Creep Shrinkage and Prestress Losses

School of Civil and Environmental Engineering

Structural Engineering, Mechanics and Materials Research Report No. 03-11

Creep, Shrinkage, and Prestress Losses of High-Performance Lightweight Concrete

Task 3 Report – Lightweight Concrete for High-Strength/High- Performance Precast Prestressed Bridge Girders

Prepared for

Office of Materials and Research Georgia Department of Transportation

GDOT Research Project No. 2004

by

Mauricio Lopez, Lawrence F. Kahn, Kimberly E. Kurtis, and James S. Lai

July 2003 Revised December 2003

Contract Research GDOT Research Project No. 2004

Creep, Shrinkage and Prestress Losses of High Performance Lightweight Concrete

Task 3 Report: Lightweight Concrete for High-Strength/High-

Performance Precast Prestressed Bridge Girders

Prepared for

Office of Materials and Research Georgia Department of Transportation

by

Mauricio Lopez, Lawrence F. Kahn, Kimberly E. Kurtis, and James S. Lai

July 2003 Revised December 2003

The contents of the report reflect the views of the authors who are responsible for the facts and the accuracy of the data presented herein. The contents do not necessarily reflect the official views or policies of the Georgia Department of Transportation. This report does not constitute a standard, specification, or regulation.

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Executive Summary

The creep, shrinkage and prestress losses of high performance lightweight concrete

(HPLC) were investigated. The creep was less than that of normal weight high performance

concrete while the shrinkage was somewhat greater. Generally prestress losses measured on

AASHTO Type II girders made with HPLC were less than those predicted using AASHTO,

PCI and ACI-209 relations.

Two different HPLC mixes were developed using Type III cement, silica fume, class

F fly ash, expanded slate as coarse aggregate, natural sand, and chemical admixtures. The

first mix was an 8,000-psi HPLC (FHWA HPC Grade 2) with an “air dry” unit weight of 117

lb/ft3. The second mix was a 10,000-psi HPLC (FHWA HPC Grade 3) with an “air-dry” unit

weight of 119 lb/ft3.

In the fresh state, the two HPLC mixes performed adequately for casting precast

prestressed concrete girders. The 56-day specified strength was reached in most cases at 28

days. As expected, modulus of elasticity was up to 20% lower than that of HPC of similar

strength. Modulus of rupture was higher than the value given by AASHTO equation for

normal weight concrete.

The 620-day creep of 8,000-psi HPLC was about 1,650 µε and 2,000 µε when loaded

to 40% and 60% of initial strength, respectively. On the other hand, the 620-day creep of

10,000-psi HPLC was approximately 1,160 µε and 1,500 µε when loaded to 40% and 60% of

initial strength. Fifty and ninety percent of the 620-day creep were reached after

approximately 10 and 250 days of loading, regardless the type of HPLC.

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The 10,000-psi HPLC had a specific creep similar to that of a normal weight HPC of

the same grade, but with less cement paste content; and it had significantly less creep than an

HPC of the same grade and similar cement paste content.

The 620-day shrinkage was approximately 820 µε for the 8,000-psi HPLC mix and

610 µε for the 10,000-psi HPLC mix. Fifty and ninety percent of the 620-day shrinkage were

reached after approximately 30 and 260 days of drying, regardless the type of HPLC.

Considering creep and shrinkage performance, the Shams and Kahn (2000) model

was the best model for predicting long-term strains of HPLC made with locally available

materials in Georgia.

The AASHTO-LRFD refined method for estimating prestress losses was conservative

when compared to measured long-term losses found in six AASHTO Type II precast,

prestressed girders made with HPLC. The AASHTO-LRFD lump sum method was

conservative for estimating prestress losses on the 10,000-psi girders made with HPLC. For

8,000-psi girders made with HPLC the AASHTO-LRFD lump sum method underestimated

total loses by 1.2%.

Overall, the AASHTO-LRFD refined method may be used conservatively for

predicting prestress losses in girders made of high performance lightweight concrete.

iii

Acknowledgements

The Georgia Department of Transportation sponsored the research reported herein

through Georgia DOT research project no. 2004, Task Order no. 97-22. Tindall Corporation

constructed all prestressed girders. For laboratory phases of the overall research project,

LaFarge Cement, Boral Material Technologies, and Grace Construction Products donated

cement, flyash, and concrete admixtures, respectively. Carolina Stalite Company donated all

expanded slate lightweight aggregate. The support provided by the sponsors is gratefully

acknowledged.

The findings and conclusions reported herein are those of the authors and do not

necessarily represent the opinions, conclusions, specifications, or policies of the Georgia

Department of Transportation, or any other sponsoring or cooperating organization.

Mr. Paul Liles, GDOT Bridge Engineer, provided valuable suggestions and guidance.

Lt. Col. Karl F. Meyer, Ph.D., P.E., Mr. Brandon Buchberg, and Mr. Adam Slapkus assisted

with specimen preparation, strain measurements, and physical testing. Mr. Charles Freeman

and Ken Harmon of Carolina Stalite provided valuable advice. Ms. Maria Wilmhof and

several other students in the School of Civil and Environmental Engineering at Georgia Tech

also assisted in the construction and testing phases of the research. Their assistance is

gratefully acknowledged.

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Table of Contents

Executive Summary........................................................................................................ i

Acknowledgements ....................................................................................................... iii

Table of Contents .......................................................................................................... iv

List of Tables ................................................................................................................ xii

List of Figures.............................................................................................................. xiv

1. Introduction................................................................................................................1

2. Background Review...................................................................................................5

2.1 Creep and Shrinkage of HPLC ........................................................................ 5

2.1.1. Creep of HPLC ......................................................................................... 5

2.1.2. Shrinkage of HPLC................................................................................... 6

2.2 Creep and Shrinkage Models ........................................................................... 7

2.3 Prestress Losses ............................................................................................... 8

3. Experimental Program, Results, and Short-term Properties ..............................11

3.1 HPLC Mixes for short and long-term properties ........................................... 11

3.2 Plastic Properties............................................................................................ 13

3.3 Unit Weight.................................................................................................... 13

3.4 Compressive Strength .................................................................................... 14

3.5 Modulus of Elasticity..................................................................................... 16

3.6 Modulus of Rupture ....................................................................................... 17

3.7 Chloride Permeability .................................................................................... 18

3.8 Coefficient of Thermal Expansion................................................................. 19

4. Creep and Shrinkage Results and Analysis...........................................................21

4.1 Creep Results and Analysis ........................................................................... 21

4.1.1 Creep Behavior of Laboratory HPLC vs. Field HPLC............................ 22

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4.1.2 Creep Behavior of 8,000-psi HPLC vs. 10,000-psi HPLC...................... 25

4.2 Shrinkage Results and Analysis..................................................................... 26

4.3 Creep and Shrinkage Test Results vs. Model Estimates................................ 29

4.3.1. Creep and Shrinkage Models Results ..................................................... 29

4.3.2. Creep Models Compared ........................................................................ 30

4.3.3. Shrinkage Models Compared.................................................................. 35

4.4 Comparison of Creep and Shrinkage of HPLC with HPC............................. 38

4.4.1. Creep Comparison .................................................................................. 39

4.4.2. Shrinkage Comparison............................................................................ 40

4.4.3. Total Strain Projection ............................................................................ 42

5. Prestress Losses........................................................................................................43

6. Conclusions and Recommendations.......................................................................49

6.1. Conclusions................................................................................................... 49

6.1.1. High Performance Lightweight Concrete Material Properties ............... 49

6.1.2. Creep and Shrinkage Behavior ............................................................... 50

6.1.3. Prestress Losses ...................................................................................... 51

6.2. Recommendations......................................................................................... 52

6.2.1. Design Recommendations ....................................................................... 52

6.2.2. Future Research ....................................................................................... 52

7. References.................................................................................................................55

Appendix A. Introduction ...........................................................................................61

A.1 Introduction to Task 3: Short and Long-term Properties of High Performance

Lightweight Concrete Mixes......................................................................................... 61

A.2 Introduction to High Performance Concrete (HPC) ..................................... 62

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A.3 Introduction to Structural Lightweight Concrete (SLC) ............................... 65

A.4 Introduction to High Performance Lightweight Concrete (HPLC) .............. 66

Appendix B. Creep and Shrinkage - Background ....................................................69

B.1 Long-term strains in concrete........................................................................ 69

B.2 Creep ............................................................................................................. 70

B.2.1. Basic Creep ............................................................................................ 71

B.2.2. Drying Creep .......................................................................................... 72

B.2.3. Factors Influencing Creep ...................................................................... 72

B.2.4. Creep Mechanisms ................................................................................. 75

B.3 Shrinkage....................................................................................................... 78

B.3.1. Autogenous Shrinkage ........................................................................... 78

B.3.2. Drying Shrinkage ................................................................................... 79

B.3.3. Factors Influencing Shrinkage ............................................................... 79

B.3.4. Shrinkage Mechanisms .......................................................................... 80

B.4 Long-Term Strains of HPC ........................................................................... 81

B.4.1. Creep of HPC ......................................................................................... 82

B.4.2. Shrinkage of HPC................................................................................... 84

B.5 Long-Term Strains of SLC............................................................................ 86

B.5.1. Creep of SLC.......................................................................................... 86

B.5.2. Shrinkage of SLC................................................................................... 90

B.6 Long-Term Strains of HPLC......................................................................... 92

B.6.1. Creep of HPLC....................................................................................... 92

B.6.2. Shrinkage of HPLC ................................................................................ 96

Appendix C. Creep and Drying Shrinkage Models ..................................................97

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C.1 Models for Normal Strength Concrete .......................................................... 98

C.1.1. ACI-209 Method .................................................................................... 98

C.1.2. AASHTO-LRFD Method..................................................................... 102

C.1.3. CEB-FIP Method.................................................................................. 104

C.1.4. Bažant and Panula’s - BP Method........................................................ 108

C.1.5. Bažant and Baweja’s - B3 Method....................................................... 115

C.1.6. Gardner and Lockman’s - GL Method................................................. 119

C.1.7. Sakata’s - SAK 93 Method................................................................... 120

C.2 Models for High Strength Concrete ............................................................ 123

C.2.1 CEB-FIP Method as modified by Yue and Taerwe (1993)................... 123

C.2.2. Bažant and Panula’s - BP Method........................................................ 124

C.2.3. Sakata’s - SAK 01 Method................................................................... 126

C.2.4. AFREM Method................................................................................... 128

C.2.5. AASHTO-LRFD as modified by Shams and Kahn (2000).................. 130

C.3 Models for Lightweight Concrete ............................................................... 133

C.3.1. ACI-209 Method .................................................................................. 133

C.3.2. AASHTO-LRFD Method..................................................................... 133

C.3.3. Gardner and Lockman’s - GL Method................................................. 133

Appendix D. Prestress Losses - Background...........................................................135

D.1 Prestress Losses........................................................................................... 135

D.1.1. Introduction to Prestress Losses........................................................... 135

D.1.2. Prestress Losses in Normal Weight Normal Strength Concrete .......... 136

D.1.3. Prestress Losses in Special Concretes.................................................. 137

D.2 Codes........................................................................................................... 138

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D.2.1. PCI Method.......................................................................................... 138

D.2.2. AASHTO-LRFD Refined Estimates of Time-Dependent Losses ....... 142

D.2.3. AASHTO-LRFD Lump Sum Estimate of Time-Dependent Losses.... 145

D.2.4. ACI-209 Method.................................................................................. 146

Appendix E. Concrete Properties – Experimental Program ................................151

E.1 Introduction ................................................................................................. 151

E.2 Mix Design .................................................................................................. 151

E.3 Test Procedures ........................................................................................... 152

E.4 Creep Test Procedures................................................................................. 154

E.5 Shrinkage Test Procedures .......................................................................... 157

E.6 Coefficient of Thermal Expansion Test Procedures.................................... 157

Appendix F. Experimental Results and Analysis....................................................159

F.1 Plastic Properties ......................................................................................... 159

F.2 Unit Weight ................................................................................................. 159

F.3 Compressive Strength.................................................................................. 161

F.4 Modulus of Elasticity................................................................................... 165

F.5 Modulus of Rupture..................................................................................... 166

F.6 Chloride Ion Permeability............................................................................ 168

F.7 Coefficient of Thermal Expansion............................................................... 169

F.8 Creep............................................................................................................ 170

F.8.1. Creep of 8L and 10L HPLC.................................................................. 170

F.8.2. Creep of 8F and 10F HPLC.................................................................. 178

F.9. Shrinkage .................................................................................................... 186

F.9.1. Shrinkage of 8L and 10L HPLC........................................................... 188

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F.9.2. Shrinkage of 8F and 10F HPLC ........................................................... 189

Appendix G. Analysis of Creep and Shrinkage .....................................................193

G.1 Comparison of Creep Performance of Laboratory HPLC with Field HPLC193

G.1.1. Comparison of Creep Performance of 8L HPLC with 8F HPLC ........ 194

G.1.2. Comparison of Creep Performance of 10L HPLC with 10F HPLC .... 196

G.2 Comparison of Creep of 8,000-psi HPLC with 10,000-psi HPLC ............. 198

G.3 Comparison of Shrinkage of 8,000-psi HPLC with 10,000-psi HPLC....... 202

G.4 Comparison of Creep and Shrinkage Test Results with Code Models ....... 205

G.4.1. Creep and Shrinkage Models Results .................................................. 205

G.4.2. Creep Models Performance Comparison ............................................. 208

G.4.3. Shrinkage Models Performance Comparison ...................................... 214

G.5 Comparison of Creep and Shrinkage of HPLC with HPC.......................... 219

G.5.1. Creep Comparison................................................................................ 220

G.5.2. Shrinkage Comparison......................................................................... 224

G.5.3. Total Strain Projection ......................................................................... 226

Appendix H. Comparison of Estimated Prestress Losses with Experimental Results 229

H.1. Experimental Results ................................................................................. 229

H.2. Prestress Losses Calculations from Standards ........................................... 233

H.3. Estimates vs. Experimental Laboratory Results ........................................ 237

Appendix I. Creep and Drying Shrinkage Models S.I. units .................................241

I.1 Models for Normal Strength Concrete .......................................................... 241

I.1.1. ACI-209 Method.................................................................................... 241

I.1.2. AASHTO-LRFD Method...................................................................... 244

I.1.3. CEB-FIP Method................................................................................... 246

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I.1.4. Bažant and Panula’s - BP Method......................................................... 249

I.1.5. Bažant and Baweja’s - B3 Method ........................................................ 256

I.1.6. Gardner and Lockman’s - GL Method .................................................. 260

I.1.7. Sakata’s - SAK Method......................................................................... 261

I.2 Models for High Strength Concrete............................................................... 263

I.2.1. CEB-FIP Method as modified by Yue and Taerwe (1993) ................... 263

I.2.2. Bažant and Panula’s - BP Method......................................................... 264

I.2.3. Sakata’s - SAK Method......................................................................... 266

I.2.4. AFREM Method.................................................................................... 268

I.2.5. AASHTO-LRFD method as modified by Shams and Kahn (2000)...... 270

Appendix J. Analysis of Variance - ANOVA...........................................................273

J.1. Three-Factor ANOVA: Creep of 8L HPLC................................................ 273

J.2. Three-Factor ANOVA: Creep of 10L HPLC.............................................. 274

J.3. Two-Factor ANOVA: Creep of 8F HPLC .................................................. 275

J.4. Two-Factor ANOVA: Creep of 10F HPLC ................................................ 276

J.5. Four-Factor ANOVA: Creep of Laboratory HPLC (8L & 10L)................. 277

J.6. Three-Factor ANOVA: Shrinkage of Laboratory HPLC (8L & 10L) ........ 278

J.7. Three-Factor ANOVA: Creep of 8,000-psi HPLC (8L & 8F) .................... 279

J.8. Two-Factor ANOVA: Shrinkage of 8,000-psi HPLC (8L & 8F) ............... 280

J.9. Three-Factor ANOVA: Creep of 10,000-psi HPLC (10L & 10F) .............. 281

J.10. Three-Factor ANOVA: Shrinkage of 10,000-psi HPLC (10L & 10F) ..... 282

J.11. Three-Factor ANOVA: Creep of Field HPLC (8F & 10F) ....................... 283

J.12. Two-Factor ANOVA: Shrinkage of Field HPLC (8F & 10F) .................. 284

Appendix K. Experimental Results ..........................................................................285

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K.1. Compressive Strength ................................................................................ 285

K.2. Modulus of Elasticity ................................................................................. 286

K.3. Modulus of Rupture ................................................................................... 286

K.4. Chloride Ion Permeability.......................................................................... 287

K.5. Coefficient of Thermal Expansion............................................................. 287

K.6. 8L Creep and Shrinkage............................................................................. 288

K.7. 8F Creep and Shrinkage............................................................................. 291

K.8. 10L Creep and Shrinkage........................................................................... 293

K.9. 10F Creep and Shrinkage........................................................................... 296

K.10. 8,000-psi HPLC girders Experimental Strains......................................... 298

K.11. 10,000-psi HPLC girders Experimental Strains....................................... 299

Appendix L. Model Comparison ..............................................................................301

L.1. Normal Strength Concrete Creep Models for 8,000-psi HPLC .................. 301

L.2. High Strength Concrete Creep Models for 8,000-psi HPLC....................... 304

L.3. Shrinkage Models for 8,000-psi HPLC....................................................... 307

L.4. Normal Strength Concrete Creep Models for 10,000-psi HPLC ................ 310

L.5. High Strength Concrete Creep Models for 10,000-psi HPLC..................... 313

L.6. Shrinkage Models for 10,000-psi HPLC..................................................... 316

Appendix M. Comparison between HPC and HPLC.............................................319

M.1. Creep and Shrinkage Results HPC-3 and HPC-6....................................... 319

M.2. Best Creep and Shrinkage Fits for HPC-3, HPC-6, and HPLC ................. 320

xii

List of Tables

Table 3.1. Actual mixes used in the laboratory specimens (8L and 10L) and used to cast the

girders tested in Task 5 (8F and 10F) ............................................................................. 11

Table 3.2. Fresh concrete Properties...................................................................................... 13

Table 4.1. Long-term shrinkage and creep coefficient .......................................................... 30

Table 4.2. Mix design and properties of HLPC and HPC, for one cubic yard ...................... 38

Table 4.3. Ultimate strain estimates for HPLC and HPC loaded at 40% and 60% of its initial

strength............................................................................................................................ 42

Table 5.1 Comparison between experimental and estimated prestress losses of 8,000-psi

HPLC prestressed girders ............................................................................................... 44

Table A.1. Designed high performance lightweight concrete mixes (SSD condition).......... 61

Table A.2. High performance concrete bridge mix specifications (Goodspeed et al., 1996) 63

Table D.1. Loss of prestress ratios for different concretes and time under loading conditions

....................................................................................................................................... 148

Table E.1. Actual mixes used in the laboratory specimens (8L and 10L) and used to cast the

girders tested on Task 5 (8F and 10F) .......................................................................... 151

Table F.1. Fresh concrete properties of HPLC mixes.......................................................... 159

Table F.2. Compressive strength of HPLC mixes (psi) ....................................................... 162

Table F.3. Rupture modulus of HPLC mixes ...................................................................... 168

Table G.1. ANOVA results for creep of 8,000-psi HPLC................................................... 194

Table G.2. ANOVA results for creep of 10,000-psi HPLC................................................. 196

Table G.3. ANOVA results for creep of HPLC................................................................... 199

Table G.4 ANOVA results for shrinkage of HPLC............................................................. 202

xiii

Table G.5. Parameters used in creep prediction equations .................................................. 206

Table G.6. Long-term shrinkage and specific creep ............................................................ 206

Table G.7. Sum of squared error and coefficient of determination of creep coefficient models

....................................................................................................................................... 213

Table G.8 Sum of squared error and coefficient of determination of shrinkage models..... 218

Table G.9. Mix design and properties of HPLC and HPC, for one cubic yard ................... 220

Table G.10. Ultimate strain estimates for HPLC and HPC loaded at 40 and 60% of its initial

strength.......................................................................................................................... 226

Table H.1 Experimental strains of 39-ft long girders (µε).................................................... 230

Table H.2 Comparison between experimental and estimated prestress losses of 8,000-psi

HPLC prestressed girders ............................................................................................. 233

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List of Figures

Figure 3.1. Unit weight of HPLC under different moisture conditions. ................................ 14

Figure 3.2. Compressive strength vs. time of 8,000-psi and 10,000-psi HPLC mixes for

accelerated and ASTM curing methods. ......................................................................... 15

Figure 3.3. Elastic modulus of 8,000 and 10,000-psi mixes.................................................. 16

Figure 3.4. 56-day elastic modulus of 8,000 and 10,000-psi mixes ..................................... 17

Figure 3.5. Rupture modulus of 8,000 and 10,000-psi mixes................................................ 18

Figure 3.6. Chloride Permeability of 8,000 and 10,000-psi mixes ........................................ 19

Figure 4.1. Creep test set-up and working principle.............................................................. 21

Figure 4.2. Creep coefficient of 8L and 8F HPLC in logarithmic time scale........................ 23

Figure 4.3. Creep coefficient of 10L and 10F HPLC in logarithmic time scale.................... 24

Figure 4.4. Average creep coefficient of 8,000-psi and 10,000-psi HPLC in logarithmic time

scale................................................................................................................................. 26

Figure 4.5. Shrinkage of 8,000-psi and 10,000-psi HPLC (a) laboratory mixes and (b) field

mixes. .............................................................................................................................. 27

Figure 4.6. Average shrinkage of 8,000-psi and 10,000-psi HPLC in logarithmic time scale.

