isto establish tolerances that are consistent withmodern construction practice, yet are governedby the effect that permissible deviations willhave upon the structural action or operationalfunction of the structure. Deviations from theestablished lines, grades, and dimensions will bepermitted to the extent set forth herein:Provided, that the Contracting Authorityreserves the right to diminish the tolerances setforth herein if such tolerances impair thestructural action or operational function of astructure or portion thereof.

Where specific tolerances are not stated inthese specifications or shown on the drawingsfor a structure, portion of a structure, or otherfeature of the work, permissible deviations willbe interpreted conformably to the tolerancesstated in this section for similar work. Specificmaximum or minimum tolerances shown onthe drawings in connection with any dimensionshall be considered as supplemental to thetolerances specified in this section, and shallgovern. The contractor shall be responsible forsetting and maintaining concrete forms withinthe tolerance limits necessary to insure that thecompleted work will be within the tolerancesspecified. Concrete work that exceeds thetolerance limits specified in these specificationsor shown on the drawings shall be remedied orremoved and replaced at the expense of and bythe contractor.


(b) Tolerances for Dam Structures.-

(1) Variation of constructed linear outline fromestablished position in plan

In any length of 20 feet,except in buriedconstruction . . . . . .

Maximum for entire length,except in buriedconstruction . . . . . .

In buried construction . .

. . . . % inch

(2) Variation of dimensions to individualstructure features from establishedpositions

(3) Variation from plumb, specified batter, orcurved surfaces for all structures, includ-ing lines and surfaces of columns, walls,piers, buttresses, arch sections, verticaljoint grooves, and visible arrises

(4) Variation from level or from grades indicatedon the drawings for slabs, beams, soffits,horizontal joint grooves, and visible arrises

(5) Variation in cross-sectional dimensions ofcolumns, beams, buttresses, piers, andsimilar members

Minus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ?A inchPlus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . %inch

(6) Variation in the thickness of slabs, walls, Minus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . %incharch sections, and similar members Plus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . %inch

(7) Footings for columns, piers, walls, buttresses,and similar members:

(a) Variation of dimensions in plan Minus . . . . . . . . . . . . . . . . . . . . . . . . . %inchPlus . . . . . . . . . . . . . . . . . . . . . . . . . 2 inches

(b) Misplacement or eccentricity

. .

. . .

. . .. % inchtwice the above

amounts

Maximum for overall dimen-sion, except in buriedconstruction . . . . . . . . . . . . . . . . 1% inches

In buried construction . . . . . . . . . . . . . . 2% inches

In any length of 10 feet,except in buriedconstruction . . . . . .

In any length of 20 feet,except in buriedconstruction . . . . . . .

Maximum for entire length,except in buriedconstruction . . . . . .

In buried construction .

In any length of 10 feet,except in buriedconstruction . . . . . . .

Maximum for entire length,except in buriedc o n s t r u c t i o n . . .

In buried construction .

. . . . I/Z inch

. . . . . % inch

. . . 1% inches

. twice the aboveamounts

.

. .

. . . . . . f/4 inch

.

.. . . % inch. twice the above

amounts

2 percent of the footingwidth in the directionof misplacement but notmore than . . . . . . . . . . . . . . . . 2 inches

(c) Reduction in thickness . . . . . . . . . . . . . . . . . . . . . . . . 5 percent of specifiedthickness

(8) Variation from plumb or level for sills andsidewalls for radial gates and similarwatertight joints*

(9) Variation in locations of sleeves, flooropenings, and wall openings

. . . . . . . . . . . . . . . . . . . . . . . . . Not greater than a rateof ‘18 inch in 10 feet

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . % inch

*Dimensions between sidewalls for radial gates shall be not more than shown on the drawings at the sills and not less thanshown on the drawings at the top of the walls.


(10) Variation in sizes of sleeves, flooropenings, and wall openings . . . . . . . . . . . . . . . . . . . . .

(c) Tolerances for Tunnel Lining.-

(1) Departure from established alinement or fromestablished grade

Free-flow tunnels and conduits . .High-velocity tunnels and

conduits . . . . . . . . . . . . . .

(2) Variation in thickness, at any point Tunnel lining . . . . . . . .Conduits . . . . . . . . . . .

Conduits . . . . . . . . .

(3) Variation from inside dimensions . . . . . . . . . . . . . . . . . . .

(d) Tolerances for Placing Reinforcing Bars and Fabric.-

(1) Reinforcing steel, except for bridges:

(a) Variation of protective covering

(b) Variation from indicated spacing

(2) Reinforcing steel for bridges:

(a) Variation of protective covering

(b) Variation from indicated spacing

H - 1 6 . R e i n f o r c i n g B a r s a n dFabric. -(a) Furnishing. -The contractor shallfurnish all the reinforcing bars and fabricr e q u i r e d f o r c o m p l e t i o n o f t h e w o r k .Reinforcing bars shall conform to ASTMDesignation A 615, grade 40 or 60, or ASTMDesignation A 6 17, grade 40 or 60. (Seereference [3] or [4] .) Fabric shall beelectrically welded-wire fabric and shallconform to ASTM Designation A 185 [ 21.

(b) PZacing. -Reinforcing bars and fabricshall be placed in the concrete where shown onthe drawings or where directed. Splices shall bel o c a t e d w h e r e s h o w n o n t h e d r a w i n g s :Provided, that the location of splices may bealtered subject to the written approval of theContracting Authority, and Provided further,that, subject to the written approval of theAuthority, the contractor may splice bars at

With cover of 2% inchesor less . . . . . . . . . . . . . .

With cover of more than2% inches . . . . . . . . . .

. . . . .

. . .

. . . .

. . . 1 inch

. . r% inch

. minus 0. minus 2% percent

or ?4 inch, whicheveris greater

. plus 5 percent or% inch, which-ever is greater

. % inch

. . r/z of 1 percent

. . . . ‘A inch

. . . % inch

. . . 1 inch

With cover of 2% inchesor less . . . . . . . . . . .

With cover of more than2% inches . . . . . . . . . . . . . . .

. . . . . . . . . . . . % inch

. . . . . . . . . ?L, inch

. . . . . . . . . 1 inch

additional locations other than those shown onthe drawings. Reinforcing bars in spliceslocated where shown on the drawings, inrelocated splices approved by the Authority, ori n addit ional splices a p p r o v e d b y t h eA u t h o r i t y , will be included in themeasurement, for payment, of reinforcing bars.

Unless otherwise prescribed, placementdimensions shall be to the centerlines of thebars. Reinforcement will be inspected forcompliance with requirements as to size, shape,length, splicing, position, and amount after ithas been placed.

Before the reinforcement is embedded inconcrete, the surfaces of the bars and thesurfaces of any bar supports shall be cleaned ofheavy flaky rust, loose mill scale, dirt, grease,or other foreign substances which, in theopinion of the Authority, are objectionable.

530 DESIGN 06 GRAVITY DAMS

drawings may not be available in time to enablethe contractor to purchase prefabricatedreinforcing bars, it may be necessary for thecontractor to purchase bars in stock lengths,and to cut and bend the bars in the field.

At leas t days before scheduledconcrete placement, the contractor shallsubmit to the Authority for approval threeprints of each of his reinforcement detaildrawings. The contractor’s reinforcement detaildrawings shall be prepared following therecommendations established by the AmericanConcrete Institute’s “Manual of StandardPractice for Detailing Reinforced ConcreteStructures” (AC1 3 15-65) unless otherwiseshown on the reinforcement design drawings.The contractor’s drawings shall show necessarydetails for checking the bars during placementand for use in establishing payment quantities.Re in fo rcemen t s h a l l c o n f o r m t o t h erequirements shown on the reinforcementdesign drawings.

The contractor’s reinforcement detaildrawings shall be clear, legible, and accuratea n d c h e c k e d b y t h e c o n t r a c t o r b e f o r esubmittal. If any reinforcement detail drawingor group of drawings is not of a qualityacceptable to the Authority, the entire set orgroup of drawings will be returned to thecontractor, without approval, to be correctedand resubmitted. Acceptable reinforcementdetail drawings will be reviewed by theContracting Authority for adequacy of generaldesign and controlling dimensions. Errors,omissions, or corrections will be marked on theprints, or otherwise relayed to the contractor,and one print of each drawing will be returnedt o t h e c o n t r a c t o r f o r c o r r e c t i o n . T h econtractor shall make all necessary correctionsshown on the returned prints. The correcteddrawings need not be resubmitted unless thec o r r e c t i o n s are extensive enough, asdetermined by the Authority, to warrantresubmittal. Such Authority review andapproval shall not relieve the contractor of hisresponsibility for the correctness of details orfor conformance with the requirements ofthese specifications.

(d) Measurement and Payment.-Measure-ment, for payment, of reinforcing bars and

Heavy flaky rust that can be removed by firmrubbing with burlap or equivalent treatment isconsidered objectionable.

Reinforcement shall be accurately placedand secured in position so that it will not bedisplaced during the placing of the concrete,and special care shall be exercised to preventany disturbance of the reinforcement inconcrete that has already been placed. Weldingor tack welding of grade 60 or grade 75reinforcing bars will not be permitted except atlocations shown on the drawings. Chairs,hangers, spacers, and other supports forreinforcement may be of concrete, metal, orother approved material. Where portions ofsuch supports will be exposed on concretesurfaces designated to receive F2 or F3 finish,the exposed portion of the supports shall be ofgalvanized or other corrosion-resistant material,except that concrete supports will not bepermitted. Such supports shall not be exposedon surfaces designated to receive an F4 finish.Unless otherwise shown on the drawings, thereinforcement in structures shall be so placedthat there will be a clear distance of at least 1inch between the reinforcement and anyanchor bolts, form ties, or other embeddedmetalwork.

(c) Reinforcement Drawings to be Preparedby the Contractor. -The contractor shallprepare and submit for approval of theAuthority reinforcement detail drawings for allstructures including bar-placing drawings,bar-bending diagrams, and bar lists.

The contractor’s reinforcement detaildrawings shall be prepared from reinforcementdes ign d rawings i n c l u d e d w i t h t h e s especifications a n d f r o m supplementalreinforcement design drawings to be furnishedby the Authority. The position, size, and shapeof reinforcing bars are not shown in all cases onthe drawings included with these specifications.Supplemental reinforcement design drawings insufficient detail to permit the contractor toprepare his reinforcement detail drawings willb e f u r n i s h e d t o t h e c o n t r a c t o r b y t h eAuthority after final designs have beencompleted and after equipment data arereceived from equipment manufacturers. Ast h e s u p p l e m e n t a l reinforcement design


fabric will be made only of the weight of thebars and fabric placed in the concrete inaccordance with the drawings or as directed.

Paymen t fo r fu rn i sh ing and p l ac ingreinforcing bars will be made at the applicableunit price per pound bid in the schedule for thevarious sizes of reinforcing bars and fabric,which unit prices shall include the cost ofpreparing reinforcement detail drawings,including bar-placing drawings and bar-bendingdiagrams; of submitting the drawings to theAuthority; of preparing all necessary bar listsand cutting lists; of furnishing and attachingwire ties and metal or other approved supports,if used; and of cutting, bending, cleaning, andsecuring and maintaining in position, allreinforcing bars and fabric as shown on thedrawings.

H - 17. Preparations for Placing. -(a) General.-No concrete shall be placed untilall formwork, installation of parts to beembedded, and preparation of surfacesinvolved in the placing have been approved. Noconcrete shall be placed in water except withthe written permission of the ContractingAuthority, and the method of depositing theconcrete shall be subject to his approval.Concrete shall not be placed in running waterand shall not be subjected to the action ofrunning water until after the concrete hashardened. All surfaces of forms and embeddedmaterials that have become encrusted withdried mortar or grout from concrete previouslyplaced shall be cleaned of all such mortar orgrout before the surrounding or adjacentconcrete is placed.

(b) Foundation Surfaces. -Immediatelybefore placing concrete, all surfaces offoundations upon or aga ins t wh ich theconcrete is to be placed shall be free fromstanding water, mud, and debris. All surfaces ofrock upon or against which concrete is to beplaced shall, in addition to the foregoingrequirements, be clean and free from oil,o b j e c t i o n a b l e coatings, a n d l o o s e ,semidetached, or unsound fragments. Earthfoundations shall be free from frost or icewhen concrete is placed upon or against them.The surfaces of absorptive foundations againstwhich concrete is to be placed shall be

531

moistened thoroughly so that moisture will notbe drawn from the freshly placed concrete.

(c) Surfaces o f C o n s t r u c t i o n a n dContraction Joints. -Concrete surfaces upon oragainst which concrete is to be placed and towhich new concrete is to adhere, that havebecome so rigid that the new concrete cannotbe incorporated integrally with that previouslyplaced, are defined as construction joints.

All construction joints shall be cured bywater curing or by application of wax basecuring compound in accordance with theprovisions of section H-22 (Curing). Wax basecuring compound, if used on these joints, shallbe removed in the process of preparing thejoints to receive fresh concrete. The surfaces ofthe construction joints shall be clean, rough,and surface dry when covered with freshconcrete. Cleaning shall consist of the removalof all laitance, loose or defective concrete,coatings, sand, curing compound if used, andother foreign material. The cleaning androughening shall be accomplished by wetsandblasting, washing thoroughly withair-water jets, and surface drying prior toplacement of adjoining concrete: Provided,that high-pressure water blasting utilizingpressures not less than 6,000 pounds per squareinch may be used in lieu of wet sandblastingfor preparing the joint surfaces if it isdemonstrated to the satisfaction of theAuthority that the equipment proposed for usewill produce equivalent results to thoseobtainable by wet sandblasting. High-pressurewater blasting equipment, if used, shall beequipped with suitable safety devices forcontrolling pressures, including shutoffswitches at the nozzle that will shut off thepressure i f t h e n o z z l e i s d r o p p e d . T h esandblasting (or high-pressure water blasting ifapproved), washing, and surface drying shall beperformed at the last opportunity prior toplacing of concrete. Drying of the surface shallbe complete and may be accomplished by airjet. I n t h e p r o c e s s of wet sandblastingconstruction joints, care shall be taken toprevent undercutting of aggregate in theconcrete.

The surfaces of all contraction joints shall becleaned thoroughly of accretions of concrete or


other foreign material by scraping, chipping, orother means approved by the Authority.

H- 18. Placing. -(a) Transporting. -Themethods and equipment used for transportingconcrete and the time that elapses duringtransportation shall be such as will not causeappreciable segregation of coarse aggregate, orslump loss in excess of 1 inch, in the concreteas it is delivered into the work. The use ofaluminum p i p e f o r d e l i v e r y o f p u m p e dconcrete will not be permitted.

(b) Placing. -The contractor shall keep theContracting Authority advised as to whenplacing of concrete will be performed. Unlessinspection is waived in each specific case,placing of concrete shall be performed only inthe presence of a duly authorized Authorityinspector.

The surfaces of all rock against whichconcrete is to be placed shall be cleaned and,except in those cases where seepage or otherwater precludes drying of the rock face, shallbe dampened and brought to a surface-drycondition. Except for tunnels, surfaces ofhighly porous or absorptive horizontal ornearly horizontal rock foundations to whichconcrete is to be bonded shall be covered witha layer of mortar approximately three-eighthsof an inch thick prior to placement of theconcrete. The mortar shall have the sameproportions of water, air-entraining agent,cement, pozzolan, and sand as the regularconcrete mixture, unless otherwise directed.The water-cement plus pozzolan ratio of themortar in place shall not exceed that of theconcrete to be placed upon it , and theconsistency of the mortar shall be suitable forplacing and working in the manner hereinafterspecified. The mortar shall be spread and shallbe worked thoroughly into all irregularities oft h e s u r f a c e . Concrete shall be placedimmediately upon the fresh mortar.

A mortar layer shall not be used on concreteconstruction joints. Unless otherwise directedin formed work, structural concrete placementsshall be started with an oversanded mixcontaining %-inch maximum-size aggregate; amaximum net water-cement plus pozzolanratio of 0.47, by weight; 6 percent air, byvolume of concrete; and having a maximum

slump of 4 inches. This mix shall be placedapproximately 3 inches deep on the joint at thebottom of the placement.

Retempering of concrete will not bepermitted. Any concrete which has become sostiff that proper placing cannot be assured shallbe wasted. Concrete shall be deposited in allcases as nearly as practicable directly in its finalposition and shall not be caused to flow suchthat the lateral movement will permit or causesegregation of the coarse aggregate from theconcrete mass. Methods and equipmentemployed in depositing concrete in forms shallbe such as will not result in clusters or groupsof coarse aggregate particles being separatedfrom the concrete mass, but if clusters dooccur they shall be scattered before theconcrete is vibrated. Where there are a fewscattered individual pieces of coarse aggregatethat can be restored into the mass by vibration,this will not be objectionable and should bedone.

Concrete in tunnel lining may be placed bypumping or any other approved method. Wherethe concrete in the invert is placed separatelyfrom the concrete in the arch and withoutinside forms, it shall not be placed bypneumatic placing equipment unless anapproved type of discharge box which preventssegregation i s p r o v i d e d a n d u s e d . T h eequipment used in placing the concrete and themethod of its operation shall be such as willpermit introduction of the concrete into theforms without high-velocity discharge andresultant separation. After the concrete hasbeen built up over the arch at the start of aplacement, the end of the discharge line shallbe kept well buried in the concrete duringplacement of the arch and sidewalls to assurecomplete filling. The end of the discharge lineshall be marked so as to indicate the depth ofburial at any time. Special care shall be takento force concrete into all irregularities in therock surfaces and to completely fill the tunnelarch. Placing equipment shall be operated byexperienced operators only.

Where tunne l l i n ing p l acemen t s a r eterminated with sloping joints, the contractorshall thoroughly consolidate the concrete atsuch joints to a reasonably uniform and stable


slope while the concrete is plastic. If thoroughconsolidation at the sloping joints is notobtained, as determined by the Authority, theAuthority reserves the right to require the useof bulkheaded construction joints. Theconcrete at the surface of such sloping jointsshall be clean and surface dry before beingcovered with fresh concrete. The cleaning ofsuch sloping joints shall consist of the removalof all loose and foreign material.

Except as intercepted by joints, all formedconcrete other than concrete in tunnel lining,including mass concrete in the dam, shall beplaced in continuous approximately horizontallayers. The depth of layers for mass concreteshall generally not exceed 18 inches, and thedepth for all other concrete shall generally notexceed 20 inches. The Authority reserves theright to require lesser depths of layers whereconcrete in 20-inch layers cannot be placed inaccordance with the requirements of thesespecifications. Except where joints arespecified herein or on the drawings, care shallbe taken to prevent cold joints when placingconcrete in any portion of the work. Theconcrete placing rate shall be such as to ensurethat each layer is placed while the previouslayer is soft or plastic, so that the two layerscan be made monolithic by penetration of thev i b r a t o r s . T o p r e v e n t featheredges,construction joints that are located at the topsof horizontal lifts near sloping exposedconcrete surfaces shall be inclined near theexposed surface, so that the angle betweensuch inclined surfaces and the exposedconcrete surface will be not less than 50’.

In placing unformed concrete on slopes sosteep as to make internal vibration of theconcrete impracticable without forming, theconcrete shall be placed ahead of a nonvibratedslip-form screed extending approximately 2%feet back from its leading edge. Concrete aheadof the slip-form screed shall be consolidated byinternal vibrators so as to ensure completetilling under the slip-form.

In placing mass concrete in the dam, thecontractor shall, when required, maintain theexposed area of fresh concrete at the practicalminimum, by first building up the concrete insuccessive approximately horizontal layers to

the full width of the block and to full height ofthe lift over a restricted area at the downstreamend o f t he b lock , and t hen con t inu ingupstream in similar progressive stages to thefull area of the block. The slope formed by theunconfined upstream edges of the successivelayers of concrete shall be kept as steep aspracticable in order to keep its area to aminimum. Concrete along these edges shall notbe vibrated until adjacent concrete in the layeris placed, except that it shall be vibratedimmediately when weather conditions are suchthat the concrete will harden to the extent thatit is doubtful whether later vibration will fullyconsolidate and integrate it with more recentlyplaced adjacent concrete. Clusters of largeaggregate shall be scattered before newconcrete is placed over them. Each deposit ofconcrete shall be vibrated completely beforeanother deposit of concrete is placed over it.