......................................................................................................................................... 28

Figure 4.7. Comparison between measured creep coefficient and estimated from models for

normal strength concrete: (a) 8,000-psi HPLC, (b) 10,000-psi HPLC. .......................... 31

Figure 4.8. Comparison between measured creep coefficient and estimated from models for

high strength concrete: (a) 8,000-psi HPLC, (b) 10,000-psi HPLC. .............................. 33

xv

Figure 4.9. Comparison between measured shrinkage of 8L HPLC and estimated from

models for normal and high strength concrete................................................................ 36

Figure 4.10. Comparison between measured shrinkage of 10L HPLC and estimated from

models for normal and high strength concrete................................................................ 37

Figure 4.11. Comparison between specific creep of HPLC and HPC mixes in logarithmic

time scale ........................................................................................................................ 39

Figure 4.12. Comparison between creep coefficients of HPLC and HPC mixes in logarithmic

time scale ........................................................................................................................ 40

Figure 4.13. Comparison between shrinkage of HPLC and HPC mixes in logarithmic time

scale................................................................................................................................. 41

Figure 5.1. Experimental strains over time for the 8,000-psi and 10,000-psi HPLC 39-foot

girders. ............................................................................................................................ 44

Figure 5.2. Comparison between estimated prestress losses from PCI, AASHTO and ACI-

209 models ...................................................................................................................... 46

Figure B.1. Relation between various strains in concrete with time. ................................... 69

Figure B.2. Representation of three stages of creep. ............................................................ 71

Figure B.3: Relationship between creep of concrete and aggregate content (Neville, Dilger

and Brooks, 1983)........................................................................................................... 74

Figure B.4. Representation of cement paste microstructure (Mehta and Monteiro, 1993) ... 76

Figure B.5. Effect of water and cement content on shrinkage (Neville, 1996). .................... 80

Figure B.6: Relationship between 28-day compressive strength and one-year specific creep

for SLC and NWC. ......................................................................................................... 87

xvi

Figure B.7: Relationship between aggregate elastic modulus and relative creep of concrete

(Pfeifer, 1968). ................................................................................................................ 89

Figure B.8: Relationship between 28-day compressive strength and one-year drying

shrinkage for SLC and NWC.......................................................................................... 91

Figure B.9: Ultimate drying shrinkage values for different lightweight concretes (Pfeifer,

1968). .............................................................................................................................. 92

Figure D.1. Example of initial and long-term strains in prestressed concrete..................... 136

Figure E.1. Elastic modulus test .......................................................................................... 153

Figure E.2. Rupture modulus test ........................................................................................ 153

Figure E.3. Chloride permeability test set up. ..................................................................... 153

Figure E.4. Creep frames components and working principle............................................. 155

Figure E.5. Creep specimens during loading process and under load in creep frames........ 155

Figure E.6. Steel mold used in casting 4” X 15” cylinders.................................................. 156

Figure E.7. Shrinkage and coefficient of thermal expansion specimens ............................. 157

Figure E.8. DEMEC gage reader for creep, shrinkage and coefficient of thermal expansion.

....................................................................................................................................... 158

Figure F.1. Unit weight of HPLC under different moisture conditions............................... 161

Figure F.2. Compressive strength vs. time of 8L mix for accelerated and ASTM curing

methods. ........................................................................................................................ 163

Figure F.3. Compressive strength vs. time of 8F mix for accelerated and ASTM curing

methods. ........................................................................................................................ 163

Figure F.4. Compressive strength vs. time of 10L mix for accelerated and ASTM curing

methods ......................................................................................................................... 164

xvii

Figure F.5. Compressive strength vs. time of 10F mixes for accelerated and ASTM curing

methods compressive strength vs. time ........................................................................ 164

Figure F.6. Elastic modulus of 8,000 and 10,000-psi HPLC mixes .................................... 166

Figure F.7. Rupture modulus of HPLC mixes and design values (ACI-318)...................... 167

Figure F.8. Chloride ion permeability of 8,000 and 10,000-psi HPLC mixes.................... 168

Figure F.9. Coefficient of thermal expansion of 8,000 and 10,000-psi HPLC mixes ......... 169

Figure F.10. 8L HPLC Total strain (a) linear scale and (b) logarithmic scale. ................... 171

Figure F.11. 10L HPLC Total strain (a) linear scale and (b) logarithmic scale. ................. 172

Figure F.12. Creep of HPLC loaded at 16 and 24 hours (a) 8L HPLC stress-to-strength ratio

of 40% and 60% (b)10L HPLC for stress-to-strength ratio of 40% and 60%. ............. 174

Figure F.13. Specific creep of 8L HPLC (a) and 10L HPLC (b) and limits for FHWA HPC

Grade 2 and 3. ............................................................................................................... 176

Figure F.14. Creep coefficient of 8L HPLC (a) and 10L HPLC (b).................................... 177

Figure F.15. 8F HPLC Total strain (a) linear scale and (b) logarithmic scale..................... 179

Figure F.16. 10F HPLC Total strain (a) linear scale and (b) logarithmic scale................... 181

Figure F.17. Creep of HPLC loaded at 16 and 24 hours (a) 8F HPLC stress-to-strength ratio

of 40% and 60% (b)10F HPLC for stress-to-strength ratio of 40% and 50%. ............. 182

Figure F.18. Specific creep of 8F HPLC (a) and 10F HPLC (b) and limits for FHWA HPC

Grade 2 and 3 ................................................................................................................ 184

Figure F.19. Creep coefficient of 8F HPLC (a) and 10F HPLC (b). .................................. 185

Figure F.20. Shrinkage of 8L HPLC (a) and 10L HPLC (b) and limits for FHWA HPC

Grade 2 and 3. ............................................................................................................... 187

xviii

Figure F.21. Shrinkage of 8F HPLC (a) and 10F HPLC (b) and limits for FHWA HPC Grade

2 and 3........................................................................................................................... 190

Figure G.1. Creep coefficient of 8L and 8F HPLC (a) linear time scale and (b) logarithmic

time scale. ..................................................................................................................... 195

Figure G.2. Creep coefficient of 10L and 10F HPLC (a) linear time scale and (b)

logarithmic time scale. .................................................................................................. 197

Figure G.3. Creep coefficient of 8L and 10L HPLC (a) linear time scale and (b) logarithmic

time scale. ..................................................................................................................... 200

Figure G.4. Average creep coefficient of 8,000-psi and 10,000-psi HPLC in logarithmic time

scale............................................................................................................................... 201

Figure G.5. Shrinkage of 8,000-psi and 10,000-psi HPLC (a) laboratory mixes and (b) field

mixes. ............................................................................................................................ 204

Figure G.6. Average shrinkage of 8,000-psi and 10,000-psi HPLC in logarithmic time scale

....................................................................................................................................... 205

Figure G.7. Predicted-to-measured ratio of 620-day specific creep and shrinkage of HPLC

....................................................................................................................................... 207

Figure G.8. Comparison between measured creep coefficient and estimated from models for

normal strength concrete: (a) 8,000-psi HPLC, (b) 10,000-psi HPLC. ........................ 209

Figure G.9. Comparison between measured creep coefficient and estimated from models for

high strength concrete: (a) 8,000-psi HPLC, (b) 10,000-psi HPLC. ............................ 211

Figure G.10. Comparison between measured shrinkage of 8L HPLC and estimated from

models for normal and high strength concrete.............................................................. 216

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Figure G.11. Comparison between measured shrinkage of 8L HPLC and estimated from

models for normal and high strength concrete.............................................................. 217

Figure G.12. Comparison between specific creep of HPC and HPLC mixes (a) linear time

scale and (b) logarithmic time scale.............................................................................. 222

Figure G.13. Comparison between creep coefficient of HPC and HPLC mixes (a) linear time

scale and (b) logarithmic time scale.............................................................................. 223

Figure G.14. Comparison between shrinkage of HPC and HPLC mixes (a) linear time scale

and (b) logarithmic time scale....................................................................................... 225

Figure G.15. Best fit regressions for HPC and HPLC mixes (a) specific creep and (b)

shrinkage. ...................................................................................................................... 227

Figure H.1. Vibrating wire strain gage used to measure internal strains in the girders....... 229

Figure H.2 Measuring strains in the AASHTO Type II precast prestressed HPLC girders.230

Figure H.3 Experimental strains over time for the 8,000-psi and 10,000-psi HPLC 39-ft

girders ........................................................................................................................... 231

Figure H.4 Experimental creep and shrinkage and exponential regression for the 8,000-psi

and 10,000-psi HPLC 39-ft girders (a) linear time scale (b) logarithmic time scale.... 232

Figure H.5. Comparison between estimated prestress losses from AASHTO-LRFD, PCI,

and ACI-209 methods (a) 8,000-psi HPLC girders, (b) 10,000-psi HPLC girders ...... 235

Figure H.6. Predicted-to-measured ratio of prestress losses from AASHTO-LRFD, PCI, and

ACI-209 models............................................................................................................ 236

Figure H.7 Comparison between 8,000-psi HPLC experimental strains and those estimated

by AASHTO-LRFD refined, PCI, and ACI-209 models.............................................. 238

xx

Figure H.8 Comparison between 10,000-psi HPLC experimental strains and those estimated

by AASHTO-LRFD refined, PCI, and ACI-209 models.............................................. 240

1

1. Introduction

The overall purpose of the research was to determine if lightweight aggregate, high

strength / high performance concrete is applicable for construction of precast prestressed

bridge girders. The specific goal of this final phase of the research was to investigate the

time-dependent behavior of high performance lightweight concrete and how that long-term

behavior affects the prestress losses in HPLC precast prestressed bridge girders.

Other objectives of this final phase were to determinate the compressive strength of

high performance lightweight concretes selected in Task 2, their elastic modulus, rupture

modulus, chloride permeability, and their creep and shrinkage characteristics.

The selected mixes from Task 2 had design strengths of 8,000 psi, 10,000 psi, and

12,000 psi. After the mix design stage, it was concluded (Meyer, Kahn, Lai, and Kurtis,

2002) that the 12,000 psi design strength was not possible with the expanded slate (Stalite 1/2-

inch aggregate) used in the research. The existence of a strength ceiling of about 11,500 psi

limits the specifiable design strength to 10,000 psi. The 8,000 psi and 10,000 psi mix designs

are presented in Table A.1 of Appendix A.

High Performance Concrete (HPC): American Concrete Institute (ACI) Committee

363 (1997) defined high strength concrete (HSC) as a concrete with a cylinder compressive

strength that exceeds 6,000 psi. ACI Committee 116 (2000) defined HPC as “concrete

meeting special combinations of performance and uniformity requirements that cannot

always be achieved routinely using conventional constituent materials and normal mixing,

placing, and curing practices”. Federal Highway Administration (FHWA) went further in its

definition of HPC and stated that it is defined not only by the strength, but by seven other

parameters.

2

The advantages of HPC have been recognized by several authors (See Appendix A,

Section A.2). They can be summarized for bridge structures as: (1) lengthening of span

length for the same size pretensioned girder; (2) use of wider girder spacing for the same size

member; (3) improvement in durability and long-term service performance under static,

dynamic, and fatigue loading; and overall cost reduction of highway bridges.

Structural Lightweight Concrete (SLC): ACI Committee 213 (ACI-213, 1999)

defined structural lightweight concrete as structural concrete made with lightweight

aggregate, with an air-dried density at 28 days in the range of 90 and 115 lb/ft3 and a

compressive strength above 2,500 psi.

The three main advantages of SLC are: (1) reduction in structure dead load, which

leads to a reduction in the foundation size and seismic forces; (2) reduction in member size,

resulting in an increase in rentable space; and (3) development of a precast technology as a

result of self-weight reduction that facilitates the transport and lifting of structural members.

High Performance Lightweight Concrete (HPLC): HPLC can be conceptualized as a

combination of the above concretes. As found by Meyer and Kahn (2002) the use of 8,000-

to-10,000-psi HPLC would permit easier and more economic transportation of long -span

precast bridge girders. Modified BT-63, BT-72, and modified BT-72 sections could be

constructed for spans exceeding 150 ft with girder weight plus that of the transport vehicle

less than 150,000 lb. Special superload permit would not be required. Nevertheless, the use

of lightweight coarse aggregate would limit some of the mechanical properties attainable by

normal weight HPC. Nilsen and Aïtcin (1992) and Zhang and Gjørv, (1990) developed

HPLC with compressive strength slightly below and above 14,500 psi, respectively.

3

According to Aïtcin (1998), this strength level represents the upper strength boundary of

HPLC.

Hoff (1990) concluded that the use of HPLC will not expand unless designers have

confidence in their knowledge of its expected properties. Currently the codes do not

specifically consider HPLC. Rather, HPLC is specified as SLC by applying a capacity

reduction factor to the formulas commonly used in the design. Hoff (1990) stated that such as

practice might lead to very conservative values, undermining the HPLC application.

4

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5

2. Background Review

2.1 Creep and Shrinkage of HPLC

2.1.1. Creep of HPLC

A detailed description of creep, its factors, and mechanisms is given in Appendix B,

Section B.2.

While it is clear that HPLC can be produced, its creep characteristics have not been

extensively or systematically investigated. Creep is typically reduced in HPC (see Appendix

B, Section B.4), but creep is typically greater in lightweight concrete (see Appendix B,

Section B.5). These competing effects make creep in HPLC difficult to predict. Moreover,

some observations and recommendations presented in the literature are not consistent. For

instance, Berra and Ferrada (1990) concluded that specific creep in HPLC is twice that of

normal weight concrete of the same strength. On the other hand, Malhotra (1990) gave values

of creep of fly ash HPLC in the range 460 to 510 µε. These values are fairly close to those

obtained by Penttala and Rautamen (1990) for HPC, and they are significantly lower than the

values between 878 and 1,026 µε reported for HPC by Huo et al. (2001).

There are only a few research works done in creep of HPLC. However, conclusions

from different researchers are sometimes opposed which makes the prediction of creep in

HPLC extremely difficult. Section B.6 of Appendix B presents a detailed literature review.

The two principle phases of HPLC, high performance matrix and lightweight

aggregate, have several possible specific implications on creep of concrete. It is commonly

assumed that normal weight aggregate does not creep at the stress levels present in concrete.

However, in HPLC, the higher stress placed on the member might induce creep in the

6

lightweight aggregate, due to its lower modulus and strength. Also, improvements in the

interfacial transition zone, afforded by the use of ultra-fine pozzolanic particles and

lightweight aggregate, can alter the mechanisms for creep. Particularly, they can alter

mechanisms compared to normal strength concrete, but also compared to high strength

concrete due to improved compatibility between the aggregate and paste. Finally, the

increased aggregate porosity and the effect of “internal curing” when using saturated

lightweight aggregate can influence moisture movements during creep. These possible

changes in expected behavior as compared to normal concrete and high strength concrete

which result from the use of high performance matrix and lightweight aggregate are

described in detail in Section B.6.1.

2.1.2. Shrinkage of HPLC

Section B.3 presents a detailed discussion of shrinkage, and Section B.6.2 deals with

shrinkage of HPLC. As occurs with creep of HPLC, there are only a few articles regarding

shrinkage of HPLC. Also, the authors usually do not report autogenous and drying shrinkage

separately, but as overall shrinkage. Berra and Ferrada (1990) found that compared with

HPC, HPLC had a lower shrinkage rate, but a higher ultimate value. According the authors,

the lower rate was caused by the presence of water in the aggregate which delays drying.

Holm and Bremner (1994) also observed that the HSLC mix lagged behind at early ages, but

one-year shrinkage was approximately 14% higher than the HPC counterpart. Holm and

Bremner (1994) measured a higher shrinkage when they incorporated fly ash to the HSLC

mix. Malhotra’s (1990) results, on the other hand, showed that fly ash particles in the HPLC

helped to reduce shrinkage after one year. Other authors (Section B.6.2) also concluded the

beneficial effect, less drying shrinkage when using saturated lightweight aggregate.

7

2.2 Creep and Shrinkage Models

According Findley, Lai and Onaran (1989), creep was first systematically observed

by Vitac (1834), but Andrade (1910) was the first in proposing a creep law. After Andrade,

several more models have been developed. Some models are general mechanistic models

which include constants for different materials and properties while other models are more

empirical for specific materials. The most used models for creep in concrete fall in the

second category, empirical models.

On the other hand, drying shrinkage of concrete was identified by the first creep

studies when they measured a higher creep rate and strain on concrete under drying

conditions. Since then, several investigators have proposed models in order to describe and

predict shrinkage.

Among the variety of methods proposed for creep and shrinkage in concrete, seven of

them are presented in this report: American Concrete Institute Committee 209 (ACI-209,

1997; Section C.1.1), American Association of State Highway and Transportation Officials

(AASHTO-LRFD, 1998; Section C.1.2), Comite Euro-Internacional du Beton and Federation

Internationale de la Precontrainte (CEB-FIP, 1990; Section C.1.3), Bažant and Panula’s (BP,

1978; Section C.1.4), Bažant and Baweja’s (B3, 1995; Section C.1.5), Gardner and

Lockman’s (GL, 2001; Section C.1.6), and Sakata’s model (SAK, 1993; Section C.1.7).

Finally, five methods aimed to be used for high strength concrete are presented: CEB-FIP as

modified by Yue and Taerwe (1993; Section C.2.1), BP as modified by Bažant and Panula

(1984; Section C.2.2), SAK as modified by Sakata et al. (2001; Section C.2.3), Association

Française de Recherches et d'Essais sur les Matériaux de Construction (AFREM, 1996;

8

Section C.2.4), and Shams and Kahn’s method which is a modification of AASHTO-LRFD

method for HSC (Shams and Kahn, 2000; Section C.2.5).

Even though there are not models specifically developed for lightweight concrete,

ACI-209, AASHTO-LRFD, and GL methods (presented in Section C.1) consider some

corrections when lightweight aggregate are being used. Creep and shrinkage prediction

equations proposed by the ACI-209 (Equations C.1 and C.3) were based on research done in

normal weight concrete and structural lightweight concrete, so they are entirely applicable to

normal weight, “sand-lightweight”, and “all-lightweight” concrete. Since the AASHTO-

LRFD method is an updated version of the ACI-209 method (see Section C.1.2), equations

C.5 and C.6 are applicable to SLC, too. Finally, Gardner and Lockman (2001) proposed a

way to incorporate aggregate stiffness in their creep and shrinkage prediction equations as

explained in Appendix C, Section C.3.3.

2.3 Prestress Losses

The prestressing force in a prestressed concrete member continuously decreases with

time (Zia et al., 1979). The Precast Prestressed Concrete Institute (PCI) Committee on

Prestress Losses, identified the factors influencing prestress losses as friction in post-

tensioning operations, movement of the prestressing steel at the end anchorage, elastic

shortening at transfer, effect due to connection of the prestressed member with other

structural member, and time dependent losses due to steel relaxation, creep and shrinkage of

the concrete (PCI Committee on Prestress Losses, 1975). The same committee pointed out

that the determination of stress losses in prestressed members is an extremely complicated

problem because the effect of one factor is continuously being altered by changes in stress

due to other factors. The contribution of each loss factor to the total losses depends on the

9

structural design, material properties (concrete and steel), prestressing method (pretensioned

or posttensioned), concrete age at stressing, and the method of prestress computation (PCI,

1998).

Section D.1 presents the literature review of prestress losses in normal strength

normal weight concrete (NSNWC), as well as HPC, SLC, and HPLC. To the authors’

knowledge, there is no previous research on prestress losses of HPLC; however, from the

concrete material properties some conclusions can be drawn. Elastic shortening losses are

expected to be similar or less than NWNSC but more than HPC. Creep and shrinkage losses

would be similar to those of HPC. Steel relaxation losses would tend to be higher than losses

in NWNSC because the previous losses are lower.

10


11

3. Experimental Program, Results, and Short-term Properties

3.1 HPLC Mixes for short and long-term properties

The main objective of Task 3 was to characterize the HPLC mixes obtained from

Task 2. This characterization included: slump, air content, and unit weight for the plastic

state, and compressive strength, elastic modulus, rupture modulus, chloride permeability,

creep and non-stress dependent strains such as shrinkage and coefficient of thermal

expansion for the hardened state.

Two HPLC mixes were suggested at the end of Task 2: (1) 8,000-psi compressive

strength (8L made in the laboratory and 8F made in the field); and (2) 10,000-psi

compressive strength (10L made in the laboratory and 10F made in the field). The mix

proportions are presented in Table 3.1.

Table 3.1. Actual mixes used in the laboratory specimens (8L and 10L) and used to cast the girders tested in Task 5 (8F and 10F)

Component Type 8L 8F 10L 10F cement, Type III (lb/yd3) 783 780 740 737 Fly ash, class F (lb/yd3) 142 141 150 149 Silica Fume, (lb/yd3) 19 19 100 100 Natural sand (lb/yd3) 1022 1018 1030 1025 3/8" Lightweight aggregate (lb/yd3) 947 944 955 956

Water (lb/yd3) 268 284 227 260

AEA, Daravair 1000 (fl oz/yd3) 7.8 7.8 7.4 5.5 Water reducer, WRDA 35 (fl oz/yd3) 47 46.8 44.4 44.2 HRWR, Adva 100 (fl oz/yd3) 47.5 53.4 102 95.8

All laboratory concrete specimens were taken from mixes made according to standard

procedures at the Georgia Tech Structural Engineering Laboratory. All field concrete

specimens were taken from actual field batches used in the girders made at Tindall

12

Corporation precast plant at Jonesboro, GA. Testing of all specimens was done at the

Georgia Tech Structural Engineering Laboratory. All specimens were cured and removed

from their forms as required. The following tests were performed:

1. Compressive Strength. Compressive strength was determined by testing 4” x 8”

cylinders according to ASTM C 39.

2. Modulus of Elasticity. The chord modulus of elasticity was tested using 6” x 12”

cylinders loaded in compression according to ASTM C 469. Figure E.1 shows elastic

modulus test.

3. Modulus of Rupture. Modulus of rupture was determined by testing 4” x 4” x 14”

beams according to ASTM C78. Figure E.2 shows modulus of rupture test.

4. Chloride Permeability. Chloride permeability was determined by testing 4” x 2”

cylinders according ASTM C1202. Figure E.3 shows the test set up.

5. Creep, Drying Shrinkage and Coefficient of Thermal Expansion. The procedures

for testing creep, drying shrinkage and coefficient of thermal expansion are given in

Sections E.4, E.5 and E.6, respectively.

The 8,000-psi and 10,000-psi compressive strength HPLC mixes were made in both

laboratory and field. The laboratory mixes were meant to characterize material properties

while the field mixes were made for casting six AASHTO Type II girders. This section

presents the most important experimental properties measured on laboratory and field mixes.

More properties and details are provided in Appendix F.

13

3.2 Plastic Properties

Slump, unit weight, and air content (ASTM C173: volumetric method) were

measured in laboratory and field batches. Table 3.2 present the average results of those tests.

Table 3.2. Fresh concrete Properties

8,000-psi HPLC 10,000-psi HPLC 8L 8F 10L 10F

Slump, in 5.0 8.0 4.0 4.5 Air Content, % 4.0 4.5 3.5 3.3

Plastic unit weight, lb/ft3 120 117 122 119 Temperature, oF 90 85 90 85

From the workability results shown above, the 8,000-psi HPLC slump might be

classified as 6.5 ± 1.5 in. The 10,000-psi mix had a slump 4.0 ± 0. 5 in. The air content, on

the other hand, averaged 4.25% for the 8,000-psi mix and 3.8% for the 10,000-psi mix.

3.3 Unit Weight

Plastic unit weight of HPLC varied from 114 to 122 lb/ft3 with most of the values

close to 120 lb/ft3. The 8,000-psi mix averaged a unit weight of 117 lb/ft3 while the 10,000-

psi HPLC an average unit weight of 119 lb/ft3. These values represent 78 and 79% of the

weight of an HPC.

ACI-213 (1999) proposed the “air-dry” condition as a standard for measuring

hardened lightweight concrete unit weight. An analysis of variance (ANOVA) of “Air-dry”

unit weight as well as “Oven dry” unit weight is shown in Section F.2.

Figure 3.1 presents measured plastic unit weight and estimated1 air-dry and oven-dry

unit weight for each mix.

1 Estimate was made based on actual results for those properties

14

Figure 3.1. Unit weight of HPLC under different moisture conditions.

3.4 Compressive Strength

Specimens used for testing mechanical properties were cured in two different ways:

ASTM C-39 (fog room and 73oF) and accelerated curing that simulates the condition within a

precast prestressed member. Compressive strength for laboratory mixes was measured using

4 x 8-in. cylinders at 16, 20 and 24 hours, and then at, 7, 28, and 56 days. For field mixes

strength was measured at 1, 7, 28, 56, and more than 100 days after casting. The average

compressive strength of 8,000-psi and 10,000-psi HPLC (including laboratory and field

mixes) is presented in Figure 3.2. Table F.2 (in Appendix F) presents the average strength

values obtained for each curing method and mix type. Figures F.2 to F.5, also in Appendix

F, show individual and average strength of three specimens tested at each age and curing

procedure.

117 119

150

75

85

95

105

115

125

135

145

155

8F 10F HPC

Uni

t Wei

ght (

lb/ft

3 )

Plastic unit weight Air-dry unit weight Oven-dry unit weight

117 119

150

75

85

95

105

115

125

135

145

155

8F 10F HPC

Uni

t Wei

ght (

lb/ft

3 )


15

Figure 3.2. Compressive strength vs. time of 8,000-psi and 10,000-psi HPLC mixes for accelerated and ASTM curing methods.

The 8,000-psi HPLC satisfied the specified strength, after the age of 28 days. At 56

days, the 8,000-psi mix reached 10,000 psi with some individual results above 10,500 psi

(Shown in Figure F.2, Appendix F). At 103 days, the 8,000-psi HPLC mix reached a

compressive strength slightly above upper limit of FHWA HPC Grade 2. At early ages,

accelerated-cured specimens presented a higher strength than the ASTM-cured ones.

However, at 28 days that relation shifts and the ASTM-cured specimens are the ones with the

higher compressive strength.

The 10,000-psi HPLC accelerated-cured specimens overcame the lower limit of the

FHWA HPC Grade 3 at 28 days with no single result below it (see Figures F.4 and F.5,

Appendix F). At 56 days the average strength was close to 11,000 psi and did not change

significantly after that. The 10,000-psi HPLC accelerated-cured specimens had a higher

strength at early ages, but lower strength than the ASTM-cured cylinders after 28 days.

0

2000

4000

6000

8000

10000

12000

0 14 28 42 56 70 84 98 112 126 140 154Age (days)

Com

pres

sive

Stre

ngth

(psi)

8,000-psi Accelerated Cure

8,000-psi ASTM Cure


10,000-psi ASTM Cure

0

2000

4000

6000

8000

10000

12000

0 14 28 42 56 70 84 98 112 126 140 154Age (days)

Com

pres

sive

Stre

ngth

(psi)


8,000-psi ASTM Cure


10,000-psi ASTM Cure

16

3.5 Modulus of Elasticity

Modulus of elasticity of concrete was measured using 6 x 12-in cylinders made from

the 8,000 and 10,000-psi mixes according ASTM C469. Specimens with accelerated curing

were tested at 16 hours, 24 hours, and 56 days while the ones under ASTM curing were

tested only at 56 days. Figure 3.3 shows the elastic modulus obtained for all the tests. Even

though there are no specifications for the concrete elastic modulus, experimental results were

lower than the limits given by FHWA for Grade 2 and 3 of 6,000 and 7,500 ksi, respectively.

These results were expected since lightweight concrete usually has lower elastic modulus

(see Section A.3, Appendix A). The average 56-day elastic modulus is shown in Figure 3.4

Figure 3.3. Elastic modulus of 8,000 and 10,000-psi mixes

3000

3200

3400

3600

3800

4000

4200

4400

0.10 1.00 10.0 100Age (days)

Mod

ulus

of E

last

icity

(ksi

)

8L Accelerated Curing 8L ASTM Curing8F Accelerated Curing 8F ASTM Curing10L Accelerated Curing 10L ASTM Curing10F Accelerated Curing 10F ASTM Curing

8L Accelerated curing average 8F Accelerated curing average10L Accelerated curing average 10F Accelerated curing average

3000

3200

3400

3600

3800

4000

4200

4400

0.10 1.00 10.0 100Age (days)

Mod

ulus

of E

last

icity

(ksi

)





17

Figure 3.4. 56-day elastic modulus of 8,000 and 10,000-psi mixes

At the age of 56 days, ASTM-cured specimens had higher modulus of elasticity than

the accelerated-cured specimens. The difference between the two curing methods ranged

from 1 to 3 %, except for 8L HPLC mix that had a difference of 9%.

Analysis of variance (ANOVA) of Poisson’s ratio indicated that none of the

considered factors (strength, age, curing procedure, and lab or field) were statistically

significant (at 90% level) in explaining variability of Poisson’s ratio. Average 56-day

Poisson’s ratio was 0.190 with 90% of the results in the range 0.188 and 0.192. Poisson’s

ratio results were higher than the range 0.142 to 0.152 obtained by Lopez and Kahn (2003)

for an equivalent HPC of normal weight.

3.6 Modulus of Rupture

Modulus of rupture (fr) was measured for the 8,000 and 10,000-psi HPLC at the age

of 56 days under accelerated and ASTM curing methods. Figure 3.5 shows the ratio of

modulus of rupture-to-squared root of compressive strength (fr / (fc′)0.5) grouped by HPLC

30003200340036003800400042004400

Acc

eler

ated

Cur

ing

AST

MC

urin

g

Acc

eler

ated

Cur

ing

AST

MC

urin

g

Acc

eler

ated

Cur

ing

AST

MC

urin

g

Acc

eler

ated

Cur

ing

AST

MC

urin

g

8L 8F 10L 10F

Mod

ulus

of E

last

icity

(ksi

)

30003200340036003800400042004400

Acc

eler

ated

Cur

ing

AST

MC

urin

g

Acc

eler

ated

Cur

ing

AST

MC

urin

g

Acc

eler

ated

Cur

ing

AST

MC

urin

g

Acc

eler

ated

Cur

ing

AST

MC

urin

g

8L 8F 10L 10F

Mod

ulus

of E

last

icity

(ksi

)

18

mix and type of curing. For the four mixes, accelerated-cured specimens presented higher

56-day rupture modulus than ASTM-cured specimens. On average, 8,000-psi mixes had

higher rupture modulus than 10,000-psi mixes as shown in Table F.3 (Appendix F).

Even though "fr / (fc′)0.5" was always higher than ACI-318 value of 7.5, as shown in

Figure 6.3, the compressive strength affected the mentioned ratio. Figure 6.3 also shows the

value of 6.375 (7.5 times the lightweight factor λ =0.85 for sand-lightweight concrete). It is

concluded that the use of '5.7 cr ff ⋅= with no reduction factor is conservative for

predicting modulus of rupture of HPLC.

Figure 3.5. Rupture modulus of 8,000 and 10,000-psi mixes

3.7 Chloride Permeability

Chloride ion permeability was measured at 56 days on 8L, 8F, 10L, and 10F

specimens. The results are presented in Figure 3.6. All HPLC mixes had a chloride ion

10.0 10.39.5

10.5 10.911.4

8.6 8.9

0

12

3

4

5

6

7

8

9

10

11

12

8L 8F 10L 10FHPLC Type

ASTM CuringAccelerated Curing

7.5: NWC

6.375 (7.5 x λ): sand-lightweight concrete

f r/(f c′)

0.5

10.0 10.39.5

10.5 10.911.4

8.6 8.9

0

12

3

4

5

6

7

8

9

10

11

12



7.5: NWC


f r/(f c′)

0.5

19

permeability classified as “very low”. The 8,000-psi HPLC results were in the range 615 -

900 coulombs while the 10,000-psi mixes presented results within the range of 100 - 350

coulombs.

Figure 3.6. Chloride Permeability of 8,000 and 10,000-psi mixes

3.8 Coefficient of Thermal Expansion

Coefficient of thermal expansion (CTE) was measured in 8F, 10L, 10F mixes at 56

days and 100% of relative humidity. The detailed results of those tests are presented in

Section F.7.

The 8F mix CTE averaged 5.14 µε/oF while 10L and 10F mixes gave slightly higher

values of 5.32 and 5.17 µε/oF. All HPLC CTE results were higher than the one reported by

Lopez and Kahn (2003) for 10,000-psi normal weight HPC (4.9 µε/oF at 100%). All results

were lower than 6.0 µε/oF commonly used for concrete.

1

10

100

1000

10000

8L 8F 10L 10F

HPLC Type

Cou

lum

bs

Negligible

Very low

LowModerateHigh

1

10

100

1000

10000

8L 8F 10L 10F

HPLC Type

Cou

lum

bs

Negligible

Very low

LowModerateHigh

20


21

4. Creep and Shrinkage Results and Analysis

4.1 Creep Results and Analysis

Eight creep specimens were cast from each laboratory mix (8L and 10L) and four

specimens from each field mix. They were loaded at different ages (16 and 24 hours) and at

different stress-to-initial strength ratios (0.4 to 0.6). Figure 4.1 illustrates the creep set-up

testing program; details are given in Sections F.8.1 and F.8.2. Four measurements were

taken from each specimen.

Figure 4.1. Creep test set-up and working principle.

22

4.1.1 Creep Behavior of Laboratory HPLC vs. Field HPLC

In this section the creep behavior of the laboratory mixes is compared with that of

field mixes. Creep strains are not compared directly because the applied stress was not the

same for laboratory and field mixes due to the different initial compressive strengths.

Nevertheless, specific creep and creep coefficient can be compared regardless the applied

stress because they are expressed in terms of stress. Specific creep is the creep strain divided

by the applied stress, while creep coefficient is the creep strain divided by the initial elastic

strain which is proportional to applied stress.

An analysis of variance (ANOVA) of specific creep (sc) and creep coefficient (øc)

was performed. The considered factors were: time under load, stress level, and whether the

mix was prepared in laboratory or field. Tables G.1, G.2, and G.3 of Section G.1 present the

ANOVA results. Among these results two parameters are of special interest: (1) the relative

contribution of each factor to the total mean squared error (MSE), denoted as “Rel MSE”,

which ranges from 0.0 to 1.0; and (2) the P-value which represents the probability that the

considered factor is not significant in explaining the variance. A P-value less than 0.05

(generally adopted as confidence limit) means that there is more than a 95% chance that the

factor is significant and should be included.

Comparison of Creep Performance of 8L HPLC with 8F HPLC: The ANOVA

between 8,000-psi mixes made in laboratory (8L) and field (8F) showed that the difference

between them was not a significant for either of the creep parameters (sc or øc). Even though

stress level had P-values below 0.05, the portion of MSE explained by stress level was only

2.0 and 2.7% for sc and øc, respectively (see Table G.1). The low contribution of stress level

23

to the variability of sc and øc was expected because the creep deformation was expressed in

terms of stress.

Figure 4.2 presents a comparison between average creep coefficient of 8L and 8F

HPLC in logarithmic time. As concluded in Section F.8, creep coefficient at 40% of initial

strength was unexpectedly higher than the one for 60% stress level. That was also seen in

ANOVA (see Table G.1) where stress level is still significant for creep coefficient.

Figure 4.2. Creep coefficient of 8L and 8F HPLC in logarithmic time scale.

The field mix had an average higher long-term creep for 40% of stress level, but

lower long-term creep for 60% stress level. Creep coefficient curves intercept each other

several times during the testing period which indicated that there is no constant trend.

From ANOVA and Figure 4.2 it can be concluded that the place of casting

(laboratory or field) was not a significant factor; therefore, 8L and 8F HPLC are the same

HPLC.

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8L 24h-60%

8F 24h-60%

24

Comparison of Creep Performance of 10L HPLC with 10F HPLC: In Table G.2

(Section G.1.2) the most relevant results from the analysis of variance (ANOVA) between

10L and 10F mixes are presented. Figure 4.3 shows the creep coefficient of each mix in a

logarithmic time scale.

Figure 4.3. Creep coefficient of 10L and 10F HPLC in logarithmic time scale.

From ANOVA it was concluded that the factor place of mixing (laboratory or field)

was significant for specific creep (sc), but it explained only 0.3% of the mean squared error

(Rel MSE=0.003). Place of mixing factor was not significant for creep coefficient (it has a P-

value of 0.492 and Relative MSE of 0.%). Stress level was not significant for any of the

creep parameters. It also can be noticed in Figure 4.3 that creep coefficient curves are not

parallel and constantly intercept each other during the testing period which shows that there

are not consistent differences over time.

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10F 24h-40%

10L 24h-60%

10F 24h-50%

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10L 24h-60%

10F 24h-50%

25

From ANOVA and Figure 4.3, it can be stated that the place of mixing (laboratory or

field) and stress level were not significant factors for creep of 10,000-psi HPLC. As a

conclusion, 10L and 10F are the same HPLC.

4.1.2 Creep Behavior of 8,000-psi HPLC vs. 10,000-psi HPLC

Following the same procedure used in Section 4.1.1 and described in Appendix G,

creep performance of 8,000-psi and 10,000-psi HPLC was compared. The factors were time

under load, stress level (40% or 60% of initial strength), compressive strength (8,000 psi or

10,000 psi), and time of application of load (16 hours or 24 hours). The analysis of variance

(ANOVA) results are shown in Table G.3 (Appendix G).

From ANOVA, it can be concluded that all four the factors were statistically

significant since none of the P-values were above 0.05. However, age of application of load

and stress level can be dropped from ANOVA without increasing MSE by more that 4%.

This means that the differences between creep of specimens loaded at 16 and 24

hours were not appreciable. Also the use of creep coefficient regardless the stress level is

also possible without making a considerable error. Figure 4.4 presents the average creep

coefficient obtained from 8,000-psi and 10,000-psi mixes in logarithmic time scale.

Figure 4.4 shows that the 620-day creep coefficient was 1.684 and 1.143 for 8,000-psi

and 10,000-psi HPLC, respectively. The 50% and 90% of the 620-day creep coefficient were

reached after 16 and 250 days regardless the type of HPLC. When specific creep of HPLC

mixes was compared with FHWA limits (Table A.2), 8,000-psi HPLC had a slightly higher

value than the 0.41 µε/psi limit (see Figure F.13, Appendix F). The specific creep of 10,000-

psi HPC was within the suggested 0.21-to-0.31 range (see Figure F.18, Appendix F)

26

Figure 4.4. Average creep coefficient of 8,000-psi and 10,000-psi HPLC in logarithmic time scale.