Concrete shall not be placed during rainssufficiently heavy or prolonged to wash mortarfrom coarse aggregate on the forward slopes ofthe placement. Once placement of concrete hascommenced in a block, placement shall not beinterrupted by diverting the placing equipmentto other uses.

Concrete buckets shall be capable ofpromptly discharging the low slump, 6-inchmass concrete mixes specified, and thedumping mechanism shall be designed topermit the discharge of as little as a%-cubic-yard portion of the load in one place.Buckets shall be suitable for attachment anduse of drop chutes where required in confinedlocations.

Construction joints shall be approximatelyhorizontal unless otherwise shown on thedrawings or prescribed by the Authority, andshall be given the prescribed shape by the useof forms, where required, or other means thatwill ensure suitable joining with subsequentwork. All intersections of construction jointswith concrete surfaces which will be exposedto view shall be made straight and level orplumb.

If concrete is placed monolithically aroundopenings having vertical dimensions greaterthan 2 feet, or if concrete in decks, top slabs,beams, or other similar parts of structures is


placed monolithically with supportingconcrete, the following instructions shall bestrictly observed:

(1) Placing of concrete shall be delayedfrom 1 to 3 hours at the top of openings and atthe bottoms of bevels under decks, top slabs,beams, or other similar parts of structureswhen bevels are specified, and at the bottom ofsuch structure members when bevels are notspecified; but in no case shall the placing bedelayed so long that the vibrating unit will notreadily penetrate of its own weight theconcrete placed before the delay. Whenconsolidating concrete placed after the delay,the vibrating unit shall penetrate and revibratethe concrete placed before the delay.

(2) The last 2 feet or more of concreteplaced immediately before the delay shall beplaced with as low a slump as practicable, andspecial care shall be exercised to effectthorough consolidation of the concrete.

(3) The surfaces of concrete where delaysare made shall be clean and free from loose andforeign material when concrete placing isstarted after the delay.

(4) Concrete placed over openings and indecks, top slabs, beams, and other similar partsof structures shall be placed with as low aslump as practicable and special care shall beexercised to effect thorough consolidation ofthe concrete.

(c) Consolidation. -Concrete shall beconsolidated to the maximum practicabledensity, so that it is free from pockets ofcoarse aggregate and entrapped air, and closessnugly against all surfaces of forms andembedded materials. Consolidation of concretei n s t r u c t u r e s s h a l l b e b y e l e c t r i c - o rpneumatic-drive, immersion-type vibrators.Vibrators having vibrating heads 4 inches ormore in diameter shall be operated at speeds ofat least 6,000 revolutions per minute whenimmersed in the concrete. Vibrators havingvibrating heads less than 4 inches in diametershall be operated at speeds of at least 7,000revolutions per minute when immersed in theconcrete. Immersion-type vibrators used inmass concrete shall be heavy duty, two-manvibrators capable of readily consolidating massc o n c r e t e of the consistency specified:

Provided, that heavy-duty, one-man vibratorsmay be used if they are operated in sufficientnumber, and in a manner and under conditionsas to produce equivalent results to thatspecified for two-man vibrators: Providedfurther, that where practicable in vibratingmass concrete, the contractor may employgang vibrators, satisfactory to the Authority,mounted on self-propelled equipment in such amanner that they can be readily raised andlowered to eliminate dragging through the freshconcrete, and provided all other requirementsof these specifications with respect to placingand control of concrete are met.

Consolidation of concrete in the sidewallsand arch of tunnel lining shall be by electric- orpneumatic-driven form vibrators supplementedwhere practicable by immersion-type vibrators.Form vibrators shall be rigidly attached to theforms and shall operate at speeds of at least8,000 revolutions per minute when vibratingconcrete.

In consolidating each layer of concrete thevibrator shall be operated in a near-verticalposition and the vibrating head shall be allowedto penetrate and revibrate the concrete in theupper portion of the underlying layer. In thearea where newly placed concrete in each layerjoins previously placed concrete, particularly inmass concrete, more than usual vibration shallbe performed, the vibrator penetrating deeplyand at close intervals into the upper portion ofthe previously placed layer along thesecontacts. In all vibration of mass concrete,vibration shall continue until bubbles ofentrapped air have generally ceased to escape.Additional layers of concrete shall not besuperimposed on concrete previously placeduntil the previously placed concrete has beenvibrated thoroughly as specified. Care shall beexercised to avoid contact of the vibrating headwith surfaces of the forms.

H-19. Repair of Concrete. -Concrete shallbe repaired in accordance with the Bureau ofReclamation “Standard Specifications forRepair of Concrete,” dated November 15,1970. Imperfections and irregularities onconcrete surfaces s h a l l b e c o r r e c t e d i naccordance with section H-20 (Finishes andFinishing).


H - 2 0 . F i n i s h e s a n d F i n i s h i n g . -(a) General. -Allowable deviations from plumbor level and from the alinement, profile grades,and dimensions shown on the drawings arespecified in section H-15 (Tolerances forConcrete Construction): these are defined as“tolerances” and are to be distinguished fromirregularities in finish as described herein. Theclasses of finish and the requirements forfinishing of concrete surfaces shall be asspecified in this section or as indicated on thedrawings. The contractor shall keep theContracting Authority advised as to whenfinishing of concrete will be performed. Unlessinspection is waived in each specific case,finishing of concrete shall be performed only inthe presence of an Authority inspector.Concrete surfaces will be tested by theAuthority where necessary to determinewhether surface irregularities are within thelimits hereinafter specified.

Surf ace irregularities are classified as“abrupt” or “gradual.” Offsets caused bydisplaced or misplaced form sheathing or liningor form sections, or by loose knots in forms orotherwise defective form lumber, will beconsidered as abrupt irregularities and will betested by direct measurements. All otherirregularities will be considered as gradualirregularities and will be tested by use of atemplate, consisting of a straightedge or theequivalent thereof for curved surfaces. Thelength of the template will be 5 feet for testingof formed surfaces and 10 feet for testing ofunformed surfaces.

(b) Formed Surfaces.-The classes of finishfor formed concrete surfaces are designated byuse of symbols F 1, F2, F3, and F4. No sackrubbing or sandblasting will be required onformed surfaces. No grinding will be requiredon formed surfaces, other than that necessaryfor repair of surface imperfections. Unlessotherwise specified or indicated on thedrawings, the classes of finish shall apply asfollows:

FI. -Finish Fl applies to formed surfacesupon or against which fill material or concreteis to be placed, to formed surfaces ofcontraction joints, and to the upstream face ofthe dam below the minimum water pool

535

elevation. The surfaces require no treatmentafter form removal except for repair ofdefective concrete and filling of holes left bythe removal of fasteners from the ends of tierods as required in section H-l 9 (Repair ofConcrete), and the specified curing. Correctionof surface irregularities will be required fordepressions only, and only for those which,when measured as described in subsection (a)above, exceed 1 inch.

F2. -Finish F2 applies to all formed surfacesnot permanently concealed by fill material orconcrete, or not required to receive finishes F 1,F3, or F4. Surface irregularities, measured asdescribed in subsection (a) above, shall notexceed one-fourth of an inch for abruptirregularities and one-half of an inch forgradual irregularities: Provided, that surfacesover which radial gate seals will operatewithout sill or wall plates shall be free fromabrupt irregularities.

F.3. -Finish F3 applies to formed surfaces,the appearance of which is considered by theAuthority to be of special importance, such assurfaces of structures prominently exposed topublic inspection. Included in this category aresuperstructures of large powerplants andpumping plants, parapets, railings, anddecorative features on dams and bridges andpermanent buildings. Surface irregularities,measured as described in subsection (a) aboveshall not exceed one-fourth of an inch forgradual irregularities and one-eighth of an inchfor abrupt irregularities, except that abruptirregularities will not be permitted atconstruction joints.

F4.-Finish F4 applies to formed surfacesfor which accurate alinement and evenness ofsurface are of paramount importance from thestandpoint of eliminating destructive effects ofwater action. When measured as described insubsection (a) above, abrupt irregularities shallnot exceed one - fou r th o f an i nch fo rirregularities parallel to the direction of flow,and one-eighth of an inch for irregularities notparallel to the direction of flow. Gradualirregularities shall not exceed one-fourth of aninch. (Note: When waterflow velocities onformed concrete surfaces of outlet works,spillways, etc., are calculated to exceed 40 feet


U3. -Finish U3 (troweled finish) applies tothe inside floors of buildings, except floorsrequiring a bonded-concrete finish or a terrazzofinish, and to inverts of draft tubes and tunnelspillways. When the floated surface hashardened sufficiently to prevent an excess offine material from being drawn to the surface,steel troweling shall be started. Steel trowelingshall be performed with firm pressure so as toflatten the sandy texture of the floated surfaceand produce a dense uniform surface, free fromb l e m i s h e s a n d t r o w e l m a r k s . S u r f a c eirregularities, measured as described insubsection (a) above, shall not exceedone-fourth of an inch.

(Note: When waterflow velocities onunformed concrete surfaces of outlet works,spillways, etc., are calculated to exceed 40 feetper second, further limitations on U2 and/orU3 finishes should be considered for theallowable irregularities to prevent cavitation.)

H-2 1. Protection. -The contractor shallprotect all concrete against injury until finalacceptance by the Contracting Authority.Fresh concrete shall be protected from damagedue to rain, hail, sleet, or snow. The contractorshall provide such protection while theconcrete is still plastic and whenever suchprecipitation, either periodic or sustaining, isimminent or occurring, as determined by theAuthority.

Immediately following the first frost in thefall the contractor shall be prepared to protectall concrete against freezing. After the firstfrost, and until the mean daily temperature inthe vicinity of the worksite falls below 40’ F.for more than 1 day, the concrete shall beprotected against freezing temperatures for notless than 48 hours after it is placed.

After the mean daily temperature in thevicinity of the worksite falls below 40’ F. formore than 1 day, the following requirementsshall apply :

(a) Mass Concrete. -Mass concrete shall bemaintained at a temperature not lower than40° F. for at least 96 hours after it is placed.Mass concrete cured by application of curingcompound will r equ i r e no additionalprotection from freezing if the protection at40’ F. for 96 hours is obtained by means of

per second, further limitations should beconsidered for the allowable irregularities toprevent cavitation.)