4.2 Shrinkage Results and Analysis

Following the same procedure used in Section 4.1, shrinkage performance of 8,000-

psi and 10,000-psi HPLC was compared. Shrinkage results are shown in Figure 4.5. The

factors considered in the analysis were time under drying, compressive strength (8,000 psi or

10,000 psi), and age at the beginning of drying (16 hours or 24 hours). Table G.4 (Appendix

G) presents the most relevant ANOVA results from four different comparisons: (1) Place of

mixing for 8,000-psi HPLC (8L vs. 8F); (2) Compressive strength for laboratory mixes (8L

vs. 10L); (3) Compressive strength for field mixes (8F vs. 10F); and (4) Place of mixing for

10,000-psi HPLC (10L vs. 10F).

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10,000-psi HPLC

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27

Figure 4.5. Shrinkage of 8,000-psi and 10,000-psi HPLC (a) laboratory mixes and (b) field mixes.

ANOVA revealed that the place of mixing was not a significant factor for shrinkage

of 8,000-psi HPLC. The factor age at the beginning of drying (16 or 24 hours) was not a

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28

statistically significant factor either. Compressive strength of the mix was a significant factor

affecting shrinkage for the laboratory mix, but not for the field mix.

In addition, a significant difference was detected when comparing 10L and 10F

HPLC; P-value was less than 0.05 and relative MSE was 2.8%. Therefore, place of mixing

(laboratory or field) affected shrinkage of the 10,000-psi HPLC.

Figure 4.5 presents the shrinkage results obtained for each HPLC. As concluded

from ANOVA, there is a clear difference between 8L and 10L HPLC at any time of drying

while shrinkage of field mixes is overlapped. The 8L and 8F mixes had a similar average

value though the variance of the 8F shrinkage result was higher than the one of 8L HPLC.

Figure 4.6. Average shrinkage of 8,000-psi and 10,000-psi HPLC in logarithmic time scale.

Figure 4.6 presents the average shrinkage obtained from 8,000-psi and 10,000-psi

mixes in logarithmic time scale. The 620-day shrinkage was 818 and 610 µε for 8,000-psi

and 10,000-psi HPLC, respectively. At very early ages (less than one day), shrinkage of the

0

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800

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29

10,000-psi mix was considerably greater than 8,000-psi mix. After one day, shrinkage rate of

the 10,000-psi mix slowed down, and measured shrinkage was much lower than for the

8,000-psi HPLC. The 50% and 90% of the 620-day shrinkage was reached after 27 and 170

days for 8,000-psi HPLC and after 55 and 170 days for 10,000-psi mix.

Compared with FHWA limits shown in Figure 4.6, 8,000-psi and 10,000-psi HPLC

mixes overcame the upper limit of each respective grade.

4.3 Creep and Shrinkage Test Results vs. Model Estimates

4.3.1. Creep and Shrinkage Models Results

Models presented in Chapter 2 for normal and high strength concrete were used to

predict creep of 8,000-psi and 10,000-psi HPLC. Since the last experimental results were

taken after at least 620 days of drying and loading, Table 4.1 presents measured and

predicted shrinkage and creep coefficient at that age. Table 4.1 also presents the predicted

values at 40 years which was taken as the ultimate creep and shrinkage states. More details

of the models and their results are presented in Appendices C and G, respectively.

The best shrinkage estimate was given by AASHTO-LRFD and Shams and Kahn’s

model, for 8,000-psi and 10,000-psi HPLC, respectively. Those models underestimated

shrinkage by only 5 and 4%, respectively. Creep coefficient of 8,000-psi HPLC was best

predicted by AASHTO-LRFD model with an underestimate of 8% while creep coefficient of

10,000-psi HPLC was best predicted by Shams and Kahn with 6% overestimate. The

AASHTO-LRFD and Shams and Kahn’s models were used to estimate2 the 8,000-psi and

2 See Section G.4.1 of Appendix G for details of the estimate.

30

10,000-psi ultimate strains, by modifying each model to yield the same shrinkage and creep

coefficient as those measured. Based on the modified relationships, the ultimate shrinkage

would be 795 and 625 µε for 8,000-psi and 10,000-psi HPLC, respectively. In addition, the

ultimate creep coefficient would be 1.925 and 1.431 for 8,000-psi and 10,000-psi HPLC,

respectively.

Table 4.1. Long-term shrinkage and creep coefficient

Parameter 620-day shrinkage

µε

620-day creep coefficient

40-year shrinkage

µε

40-year creep coefficient

HPLC mix (psi) 8,000 10,000 8,000 10,000 8,000 10,000 8,000 10,000 Measured 763 610 1.66 1.29

AASHTO-LRFD 725 725 1.965 1.852 755 755 1.529 1.439 ACI-209 644 640 1.739 1.639 698 694 2.305 2.173

AFREM - HSC 396 350 1.137 0.941 408 359 1.215 1.051 B3 385 329 4.465 4.511 390 334 5.325 5.392 BP 322 298 3.928 3.807 330 310 4.746 4.65

BP - HSC 322 298 3.357 3.254 330 310 4.649 4.519 CEB-FIP 381 313 3.727 3.564 407 334 4.202 4.019

CEB-FIP - HSC 381 313 2.896 2.707 407 334 3.279 3.058 GL 555 530 5.112 5.111 594 568 5.585 5.585

SAK-2001 - HSC 512 357 1.451 1.027 553 382 2.164 1.531 SAK-93 291 230 4.464 2.815 297 234 4.528 2.856

Shams & Kahn 590 585 1.479 1.373 604 599 1.634 1.523

4.3.2. Creep Models Compared

Figure 4.7 presents a comparison between measured creep coefficient versus time and

predicted values using models for normal strength concrete. Figure 4.7a shows results for

8,000-psi HPLC and Figure 4.7b does it for 10,000-psi HPC. A more detailed comparison

for each model is presented in Appendix G, section G.4.2.

When comparing model performance from Figure 4.7a, it can be concluded that ACI-

209 model had the best overall performance closely followed by AASHTO-LRFD model.

31

Figure 4.7. Comparison between measured creep coefficient and estimated from models for normal strength concrete: (a) 8,000-psi HPLC, (b) 10,000-psi HPLC.

Even though the ACI-209 model underestimated creep for time under load less than

10 days and overestimated creep for times greater than 100 days, it was the one with best

0.01 0.10 1.00 10.0 100 1000 10000Time under Load (days)

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Bažant Panula

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Sakata 93

8,000-psi Measured


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Sakata 93

10,000-psi Measured


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8,000-psi Measured


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Sakata 93

8,000-psi Measured


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Sakata 93

10,000-psi Measured


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Bažant Panula

Bažant Baweja

Sakata 93

10,000-psi Measured

32

overall agreement with the experimental data. The second best model was AASHTO-LRFD

model which followed the same tendency as ACI-209 at early ages, but continued

underestimating creep at all ages.

The good performance presented by ACI-209 model might be due to that model is

explicitly including SLC in its database. However, because the model was largely based on

work done between 1957 and 1970, it can be assumed that high strength concrete and

supplementary cementing materials were not part of the database.

All the other models greatly overestimated creep of 8,000-psi HPLC especially after

10 days under load. Figure 4.7b shows the same general tendencies as Figure 4.7a. The best

model among the models for normal strength concrete was AASHTO-LRFD. For 10,000-psi

HPLC, that model was in good agreement with experimental data for any time under load

between 1 and 600 days. The ACI-209 model, the second best, tended to overestimate creep

coefficient for times under load greater than 30 days.

Figure 4.8 shows a comparison between experimental creep coefficient and estimated

creep coefficient using models for high strength concrete (Section C.2). Again, part (a) of

Figure 4.8 compares data from 8,000-psi HPLC and part (b) compare 10,000-psi HPLC data

(for more details see Appendix G).

In Figure 4.8 it can be seen that the performance of creep models for HSC was better

than the ones for normal strength concrete. Even though BP and CEB-FIP were modified for

HSC, they still greatly overestimated creep of HPLC. The BP modified for HSC

overestimated creep at all ages while the CEB-FIP modified for HSC overestimated creep for

ages greater than 20 days.

33

Figure 4.8. Comparison between measured creep coefficient and estimated from models for high strength concrete: (a) 8,000-psi HPLC, (b) 10,000-psi HPLC.

0.0

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AFREM

Sakata 2001

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AFREM

Shams &Kahn

b

8,000-psi Measured

Shams &Kahn

CEB-FIP MOD-HSC

Sakata 2001

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Shams &Kahn

CEB-FIP MOD-HSC

Sakata 2001

34

The AFREM model, on the other hand, tended to underestimate creep. As shown in

Table 4.1 and Figure 4.8, the 620-day creep coefficient predicted by AFREM was

approximately 68 and 73% of the measured value for 8,000-psi and 10,000-psi HPLC,

respectively. Shams and Kahn’s model (2000) and Sakata’s model (2001) gave the best

estimates of the 620-day creep coefficient of 8,000-psi HPLC. Despite the fact that the two

models gave a very similar 620-day estimate, from Figure 4.8a Sakata’s model

underestimated creep for time under load less than 300 days.

The best model among the models for HSC was Shams and Kahn model which not

only gave a good 620-day estimate, but also followed the shape of the experimental data as

well.

Figure 4.8b presents a similar scenario as Figure 4.8a, Sakata’s model and Shams and

Kahn’s model gave the two best estimates after 620-day under load. The AFREM model

also gave reasonable estimates for 10,000-psi HPLC. However, the best model, including

early and late ages, was the Shams and Kahn’s model.

Overall, the model with the best performance for estimating creep of 8,000-psi and

10,000-psi HPLC, including models for NSC and HSC, was the Shams and Kahn’s model.

Table G.7 of Section G.4.2 presents the sum of squared error (SSE) and coefficient of

determination (R2) between experimental data and creep models for 8,000-psi and 10,000-psi

HPLC. This statistical comparison indicated that the best model for estimating creep of

HPLC was Shams & Kahn model which presented the largest R2 (0.922 and 0.946, for 8,000-

psi and 10,000-psi HPLC, respectively). The AASHTO-LRFD model presented the second

best overall performance with an average3 R2 of 0.899.

3 Average of the parameter obtained for 8,000-psi and 10,000-psi HPLC

35

The two models that better estimate creep of HPLC, utilized the maturity of concrete

at loading rather than age. Age of loading is an important factor in determining creep. For

precast prestressed concrete members, the age of application of load can be as low as 16

hours, so creep becomes very dependant of concrete mechanical properties at the moment of

loading. HPC usually includes high contents of cementitious materials which generate a high

heat of hydration. This heat of hydration is responsible for raising concrete temperature to

levels as high as 145 oF; this heat accelerates the hydration process. This self feeding

reaction increases concrete mechanical properties above the expected values. Hence,

maturity leads to more accurate estimate of concrete performance. The Shams and Kahn and

AASHTO-LRFD models were able to better estimate creep because 8,000-psi and 10,000-psi

HPLC had a maturity at 24 hours equivalent to 147 and 158 hours (6.1 and 6.6 days).

4.3.3. Shrinkage Models Compared

Figure 4.9 presents a comparison between measured shrinkage in 8L HPLC and

predicted values using normal strength concrete and HSC models (Section C.1 and C.2). A

more detailed comparison for each model is presented in Appendix G, section G.4.3.

The AASHTO-LRFD model gave the best shrinkage estimate for anytime greater

than 30 days. Shams and Kahn’s model also presented good performance in the range 5 to

100 days of drying. After 100 days, however, Shams and Kahn’s model tended to

underestimate shrinkage of 8,000-psi HPLC.

36

Figure 4.9. Comparison between measured shrinkage of 8L HPLC and estimated from models for normal and high strength concrete.

All models (for NSC and HSC) greatly underestimated shrinkage at early ages (less

than 3 days). A possible explanation of this poor performance at early ages might be due to

autogenous shrinkage. As explained in Section B.4.2, a large portion of autogenous

shrinkage might be included in shrinkage measurements when testing started at early ages.

Figure 4.10 presents a comparison between shrinkage of 10,000-psi specimens and

the values predicted using the models. As seen in Figure 4.10, ACI-209, Shams and Kahn’s

and Gardner and Lockman’s (GL) models gave fairly good estimates of shrinkage for any

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Sakata 93

8,000-psi Measured

AFREM Sakata 2001

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Bažant Panula

Bažant Baweja

Sakata 93

8,000-psi Measured

AFREM Sakata 2001

37

time except for the first 24 hours. The AASHTO-LRFD model overestimated shrinkage for

drying periods longer than 10 days.

Figure 4.10. Comparison between measured shrinkage of 10L HPLC and estimated from models for normal and high strength concrete.

All the rest of the models greatly underestimated shrinkage for times greater than 100

days of drying regardless whether they were meant for HSC or not.

The highest R2 values were very similar for 8,000-psi and 10,000-psi HPLC (As

shown in Table G.8, Appendix G) and were obtained by AASHTO-LRFD and GL model,

respectively. Shams and Kahn‘s model, which had the second best performance for 8,000-

psi mix, was the third best for 10,000-psi mix. When R2 values from each mix were

0

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700


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Bažant Panula

Bažant Baweja

Sakata 93

10,000-psi Measured

Sakata 2001

AFREM

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Shams&Kahn

Bažant Panula

Bažant Baweja

Sakata 93

10,000-psi Measured

Sakata 2001

AFREM

38

averaged in order to obtain an overall performance, Shams and Kahn’s and ACI-209 models

had the two highest R2 average values with 0.830 and 0.811, respectively.

4.4 Comparison of Creep and Shrinkage of HPLC with HPC

This section presents a comparison between creep and shrinkage of 10,000-psi HPLC

and two HPC mixes (called HPC-3 and HPC-6) of equivalent mechanical properties from an

HPC project carried out by Georgia Institute of Technology for the Georgia Department of

Transportation. Mix designs, mechanical properties, and properties of fresh concrete of HPC

mixes are given in Table 4.2. Section G.5 also discusses the main differences and similarities

among these three mixes.

Table 4.2. Mix design and properties of HLPC and HPC, for one cubic yard

Amount 10,000-psi HPLC

HPC-3 HPC-6

Cement, Type I (lbs) 675 796 Cement, Type III (lbs) 740 Fly ash, class F (lbs) 150 100 98

Silica Fume, Force 10,000 (lbs) 100 33 70 Brown Brothers #2 sand (lbs) 1030 1,000 965

Coarse Aggregate (lbs) 955 1,750 1837 Water (lbs) 227.3 208 237

Water-to-cementitious ratio 0.230 0.257 0.246 Cement paste volume (yd3) 0.458 0.381 0.443

Air entrainer (oz) 9.5 16 7 Retarder (oz) 0 21 0

Water reducer (oz) 57 0 35 High-range water reducer (oz) 132 188 169

ASTM-cured 56-day compressive strength (psi) 10,250-11,500

11,619 13,618

Accelerated-cured 24-hour compressive strength (psi) 8,300-11,100

7,957 8,455

ASTM-cured 56-day elastic modulus (ksi) 4,050-4,330 4,748 4,973 Accelerated-cured 24-hour elastic modulus (ksi) 3,550-4,250 4,244 3,410

Slump (in) 4-6 7 4.6 Air content (%) 3.5-4.5 5 4.2

Unit weight (lb/ft3) 114-122 144 147

39

HPC-3 and HPC-6 as well as 10,000-psi HPLC might be classified as HPC Grade 3

according the strength limits given by FHWA. The HPC-6 mix had about the same paste

volume and total cementitious content as the HPLC mix; therefore it was regarded as most

similar.

4.4.1. Creep Comparison

Figures 4.11 and 4.12 present a comparison of creep of each mix in logarithmic time

scale expressed as specific creep and creep coefficient, respectively.

Figure 4.11. Comparison between specific creep of HPLC and HPC mixes in logarithmic time scale

Average specific creep of HPLC was much lower than specific creep of HPC-6 and

slightly lower than creep of HPC-3. This was true for at any time after 40 days under load.

At early times after loading (less than 10 days) HPC-3 and HPLC had equivalent specific

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40

creep. Figures 4.11 and 4.12 show that after 3 days, the creep curves of HPC-3 and HPLC

are not parallel which implies that creep rate of HPLC was lower than the one of HPC.

Figure 4.12. Comparison between creep coefficients of HPLC and HPC mixes in logarithmic time scale

Because HPLC had a lower average elastic modulus than the normal weight

counterpart of similar strength, creep coefficient enlarges the differences between HPLC and

HPC-3. Further details are provided in Appendix G, section G.5.

4.4.2. Shrinkage Comparison

Figure 4.13 compares shrinkage of HPLC and the two HPC mixes in logarithmic time

scale. Average shrinkage of HPC-3, HPC-6 and HPLC was of the same magnitude for any

time up to 480 days of drying. After 480 days only HPC-6 and HPLC experimental results

are available, and they show an increasing difference as time increases. Shrinkage of HPC-6

did not increase significantly after one year while HPLC shrinkage went from 550 to 600 µε

0.01 0.10 1.00 10.0 100 1000Time (days)

0.0

0.5

1.0

1.5

2.0

Cre

ep C

oeffi

cien

t

HPLC

HPC-3

HPC-6

0.01 0.10 1.00 10.0 100 1000Time (days)

0.0

0.5

1.0

1.5

2.0

Cre

ep C

oeffi

cien

t

HPLC

HPC-3

HPC-6

0.0

0.5

1.0

1.5

2.0

Cre

ep C

oeffi

cien

t

HPLC

HPC-3

HPC-6

41

during the 365-to-600-day period. After 250 days shrinkage of HPLC was higher than

shrinkage of the other two normal weight mixes. In figure 4.13, each data point is an average

of eight readings taken on two specimens.

Figure 4.13. Comparison between shrinkage of HPLC and HPC mixes in logarithmic time scale.

HPC-3 and HPLC presented very similar shrinkage rates. Figure 4.13 shows that the

two shrinkage curves were fairly parallel. HPC-6, on the other hand, showed a much faster

shrinkage rate until 100 days of drying, and after that it showed almost no increase in

shrinkage.

From creep comparison it was concluded that creep of 10,000-psi HPLC was either

lower or very similar than creep of the HPC of the same strength. On the other hand, from

shrinkage comparison, it seems that long-term shrinkage of HPLC was about 20% higher

than the HPC counterparts.

0

100

200

300

400

500

600

0.01 0.10 1.00 10.0 100 1000Time (days)

Shrin

kage

(µε)

HPLC

HPC-3

HPC-6

0

100

200

300

400

500

600

0.01 0.10 1.00 10.0 100 1000Time (days)

Shrin

kage

(µε)

HPLC

HPC-3

HPC-6

42

4.4.3. Total Strain Projection

Various mathematical models (logarithmic, hyperbolic, and exponential) were fitted

to specific creep and shrinkage of HPLC and the two HPC mixes. All details are shown in

Section G.5.3. With the best fit curves (shown in Figure G.15), values at ultimate (40 years)

were estimated for specific creep and shrinkage of HPLC and HPC as shown in Table 4.3.

Table 4.3. Ultimate strain estimates for HPLC and HPC loaded at 40% and 60% of its initial strength.

HPLC HPC-3 HPC-6 Stress

40% Stress 60%

Stress 40%

Stress 60%

Stress 40%

Stress 60%

Elastic Modulus1 3,663 3,949 3,350 Elastic Strain2 (µε) 1,092 1,638 1,013 1,519 1,191 1,786

Shrinkage3 (µε) 607 504 539 Specific creep3 (µε/psi) 0.371 0.367 0.650

stress (psi) 4,000 6,000 4,000 6,000 4,000 6,000 Creep strain4 (µε) 1,484 2,227 1,467 2,200 2,599 3,898 Total strain (µε) 3,184 4,472 2,984 4,224 4,328 6,226

Note: 1 measured from creep specimens; 2 elastic modulus times applied stress; 3 estimated from best fit; 4 specific creep multiplied by applied stress

Total strain of HPLC at 40 years stressed with 40% and 60% of its ultimate strength

was estimated to be 3,184 and 4,472 µε, respectively. On the other hand, the strains under

the same condition for HPC-3 were slightly lower: 2,984 µε and 4,224 µε for 40% and 60%

stress level, respectively. Finally, total strain after 40 years of HPC-6 was estimated to be

4,328 µε and 6,226 µε, respectively.