(c) Unformed Surfaces. -The classes offinish for unformed concrete surfaces aredesignated by the symbols Ul, U2, and U3.Interior surfaces shall be sloped for drainagewhere shown on the drawings or directed.Surfaces which will be exposed to the weatherand which would normally be level, shall besloped for drainage. Unless the use of otherslopes or level surfaces is indicated on thedrawings or directed, narrow surfaces such astops of walls and curbs, shall be slopedapproximately three-eighths of an inch per footof width; broader surfaces such as walks,roadways, platforms, and decks shall be slopedapproximately one-fourth of an inch per foot.Unless otherwise specified or indicated on thedrawings, these classes of finish shall apply asfollows:

Ul.-Finish Ul (screeded finish) applies tounformed surfaces that will be covered by fillmaterial or by concrete. Finish Ul is also usedas the first stage of finishes U2 and U3.Finishing operations shall consist of sufficientl e v e l i n g a n d screeding t o p r o d u c e e v e n ,un i fo rm surfaces. Surface irregularitiesmeasured as described in subsection (a) above,shall not exceed three-eighths of an inch.

K?. -Finish U2 (floated finish) applies tounformed surfaces not permanently concealedby fill material or concrete, or not required toreceive finish Ul or U3. U2 is also used as thesecond stage of finish U3. Floating may beperformed by use of hand- or power-drivenequipment. Floating shall be started as soon asthe screeded surface has stiffened sufficiently,and shall be the minimum necessary to producea surface that is free from screed marks and isuniform in texture. If finish U3 is to beapplied, floating shall be continued until asmall amount of mortar without excess water isbrought to the surface, so as to permit effectivetroweling. Surface irregularities, measured asdescribed in subsection (a) above, shall notexceed one-fourth of an inch. Joints and edgesof gutters, sidewalks, and entrance slabs, andother joints and edges shall be tooled whereshown on the drawings or directed.


approved insulation in contact with the formsor concrete surfaces; otherwise, the concreteshall be protected against freezing temperaturesfor 96 hours immediately following the 96hours protection at 40’ F. Mass concrete curedby water curing shall be protected againstf r e e z i n g t e m p e r a t u r e s f o r 9 6 h o u r si m m e d i a t e l y f o l l o w i n g t h e 9 6 h o u r s o fp r o t e c t i o n a t 40’ F . D i s c o n t i n u a n c e o fprotection of mass concrete against freezingtemperatures shall be such that the drop intemperature of any portion of the concrete willbe gradual and will not exceed 20° F. in 24hours. After March 15, when the mean dailytemperature rises above 40° F. for more than 3successive d ws, the specified 96-hourprotection at a temperature not lower than 40°F. for mass concrete may be discontinued foras long as the mean daily temperature remainsabove 40’ F.: Provided, that the specified dropin temperature limitation is met, and that thec o n c r e t e i s p r o t e c t e d against freezingtemperatures for not less than 48 hours afterplacement.

( b ) C o n c r e t e O t h e r T h a n M a s sConcrete. -All concrete other than massconcrete shall be maintained at a temperaturenot lower than 50’ F. for at least 72 hoursafter it is placed. Such concrete cured byapplication of curing compound will require noadditional protection from freezing if theprotection at 50’ F. for 72 hours is obtainedby means of approved insulation in contactwith the forms of concrete surfaces; otherwise,the concrete shall be protected against freezingtemperatures for 72 hours immediatelyfollowing the 72 hours protection at 50’ F.Concrete other than mass concrete cured bywater curing shall be protected against freezingtemperatures for 72 hours immediatelyfollowing the 72 hours protection at 50’ F.Discontinuance of protection of such concreteagainst freezing temperatures shall be such thatthe drop in temperature of any portion of theconcrete will be gradual and will not exceed40° F. in 24 hours. After March 15, when themean daily temperature rises above 40’ F. formore than 3 successive days, the specified72-hour protection at a temperature not lowerthan 50’ F. may be discontinued for as long as

537

the mean daily temperature remains above 40°F.: Provided, that the specified drop intemperature limitation is met, and that thec o n c r e t e i s p r o t e c t e d against freezingtemperatures for not less than 48 hours afterplacement.

( c ) U s e of Unvented Heaters. -Whereartificial heat is employed, special care shall betaken to prevent the concrete from drying. Useof unvented heaters will be permitted onlywhen unformed surfaces of concrete adjacentto the heaters are protected for the first 24hours from an excessive carbon dioxidea t m o s p h e r e b y a p p l i c a t i o n o f c u r i n gcompound: Provided, that the use of curingcompound on such surfaces for curing of theconcrete is permitted by and the compound isapplied in accordance with section H-22(Curing). (Include this proviso only when theuse of sealing compound is not permitted onsome concrete surfaces.)

H-22. Curing. -(a) General. -Concrete shallbe cured either by water curing in accordancewith subsection (b) or by application of waxbase curing compound in accordance withsubsection (c), except as otherwise hereinafterprovided.

The unformed top surfaces of walls and pierss h a l l b e m o i s t e n e d b y c o v e r i n g w i t hwater-saturated material or by other effectivemeans as soon as the concrete has hardenedsufficiently to prevent damage by water. Thesesurfaces and steeply sloping and verticalformed surfaces shall be kept completely andcontinually moist, prior to and during formremoval, by water applied on the unformed topsurfaces and allowed to pass down between theforms and the formed concrete faces. Thisprocedure shall be followed by the specifiedwater curing or by application of curingcompound.

(b) Water Curing. -Concrete cured withwater shall be kept wet for at least 21 days forconcrete containing pozzolan and for at least14 days for concrete not containing pozzolan.Water curing shall start as soon as the concretehas hardened sufficiently to prevent damage bymoistening the surface, and shall continue untilcompletion of the specified curing period oruntil covered with fresh concrete: Provided,


surfaces, the surfaces shall be moistened with alight spray of water immediately after theforms are removed and shall be kept wet untilthe surfaces will not absorb more moisture. Assoon as the surface film of moisture disappearsbut while the surface still has a dampappearance, the curing compound shall beapplied. Special care shall be taken to insureample coverage with the compound at edges,corners, and rough spots of formed surfaces.After application of the curing compound hasbeen completed and the coating is dry totouch, any required repair of concrete surfacesshall be performed. Each repair, after beingfinished, shall be moistened and coated withcuring compound in accordance with theforegoing requirements.

Equipment for applying curing compoundand the method of application shall be inaccordance with the provisions of chapter VIo f t h e e i g h t h e d i t i o n o f t h e B u r e a u o fReclamation Concrete Manual [ 11. Traffic andother operations by the contractor shall besuch as to avoid damage to coatings of curingcompound for a period of not less than 28days. Where i t is impossible because ofconstruction operations to avoid traffic oversurfaces coated with curing compound, thefilm shall be protected by a covering of sand orearth not less than 1 inch in thickness or byother effective means. The protective coveringshall not be placed until the applied compoundis completely dry. Before final acceptance ofthe work, the contractor shall remove all sandor earth covering in an approved manner. Anycuring compound that is damaged or that peelsfrom concrete surfaces within 28 days afterapplication, shall be repaired without delay andin an approved manner.

(d) Costs. -The costs of furnishing andapplying all materials used for curing concreteshall be included in the price bid in theschedule for the concrete on which the curingmaterials are used.

H - 2 3 . M e a s u r e m e n t o fConcrete. -Measurement, for payment, ofconcrete required to be placed directly upon oragainst surfaces of excavation will be made tothe lines for which payment for excavation is

that water curing of concrete may be reducedto 6 days during periods when the mean dailytemperature in the vicinity of the worksite isless than 40’ F.: Provided further, that duringthe prescribed period of water curing, whentemperatures are such that concrete surfacesmay freeze, water curing shall be temporarilydiscontinued. The concrete shall be kept wetby covering with water-saturated material or bya system of perforated pipes, mechanicalsprinklers, or porous hose, or by any otherapproved method which will keep all surfacesto be cured continuously (not periodically)wet. Water used for curing shall be furnishedby the contractor and shall meet therequirements of these specifications for waterused for mixing concrete in accordance withsection H-7 (Water).

(c) Wax Base Curing Compound. -Wax basecuring compound shall be applied to surfacesto form a water-retaining film on exposedsurfaces of concrete, on concrete joints, andwhere specified, t o p r even t bond ing o fconcrete placed on or against such joints. Thecuring compound shall be white pigmented andshall conform to Bureau of Reclamation“ S p e c i f i c a t i o n s f o r W a x - B a s e C u r i n gC o m p o u n d , ” d a t e d M a y 1 , 1 9 7 3 . T h ecompound shall be of uniform consistency andquality within each container and fromshipment to shipment.

Curing compound shall be mixed thoroughlyand applied to the concrete surfaces byspraying in one coat to provide a continuous,uniform membrane over all areas. Coverageshall not exceed 150 square feet per gallon, andon rough surfaces coverage shall be decreasedas necessary to obtain the required continuousmembrane. Mortar encrustations and fins onsurfaces designated to receive finish F3 or F4shall be removed prior to application of curingcompound. The repair of all other surfaceimperfections shall not be made until afterapplication of curing compound.

When curing compound is used on unformedconcrete surfaces, application of the compoundshall commence immediately after finishingoperations are completed. When curingcompound is to be used on formed concrete


made. Measurement, for payment, of all otherconcrete will be made to the neatlines of thestructures, unless otherwise specifically shownon the drawings or prescribed in thesespecifications. In the event cavities resultingfrom careless excavation, as determined by theContracting Authority, are required to be filledwith concrete, the materials furnished by theAuthority and used for such refilling will becharged to the contractor at their cost to theAuthority at the point of delivery to thecontractor. In measuring concrete for payment,the volume of all openings, recesses, ducts,embedded pipes, woodwork, and metalwork,each of which is larger than 100 square inchesin cross section will be deducted.

H-24. Payment for Concrete. -Payment forconcrete in the various parts of the work willbe made at the unit prices per cubic yard bidtherefor in the schedule, which unit prices shallinclude the cost of all labor and materialsrequired in the concrete construction, exceptthat payment for furnishing and handlingcement, and payment for furnishing andplacing reinforcing bars will be made at theunit prices bid therefor in the schedule.

539

H-25. Bibliography.

111

PI

131

[41

[51

161

171

181

191

1101

1111

Bureau of Reclamation

“Concrete Manual,” eighth edition, 1975.