43

5. Prestress Losses

One goal of this research was to determine how the use of HPLC would affect the

loss of prestressing force in bridge girders. The creep and shrinkage data found from HPLC

cylinders and from AASHTO Type II girders made with HPLC were used to estimate

prestress losses in bridge girders. These experimental losses are compared with four models:

AASHTO refined and AASHTO lump sum (AASHTO-LRFD, 1998), ACI Committee 209

(ACI-209, 1997), and the PCI method (PCI, 1998), which are presented in detail in appendix

D. For comparison purposes, ACI-209 estimates were computed for 40 years after

prestressing assuming that time as the final state of losses. Actual losses were computed

from measured, experimental strains of AASHTO Type II girders. The experimental data did

not include steel relaxation losses. Experimental strains were projected to the 40-year

condition for comparison with the estimates from the standards.

Six AASHTO Type II girders were cast using HPLC: three each with 8,000-psi and

10,000-psi mixes. Four were 39-ft long and two were 43-ft long. Each was reinforced with

ten 0.6-inch diameter 270 ksi low relaxation strands. Approximately two months after girder

fabrication, a normal weight, 3,500-psi composite deck slab was cast at top each girder. The

girders were tested to determine flexure and shear strengths and to find strand transfer and

development length about six month after initial construction. Each girder was instrumented

to measure internal and external strains (Meyer et al., 2002).

Strain measurements of those girders as shown in Figure 5.1 provided experimental

data for actual prestress computations. Table 5.1 presents the comparison between measured

and estimated prestress losses for the 8,000-psi HPLC girder. Comparison for 10,000-psi

HPLC girder is presented in Appendix H (Table H.2).

44

Figure 5.1. Experimental strains over time for the 8,000-psi and 10,000-psi HPLC 39-foot girders.

Table 5.1 Comparison between experimental and estimated prestress losses of 8,000-psi HPLC prestressed girders

Measured AASHTO refined

AASHTO Lump sum PCI ACI 209 8,000-psi HPLC

Girders (ksi) (%) (ksi) (%) (ksi) (%) (ksi) (%) (ksi) (%)

After Jacking 202.5 100.0 202.5 100.0 202.5 100.0 202.5 100.0 202.5 100.0 Elastic Shortening -17.0 -8.4 -11.2 -5.5 -10.4 -5.2 -10.5 -5.2 -12.0 -5.9

Creep -16.4 -8.1 -14.1 -7.0 -14.8 -7.3 Shrinkage

not measured separately -6.5 -3.2 -5.1 -2.5 -11.3 -5.6

CR+SH -8.8 -4.3 -22.9 -11.3 -19.2 -9.5 -26.1 -12.9 Relaxation -11.54 -5.74 -18.7 -9.2

not estimated separately

-3.8 -1.9 -5.6 -2.8

Total Time-dependent -20.2 -10.0 -41.5 -20.5 -24.2 -12.0 -23.0 -11.3 -31.7 -15.7

Total Losses -37.2 -18.4 -52.8 -26.1 -34.7 -17.1 -33.5 -16.5 -43.7 -21.6

Experimental “total losses” for 8,000-psi girders made with HPLC was 37.2 ksi. The

AASHTO-LRFD refined and ACI-209 method overestimated losses by 15.6 and 6.5 ksi,

respectively. The AASHTO-LRFD lump sum and PCI methods were close to experimental

4 Experimental relaxation was determinate with Equation D.11 and experimental ES, CR and SH.

-1000

-800

-600

-400

-200

00 20 40 60 80 100 120 140

Age (Days)

Mic

rost

rain

s (in

/in x

10-6

)

8,000-psi Individual Girder Result10,000-psi Individual Girder Result

Deck pouring

-1000

-800

-600

-400

-200

00 20 40 60 80 100 120 140

Age (Days)

Mic

rost

rain

s (in

/in x

10-6

)


Deck pouring

45

data, but they underestimated total losses by 2.5 and 3.7 ksi, respectively. Those differences

expressed as percentage of the initial stress before losses are: 7.7, 3.2, -1.2, and -1.8%, for

the AASHTO-LRFD refined, ACI-209, AASHTO-LRFD lump sum and PCI techniques,

respectively. A positive difference indicates a predicted value greater than experimental.

The experimental prestress losses in the 10,000-psi girders were 29.6 ksi which was

lower than that of 8,000-psi girders by 7.6 ksi. The four methods overestimated the

experimental data. AASHTO-LRFD refined and lump sum methods overestimated total

loses by 22.3 and 3.7 ksi, respectively (see Figure H.5, Appendix H).

In Figure 5.2, the predicted-to-measured ratio is shown. Losses are grouped in elastic

shortening, creep and shrinkage, total time dependent and total losses. Overestimates appear

as a predicted-to-measured ratio greater than one, and the underestimates as lower than one.

The four methods underestimated elastic shortening losses regardless the type of

HPLC. The AASHTO-LRFD refined, PCI and ACI-209 overestimated creep and shrinkage

losses by at least 100%. The underestimate in steel relaxation losses given by the PCI and

ACI-209 methods was probably due to the much higher creep and shrinkage losses that they

predicted which decreased relaxation in the steel.

The fact that all methods underestimated elastic shortening was probably a

consequence of the procedures for measuring elastic shortening. The strain measurement

was taken after prestress transfer, which took approximately one hour. Therefore, the first

reading after transfer included not only instantaneous elastic strain, but also early creep and

shrinkage. The same argument can be used to explain that all methods overestimated time

dependant losses.

46

Figure 5.2. Comparison between estimated prestress losses from PCI, AASHTO and ACI-209 models

Within time-dependant losses (TD), differences between estimates were due primarily

to shrinkage losses. The PCI method estimated shrinkage losses as 5.1 ksi (2.5%) while

ACI-209 method estimated it to be 11.3 ksi (5.6%).

As described in Chapter 4, creep and shrinkage tests were conducted on HPLC mixes.

Therefore, estimates for creep and shrinkage using prestress losses models can be compared

separately with experimental results to evaluate the performance of the models. The details

are given in Section H.3.

The three models underestimated elastic shortening by less than 10%. This difference

can be explained based on the size of the creep specimens (see Section H.3).

The largest relative differences were obtained on the shrinkage portion where PCI and

AASHTO refined methods underestimated shrinkage losses by approximately 65%. The PCI

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

8,000-psiHPLC

10,000-psiHPLC

8,000-psiHPLC

10,000-psiHPLC

8,000-psiHPLC

10,000-psiHPLC

8,000-psiHPLC

10,000-psiHPLC

AASHTO refined AASHTO lump sum PCI ACI 209

Pred

icte

d-to

-mea

sure

d ra

tio Elastic ShorteningCreep & ShrinkageTotal Time DependentTotal Losses

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

8,000-psiHPLC

10,000-psiHPLC

8,000-psiHPLC

10,000-psiHPLC

8,000-psiHPLC

10,000-psiHPLC

8,000-psiHPLC

10,000-psiHPLC


Pred

icte

d-to

-mea

sure

d ra


47

method was the least accurate method to estimate creep. The AASHTO refined method also

underestimated creep losses, but by less than the PCI method. As expected, the ACI-209

method gave the best creep estimate with an only 4.4% underestimate. The fact that PCI and

AASHTO refined method underestimated creep strains in such proportion is probably

because those design methods are estimating what happens on a prestressed concrete member

rather than testing specimens. On a prestressed member creep of concrete occurs at a

decreasing stress because creep, shrinkage and steel relaxation decrease the effective stress

on concrete. That does not happen in creep testing of cylinders.

Summarizing, each of the methods for estimating prestress losses overestimated the

actual losses due to elastic shortening, creep and shrinkage measured in 8,000-psi and

10,000-psi HPLC AASHTO Type II prestressed girders. For total losses, all experimental

losses5 were overestimated by the standards. The only exceptions were the AASHTO lump

sum and PCI methods that underestimated total losses in 8,000-psi girders by 1.2 and 1.8%.

In particular, the AASHTO refined and lump sum methods were conservative in

predicting prestress losses in HPLC girders. As explained in Section D.2, AASHTO methods

do not consider lightweight concrete, so they estimate losses for a normal weight HPC.

5 Experimental relaxation was determinate with Equation D.11 and experimental ES, CR and SH.

48


49

6. Conclusions and Recommendations

The long-term performance of high performance lightweight concrete (HPLC) for use

in prestressed bridge girders was studied. Two different HPLC mixes were developed using

Type III cement, silica fume, class F fly ash, expanded slate as coarse aggregate, natural

sand, and chemical admixtures. The first mix was an 8,000-psi HPLC (FHWA HPC Grade

2) with an “air dry” unit weight of 117 lb/ft3. The second mix was a 10,000-psi HPLC

(FHWA HPC Grade 3) with an “air dry” unit weight of 119 lb/ft3.

Conclusions drawn from this study are divided into three areas: HPLC material

properties, creep and shrinkage behavior, and prestress losses.

6.1. Conclusions

6.1.1. High Performance Lightweight Concrete Material Properties

In the fresh state, the two HPLC mixes performed adequately for casting precast

prestressed concrete girders. They had a slump ranging from 4 to 8 inches and air content

within the range 3.5 to 4.5 %. The specified 56-day compressive strength for HPLC Grade 2

was reached after 28 days and the one for HPLC Grade 3 was reached at the age of 56 days.

The 8,000-psi HPLC mix had a 24-hour and 56-day compressive strength of 7,400 and

10,000 psi; 24-hour and 56-day modulus of elasticity were approximately 3,600 and 4,100

ksi. The 10,000-psi HPLC had a compressive strength of 9,000 psi at 24 hours and 11,500

psi af 56 days. The 24-hour and 56-day modulus of elasticity were 3,800 and 4,200 ksi. As

expected, modulus of elasticity was between 15 to 20% lower than that of an HPC of similar

strength. Measured modulus of rupture in both HPLC mixes was 33% higher than the value

given by the AASHTO equation ( '5.7 cr ff ⋅= ), and 57% higher than the same equation

50

when the reduction factor for sand-lightweight concrete was included. Chloride ion

permeability was within the range 100 - 1,000 coulomb which is classified as very low

permeability. The coefficient of thermal expansion at 100% RH ranged from 5.0 to 5.5

µε/oF.

6.1.2. Creep and Shrinkage Behavior

Creep was measured on 24 specimens stored at 50% relative humidity and 70 oF for a

period of 620 days. Twelve 4” x 15” cylinder specimens were made of 8,000-psi HPLC, and

twelve of 10,000-psi HPLC. Half of the specimens were loaded to 40% of the initial

compressive strength and the other half to 60% of the initial strength. Within each group

some specimens were loaded at 16 hours and some at 24 hours after casting.

Creep of 8,000-psi HPLC after 620 days under load was close to 1,650 µε for 40% of

initial strength and approximately 2,000 µε for 60% of initial strength. Creep of 10,000-psi

HPLC after 620 days under load was 1,160 µε for 40% of initial strength and 1,500 µε for

60% of initial strength. Fifty and ninety percent of the 620-day creep was reached after

approximately 16 and 250 days of loading, regardless the type of HPLC.

Experimental creep coefficient was compared with several empirical models

presented in the literature. Shams and Kahn’s and AASHTO-LRFD models most accurately

estimated creep of HPLC. Their respective average6 coefficients of determination (R2) were

0.934 and 0.899, respectively. One of the reasons behind the better performance of these two

models was that they incorporate maturity of concrete instead of age of concrete.

6 Average between the values obtained for 8,000-psi and 10,000-psi HPLC

51

Shrinkage after 620 days of drying was approximately 820 µε for the 8,000-psi HPLC

mix and 610 µε for the 10,000-psi HPLC mix. Fifty and ninety percent of the 620-day

shrinkage was reached after approximately 30 and 260 days of drying for both 8,000-psi and

10,000-psi HPLC. Experimental results and estimates from several models were compared.

AASHTO-LRFD model gave the best overall estimate of 8,000-psi HPLC shrinkage. On the

other hand, for the 10,000-psi HPLC mix, the Gardner and Lockman model gave the best

overall performance. However, when the two HPLC mixes were analyzed together and when

the average coefficient of determination (R2) was used, the Shams and Kahn model resulted

in the best prediction.

Grade 3 HPLC (10,000-psi HPLC) had a specific creep similar to that of an HPC of

the same grade, but with less cement paste content, and it had significantly less creep than an

HPC of the same grade and similar cement paste content. The shrinkage of the HPLC was

about 20% greater than the HPC after 620 days. Therefore, the HPLC had less creep yet

somewhat more shrinkage than comparable HPC.

6.1.3. Prestress Losses

Final prestress losses were estimated using AASHTO refined, AASHTO lump sum,

PCI, and ACI-209 methods. All of them overestimated the measured time dependant losses

in 8,000-psi and 10,000-psi AASHTO Type II prestressed girders made with HPLC. This

result means that those methods are conservative for estimating time dependant losses of

HPLC. Total losses, however, were underestimated by the AASHTO lump sum and PCI

method by 1.2 and 1.8% for 8,000-psi girders, respectively.

52

6.2. Recommendations

6.2.1. Design Recommendations

The method that gave the best results for predicting creep of HPLC was Shams and

Kahn’s method (Shams and Kahn, 2000) which can be regarded as a modification of

AASHTO-LRFD model for HPC. The average coefficient of determination (R2) of Shams

and Kahn’s model was 0.934 while the one from AASHTO LRFD (1998), the second best

model, was 0.899. The best method for predicting shrinkage of HPLC was Shams and

Kahn’s method, but the AASHTO LRFD and Gardner and Lockman’s methods gave better

particular estimates for 8,000-psi and 10,000-psi HPLC, respectively.

Considering creep and shrinkage performance, the Shams and Kahn model was the

best model for predicting long-term strains of HPLC made with locally available materials in

Georgia.

The AASHTO-LRFD refined method for estimating prestress losses was

conservative. The AASHTO-LRFD lump sum method gave a good estimate of total losses

slightly underestimation total losses of 8,000-psi HPLC girders by 1.3%.

Overall, the AASHTO-LRFD refined method may be used conservatively for

predicting prestress losses in girders made of high performance lightweight concrete.

6.2.2. Future Research

The use of supplementary cementitious materials (SCM’s), chemical admixtures and

expanded slate as coarse aggregate is a key issue in the production of high performance

lightweight concrete. However, most of the research for development of models for

estimating long-term strains in concrete included none of them as a factor. Future research

53

needs to understand the role of SCM’s and additives on creep and shrinkage in order to

improve the current models.

It is widely accepted that water has a main role in basic creep, drying creep,

autogenous shrinkage, and drying shrinkage. Because of the use of SCM’s, and particularly

the use of silica fume, provides low permeability, it is recommended to investigate the

relationship between water permeability and long-term strains of HPLC.

The lower specific creep showed by HPLC in relation to HPC of similar mechanical

properties needs to be further investigated. The literature presents very little research on

long-term strains of high performance / high strength lightweight concrete. Some of the

previous results support the conclusions of this research, but others do not. Therefore, it is

recommended to investigate the effect of replacing normal weight coarse aggregate by

expanded slate under long-term deformation and under different drying conditions.

54


55

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Findley, W. N., Lai J. S. and Onaran K. (1989) "Creep ands Relaxation of Nonlinear Viscoelastic Materials", Dover Publications, Inc, New York.

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61

Appendix A. Introduction

A.1 Introduction to Task 3: Short and Long-term Properties of High

Performance Lightweight Concrete Mixes

The goal of Task 3 was to determinate the compressive strength of high performance

lightweight concretes (HPLC) selected in Task 2, their elastic modulus, rupture modulus,

chloride permeability, and their creep and shrinkage characteristics.

The selected mixes from Task 2 had design strengths of 8,000 psi, 10,000 psi, and

12,000 psi. Those were HPC Grades 2 and 3 (see Section A.2 for grade definitions). After

mix design stage, it was concluded (Meyer et al. , 2002) that the 12,000 design strength was

not possible with the expanded slate used in the research. The existence of a strength ceiling

of about 11,500 psi limits the specifiable strength to just 10,000 psi. The 8,000 and 10,000-

psi mix designs are presented in Table A.1.

Table A.1. Designed high performance lightweight concrete mixes (SSD condition)

8,000 psi design mix

10,000 psi design mix

Type III cement (lb/yd3) 783 740 class "F" fly ash (lb/yd3) 142 150 silica fume (lb/yd3) 19 100 1/2-in. lightweight aggregate (lb/yd3) 947 955 concrete sand (lb/yd3) 1022 1030 water (lb/yd3) 267.8 227.3 water reducer (fl oz/yd3) 57 57 superplasticizer (fl oz/yd3) 57.4 131.8 air entrainer (fl oz/yd3) 9.5 9.5 water/cementitious ratio 0.284 0.23 cement paste content (%) 39 39 coarse/fine ratio 1.5 1.5 theoretical unit weight (lb/ft3) 118 119

62

The 8,000-psi mix design was named as “8L” when mixed in the laboratory and “8F”

when mixed in the field. The 10,000-psi mix was named as “10L” and “10F” when made in

laboratory and field, respectively.

This report is focused on time-dependent strains of the high performance lightweight

concretes described above and on how those strains influence the prestress losses in the HPC

precast prestressed bridge girders.

A.2 Introduction to High Performance Concrete (HPC)

ACI Committee 363 (1997) defined high strength concrete (HSC) as a concrete with a

cylinder compressive strength that exceeds 6,000 psi, while ACI Committee 116 (2000)

defined HPC as “concrete meeting special combinations of performance and uniformity

requirements that cannot always be achieved routinely using conventional constituent

materials and normal mixing, placing, and curing practices. The requirements may involve

enhancements of placement, compaction without segregation, long-term mechanical

properties, early-age strength, volume stability, or service life in severe environments.”

Goodspeed et al. (1996), went further in its definition and stated that HPC is defined not

only by the strength, but by seven more parameters: freeze-thaw durability, scaling

resistance, abrasion resistance, chloride penetration, creep, shrinkage, and modulus of

elasticity. Table A.2 presents a summary of HPC grade 2 and 3 specifications according to

Goodspeed et al. (1996).

From the definitions above it can be concluded that HPC is a broad concept that may

include HSC, but HSC is not equivalent to HPC. To avoid confusions Aïtcin (1998)

proposed for HPC the term low water-to-binder ratio concrete because when concrete has a

very low water to binder ratio (less than 0.4) not only achieves higher strength, but also

63

several improved characteristics, such as higher flexural strength, lower permeability,

improved abrasion resistance and better durability.

Table A.2. High performance concrete bridge mix specifications (Goodspeed et al., 1996)

Grade 2 Grade 3 Property lower

limit upper limit

lower limit

upper limit

MPa 55 69 69 97 Compressive strength 56 days is recommended psi 8,000 10,000 10,000 14,000

GPa 35 40 40 50 Elastic modulus ksi 5,075 5,800 5,800 7,250 Freeze/thaw durability (%) 70 80 80 90

Chloride permeability (coulombs) 2000 800 800 500 Scaling resistance (visual rating) 2 1 1 0

Abrasion resistance (depth of wear, mm) 1.0 0.5 0.5 0.25 µε/MPa 60 45 45 30 Specific creep

at 180 days loading µε/psi 0.41 0.31 0.31 0.21 Shrinkage (µε) at 180 days drying 600 500 500 400

Several authors (Aïtcin, 1998; Shah and Ahmad, 1994; ACI-363, 1997; Neville,

1996; Nawy, 2001; Mehta and Monteiro, 1993; Carrasquillo and Carrasquillo, 1988;

Carrasquillo et al., 1981) have summarized the advantages of the HPC with low water-to-

cement ratio with respect to the normal strength concrete. Some of the most important

advantages follow:

• Reduction in member size, resulting in an increase in rentable space and a decrease

in the volume of concrete required

• Reduction in axial shortening of compression supporting members

• Improvement in long-term service performance under static, dynamic, and fatigue

loading

• Reduction of creep and shrinkage

64

• Improved durability

• Increased stiffness as a result of a higher modulus of elasticity7

• Reduction in cost for a given load capacity

Although HPC presents advantages over conventional concrete, it requires special

care during the production process in order to assure its quality. ACI Committee 363

recognized this, and in 1998 prepared the report “Guide to Quality Control and Testing of

High-Strength Concrete”. Moreover, Aïtcin (1998) stated that “HPC is not a cheap concrete

that can be produced by anyone; on the contrary, it is becoming an engineered, high-tech

material.”