Amen’can Society for Testing and Materials

ASTM Designation: A 185, “Welded Steel Wire Fabricfor Concrete Reinforcement.”ASTM Designation: A 615, “Deformed Billet-Steel Barsfor Concrete Reinforcement.”ASTM Designation: A 617, “Axle-Steel Deformed Barsfor Concrete Reinforcement.”ASTM Designation: C 184, “Standard Method of Testfor Fineness of Hydraulic Cement by the No. 100 and200 Sieves.”ASTM Designation: C 260, “Standard Specifications forAir-Entraining Admixtures for Concrete.”ASTM Designation: E-l 1, “Standard Specifications forWire-Cloth Sieves for Testing Purposes.”

General Services Administration(Federal Supply Service)

Federal Specification AAA-S-12ld, “Scale (weighing;General Specifications for).”Federal Specification SK-192G (Including Amendment3), “Portland Cement.”Federal Specification SS-P-570B, “Pozzolan (for Use inPortland Cement Concrete).”Federal Test Method Standard No. 158A, ‘Cements,Hydraulic; Sampling, Inspection, and Testing.”

U.S. Department of Commerce, Bureau of Standards

[12] Product S tandard PS l -66 , “Sof twood Plywood,Construction and Industrial.”

<<Appendix I

Sample Spec i f icat ions for Contro l l ing

W a t e r a n d A i r P o l l u t i o n

I - l . Scope. -The fo l lowing sample prevention and control of air pollution. Theyspecifications prescribe water quality controls are written in the form of mandatoryand preventive measures for discharge of wastes provisions which should be required of theand/or pollution into a river, lake, or estuary contractor.due to construction operations; and the

A. PREVENTION OF WATER POLLUTION

I-2. General. -The contractor shall complywith applicable Federal and State laws, orders,and regulations concerning the prevention,control, and abatement of water pollution.Permits to discharge wastes into receivingwaters shall be obtained by the contractoreither from the State water pollution controlagency or from the Environmental ProtectionAgency.

The contractor’s construction activities shallbe performed by methods that will prevententrance or accidental spillage of solid matter,contaminants, debris, and other objectionablepollutants and wastes into streams, flowing ordry watercourses, lakes, and undergroundwater sources. Such pollutants and wastesinclude but are not restricted to refuse,garbage, cement, concrete, sewage effluent,industrial waste, radioactive substances,mercury, oil and other petroleum products,aggregate processing tailings, mineral salts, andthermal pollution. Pollutants and wastes shallbe disposed of at sites approved by theContracting Authority.

The contractor shall control his construction

activities so that turbidity resulting from hisoperations shall not exist in concentrationsthat will impair natural or developed watersupplies, fisheries, or recreational facilitiesdownstream from the construction area.

At least 40 days prior to beginning ofconstruction of each phase of work, thecontractor shall submit for approval two copiesof his plans for the treatment and disposal ofall waste and for control of turbidity in the

River which may result from hisoperations. The plans shall be submitted to theConstruction Engineer, Post Office Box ,

. The plans shallinclude coiplete design and constructiondetails of turbidity control features. Such plansshall also show the methods of handling anddisposal of oils or other petroleum products,chemicals, and similar industrial wastes.

Except as otherwise provided in section1-4(a) below, approval of the contractor’s plansshall not relieve the contractor of theresponsibility for designing, constructing,operating, and maintaining pollution andturbidity control features in a safe and

541


systematic manner, and for repairing at hisexpense any damage to, or failure of, thepollution and turbidity control structures andequipment caused by floods or storm runoff.

I-3. Control of Turbidity.-Turbidityincreases above the natural turbidities in the

River that are caused byconstruction activities shall be limited to thoseincreases resulting from performance ofrequired construction work in the river channeland will be permitted only for the shortestpracticable period required to complete suchwork and as approved by the ContractingAuthority. This required construction workwill- include such work as diversion of the river,construction or removal of cofferdams andother specified earthwork in or adjacent to theriver channel, pile driving, and construction ofturbidity control structures.

The spawning period for trout (or othergame fish) in the River isnormally during the period through

Accordingly, no change in thediversion or channelization of the river will bepermitted during this particularly sensitiveperiod.

Mechanized equipment shall not be operatedin flowing water except as necessary toconstruct approved crossings or to perform therequired construction, as outlined above.

The contractor’s methods of unwatering, ofexcavating foundations, of operating in theborrow areas, and of stockpiling earth and rockmaterials shall include preventive measures tocontrol siltation and erosion, and to interceptand settle any runoff of muddy waters. Wastewaters from construction of dam andappurtenances, aggregate processing, concretebatching and curing, drilling, grouting, andsimilar construction operations shall not enterflowing or dry watercourses without the use ofspecial approved turbidity control methods.

I - 4 . T u r b i d i t y C o n t r o lMethods. -(a) General.-Turbidity controlshall be accomplished through the use of plansapproved by the Contracting Authority inaccordance with section N-2 above.

The Bureau of Reclamation’s methods forcontrol of turbidity during construction at thedamsite as set forth in (c) below are acceptable

methods. The contractor may adopt thesemethods or he may submit for approvalalternative methods of equivalent adequacy. Ifthe contractor elects to utilize the Bureau’smethods and his plans for implementation areapproved by the Contracting Authority, and ifsuch approved plans do not effectively controlturbidity due to no fault of the contractor,additional work will be directed for whichpayment will be made in accordance with the“ G e n e r a l P r o v i s i o n s ” p o r t i o n o f t h especifications. If the contractor elects topropose for approval different methods ofturbidity control, the contractor shall bear thefull responsibility for their satisfactoryoperation in controlling turbidity. Theapproval of the contractor’s alternate proposalsby the Contracting Authority shall not beconstrued to relieve the contractor from hisresponsibility.

The contractor’s plans, submitted inaccordance with section I-2 above, shall showcomplete design and construction details forimplementing either the Bureau’s methods orthe contractor’s alternative methods.

(b) Requirements for Turbidity ControlDuring Construction at the Damsite.-Theturbidity control method to be used duringconstruction at the damsite shall: (1) Providefor treatment of all turbid water at the damsiteresulting from construction of dam andappurtenances; washing of aggregate obtainedfrom approved sources, if such washing isperformed at the damsite; drilling; grouting; orsimilar construction operations: Provided, thatthe Contracting Authority may direct thatclear water removed from foundations bedischarged directly to the river withouttreatment. The treatment plant shall have acapacity to treat 0 to gallons of turbidwater per minute so that the turbidity of anyeffluent discharged to the river does not exceed-Jackson turbidity units.

(2) Include bypass and control equipmentsuitable for blending treated and untreatedwaste waters and obtaining effluents of varyingdegrees of turbidity. The decision to dischargeto the river completely treated effluent or ablend of treated and untreated effluent will bethe responsibility of the Contracting

SAMPLE SPECIFICATIONS FORCONTROLLING WATER AND All?POLLUTION-Sec. I-5

Authority, and will depend on the naturalturbidity existing in the river at any particulartime.

(3) Have a capability of adjusting the pHand alkalinity values of any effluent dischargedto the river.

(4) Use only chemicals which have beenapproved by the Environmental ProtectionAgency for use in potable water and whichhave been proven to be harmless to terrestrialwildlife and aquatic life.

(5) Have provisions for accumulating,transporting, and depositing sludge in disposalareas so that the material will not wash into theriver by high flows or storm runoff, asapproved by the Contracting Authority.

(6) Provide for removal of the treatmentplant, cleanup of the site, and restoration ofthe site to its original condition as approved bythe Contracting Authority. All materials, plant,and appurtenances used for turbidity controlshall remain the property of the contractor.

(c) Bureau’s Methods of Turbidity Controlat the Damsite.-The Bureau of Reclamation’smethods for controlling turbidity duringconstruction at the damsite are based oncollecting turbid waters in sumps, andpumping from the sumps to: (1) A waterclarification plant, Dorr-Oliver’ Pretreater(--foot diameter by--foot water depth), orequal, with automatic chemical dosage feedersfor hydrated lime, alum, and an acid orcoagulant aid if needed; or

(2) A treatment plant consisting ofequalizing tanks, sedimentation flumes, settlingtanks, and ponds combined with innocuousstabilizing and flocculating chemicals asrequired. Such a treatment plant shall be theDow Turbidity Control System, as proposed byDow Chemical U.S.A.,’ or equal.

(d) Sampling and Testing of WaterQuality. -The Contracting Authority will dosuch water quality sampling and testing inconnection with construction operations as isnecessary to insure compliance with the waterquality standards of the State ofand the Environmental Protection Agency.

1 Mention of these firms should not be construed as anindication that they are the only suppliers of these or similarproducts nor as an endorsement by the Bureau of Reclamation.

543

Turbidities of all effluents discharged to theriver from the contractor’s constructionoperations shall be monitored by continuousrecorders such as the HACH 6491 or 7855 stripchart recorder provided with CR SurfaceScatter Turbidimeter Model 2411 or 2426, ’ orequal, which shall be furnished, installed, andoperated by the contractor. Locations of therecorders shall be as approved by theContracting Authority.

Copies of the recordings shall be submitteddaily to the Contracting Authority and shallinclude the date, time of day, and name ofperson or persons responsible for operation ofthe equipment and recorder.

Sampling and testing by the ContractingAuthority in no way relieves the contractor ofthe responsibility for doing such monitoring asis necessary for the controlling of hisoperations to prevent violation of the waterquality standards.

I-5. Payment.-Payment for control ofturbidity during construction at the damsitewill be made at the applicable lump-sum pricebid therefor in the schedule, which lump-sumprice shall include the cost of furnishing alllabor, equipment, and materials for designing,con strutting, operating, maintaining, andremoving all features necessary for control ofturbidity in accordance with these sections.

Payment of percentages of the lump-sumprice for control of turbidity duringconstruction at the damsite will be made asfollows:

( 1) Fifty percent of the lump sum inthe first monthly progress estimate aftercompletion of the initial installation ofthe approved plant for treatment of theturbid water.

(2) Twenty-five percent of the lumpsum in the first monthly progress estimateafter completion of all concreteplacement in the dam.

(3) Twenty-five percent of the lumpsum in the first monthly progress estimateafter completion of the turbidity controloperation at the damsite, and removal ofequipment.

The costs of all other labor, equipment, andmaterials necessary for control of turbidity at


locations other than the damsite and for prices bid in the schedule for other items ofprevention of water pollution for compliance work.with these sections shall be included in the

B. ABATEMENT OF AIR POLLUTION

I-6. General. -The contractor shall complywith applicable Federal, State, and local lawsand regulations concerning the prevention andcontrol of air pollution.

In his conduct of construction activities andoperation of equipment, the contractor shallutilize such practicable methods and devices asare reasonably available to control, prevent,and otherwise minimize atmospheric emissionsor discharges of air contaminants.

The emission of dust into the atmospherewill not be permitted during the manufacture,handling, and storage of concrete aggregates,and the contractor shall use such methods andequipment as are necessary for the collectionand disposal, or prevention, of dust duringthese operations. The contractor’s methods ofstoring and handling cement and pozzolansshall also include means of eliminatingatmospheric discharges of dust.

Equipment and vehicles that show excessiveemissions of exhaust gases due to poor engineadjustments, or other inefficient operatingconditions, shall not be operated untilcorrective repairs or adjustments are made.

Burning shall be accomplished only at timesand at locations approved by the ContractingAuthority. Burning of materials resulting fromclearing of trees and brush, combustibleconstruction materials, and rubbish will bepermitted only when atmospheric conditionsfor burning are considered favorable byappropriate State or local air pollution or fireauthorities. In lieu of burning, suchcombustible materials may be removed fromthe site, chipped, or buried as provided insection

Where open burning is permitted, the burnpiles shall be properly constructed to minimizesmoke, and in no case shall unapproved

materials such as tires, plastics, rubberproducts, asphalt products, or other materialsthat create heavy black smoke or nuisanceodors be burned.

Storage and handling of flammable andcombustible materials, provisions for fireprevention, and control of dust resulting fromdrilling operations shall be done in accordancew i t h t h e applicable provisions o f t h eDepartment of Labor “Safety and HealthRegulation for Construction” and the Bureauof Reclamation Supplement thereto.

Dust nuisance resulting from constructionactivities shall be prevented in accordance withsection

The costs of complying with this sectionshall be included in the prices bid in theschedule for the various items of work.

I - 7 . D u s t A b a t e m e n t . -Dur ing theperformance of the work required by thesespecifications or any operations appurtenantthereto, whether on right-of-way provided bythe Contracting Authority or elsewhere, thecontractor shall furnish all the labor,equipment, materials, and means required, andshall carry out proper and efficient measureswherever and as often as necessary to reducethe dust nuisance, and to prevent dust whichhas originated from his operations fromdamaging crops, orchards, cultivated fields, anddwellings, or causing a nuisance to persons. Thecontractor will be held liable for any damageresulting from dust originating from hisoperations under these specifications onAuthority right-of-way or elsewhere.

The cost of sprinkling or of other methodsof reducing formation of dust shall be includedin the prices bid in the schedule for other itemsof work.

INDEXAbsolute head, 417Absorption, 109Abutment contraction coefficient, 173Accelerations, earthquake

horizontal, 70vertical, 70

Accelerators, 283Accelerogram, 29Adiabatic temperature, 116, 119, 120, 124Admixtures in concrete, 282Aesthetic, 294Aggregates for concrete (see Concrete, aggregates for)Air bubbling systems, 221.238Air-entraining agents, 283

specifications for, 517Air pollution (see Control of Water and Air Pollution)Alkali-aggregate reaction, 282Allowable stress, safety factors for, 31Ambient air temperatures, 108,115, 131Amplitudes of concrete temperatures, 116Analysis

curved gravity dams, 68‘dynamic, 68Finite Element Method, 70, 76, 79foundation, 76,79Trial-load Twist Method of, joints grouted, 61Trial-load Twist Method of, joints ungrouted, 43

Artifical cooling, 131Attenuation, 29Auxiliary spillway (see Spillways)Baffle blocks, 192, 198Batter on upstream face of dam, 12Beam elements, 64Bend losses in conduits, 231Bernoulli’s theorem (equation)

defined, 180,417,425equations, 180,417,425for flow in closed pipe systems, 429for flow in open channels, 417,425

Blocks, size of, 126Bridges, 25 1Broad-crested weir, 169Cantilever structure, 60Carlson-type meters, 264Cavitation, 174, 186, 192

protection against, 186Cement

low heat, 108, 112,282types of, 282type to reduce alkali aggregate reaction, 282

Channels (see also Spillway components)hydraulic design of, 4 17

Chezy Formula, 180,423Chute spillways, 156,160

design of, 180Classification of gravity dams

by alinement, 1by structural height, 1

Climatic effectsdata to be submitted, 10

general considerations, 10on temperature studies, 114

Closureslots, 131temperature, 125

Coefficient of abutment contraction, 173Coefficient of discharge

broad-crested weir, 169circular crest, 205conduit entrances, 231effect of depth of approach on, 168for flow under gates, 175for head differing from design head, 17 1ogee crest with sloping face, 169ogee crest with vertical face, 165reduction of, due to downstream apron interference, 169reduction of, due to submergence, 169sharpcrested weir, 168

Coefficient of internal friction (tangent of angle offriction), 24

Coefficient of pier contraction, 173Coefficient of roughness (see Roughness coefficient)Cofferdams, 92

design of, 92types of, 94

Cohesion, 24Collimation, 262, 273Comparison of results by Gravity and Trial-load Methods

maximum sliding factors, 381maximum stresses, 381minimum shear-friction factors, 381

Compression, 3 1Concrete

aggregates for, 282average concrete properties, 22batching and mixing of, 283cement for, 282elastic properties, 22control of, 281curing and protection of, 284density, 22dynamic properties, 22finishes and finishing for, 284other properties, 22placing of, 284Poisson’s ratio, 22repair of, 285sample specifications for, 511strength of, 21thermal expansion, coefficient of, 22thermal properties, 22tolerances of, 285

Concrete, sample specifications, 5 11admixtures, 517batching, 522cement, 5 14coarse aggregate, 519composition, 512contractors’ plants, equipment, and construction

procedures, 5 11

545

546 INDEX

curing, 537finishes and finishing, 535forms, 525measurement, 528mixing, 524payment, 539placing, 532pozzolan, 516preparations for placing, 5 3 1production of sand and gravel aggregate, 520protection, 536reinforcement bars and fabric, 529repair of concrete, 534temperature of concrete, 525tolerances for construction, 527

Conductivity, 109Conduits (see Outlet works or river diversion methods)Configuration of dam

nonoverflow section, 12overflow section, 12

Conjugate depth, 187,188, 195, 198Conservation of linear momentum, 178Consolidation grouting (“B” hole), 101

grouting pressures of, 104layout of, 101water cement ratio for, 104

Construction aspects, 17construction schedule, 17

Construction jointsdefined, 138specification for, 531,533

Construction materialsconcrete aggregates, 11data to be submitted, 11water for construction purposes, 11

Construction operationscuring, 135forms and form removal, 134foundation irregularities, 134insulation, 135openings in dam, 134temperature control operations, 131

Consumptive use (see Evapotranspiration)Contraction joints, 137

drains in, 145analysis of dam with grouted, 61grout grooves and cover plates for, 146grouting of, 107,145keys in, 141seals for, 145specifications for, 5 3 1analysis of dam with ungrouted, keyed, 43

Contraction joint grouting (see Grouting contraction joints)Contraction joint seals

asphalt, 143metal, 143polyvinylchloride, 143purpose of, 143rubber, 143

Contraction losses in pressure pipes, 231Control of water and air pollution, sample specifications, 541

abatement of air pollution, 544prevention of water pollution, 541

Control structure for spillways, 157Conversion factors (table of), 418Cooling of concrete, 111Cracking

due to loadings, 32

in mass concrete, 134repair of, 285temperature, 109

Creep, 22,270Crests of spillways

drop inlet spillway, 203ogee shape for, 159, 164structural design of, 214

Criteria, forgravity dam design, 21

Critical flow, 420critical depth, 188, 421critical discharge, 420critical slope, 421critical velocity, 188,421in conduits, 426

Curing of mass concrete, 135membrane (curing compounds), 135water, 135

Curtain grouting, 104“A” holes, 104“C” holes, 104grouting pressures in, 105layout of, 104stage grouting for, 105

Curved gravity dams, 68Cutoff shafts, 100Darcy-Weisbach equation, 228,431Darcy-Weisbach friction loss coefficient, 431Dead load, 28Deflector buckets, 198Deformation meter, 267Deformation modulus, 23Density

concrete, 28,109(see also Concrete, average properties)

silt, 29Dental treatment of foundation, 97Design considerations, 3

climatic effects, 10configuration of dam, 12construction aspects, 17construction materials, 11factors in site selection, 11foundation investigations, 13hydrologic data, 4local conditions, 3maps and photographs, 3miscellaneous considerations, 17reservoir capacity, elevation, and operation, 7

Design data and criteriabasic assumptions, 21

Design flood (see Inflow design flood)Design, gravity dam

batter, upstream face, 36nonoverflow section, 36spillway section, 36

Design storm studies, 468probable maximum precipitation or probable maximum

storm estimates for a watershed, 473procedure for storm maximization

plains-type terrain, 471Diffusivity, 108,116,119, 121Discharge channels for spillways, 157

convergence in, 183divergence in, 183freeboard for, 183hydraulic design of, 180

INDEX 547

limitations of vertical curvature for, 181losses in, 180selection of profile for, 181

Discharge coefficients (see Coefficient of discharge)Discharge formulas for

circular crests, 205flow over gate-controlled ogee crests, 174outlet works conduits, 226uncontrolled ogee crests, 165

Discharge over an uncontrolled overflow ogee crest, 165coefficient of discharge for, 165effect of downstream apron interference and downstream

submergence on, 169effect of heads differing from design head on, 171effect of upstream face slope on, 169pier and abutment effects on, 171

Divergence in spillway discharge channels, 183Diversion (see River diversion)Diversion conduits through dam, 88

closures of, 88Diversion tunnels, 85

linings in, 86tunnel closures for, 88

Drains, size, location, and spacing effects on internal hydro-static pressures, 27