One problem associated with some HPC is an increase in the autogenous shrinkage

with respect to normal strength concrete (Aïtcin, 1998). This increase can be explained

based on the creation of strong menisci in small capillaries when the cement particles

demand more water. Because normal strength concrete has larger capillaries, the autogenous

shrinkage is not an issue. Bentz and Snyder (1999) pointed out that the self-desiccation and

autogenous shrinkage may be increased by the use of low water-to-binder ratios and by

addition of silica fume. In addition to higher autogenous shrinkage, HPC also presents a

lower relaxation and a higher modulus of elasticity. The last two characteristics lead to a

decrement in the concrete extensibility. Another disadvantage of HPC is poor fire resistance

compared with normal strength concrete (Gjørv, 1994). This poor behavior is due to the very

7 A higher modulus of elasticity may be an advantage when a dimensional stability is desired, and the

concrete element is free to deform. However, it may be a disadvantage when it is associated with deformation

restraints because the higher modulus of elasticity decreases extensibility.

65

low permeability of HPC, which does not allow the egress of steam formed from water at

high temperatures in the hydrated cement paste.

A.3 Introduction to Structural Lightweight Concrete (SLC)

Lightweight concrete was used first by the Greeks and the Romans circa 250 B.C.,

but the main development of such a material was in the 1920’s with the first manufactured

lightweight aggregate (Holm and Bremner, 2000). ACI Committee 213 (ACI-213, 1999)

defined structural lightweight concrete as structural concrete made with lightweight

aggregate, with an air-dried density at 28 days in the range of 90 and 115 lb/ft3 and a

compressive strength above 2,500 psi.

Several authors (Holm and Bremner, 2000; ACI-213, 1999; Neville, 1996; Holm,

1995; Mehta and Monteiro, 1993; Zhang and Gjørv, 1991; Short and Kinniburgh, 1963)

have studied the advantages of SLC. The most important advantages are the following:

• Reduction in structure dead load, which leads to a reduction the foundation size

• Reduction in member size, resulting in an increase in rentable space and a decrease

in the volume of concrete required

• Development of a precast technology as a result of self-weight reduction that

facilitates the transport and lifting of structural members

• Reduction in the seismic forces that are proportional to the mass of the structure

• Increase in thermal insulation

• Increase in fire resistance

As occurs with HPC, SLC also has disadvantages when it is compared with ordinary

concrete (Videla and Lopez, 2002; Holm and Bremner, 2000; Videla and Lopez, 2000;

66

Curcio et al., 1998; Neville, 1995; Short and Kinniburgh, 1967). Some of these

disadvantages follow:

• Reduction in the modulus of elasticity for the same strength level

• Increase in shrinkage and creep for the same strength level

A.4 Introduction to High Performance Lightweight Concrete (HPLC)

According to Holm and Bremner (1994), the first use of high strength lightweight

concrete was during World War I, when an American corporation built lightweight concrete

ships with strength of 5,000 psi. At that time the commercial strength of normal weight

concrete (NWC) was only around 2,000 psi. The same authors and Curcio et al. (1998)

pointed out that the principal advantage of HPLC is the structural efficiency given by a

favorable strength-to-unit weight ratio. Malhotra (1990) obtained HPLC with compressive

strength higher than 8,700 psi at one year with relatively moderate amount cementitious

materials (cement, silica fume, and fly ash). In addition, Nilsen and Aïtcin (1992) and Zhang

and Gjørv, (1990) presented HPLC with compressive strength slightly below and above

14,500 psi, respectively. According to Aïtcin (1998), this strength level represents the upper

strength boundary of HPLC.

Hoff (1990) reviewed five major joint-industry research programs using HPLC, and

concluded that lightweight concretes having compressive strength in excess of 7,250 psi can

readily be made using a competent lightweight aggregate. He also pointed out that the

addition of silica fume and superplasticizers in the mix provide significant benefits.

Malhotra (1990) concluded that HPLC with compressive strength of 10,000 psi and a density

of 125 lb/ft3 can be made with expanded slate from Canada. The same author highlighted

67

that the most promising mix that he obtained had ASTM Type III cement, fly ash and silica

fume.

According to Holm and Bremner (2000), the replacement of normal weight aggregate

by lightweight aggregate improves the mechanical properties of the concrete. This

improvement is due to enhanced elastic matching between lightweight aggregate and

cementitious matrix (conventional and high strength matrix). The elastic matching reduces

the fracture initiation in the interfacial transition zone (ITZ). However, the use of an ultra-

high-strength matrix, with a very high stiffness, produces an elastic mismatch, resulting in

fractures in the lightweight aggregate.

Although HPLC may reach a modulus of elasticity of 3,600 ksi (Malhotra, 1990),

which is fairly similar to a commercial NWC, this value is only 80% of that expected from an

HPC of the same strength. In fact, Meyer and Kahn (2002) and Morales (1982) have

proposed equations for the estimation of the elastic modulus of HPLC that includes a

correction factor for densities below 155 lb/ft3.

Hoff (1990) concluded that the use of HPLC will not expand unless designers have

confidence in their knowledge of its expected properties. Currently the codes do not

specifically consider HPLC. Rather, HPLC is specified as SLC by applying a capacity

reduction factor to the formulas commonly used in the design. Hoff (1990) stated that such as

practice might lead to very conservative values, undermining the HPLC application.

68


69

Appendix B. Creep and Shrinkage - Background

B.1 Long-term strains in concrete

Concrete as any other civil engineering material presents an instantaneous

deformation upon loading. However, it also presents other kinds of deformation because of

its aging and hygroscopic nature. Among those are stress and drying induced deformations.

Figure B.1 presents the change of such deformation with time.

Figure B.1. Relation between various strains in concrete with time.

As shown in Figure B.1, total strain in concrete at any given time can be broken into

three portions: initial strain which is the instantaneous response upon loading, shrinkage

which in comprised of autogenous and drying shrinkage, and creep which has basic and

drying creep portions.

time

Con

tract

ion

Drying Creep

Basic Creep

Drying Shrinkage

Autogenous Shrinkage

Elastic Strain

Beginning of drying (to) and loading (t′)

time

Con

tract

ion

Drying Creep

Basic Creep

Drying Shrinkage

Autogenous Shrinkage

Elastic Strain

Beginning of drying (to) and loading (t′)

70

Creep and shrinkage are usually discussed together because they are influenced by the

same factors in similar ways: both are originated in the cement paste, and both have similar

changes with time. Nevertheless, in this report they are analyzed separately because creep is

a stress-dependent strain and shrinkage is not.

B.2 Creep

In describing creep, Findley, Lai and Onaram (1976) stated that most materials

behave elastically or nearly so under small stresses and upon loading immediate elastic

(recoverable) strain response is obtained. However, when higher stresses are applied, a slow

and continuous increase in strain at a decreasing rate also occurs in some materials. These

are referred to as “viscoelastic materials”. Among these materials are different kinds of

plastics, wood, natural and synthetic fibers, concrete, and metals. Metals behave

viscoelastically only at elevated temperatures.

Creep in materials can be described in terms of three stages as shown in Figure B.2.

In the primary stage, creep occurs at a decreasing rate; in the secondary stage, creep is at

fairly constant rate; and finally, in the tertiary stage the creep rate accelerates and leads to

failure. According to Neville, Dilger and Brooks (1983), for the normal stress level present

in concrete, primary and secondary stages cannot be distinguished and tertiary stage does not

exist.

71

Figure B.2. Representation of three stages of creep.

ACI Committee 209 (1997) defined creep in concrete as the time dependent increase

in strain in hardened concrete subjected to sustained stress. Several authors (ACI Committee

209, 1997; Neville, 1996; Mehta and Monteiro, 1993; Bažant, 1988; Neville, Dilger, and

Brooks, 1983) have divided creep in concrete into “basic creep”, which takes place under

conditions of no moisture exchange with the environment, and “drying creep”, which is

additional creep caused by drying (Figure B.1).

B.2.1. Basic Creep

Basic creep can be conceptualized as a constitutive concrete property since it depends

on the material characteristics and stress, but not on member size or ambient conditions.

Under normal loading conditions where the loading process is not instantaneous, the so-

called “instantaneous strain” is actually comprised of elastic strain and early creep.

Therefore, an accurate measure of basic creep is not possible. Moreover, the actual elastic

strain decreases with time because the modulus of elasticity increases as the hydration

Time

Cre

ep st

rain

, Cre

ep ra

te

CreepCreep rate

Primary Secondary Tertiary

Time

Cre

ep st

rain

, Cre

ep ra

te

CreepCreep rate

Primary Secondary Tertiary

72

process develops. Consequently, basic creep, defined as the difference between total and

elastic strain under no drying conditions, is not easy to measure accurately (Neville, 1996).

Even though there are some inaccuracies in measuring basic creep, for practical purposes it is

only important to accurately determine the total strain over time.

B.2.2. Drying Creep

Sometimes referred to as the Pickett effect, drying creep not only depends on mixture

characteristics, but also on environmental parameters (relative humidity and temperature) and

member dimensions. As shown in Figure B.1, drying creep is the time-dependent

deformation of stressed concrete in drying environment, which is in excess of basic creep and

drying shrinkage (Carreira and Burg, 2000). Therefore, the only way to measure drying

creep is by measuring total strain and by subtracting the elastic strain, basic creep, and

shrinkage (autogenous and drying).

Frequently creep and shrinkage are assumed to be additive which is a convenient

simplification, but in reality they are not independent phenomena to which the superposition

principle can be applied. Again, because they occur simultaneously and from the practical

standpoint, the treatment of the two together is convenient and accurate. Bažant (2001)

referred to this phenomenon as follows: “Aside from aging, the most difficult aspect of creep

is the humidity variation, particularly the drying creep effect.”

B.2.3. Factors Influencing Creep

Creep characteristics of any type of concrete are mainly influenced by aggregate-to-

cement paste proportion, aggregate characteristics, water and cement content, age (maturity)

at time of loading, type of curing, storage conditions which influence the water migration

73

conditions, amount and type of chemical and mineral admixtures, and applied stress-to-

strength ratio (Neville, 1996).

Neville, Dilger, and Brooks (1983) explained the importance of the aggregate-to-

cement paste ratio on creep by concluding that cement paste phase is the source of creep of

concrete and aggregate acts as a restraint to that movement. The authors concluded that the

restraining effect of aggregate on deformation is independent of whether the deformation is

due to shrinkage or creep. Therefore, the expressions proposed by Pickett (1956) and Power

(1961) are entirely applicable to creep.

Powers’ expression (Power, 1961) modified by Neville (1964) for describing creep is

presented in Equation B.1a (power form) and B.1b (logarithmic form).

( )αgcc

p

c −= 1 (B.1a)

( ) ( )

−

⋅−=g

cc epece 11logloglog α (B.1b)

where

cp: creep of neat cement paste

cc: creep of concrete

g: fraction of aggregate

α: constant representing aggregate restraining effect; it depends on aggregate properties

Mehta and Monteiro (1993) reported values for “α” measured by L’Hermite (1962)

between 1.2 and 1.7, depending on the normal weight aggregate used.

According Mehta and Monteiro (1993), Equation B.1 applies to concretes of constant

water-to-cement ratio and loaded to the same stress-to-strength ratio. Figure B.3 shows the

relationship between basic creep at 28 days under load and content of aggregate “g” for

74

concrete made with portland cement, loaded at 14 days to a stress-to-strength ratio of 0.5.

Figure B.3 also compares experimental data and Equation B.1b.

Figure B.3: Relationship between creep of concrete and aggregate content (Neville, Dilger and Brooks, 1983).

From Figure B.3, it can be concluded that the aggregate content (or cement paste

content), explained an important proportion of the variance in creep of concrete, but there is

still an unexplained variability around the line in the plot ( Equation B.1b with α=1.71). The

variability might be due to “α”, which can be conceptualized as the restraining effect of the

aggregate.

In spite of the fact that many of the factors affecting creep have been identified, the

mechanisms are not yet fully understood. According to Neville, Dilger, and Brooks (1983),

“A number of theories have been proposed over the years, but it is probably justified to say

that, as they stand, none is capable of accounting for all the observed facts. Yet each

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.82.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

75

explains a number of observations and accords fully with some or other of the experimental

results. It is possible that the actual creep involves two or more mechanisms. Before

accepting such a combined theory, further verifications are, however, necessary.”

Bažant (2001) introduced the difficulty of predicting creep saying that “much

research has been devoted to this complex problem ever since. However, despite major

successes, the phenomenon of creep and shrinkage is still far from being fully understood,

even though is has occupied some of the best minds in the field on cement and concrete

research and materials science.”

Altoubat and Lange (2001) in their research for the Federal Aviation Administration

also concluded that although several theories have been proposed over the years to explain

the creep mechanism, none has adequately explained all the observed information regarding

creep in concrete.

B.2.4. Creep Mechanisms

According to the American Concrete Institute (ACI-209, 1971) the primary

mechanisms that describe creep are the following:

1. Viscous flow theory. First postulated by Thomas (1937), this theory stated that the

cement paste is a fluid with a high viscosity that flows under load. Since concrete also

includes aggregate, which typically (i.e., normal weight natural aggregates) do not flow, the

load is gradually transmitted from paste to aggregate decreasing the flow rate (Neville,

Dilger, and Brooks, 1983). When analyzing this theory, Han (1996) concludes that it is not

completely correct because viscous flow requires constant volume, which is not the case in

concrete.

76

2. Seepage theory. First postulated by Lynam (1934), this theory stated that creep is

due to seepage of water from the physically adsorbed layers to capillary voids. The applied

stress changes the pressure of the physically adsorbed water, and to obtain equilibrium, the

water is reorganized. One problem of this theory is that it predicts a total recovery after

unloading, which does not happen in concrete (Han, 1996). One possible explanation of this

inconsistency may be the formation of new bonds in calcium silicate hydrates (C-S-H) that

would prevent the strain recovery. The Figure B.4 is an illustration of the cement paste

microstructure, and the different kinds of water present in cement paste.

Figure B.4. Representation of cement paste microstructure (Mehta and Monteiro, 1993)

3. Delayed elasticity. This theory rested on a two-component model of the concrete

microstructure. The first component is an elastic skeleton comprised of aggregate and

crystals hydrates while the second component is the viscous portion of the cement paste.

When the concrete is loaded the viscous component tends to take the load and progressively

deforms. Over time the load is transferred from viscous component to the elastic skeleton,

which behaves elastically. As a consequence, a delayed elastic behavior is obtained.

4. Microcracking effect. First postulated by Hsu (1956), this mechanism explained

the non-linearity in the concrete stress-strain relationship by the presence of the interface

C-S-HSheet

AdsorbedWater

CapillaryPore

InterlayerWater

C-S-HSheet

AdsorbedWater

CapillaryPore

InterlayerWater

77

between aggregate and paste. This interface is considered, by many, to be the weakest region

in the concrete. In this region, porosity and density of microcracks tend to be greater than in

the bulk paste. Hence, this theory stated that the propagation of preexisting microcracks

results in residual strain upon unloading. In addition to the permanent strain cracks, it is also

possible the formation of new bonds in C-S-H (Neville, Dilger, and Brooks, 1983), in the

same way that is presented in the seepage theory. It should be pointed out that at high

stresses the role of the microcracking becomes more important (Han, 1996).

In addition to the mechanisms discussed by ACI Committee 209, some authors have

identified additional mechanisms that may cause or influence creep: (1) plastic flow, which

is caused by sliding along planes of maximum shear stress within the crystalline components

of the cement paste (Neville, Dilger, and Brooks, 1983). Interlayer water within C-S-H

structure lubricates planes facilitating them to flow (Figure B.4). Bažant (2001) also

proposed: (2) the solid solution theory, (3) load-bearing hindered absorbed water, (4)

nonlinear deformations and cracking as a contribution to the Pickett effect, (5) solidification

theory for short term aging, (6) microprestress of creep sites in the cement C-S-H

microstructure, causing the Pickett effect and long-term aging.

Shams and Kahn (2000) concluded that researchers generally agree that viscous flow

and seepage are the main contributors to creep. However, the two theories disagree about the

role of the water in the cement paste. That is, whether the water is a fundamental cause of

creep (seepage) or whether it only modifies the movement of the C-S-H (viscous flow).

Hence, it remains that water does have a role, but fundamental research is required to better

define that role in creep mechanisms.

78

B.3 Shrinkage

Shrinkage is defined by ACI Committee 209 (1997) as the reduction of concrete

volume with time. The three types of shrinkage in hardened concrete are autogenous

shrinkage, drying shrinkage, and carbonation shrinkage. The three of them are related with

water loss, but in very different ways. The first one is caused by the absorption of water

from the capillary pores due to continued hydration. Drying shrinkage is the migration of

water from concrete to unsaturated air. Finally, carbonation shrinkage is due to the reaction

of calcium hydroxide (Ca(OH)2)with carbon dioxide (CO2) that forms calcium carbonate

(also known as calcite, CaCO3) and water. After the water evaporates, the calcium carbonate

occupies less volume than the original calcium hydroxide. In this report only autogenous and

drying shrinkage are discussed.

B.3.1. Autogenous Shrinkage

Autogenous shrinkage, also called self desiccation, is analogous to basic creep

portion found in creep. Since it depends on the concrete mix design and hydration process, it

is a constitutive property of concrete. For conventional concrete autogenous shrinkage is

relatively small with typical values of 40 µε at early ages and 100 µε at five years (Carreira

and Burg, 2000; Neville, 1996). However, it increases when rate of hydration increases, so a

higher C3A content8, a finer cement, and a lower water-to-cement ratio will increase

autogenous shrinkage.

8 C3A stands for tricalcium aluminate, and it is the cement nomenclature for (CaO)3Al2O3

79

B.3.2. Drying Shrinkage

Drying shrinkage is analogous to the drying creep portion seen above. Therefore, it is

not a constitutive property because it depends on external characteristics such as member

size, shape and the environment. For conventional concrete under standard ambient

conditions (73.4oF and 50% relative humidity), drying shrinkage, measured in 3 to 6 inch-

deep specimens, generally ranges between 400 and 800 µε after two years.

B.3.3. Factors Influencing Shrinkage

Similarly to creep, shrinkage occurs in the cement paste and the aggregate acts as a

restraint to it. Therefore, aggregate-to-paste ratio is a main factor influencing shrinkage.

Shrinkage depends not only on aggregate proportion, but also on aggregate characteristics

such as stiffness, strength and shape. Water and cement contents also have a main role in

shrinkage. At high water-to-cement ratios autogenous shrinkage decreases, but drying

shrinkage increases given an overall increase in shrinkage. On the other hand, at low water-

to-cement ratios the autogenous portion increases and the drying one decreases. Because the

concrete strength increases too, the overall effect of decreasing water-to-cement ratio is a

reduction in total shrinkage. Figure B.5 shows the water and cement content effect on

shrinkage measured after 450 days under drying (Neville, 1996).

80

Figure B.5. Effect of water and cement content on shrinkage (Neville, 1996).

As occurs with creep, chemical and mineral admixtures affect shrinkage

characteristics. Finally, curing and storage condition will affect concrete porosity and the

rate of water migration from concrete to ambient which ultimately influences shrinkage.

B.3.4. Shrinkage Mechanisms

Shrinkage is related with water loss from the cement paste. However, the change in

volume of drying concrete is not the same as the removed water volume. The latter is due to

the existence of different kinds of water in cement paste structure (Figure B.4). When free

water is removed from capillaries, little or no shrinkage takes place. The shrinkage measured

at this level is believed to be caused by the hydrostatic tension in small capillaries (Neville,

1996 and Mindess et al., 2003).

Once the water has been totally removed from the pore system, cement paste starts to

loose adsorbed water, which is directly related with volume changes. At this level, the

700

800

900

1000

1100

1200

300 400 500 600 700 800Cement Content (kg/m3)

Shrin

kage

(µε)

Water-to-Cement Ratio0.50 0.45

0.400.35

0.30

0.25

175 [295]

230

900

Water Content (kg/m

3 )

[lb/yd3 ]

700 900 1100 1300 1500Cement Content (lb/yd3)

210 [354]

190 [320]

700

800

900

1000

1100

1200

300 400 500 600 700 800Cement Content (kg/m3)

Shrin

kage

(µε)

Water-to-Cement Ratio0.50 0.45

0.400.35

0.30

0.25

175 [295]

230

900

Water Content (kg/m

3 )

[lb/yd3 ]

700 900 1100 1300 1500Cement Content (lb/yd3)

210 [354]

190 [320]

81

change in volume of unrestrained cement paste is approximately equal to the volume of water

removed.

Interlayer water can also be removed at room temperature causing a higher volume

change than the adsorbed water (Mindess et al., 2003). However, this change is highly

dependent on the C-S-H particle size. At low specific surface microstructure, as the one

obtained when high pressure steam curing is used, the observed shrinkage can be 5 to 10

times lower than similar paste cured normally (Neville, 1996).

B.4 Long-Term Strains of HPC

According most of the authors working on HPC (Aïtcin, 1998; Shah and Ahmad,

1994; ACI 363, 1997; Neville, 1995; Nawy, 2001; Mehta and Monteiro, 1993; Carrasquillo

and Carrasquillo, 1988; Carrasquillo et al., 1981, Shams and Kahn, 2000), creep and

shrinkage of such concrete is less than that of normal strength concrete (NSC). This section

presents creep and shrinkage result of HPC given in the literature and some theories behind

such results.

The fact that HPC presents lower creep and shrinkage can be attributed to its

differences with NSC. HPC has sometimes different and usually additional constituent

materials such as finer cement, high early strength cement, silica fume, slag, fly ash, and

superplasticizers. Also, it might have different mix procedures such as time of mixing, and

type of mixer. HPC might have special curing procedures such as steam curing or heating.

All the mentioned HPC characteristics affect the long-term strain behavior of such concrete.

Among the factors making a difference in HPC behavior are cement paste mechanical

properties and water permeability of concrete.

82

B.4.1. Creep of HPC

Dilger and Wang (2000) carried out a comparison between creep of NSC and creep of

high strength concrete. They concluded that for NSC creep deformation after a long time

(several years) was normally two to four times the elastic deformation (creep coefficient 2.X

to 4.X). In contrast, the creep coefficient of HPC was somewhere in the range 1.8 to 2.4.

The authors stated that NSC and HPC are affected by the same parameters in similar ways.

However, the main factors responsible for lower creep of HPC are low water-to-cementitious

materials ratio (w/cm) and silica fume addition. The same authors also concluded that the

main difference between creep in normal and HPC is given by the significantly lower drying

creep observed in HPC.

Many times HPC is produced with Type III cement or finer cement and

supplementary cementitious materials (SCM’s) in order to obtain high early strength derived

from a faster cement hydration. Mokhtarzadeh and French (1998) carried out an extensive

experimental program on high strength concrete where they varied type of cement (Type I

and III) with silica fume and/or fly ash cement replacement. They found that, as occurs with

NSC, the higher the compressive strength, the lower the specific creep.

Burg and Ost (1992) investigated silica fume and creep relationship and reported that

silica fume high strength mixes had specific creep ranging between 34 and 50% of the one

measured in non-silica fume mixes. Wolseifer (1982) found that creep of silica fume HPC

was 30% less than that of the reference non-silica fume concrete.

It is known that cement hydration is not only affected by the composition of

cementitious materials, but also by temperature. Faster cement hydration due to the use of

SCM’s, finer cement or Type III cement can lead to important increment in temperature

83

during the first hours after casting. This rise in temperature might accelerate the hydration of

the cementitious materials generating more heat. As a result, there is an increase in maturity

of concrete at the same age which would lead to a reduction in creep. On the other hand,

Mokhtarzadeh and French (1998) investigated the effect of curing temperature on creep by

using high strength concrete made with Type I cement, Type III cement and contained either

no mineral admixtures, fly ash, silica fume, or the combination of fly ash and silica fume.

The authors reported reduced specific creep for concrete cured under lower temperatures.

The authors concluded that high temperature curing had a negative effect on creep.

As mentioned above, permeability of HPC is usually much lower than NSC. Some

authors (Dilger and Wang, 2000; Ngab et al., 1981) related low permeability of HPC with

low creep. The relationship between permeability and creep can be explained based on creep

mechanisms. As explained in Section B.2.4, it is widely accepted that water plays a central

role in creep; however, theories disagree about the specific role, that is, whether water is the

fundamental cause of creep (seepage theory) or whether it just modifies the flow of C-S-H

(viscous flow theory). Since most of the times improvement in mechanical properties also

brings a reduction in water permeability, HPC is usually a low permeability concrete, too.

Reduced permeability would reduce water migration within the concrete and from the

concrete to the atmosphere. As a consequence, low permeability concrete would lose less

water more slowly which would decrease drying creep.

According to Ngab et al. (1981), under drying conditions non-silica fume HPC

presented 30 to 50% less creep than normal strength concrete (NSC). The same authors

reported that the same HPC under non-drying condition had 10 to 25% less creep than NSC.

84

They explained the higher improvement under drying conditions based on the reduced water

content and low permeability of HPC.

Buil and Acker (1985) reported a 17.5% less creep in silica fume mixes for unsealed

specimens when compared with their non-silica fume counterparts. The same authors

registered a 12% increase in creep of concrete with silica fume when they used sealed

specimens. Buil and Acker’s results would indicate that the reduction in creep of HPC,

compared with NSC, would be in the drying creep portion rather than basic creep.

B.4.2. Shrinkage of HPC

Even though HPC presents less total shrinkage than NSC, autogenous shrinkage

might be significantly increased. According Aïtcin (1998), at very low water-to-cement

ratios, as the ones used in HPC, the autogenous shrinkage can be as high as 700 µε. The

difference in autogenous shrinkage of HPC and NSC can be explained by the major

differences at the microstructure level. In NSC capillary pores are coarse, so the creation of

menisci is not very strong. Weak menisci result in a small or negligible autogenous

shrinkage. In HPC of low water-to cementitious materials ratio, hydration starts to develop

very rapidly, water is drained rapidly from capillaries that are finer. As a result, high tensile

stresses are developed leading to faster and higher autogenous shrinkage. Tazawa (1995)

concluded that for concretes with water-to-cement ratio of 0.3 and 0.4, autogenous shrinkage

was 50 and 40% of the total shrinkage, respectively.

Aïtcin (1998) concluded that HPC shrinkage is linked to the presence or absence of

curing and not to its cement content. Wolseifer (1984) reported that HPC moist-cured for 14

days presented 24.3% less shrinkage compared with NSC. However, he reported higher

shrinkage in the same mixes when moist-cured for only one day. Wolseifer’s results might

85

be explained based on autogenous shrinkage. Under the short period of curing, autogenous

shrinkage is free to develop due to the lack of water. When cured for 14 days, autogenous

shrinkage is greatly reduced as explained below.

According to de Larrand et al. (1994), there is very little information concerning

drying shrinkage of HSC. Because most shrinkage tests do not include sealed specimens, the

measured data are total shrinkage which cannot be divided into autogenous and drying

portions. The authors also pointed out that there is conflicting information of the effect of

high range water reducers (HRWR) on drying shrinkage. In first place, the use of HRWR for

reducing water content can be expected to reduce drying shrinkage. Secondly, flowing

concrete probably will require a higher cement paste content which would lead to higher

drying shrinkage.

The influence of SCM’s on drying shrinkage has also been investigated. Burg and

Ost (1992) reported a reduction of 40% of drying shrinkage when using silica fume in the

mix. Luther and Hansen (1989), concluded that drying shrinkage of HSC with silica fume is

similar and in some cases less than that of HSC made with fly ash.

Buil and Acker (1985), who investigated the effect of SCM’s on drying shrinkage,

reported a reduction up to 40% in shrinkage for unsealed specimens, but for sealed

specimens they obtained a 19% increase. Buil and Acker’s results support the idea that the

main effect of supplementary materials is through a reduction in drying shrinkage, and

autogenous shrinkage is not reduced, but increased under certain curing conditions. Aïtcin

(1998) recommended water curing or fog misting during the very first hours to reduce

autogenous shrinkage. He sealed specimens later for reducing drying shrinkage.

86

The effect of water-to-cementitious materials ratio (w/cm) on drying shrinkage of

HSC with silica fume was investigated by de Larrand et al. (1994). They obtained less

drying shrinkage when the w/cm was reduced. In contrast, they measured higher autogenous

shrinkage as the w/cm decreased, so the sum remained roughly constant. They concluded

that there is a balance between the two kinds of shrinkage.

Shams and Kahn (2000), after their literature review, concluded that “shrinkage is not

affected by the concrete strength, but rather by the water content in the mix”. Smadi et al.

(1987) indicated significant reduction in shrinkage as concrete strength increased.

B.5 Long-Term Strains of SLC

B.5.1. Creep of SLC

As described in Section B.2.3, creep of concrete can be expressed in terms of creep of

cement paste, cement paste content, and the constant “α” which represents the aggregate

restraining effect. The aggregate restraining effect depends on the aggregate modulus of

elasticity. A soft aggregate (low modulus of elasticity) would impose less restraint to cement

paste movements, so creep is expected to increase. Lightweight aggregate elastic modulus

usually ranges between 700 and 2,900 ksi while that of normal weight aggregate ranges

between 5,800 and 17,500 ksi. Based on that, creep in lightweight aggregate concrete is

expected to be greater than creep of normal concrete.

Figure B.6 presents some of the values proposed by ACI committee 213 (1999) for

one-year specific creep of SLC of different compressive strength.

87

Figure B.6: Relationship between 28-day compressive strength and one-year specific creep for SLC and NWC.

In Figure B.6 “all-lightweight” stands for lightweight concrete made with both coarse

and fine lightweight aggregate while “sand-lightweight” stands for lightweight concrete

made with coarse lightweight aggregate and normal weight fine aggregate. Figure B.6

clearly shows a decrease in one-year creep as concrete compressive strength increases. Also,

the band of “all-lightweight” concrete is wide for concrete having low compressive strength ,

but sharply decreases for higher strength concretes. “Sand-lightweight” concrete band is

narrower than “all-lightweight” band, and it also decreases in width as compressive strength

increases. Reference NWC values are close to the lower limits given for lightweight

concrete. It can be stated that, on average, lightweight concrete exhibits a higher creep than

NWC. Nevertheless, there are some individual lightweight concretes that present a lower

creep than the reference NWC.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

3000 4000 5000 600028-day compressive strength (psi)

One

-yea

r spe

cific

cre

ep (µ

ε/ps

i)All-lightweight rangeSand-lightweight rangeNWC reference values

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8


One

-yea

r spe

cific

cre

ep (µ

ε/ps

i)All-lightweight rangeSand-lightweight rangeNWC reference values

88

Results of creep on lightweight concrete by Ward et al. (1967), suggested that the

lightweight aggregate restraining effect “α” is very similar for wet and dry conditions. They

also concluded that the average “α” value for lightweight aggregates was slightly higher than

1.0, which is lower than the 1.2 to 1.7 range obtained for normal weight aggregate.

Creep of lightweight aggregate concrete has been reported by several authors

(Weigler, 1974; Pfeifer, 1968; Short and Kinniburgh, 1968; and Hummel, 1964). Among

them Pfeifer (1968) carried out a large creep and shrinkage experimental program on 47

concrete mixes made with seven different lightweight aggregates (mostly expanded shale and

clay). Detailed properties of the aggregates were not reported, but based on Holm (1995)

and CEB/FIP (1977), elastic modulus of those aggregates was probably around 1,600 ksi.

Pfeifer (1968) also tested, under the same conditions, NWC of the same strength made with

gravel (gravel elastic modulus was approximately 14,500 ksi). Pfeifer’s results are shown in

Figure B.7. The Y-axis, labeled as “relative creep”, presents ultimate creep of SLC divided

by ultimate creep of NWC.

According to Pfeifer’s results, lightweight concrete made with an aggregate with one

tenth of the stiffness of a normal weight aggregate, creeps on average 12% more than its

normal weight counterpart. When each aggregate is analyzed alone, it can be seen that 5 out

of 12 lightweight mixes had an ultimate creep coefficient lower than NWC. The best

performing mix (rotary kiln expanded shale) presented an ultimate creep coefficient 30%

lower than control concrete. On the other hand, the worst performing mix (sintering grate

expanded shale) presented creep 70% higher than control NWC.

89

Holm and Bremner (2000) reported results by Shideler (1957) and by Troxell et al.

(1958) where creep in lightweight aggregate concrete is within a wide envelope with values

up to two times that of NWC.

Figure B.7: Relationship between aggregate elastic modulus and relative creep of concrete (Pfeifer, 1968).

Van der Wegen and Bijen (1985), carried out a research on influence of artificial

pulverized fuel ash (PFA) aggregate in mechanical properties of concrete. They used two

lightweight aggregates (Aardelite and Lytag) and one normal weight aggregate (river gravel).

The authors characterized their aggregates measuring strength and absorption among other

nine properties.

When they compared creep of Aardelite concrete and NWC, they concluded that

Aardelite had 58% less compressive strength and produced a concrete with much higher

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0 1500 3000 4500 6000 7500 9000 10500 12000 13500 15000

Aggregate Elastic Modulus (ksi)

Rel

ativ

e C

reep

Lightweight aggregate Ea=1,600 ksiNormal weight aggregate Ea=14,500 ksiNormal weight average

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0 1500 3000 4500 6000 7500 9000 10500 12000 13500 15000

Aggregate Elastic Modulus (ksi)

Rel

ativ

e C

reep

Lightweight aggregate Ea=1,600 ksiNormal weight aggregate Ea=14,500 ksiNormal weight average

90

creep (approximately two times). However, the creep obtained using Lytag aggregate was

similar to the one of NWC even though Lytag aggregate strength was 51% lower than natural

river aggregate strength. The authors could not explain the better Lytag performance since

both artificial aggregates were similar. One explanation of these results might be the

pozzolanic reactivity of the two different PFA aggregates which was not measured by the

authors. A more reactive aggregate would improve the interfacial transition zone (ITZ) which

might decrease creep.

B.5.2. Shrinkage of SLC

Shrinkage of SLC is expected to be greater than NWC because of the lower modulus

of elasticity of lightweight aggregate compared with normal weight aggregate. Figure B.8

presents some of the values given by ACI committee 213 (1999) for one-year drying

shrinkage of SLC of different compressive strengths.

From Figure B.8 it can be stated that shrinkage of SLC increases as compressive

strength increases. The range of “all-lightweight” concrete was broader than “sand-

lightweight” concrete range; however, the lower limits were very similar for both types of

concrete. The observed increase in drying shrinkage might be due to the required increase in

cement paste content in order to achieve higher strengths. One-year drying shrinkage of SLC

might be in the range of 500 to 1000 µε for normal strength levels (4000 to 5000 psi). One-

year drying shrinkage of reference NWC might be close to that low bound of 500 µε.

However, some lightweight concrete may present less drying shrinkage than NWC.

91

Figure B.8: Relationship between 28-day compressive strength and one-year drying shrinkage for SLC and NWC.

Pfeifer (1968) investigated drying shrinkage on 47 lightweight concrete mixes using

seven different lightweight aggregate. Figure B.9 presents ultimate drying shrinkage

reported by Pfeifer (1968). As shown in Figure B.9, Pfeifer’s results are in agreement with

the ranges proposed by ACI-213 (1999). For 3000 psi compressive strength, there were four

expanded shale concretes (#14, #16, #18, and #7) that showed lower ultimate shrinkage than

NWC. In contrast, for 5000 psi mixes, only one of the lightweight concretes (expanded shale

#14) showed less shrinkage than NWC.

0

100

200

300

400

500

600

700

800

900

1000

1100


One

-yea

r dry

ing

shrin

kage

(µε)

All-lightweight rangeSand-lightweight rangeNWC reference values

0

100

200

300

400

500

600

700

800

900

1000

1100


One

-yea

r dry

ing

shrin

kage

(µε)

All-lightweight rangeSand-lightweight rangeNWC reference values

92

Figure B.9: Ultimate drying shrinkage values for different lightweight concretes (Pfeifer, 1968).

Holm (1995), stated that drying shrinkage of SLC is determined by the same factors

that NWC. However, SLC has three more characteristics that would affect drying shrinkage:

(1) SLC usually requires a higher cement content than NWC for a given compressive

strength; (2) stiffness of lightweight aggregate is lower than normal weight aggregate, so

lightweight aggregate allows more movement of the cement paste; and (3) SLC has a higher

water retention capacity which slows down the drying process and delays the dimensional

stabilization.

B.6 Long-Term Strains of HPLC

B.6.1. Creep of HPLC

While it is clear that HPLC can be produced with high strength lightweight concrete,

its creep characteristics have not been extensively or systematically investigated. Creep is

0

200

400

600

800

1000

1200

#14: Exp.shale

#16: Exp.shale

#18: Exp.shale

#7: Exp.shale

#6: Exp.blast

furnace slag

#15: Exp.shale

#19: Exp.clay

Normalaggregate

Aggregate type

Ulti

mat

e Sh

rinka

ge (µ

ε)3000 psi lightweight concrete 5000 psi lightweight concrete

0

200

400

600

800

1000

1200

#14: Exp.shale

#16: Exp.shale

#18: Exp.shale

#7: Exp.shale

#6: Exp.blast

furnace slag

#15: Exp.shale

#19: Exp.clay

Normalaggregate

Aggregate type

Ulti

mat

e Sh

rinka

ge (µ

ε)3000 psi lightweight concrete 5000 psi lightweight concrete

93

typically reduced in HPC (see Section B.4) but is typically greater in lightweight concrete

(see Section B.5). These competing effects make creep in HPLC difficult to predict.

Moreover, some observations and recommendations presented in the literature are not

consistent. For instance, Berra and Ferrada (1990) concluded that specific creep in HPLC is

twice that of normal weight concrete of the same strength. On the other hand, Malhotra

(1990) gave values of creep of fly ash HPLC in the range 460 to 510 µε. These values are

fairly close to those obtained by Penttala and Rautamen (1990) for HPC, and they are

significantly lower than the values between 878 and 1,026 µε reported for HPC by Huo et al.

(2001).

In a recent state-of-the-art report on high-strength, high-durability structural

lightweight concrete, Holm and Bremner (2000) remarked on the discrepancies found in the

literature. They contrasted the work of Rogers (1957) with the research done by Reichard

(1964) and Shideler (1957). In the former, creep of HSLC was found to be similar to that

measured in companion HSC while the last two found greater creep in “all lightweight”

concrete (fine and coarse lightweight aggregate), than in the normal weight concretes.

Leming (1990) compared the creep of three mixes: two 4,000-psi concrete with same

mix proportions, but with either lightweight or normal weight coarse aggregate. The third

mix was an 8,000-psi concrete with lightweight coarse aggregate. One-year creep was 1,095,

608, and 520 µε for the 4,000-psi lightweight, 4,000-psi normal weight concrete, and 8,000-

psi lightweight concrete, respectively. The result for the 8,000-psi lightweight concrete was

85% of the value obtained for the 4,000-psi normal weight concrete.

There are only a few research works done in creep of HPLC. However, conclusions

from different researchers are sometimes opposed which makes the estimate of creep in

94

HPLC extremely difficult. As a consequence, when HPLC is to be used in a certain project,

performance of a laboratory creep test for the specific mix is recommended in order to obtain

more accurate data for the design and prediction of creep in the project.

The two principle phases of HPLC: high performance matrix and lightweight

aggregate have several possible specific implications on creep in concrete. It is commonly

assumed that normal weight aggregate does not creep at the stress levels present in concrete.

However, in HSLC, the higher stress placed on the member might induce creep in the

lightweight aggregate, due to its lower modulus and strength. Also, improvements in the

interfacial transition zone, afforded by the use of ultra-fine pozzolanic particles and

lightweight aggregate, can alter the mechanisms for creep. Particularly, they can alter

mechanisms not only compared to normal strength concrete, but also compared to high

strength concrete (due to improved compatibility between the aggregate and paste). Finally,

the increased aggregate porosity and the effect of “internal curing” (when using saturated

lightweight aggregate) can influence moisture movements during creep. These possible

changes in expected behavior (as compared to normal concrete and high strength concrete)

resulting from the use of high performance matrix and lightweight aggregate are described in

further detail below.

Aggregate mechanical properties: In normal weight concrete, creep is largely a

phenomenon occurring in the paste, but its magnitude, and perhaps its temporal development,

can be affected by the quantity and quality of the aggregate. The high porosity of lightweight

aggregates may influence creep of concrete not only indirectly by reducing the elastic

modulus and strength of the concrete, but also directly by participating in the moisture

movements occurring during creep, as considered in the seepage theory.