Drains, foundations (see Foundation drainage)Drop inlet spillway (see Morning Glory)Durability of concrete, 281,282Dynamic loading (see Earthquake)Dynamic analysis

effects of vertical earthquake accelerations, 70hydrodynamic effects, 70loads due to horizontal earthquake accelerations, 70natural frequencies and mode shapes, 68response to an earthquake, 69

Earthquakeaccelerogram, 29attenuation, 29maximum credible, 29response spectrum, 29Richter magnitude, 29

Ecological balance, 287Ecological and environmental considerations, 287

fish, 288recreation, 293wildlife, 291

Elastic modulus, 23Electrical services, 257Elevator structure, 249

description, 249design of shaft, 249design of tower, 251

Embedded instrumentsCarlson-type, 264deformation meters, 267“No-stress” strainmeter, 265pore pressure meter (cells), 264resistance thermometers, 264strain meter, 264

Embedded pipe cooling systems, 107,112,130,134Energy dissipating devices (see Terminal structures)Energy gradients, 425,431Entrance loss coefficients for outlet conduits, 231Entrance losses, 229Entrance shapes for conduits, 232Envelope curves for floods, 505Environmental considerations (see Ecological)Environmental impact statement, 287

Epoxy-bonded concrete, 285Evapotranspiration, 6Excavation (see Foundation treatment, excavation)Exit losses, 232Exothermic reaction, 118Expansion losses, 231Extensometers, 262Extreme loading combination, 30

cracking, 32safety factors for, 31,33

Factors of safetyallowable stresses, 3 1cracking, 32foundation stability, 33, 100shear-friction, 31sliding stability, 31

Finishes for concrete, 284Finite Element Method, 70,76,79, 100,215,255

threedimensional, 72,74twodimensional, 72

Finite Element Method of Analysisgrid and numbering, 351input, 35 1,358layout and numbering system, 358output, 351,361threedimensional, 358two-dimensional, 35 1

First-order surveys (see Triangulation)Fish considerations (environmental), 288Fishways, 255

fish ladder, 255fish lock, 255

Floatlines (see Plumblines)Flood hydrograph (see Hydrograph)Flood routing

criteria, 507sizing spillway by, 15 1streamflow, 464

Floodsdata for determination of, 437during construction, 83,506envelope curves for, 505frequency determination of, 506from snowmelt, 499influence of retention losses, 446routing of (see Flood routing)use of precipitation data in estimating, 438use of streamflow records in estimating, 437use of watershed data in estimating, 439

Forces, 40Formed drains, 247Forms (see Concrete, sample specifications)Foundation

compressive strength of, 24constants, 47deformation modulus of, 23elastic modulus of, 23permeability of, 26shear resistance of, 24stability of, 33

Foundation analysis methods, 15, 76, 79stability, 15, 33, 76

Foundation drainage, 105collection system of, 106layout, size spacing, and depth of, 105

Foundation grouting (see Grouting foundation)Foundation investigations (see Design considerations)

construction geology, 15

548 INDEX

field investigation, 13foundation analysis methods (see Foundation analysis), 15in situ testing, 16laboratory testing, 16presentation of data, consistency of, 16purpose, 13

Foundation treatment, excavation, 97dental treatment in, 97,134protection against piping in, 100shaping of, 97

Frequencies, dynamic, 68Frequency of occurrence of floods, 506Friction, 24Friction factor (f), hydraulic, 431Friction loss, 180,241,426Froude number, 183,186,192,201,432Gage, bourdon, 275Galleries and adits, 243

drainage gutter along, 247formed drains flowing to, 247location and size of, 243purpose of, 243reinforcement around, 247stairways and slopes for, 248

Gates and valves (control devices)outlet works, 221spillway, 162

General dimensions of gravity dams, definedhydraulic height, 1length, 1structural height, 1volume, 2

Gravity dam, 1classifications of, 1general dimensions, 1terminology related to design and analysis, 2

Gravity dam definitions for trial-load analysisabutment of a beam element, 2axis, 2beam element or beam, 2cantilever element or cantilever, 2crest, 2height of cantilever, 2plan, 2profile, 2section, 2thickness of dam, 2twisted structure, 2

Gravity Method of Stress and Stability Analysisassumptions, 37computations and forms, 302conditions studied in example, 299description and use, 37example of, 299forces and moments on cantilever element, 40notations for horizontal earthquake, 39notations for normal reservoir loading, 37stress and stability equations, 40

Geology, 12Ground water, 7Grouting contraction joints. 61.107. 145

grouigrooves and cover plates, 146grout lifts, 133grout outlet units, 146layout of system, 145limiting pressures, 148operation, 146water cement ratio, 146

Grouting foundation, 101consolidation grouting (“B” hole), 101curtain grouting, 104principal objectives of, 101

Grouting temperature (see Closure temperature)Head loss (see Losses)Heat continuity, 109Heat generation, 119Heat of hydration, 108,113, 119,121,131,132,282“High pressure” grouting (see Curtain grouting), 101Horizontal beam elements, 64Hydraulic design of outlet works, 226

open flow in outlet works, 234pressure flow in outlet conduits, 227pressure flow losses in conduits, 228

Hydraulic design of power outletsintake structure, 241size determination of penstock, 241

Hydraulic formulasflow in closed conduits, 426flow in open channels, 417hydraulic jump and hydraulic jump basins, 431pressure flow in conduits, 429

Hydraulic gradient, 177,213,425Hydraulic jump, 187,192,431Hydraulic jump stilling basins, 186

basin depths by approximate methods for, 195hydraulic design of, 187hydraulic formulas for, 431rectangular versus trapezoidal, 192tailwater consideration for, 195

Hydraulic symbols, 415Hydraulics of channels, 180

open channels, 181tunnel channels, 185

Hydraulics of morning glory (drop inlet) spillway, 201crest discharge, 203crest profiles, 206orifice control, 207tunnel design, 213

Hydraulics of terminal structures, 186, 233deflector buckets, 198hydraulic jump stilling basins, 186, 233plunge pools, 201, 234submerged bucket energy dissipators, 199

Hydrodynamic effects, 70Hydrograph

inflow, 154outflow, 154synthetic unit hydrograph, 462unit hydrograph principals, 453

Hydrologic dataanalyses of, 439BlaneyCriddle Method, 6data to be submitted, list of, 4evapotranspiration, 6floodflows, 6ground water, 7hydrologic investigations, 5Jensen-Haise Solar Radiation Method, 6precipitation, 438Soil Conservation Service, 6streamflow, 437watershed, 439

Hydrologic soil groups, 446Hydrostatic pressure, 26Ice load, 28Ice prevention system (see Air bubbling systems)

INDEX 549

Inertiaconcrete, due to earthquake, 70

Inflow, design flood, 149definition of, 435spillway design using, 15 1types of, 435

Inflow design flood studies, 435analyses of basic data, 439design storm studies, 468envelope curves, 505estimates of frequency of occurrence of floods, 506final-type inflow design flood studies, 507hydrologic data for estimating floodflows, 437inflow design flood, rainfall only, 480snowmelt runoff contributions to inflow design floods, 499streamflow routing, 465synthetic unit hydrographs, 462

In situ testing, 16Instruments

Carlson-type, 264deformation meter, 267joint meter, 269“No-stress” strain meter, 265piers, 213pore pressure meter (cell), 264reinforcement meter, 269resistance thermometers, 264strain meters, 264

Intake structures for outlet works other than poweroutlets, 220

Internal hydrostatic pressure, 27Isohyetal maps, 441Joints, 61,137

construction, 138contraction, 137drains for, 145expansion, 138grouting of contraction, 145keys in (see Shear keys), 141purpose for, 137seals in, 143spacing of, 138

Keyscontraction joint, 43

Landscaping, 295Layout, gravity dam

freeboard, 36nonoverflow section, 36spillway section, 36

Leveling measurements, 274Lift thickness, 130Lining of diversion tunnel, 86Loads

bridge, 251dead load, 28earthquake, 29elevator tower, 25 1ice, 28internal hydrostatic pressures, 27reservoir and tailwater, 26silt, 29temperature, 26

Loading combinationsother studies and investigations, 30unusual and extreme loading combinations, 30,31,33usual loading combination, 30, 31, 33

Local conditions, 3data to be submitted, list of, 3

Losses (head losses), 226bend loss, 231entrance loss, 229exit loss, 232Friction loss, 228,426,431gate and valve loss, 231transition loss, 231trashrack loss. 229, ~-_

“Low pressure” grouting (see Consolidation grouting), 101Magnitude (Richter), for earthouake, 29Manning’s formula (Manning’s equation), 180,423,426,431Maps and photographs

data to be submitted, list of, 4general, 3isohyetal, 441survey control, 3

Mass curves of rainfall, 441Maximum Credible Earthquake, 29Maximum probable flood (see Inflow design flood)Mechanical services, 258Meters

Carlson-type, 264deformation, 267joint, 269“No-stress” strain, 265pore pressure (cell), 264reinforcement meter, 269strain, 264

Methods of temperature controlamount and type of cement, 112miscellaneous measures, lists of, 113post cooling, 112precooling, 111use of pozzolans, 113

Miscellaneous considerationsdata to be submitted, list of, 17other considerations, 18

Mode shapes, 68Modulus

deformation, 23elastic, 22, 23, 126

Moments, 40Morning glory (drop inlet) spillway, 161

characteristics of flow in, 201hydraulic design of, 20 1

Multilevel outlet works, 219Nappe profiles

for circular weir spillway crest, 205for ogee spillway crests, 164,174

Natural frequencies, 68Negative pressures (see Subatmospheric pressures)Nonlinear stress analysis, special methods of

experimental models, 376Lattice Analogy Method, 372photoelastic models, 377Slab Analogy Method, 37 1

Nonoverflow section. 36Ogee crest (gate-controlled), 174

discharge over an, 174Ogee crest (uncontrolled)

design heads other than maximum for an, 174discharge over an, 165shape for, 164

Ogee spillways (overflow), 159Open channels (see Discharge channels for spillways)Orifice (see Spillway-orifice control structures)Other analyses

analysis of stress concentrations due to bridging, 80

550 INDEX

capacity definitions, 9data to be submitted, 10general criteria, 7water surface elevation definitions, 7

Reservoir loading, 26Reservoir water temperature, 115Resistance thermometers, 264Resonance (see Response spectrum)Response spectrum, 29Restrooms, 25.5Retarding agents, 113Retention loss estimating, 446Reynolds number, 228Richter magnitude, 29Rigid Block Method, 77Rigid Section Method, 76River diversion, diversion requirements, 83

characteristics of streamflow, 83downstream requirements, 85hydrographs for estimating diversion requirements, 506probability of occurrence, 84regulation by an existing upstream dam, 84selection of diversion flood, 83turbidity and water pollution control, 84

River diversion, methods of diversion, 85cofferdam, 92conduits through dam, 88flumes, 88multiple stage diversion, 92tunnels, 85

River diversion, responsibilitiescontractor’s responsibility, 95designer’s responsibility, 95

River outlet works (see Outlet works)Roughness coefficient (Manning’s n), 180,425Runoff

base flow, 440channel, 440estimating, 440interflow, 440surface, 440

Safety factors (see Factors of safety)Seals (waterstops) for contraction joints, 143Sediment, 5Seismic considerations, 29Selective withdrawal, 219, 289Service installations, 255

electrical services, 257mechanical services, 258storage at dam, 258telephone and other communication systems, 258water supply lines, 258

Service spillways, 156Shear

friction factor of safety for, 31keys, 141resistance, 24strength in foundation, 100strength in concrete, 22

Shear-friction factorafter cracking, 32foundation, 33gravity dam, 31,43

Shear keys, 14 1shearing resistance of, 141water leakage prevention by, 141

Side channel control structures (see Spillway-side channelcontrol structures)

differential displacement analysis, 79Outlet works, 217

multilevel, 219outlet works other than power outlets, 218power outlets, 236types and purposes, 217

Outlet works other than power outlet, controls, 221emergency or guard gates or valves, 225operating gates and regulating valves, 225stoplogs and bulkhead gates, 225

Outlet works other than power outlet, intake structures, 220entrance and transition, 221trashrack, 220

Outlet works other than power outlets, 218conduits in, 221energy dissipating devices for, 225, 233gates and controls for, 221hydraulic design of, 226intake structures on, 220layout of, 218structural design of, 234

Overflow section, 36Overflow spillways (see Ogee spillways)Overturning, 33Partition Method, 78Penstocks, 236,240

hydraulic design of, 241structural design of, 242

Permeability, 113Photoelastic models

fringe value, 378material, 378polariscope, 378

Pier contraction coefficient, 173Piping, 100Plunge pools, 201Plumblines, 262, 270Pollutants (pollution), 84,288Pore pressure, 27Pore pressure meter (cell), 264Power outlets, 236

gates or valves for, 240hydraulic design of, 240intake structures for, 236layout of, 236penstocks for, 240structural design of, 242

Pozzolans, 108,113,119,283Precipitation data, 438Pressure

hydrodynamic, 70hydrostatic, 26ice, 29internal hydrostatic, 27pore, 27

Pressure gradient, 431Principal stress, 40Properties

concrete, 21foundation, 23thermal, 22

Radial gates for spillways, 164Rainfall excess determination, 444Reaeration, 290Recreation considerations (environmental), 293Reradiation, 109Reservoir capacity, 152Reservoir capacity and operation, 7

INDEX 551

Side channel spillwayhydraulics of, 178layout of, 176

Site selection, 11factors in, 12

Silt load, 29Size limitation of construction block for temperature

control, 126length, 126width, 127

Sliding stability, 31Slope, downstream face, 12Solar radiation effect, 109, 115Specific energy, 180, 192Specific heat, 22, 109Specifications for various items of work (refer to specific

item desired)Spectrum, dynamic response, 29Spillway components, 157

control structure, 157discharge channel, 157, 180entrance and outlet channels, 158,417terminal structure, 158, 186

Spillway-orifice control structures, 175hydraulics of, 175shape of, 175

Spillways, 149auxiliary, 156capacity of, 151design flood hydrograph for, 151flood routing to size, 15 1function of, 149inflow design flood for, 149selection of size and type of, 154, 156service, 156structural design of, 214

Spillways-controls for crests, 162drum gates, 164flashboards and stoplogs, 163radial gates, 164rectangular lift gates, 163ring gates, 164

Spillway typeschute, 156,160controlled, 159,174free overfall, 159morning glory (drop inlet), 157,161,201ogee (overflow), 157,159side channel, 156,160,176tunnel, 156,161uncontrolled, 159, 164

Stabilitycracking, 32foundation, 3 3sliding, 31,97

Stability analysesfoundation, 76methods available, 76threedimensional methods, 77twodimensional methods, 76(see also Gravity Method of Stress and Stability Analysis)

Stilling basins (see Terminal structures)Storm (see Design storm)Strain meter, 264

“No stress” strain meter, 265Streamflow

data analysis of, 450pollution of, 84

required data relating to, 437routing of, 464source of data on, 5,437

Streamflow data analysishydrograph analysis-base flol.7 separation, 455hydrograph analysis of direct runoff-

need for synthetic unit hydrographs, 455dimensionless graph computations and lag time

estimates, 457selection of hydrographs to analyze, 455unit hydrograph principals, 453

Streamflow routing, 464comparison of methods of, 468methods of, 465Tatum’s Method of, 465translation and storage method of, 466

Stoplogsfor power outlet works, 237for outlet works, 225for spillway crests, 163

Storage at dam, 258Stress in gravity dams

due to temperature, 117gravity method, 40principal stress, 40trial-load twist method, joints ungrouted, 60

Stress meter, 260, 266Structural behavior measurements

baseline, 273collimation, 262, 273drainage flow, 275embedded instruments, 260extensometers, 262instrument piers, 273joint meter, 261leveling measurements, 274plumblines, 262, 270strain, 260stress, 260, 266target, 273temperature-sensing, 262theodolite, 274triangulation, 273uplift pressure, 275

Subatmospheric pressure, 160,174,205Subcritical flow, 421Submerged bucket energy dissipators, 199Sulfate attack, 113Supercritical flow, 421Surcharge storage, 151,152Surging, 186Suiveys (see Triangulation)Symbols (see Hydraulic symbols)Tailwater loading, 26Tailwater’s relation to stilling basin depths, 195Telephone and other communication systems, 258Temperature

gradients, 116load, 26of ambient air, 115of reservoir water, 115concrete, 114studies, 114

Thiessen polygons to predict average rainfall, 443Temperature control operations, 131

initial cooling, 132intermediate and final cooling, 133warming operations, 133

552 INDEX

Temperature control methods, 111controlling rate of temperature drop, 114control of amount and type of cement, 112curing, 113limiting construction lift thickness, 113postcoolhlg, 112precooling, 111retarding agents, 113use of pozzolans, 113

Temperature control of concreteblock height differentials, 130closure slots, 131closure temperature (grouting temperature), 125concrete cooling systems, 127delays between placements, 131design data required for, 108factors to be considered in, 108lift thickness, 130methods of, 111placing temperatures, 125purposes of, 107size of block, 126volumetric changes, 107

Temperature equilibrium, 107Temperature related construction operations, 131

at openings in dam, 134concrete curing, 135forms and form removal, 134foundation irregularities, 134insulation (concrete protection), 135temperature control operations, 131

Temperature studiesartificial cooling, 120Carlson’s Method, 116,120range of concrete temperatures, 114Schmidt’s Method, 116,120temperature gradients, 116temperature rise, 118

Tension, 31Terminal structures (energy dissipating devices)

for outlet works, 225,233for spillways, 158,186

Testingin situ, 16laboratory, 16,215,286

Theodolite, 274Thermal

coefficient of expansion, 22,118,126conductivity, 22, 109density, 109diffusivity, 109properties, 22,109specific heat, 109

Thermally stratified reservoir, 219Thermocouples, 130Thermometers

electrical resistance-type, 130, 264insert-type, 130

Threedimensional finite element programapplication, 74capabilities and limitations, 74input, 75output, 75

Tolerances for concrete placing, 285Top of dam, 254

cantilever at, 254design of, 254parapets or handrails at, 254

roadway at, 254Topographic maps, 4Topography, 12Transitions in outlet conduits, 232Trashrack losses, 229,241Trashrack structures

losses through, 229,241for outlet works other than power, 220for power outlets, 237velocity through, 220,237

Trial-load twist analysis-joints groutedbeam stresses, 340beamstructure deflections, 335cantilever deflections, 323cantilever stresses, 340distribution, trial-load, 323example of, 321moment and shear due to trial loads on beams, 340stability factors, 340twisted-structure deflections, 335

Trial-load Twist Method of Analysis, joints groutedassumptions, 64description of method, 61equations, 64horizontal beam elements, 64notations, 64

Trial-load Twist Method of Analysis, joints ungroutedangular rotation of vertical twisted elements due to trial

loads on horizontal elements, 60deflections of cantilever structure, 60deflections of twisted structure, 60foundation constants, 47initial and unit deflections of cantilevers, 54keyed contraction joints, 43loads, forces, and moments, 54notations, 45selection of elements, 54stresses and stability factors, 60theory, 44trial loads, 58unit deflections of horizontal elements of twisted

structure, 57unit rotations of vertical elements of twisted structure

due to unit twisting couple, 54Triangulation, 273Tunnel spillway channels, 185

cross section for, 185morning glory spillway, 213profile of, 185

Tunnelsriver diversion, 85spillway channel, 185

Turbidity, 84Twisted structure, 60Twodimensional finite element program

application to gravity dams, 74approximations, 73capabilities, 7 3input, 73limitations, 73method, 72output, 73purpose, 7 2

Ungrouted contraction joints, 43keyed, 43unkeyed (see Gravity analysis)

Unusual loading combination, 30safety factors for, 31, 33

INDEX 553

Uplift pressures (internal hydrostatic pressures), 27drains, effect of, 27

Usual loading combination, 30safety factors for, 31,33

Valves for outlet works, 463Volumetric change in mass concrete, 107, 137Vortex, 205Wall for spillway structures, 215Water curing of concrete, 113Water for construction purposes, 11

Water pollution (see Control of water and air pollution)Water reducing agents, 283Water supply lines, 258Water temperature and quality, 219Watershed data, 439Waterstops (see Seals for contraction joints)Wave suppressors (wave dampers), 188Wildlife considerations (environmental), 291Workability of concrete, 113Young’s modulus, (modulus of elasticity), 22, 23

* “S GOVERNMENT PRINTING OFFICE: 1976 67%101

Gravity Dams

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