95

Improved interface characteristics: Micrographs of SLC showed that the boundary

between cementitious matrix and coarse aggregate was indistinguishable from the bulk paste

(Holm and Bremner, 2000). This may result from: (1) improved physical bonding between

the paste and aggregate (due to increased aggregate porosity); (2) improved chemical

bonding between the paste and aggregate (due to pozzolanic activity); (3) reduced

microcracking (due to elastic matching between aggregate and paste); and (4) reduced

bleeding. In addition, “internal curing” may improve the strength and density of the ITZ.

This occurs when presoaked lightweight aggregate provides an internal reservoir of water

maintaining favorable moisture conditions and extending the local hydration processes (ACI-

213, 1987 -reapproved 1999; Holm and Bremner, 1990). These improvements to the ITZ

could mitigate the “microcracking effect” on creep. Katz et al. (1999) postulated that an

improved ITZ can be obtained by using dry lightweight aggregate. They concluded that the

suction imposed by a dry lightweight aggregate can lead to a dense ITZ, with even some

penetration of cement particles into the shell of the aggregate.

Changes in moisture migration: the seepage theory views creep as a result of water

movement under stress from micropores to the larger capillary pores. If water migration is

the main factor in concrete creep, both the aggregate porosity (i.e., volume of pores, pore

size, and pore distribution) and the permeability of the cementitious matrix become important

factors. Several (ACI-213, 1999; Holm, 1995; Neville et al., 1983) have cited the importance

of using lightweight aggregate in a saturated condition while mixing. If the aggregate is not

saturated, a more rapid movement of water from the paste would be expected to lead to

greater creep. On the other hand, the moisture conditions given by the saturated lightweight

aggregate could replace the water lost under stress (seepage).

96

B.6.2. Shrinkage of HPLC

As occurs with creep of HPLC, there are only a few articles regarding shrinkage of

HPLC. Besides, they usually do not report autogenous and drying shrinkage separately, but

as overall shrinkage. Berra and Ferrada (1990) found that compared with HPC, HPLC had a

lower shrinkage rate, but a higher ultimate value. According the authors, the lower rate was

caused by the presence of water in the aggregate which delays drying. Holm and Bremner

(1994) also observed that HSLC mix lagged behind at early ages, but one-year shrinkage was

approximately 14% higher than the HPC counterpart. Holm and Bremner (1994) measured a

higher shrinkage when they incorporated fly ash to the HSLC mix. Malhotra’s (1990)

results, on the other hand, showed that fly ash particles in the HPLC helped to reduce

shrinkage after one year.

Leming (1990) reported one-year shrinkage of 4,000-psi and 8,000-psi lightweight

concretes, made with saturated expanded slate, of 390 and 310 µε, respectively while the

corresponding shrinkage of a 4,000-psi NWC was found to be 360 µε. Bilodeau et al. (1995)

investigated HSLC with 28-day compressive strength ranging from 7,250 to 10,000 psi and

found that the 450-day shrinkage was in the range 518 to 667 µε. Curcio et al. (1998)

reported that one-year and ultimate shrinkage of HPLC with Type III cement and fly ash was

450 and 500 µε, respectively.

Kohno et al. (1999) found out that autogenous shrinkage is reduced by the use of

lightweight fine aggregate. They concluded that this is because water lost by self-desiccation

of the cement paste is immediately replaced by moisture from lightweight aggregate.

Aïtcin (1992) reported values of shrinkage of HPLC as low as 70 and 260 µε, after a

28-day curing.

97

Appendix C. Creep and Drying Shrinkage Models

According Findley, Lai and Onaran (1989), creep was first systematically observed

by Vitac (1834), but Andrade (1910) was the first in proposing a creep law. After Andrade,

several more models have been developed. Some models are general mechanic-rheologic

models which include constants for different materials and properties while other models are

more empirical for specific materials. The most used models for creep in concrete fall in the

second category, empirical models.

On the other hand, drying shrinkage of concrete was identified by the first creep

studies when they measured a higher creep rate and strain on concrete under drying

conditions. Since then, several investigators have proposed models in order to describe and

predict shrinkage.

Among the variety of methods proposed for creep and shrinkage in concrete, seven of

them are presented in this section: American Concrete Institute committee 209 (ACI-209,

1997), American Association of State Highway and Transportation Officials (AASHTO-

LRFD, 1998), Comite Euro-Internacional du Beton and Federation Internationale de la

Precontrainte (CEB-FIP, 1990), Bažant and Panula’s (BP, 1978), Bažant and Baweja’s (B3,

1995), Gardner and Lockman’s (GL, 2001), and Sakata’s model (SAK, 1993). Finally, five

methods aimed to be used for high strength concrete are presented: CEB-FIP as modified by

Yue and Taerwe (1993), BP as modified by Bažant and Panula (1984), SAK as modified by

Sakata et al. (2001), Association Française de Recherches et d'Essais sur les Matériaux de

Construction (AFREM, 1996), and AASHTO-LRFD as modified by Shams and Kahn

(2000). Finally, the applicability of the above models to SLC and HPLC is analyzed. Most

of the expressions presented here are empirical, so they have different versions depending on

98

the unit system. US customary unit version is presented in this section while S.I. unit

version is presented in Appendix I.

C.1 Models for Normal Strength Concrete

C.1.1. ACI-209 Method

American Concrete Institute through its committee 209 “Prediction of Creep,

Shrinkage and Temperature Effects in Concrete Structures” proposes an empirical model for

predicting creep and shrinkage strain as a function of time. The two models have the same

principle: a hyperbolic curve that tends to an asymptotic value called the ultimate value.

The shape of the curve and ultimate value depend on several factors such as curing

conditions, age at application of load, mix design, ambient temperature and humidity.

Creep Model. Creep model proposed by ACI-209 has three constants that determine

the asymptotic value, creep rate and change in creep rate. The predicted parameter is not

creep strain, but creep coefficient (creep strain-to-initial strain ratio). The latter allows for

the calculation of a creep value independent from the applied load. Equation C.1 presents the

general model.

ut ttdtt

φφ ψ

ψ

⋅−+

−=

)'()'(

(C.1)

where

øt: creep coefficient at age “t” loaded at t′

t: age of concrete (days)

t′: age of concrete at loading (days)

ψ: constant depending on member shape and size

99

d: constant depending on member shape and size

øu: ultimate creep coefficient

ACI-209 recommended a value of 0.6 and 10 for ψ and d, respectively. Ultimate

creep coefficient value depends on the factors described in Section B.2. ACI proposed an

average creep coefficient value of 2.35 which is multiplied by six factors depending on

particular conditions, as shown in Equation C.2

αψλ γγγγγγφ ⋅⋅⋅⋅⋅⋅= svslau 35.2 (C.2)

where


⋅⋅

=−

−

curingsteamfortcuringmoistfort

la 094.0

118.0

'13.1'25.1

γ ; age of loading factor


≥⋅−

=otherwise

hforh00.1

40.067.027.1λγ ; ambient relative humidity factor

h: relative humidity in decimals

{ }( )SV

VS ⋅−⋅+= 54.0exp13.1132

γ ; volume-to-surface ratio factor

V: specimen volume (in3)

S: specimen surface area (in2)

ss ⋅+= 067.082.0γ ; slump factor

s: slump (in)

ψλψ ⋅+= 24.088.0 ; fine aggregate content factor

100

ψ: fine aggregate-to-total aggregate ratio in decimals

αγ α ⋅+= 09.046.0 ; air content factor

α: air content (%)

After applying the factors above, ultimate creep coefficient value is usually between

1.3 and 4.15, which means that creep strain is between 1.3 and 4.15 times the initial elastic

strain.

Drying Shrinkage Model. Similar to creep, ACI-209 shrinkage model has constants

that determine the shrinkage asymptotic value, shrinkage rate and rate change. Equation C.3

shows such a model.

ushtsh ttftt )(

)()()(

0

0 εε α

α

⋅−+

−= (C.3)

where


t0: age at the beginning of drying (days)

(εsh)t: shrinkage strain after “t-t0” days under drying (in/in)

α: constant depending on member shape and size

f: constant depending on member shape and size

(εsh)u: ultimate shrinkage strain (in/in)

ACI-209 recommends a value for f of 35 and 55, for seven days moist curing and 1 to

3 days steam curing, respectively, while a value of 1.0 is suggested for α. Ultimate shrinkage

101

value depends on the factors described in Section B.3. As shown in Equation C.4, ACI-209

proposes an average value of 780 µε for shrinkage which is multiplied by seven factors

depending on particular conditions.

αψλ γγγγγγε ⋅⋅⋅⋅⋅⋅= csvsush 780)( (C.4)

where

(εsh)u: ultimate shrinkage strain

>⋅−≤≤⋅−

=80.00.300.3

80.040.00.140.1hforh

hforhλγ ; ambient relative humidity factor


{ }SV

VS ⋅−⋅= 12.0exp2.1γ ; volume-to-surface ratio factor




s: slump (in)

>⋅−≤⋅−

=50.02.090.050.04.130.0

ψψψψ

γψ forfor

; fine aggregate content factor


cc ⋅+= 00036.075.0γ ; cement content factor

c: cement content (lb/yd3)


α: air content (%)

102

After applying the factors above, ultimate shrinkage value is usually between 415 and

1070 µε.

C.1.2. AASHTO-LRFD Method

AASHTO-LRFD method (1998) is very similar to ACI-209 method, but it

incorporates more recent data. AASHTO-LRFD method proposes slightly different

correction factors.

Creep Model. The general equation for creep coefficient is the same as ACI-209

(Equation C.1). However the expression for calculating ultimate creep coefficient differs

from ACI expression (Equation C.2). Equation C.5 presents AASHTO-LRFD expression for

ultimate creep coefficient.

fchlau kkkk ⋅⋅⋅⋅= 50.3φ (C.5)

where


curingmoistfortkla118.0'00.1 −⋅= ; age of loading factor

−∆+

−⋅∆= ∑ 65.13)(273

4000exp'

0TtT

tti

loadinguntil

i ; maturity of concrete at loading (days)

∆ti: period of time (days) at temperature T(∆ti) (oC) ( 778.17556.0 −×= FC oo )

T0: 1 oC

hkh ⋅−= 83.058.1 ; ambient relative humidity factor


103

{ } { }

⋅−⋅+⋅

+

+⋅⋅=

587.2

54.0exp77.180.1

45

36.0exp26 SV

tt

tSV

t

kc ; size factor

−∆+

−⋅∆= ∑ 65.13)(273

4000exp

0TtT

tti

ndayuntil

i ; maturity of concrete (days) after “n” days



9'67.0

1c

f fk

+= ; concrete strength factor

fc’: compressive strength of concrete cylinders at 28 days (ksi)

Drying Shrinkage Model. ASSHTO-LRFD general expression for shrinkage is the

same as ACI expression (Equation C.3) including the values for f of 35 and 55 for moist and

steam curing, respectively. The expression for calculating ultimate shrinkage is different

from ACI expression, and it is presented in Equation C.6.

hsush kkK ⋅⋅=)(ε (C.6)

where

(εsh)u: ultimate shrinkage strain (in/in)

=curingsteamforcuringmoistfor

Kµεµε

560510

; ultimate shrinkage base value

104

( ){ } ( )( )( )

⋅−⋅

−+−

−+⋅⋅

−

=923

94.01064

45

36.0exp26

0

0

0

0

SV

tttt

ttSVtt

ks ; size factor





≥⋅−<⋅−

=80.029.429.480.043.100.2

hforhhforh

kh ; ambient relative humidity factor


C.1.3. CEB-FIP Method

CEB-FIP method has a similar concept that ACI-209 in the sense that it gives a

hyperbolic change with time for creep and shrinkage, and it also uses an ultimate value

corrected according mix design and environment conditions. One difference of CEB-FIP

method with respect to the methods above is that it predicts creep strain rather than creep

coefficient.

Creep Model. CEB-FIP general model is presented in Equation C.7. This model

predicts creep strain by multiplying creep coefficient by elastic strain. Creep coefficient has

its own equation based on two parameters, as shown in Equation C.8

)',()'(

)',( 2828

ttE

ttt c

cr φσ

ε = (C.7)

105

3.0

028 )'()'(

−+

−⋅=

tttt

Hβφφ (C.8)

where



εcr: creep strain in µε

σc(t′): applied stress (ksi)

E28: 28-day elastic modulus (ksi)

ø28: creep coefficient at age “t” loaded at t′

( )2.0

310 '1.0

1

45.1'

3.5

367.0

11tf

uA

h

cc+

⋅⋅

⋅

−+=φ ; notional creep coefficient


Ac: cross sectional area (in2)

u: exposed perimeter (in)


( )[ ] 1500250508.02.11150 18 ≤+⋅⋅⋅+⋅= uAh c

Hβ ; constant depending on member size and

relative humidity

Equations C.9 and C.10 are used when strength gaining different from normal is

expected.

dayst

ttT

T 5.01)'(2

9'' 2.1 ≥

+

+=

α

(C.9)

106

−∆+

−⋅∆= ∑ 65.13)(273

4000exp'

0TtT

tti

iT (C.10)

where


t′T: adjusted age of concrete at loading

+

−=

cementstrengthearlyhighhardeningrapidforcementhardeningrapidnormalfor

cementhardeningslowlyfor

1/0

1α ; cement type parameter


T0: 1 oC

When stresses between 40 and 60% of compressive strength are applied, CEB-FIP

recommends using a high stress correction to the notional creep “ø0” as shown in Equation

C.11.

( ){ }4.05.1exp0,0 −⋅⋅= σφφ kk (C.11)

where

ø0,k: notional creep coefficient corrected by stress level

ø0: notional creep coefficient

kσ: stress-to-strength ratio at time of application of load.

Drying Shrinkage Model. Equation C.12 presents CEB-FIP expression for predicting

shrinkage.

107

)(),( 00 tttt ssos −⋅⋅= βεε (C.12)

where


t0: age of concrete at the beginning of drying (days)

RHc

scsf

ββε ⋅

−⋅⋅+=

1450'

9101600 ; notional shrinkage coefficient

=



sc

8/5

4β ; cement type parameter

[ ]

≥

≤≤−⋅−

99.025.0

99.040.0155.1:

3

hfor

hforhRHβ ; relative humidity factor



( ) ( )( )

5.0

0

00,

−+

−=

tttt

ttsH

s ββ ; shrinkage-time function

2

08.5350

⋅⋅= u

AcsHβ ; geometric factor



When temperatures above 30oC (86oF) are applied, CEB-FIP recommends using an

elevated temperature correction for βsH and βRH as shown below.

108

( ){ }2006.0exp, −⋅−⋅= TsHTsH ββ

−⋅

−+⋅=

4020

03.108.01,

ThRHTRH ββ

where

TsH ,β : geometric factor corrected by temperature

2

08.5350

⋅⋅= u

AcsHβ ; geometric factor

TRH ,β ; relative humidity factor corrected by temperature

[ ]

≥

≤≤−⋅−

99.025.0

99.040.0155.1:

3

hfor

hforhRHβ ; relative humidity factor

T: ambient temperature (oC) ( 778.17556.0 −×= FC oo )


C.1.4. Bažant and Panula’s - BP Method

First proposed in the late 1970’s (Bažant and Panula, 1978a, 1978b, 1979a), the BP

model suggested some computations quite different from ACI and CEB models. Among

those are the modeling of creep using three portions (basic, drying, and after drying creep)

based on a double power law in time and drying shrinkage based on a square-root hyperbolic

law in time (Bažant and Panula 1978b, 1978d).

Creep Model. The BP model proposed that creep of concrete is comprised of three

portions: Basic creep modeled by a double power law in time; drying creep modeled by a

hyperbolic law multiplied by drying shrinkage; and creep decrease after drying which is

109

modeled by a hyperbolic law multiplied by double power law in time. Equation C.13

presents the BP model general compliance function.

),',(),',()',(1)',( 0000

tttCtttCttCE

ttJ pd −++= (C.13)

where

J: compliance function

E0: Modulus of elasticity at the age of loading (ksi)

C0: basic creep portion [specific creep - (in/in)/ksi]

Cd: drying creep portion [specific creep - (in/in)/ksi]

Cp: creep decrease after drying [specific creep - (in/in)/ksi]

Basic Creep Model. Basic creep can be best approximated by a double power law

(Bažant and Panula, 1978a, 1978b), in the form:

( ) ( )nm tttE

ttC '')',(0

10 −⋅+⋅= − α

φ (C.14)

where





( )αφ+⋅

= −

⋅

m

n

282103

1 material parameter

( )( ) ( ) 4'1.01.2

412.0

45130

07.012.0

1

2.23

15.1

6

6

−⋅

⋅

⋅⋅+⋅=

≤

>+⋅

+

= aga

cwf

cs

ca

xxfor

xforx

x

n c

110


w: water content (lb/yd3)

a: aggregate content (lb/yd3)

s: sand content (lb/yd3)

g: coarse aggregate content (lb/yd3)


( )2'128.0cf

m += ; ( )cw⋅

=40

1α ; material parameters

a1: cement type coefficient

cementIVTypeforcementIIITypefor

cementsIIandITypefor

05.193.000.1

Drying Creep Model:

According to Bažant and Panula (1978c and 1984) drying creep can be modeled by

Equation C.15:

ncsh

shh

mdd

d

ttkt

EtttC

⋅−

∞−

−⋅

+⋅⋅⋅⋅='

101''

'),',( 2

00

τε

φ (C.15)

where




t′: age of loading (days)


dsh

dtt

φτ

φ ⋅

⋅−

+=− 2

1

0

10'

1'

111

85.0'560000008.0

07.011027.0008.0 5.1

3.13.04.1

−

⋅

⋅

⋅⋅=

≤

>⋅+

⋅+

=∞

−

scd

cw

sgf

asr

rfor

rforr

εφ







( )01

12

8.50150

600tC

CS

Vk refs

sh ⋅

⋅⋅⋅=τ ; size-dependent factor

=

cube afor 1.55sphere afor 1.30

prism squared infinitefor 1.25cylinder infinitefor 1.15

slab infinitefor 1.0

sk ; shape factor



daymmC ref /10 21 =

( )

+⋅⋅=

0701

3.605.0't

kCtC T

( ) 21712593.081

77 ≤≤−⋅⋅⋅= CccwC

−=TTT

TkT50005000exp'

00

112

T: ambient temperature oK ( 372.255556.0 +×= FK oo )

T0: 296.15 oK (reference temperature)

( )( ) ( ) 4'1.01.2

412.0

45130

07.012.0

1

2.23

15.1

6

6

−⋅

⋅

⋅⋅+⋅=

≤

>+⋅

+

= aga

cwf

cs

ca

xxfor

xforx

x

n c

( )2'128.0cf

m += ; ( )cw⋅

=40





05.193.000.1

5.15.10' hhkh −= ; humidity dependent parameter


h0: 0.98 to 1.0

εs∞: final shrinkage in µε as in Equation C.17

ncd ⋅−= 5.78.2

Creep Decrease after Drying

Creep decrease after drying follows a function of time similar to drying creep as

shows Equation C.16:

( )',1001),',( 00

"0 ttC

ttkctttC sh

hpp ⋅

−⋅

+⋅⋅=τ (C.16)

where

Cp: creep decrease after drying portion [specific creep - (in/in)/ksi]

113




83.0=pc

220'' hhkh −= humidity dependent parameter


h0: 0.98 to 1.0

( )01

12

8.50150

600tC

CS

Vk refs

sh ⋅


=




sk ; shape factor



daymmC ref /10 21 =

( )

+⋅⋅=

0701

3.605.0't

kCtC T

( ) 21712593.081

77 ≤≤−⋅⋅⋅= CccwC



−=TTT

TkT50005000exp'

00

114




Drying Shrinkage Model. Drying shrinkage can be approximate by square-root

hyperbolic law in time, as shown in Equation C.17

0

00 ),(

tttt

kttsh

hshsh −+−

⋅⋅= ∞ τεε (C.17)

where

εsh∞: ultimate shrinkage stain µε

≤≤=−≤−

=00.198.0int

00.12.098.01 3

hforerpolationlinearhforhforh

kh ; humidity-dependent factor




( )01

12

8.50150

600tC

CS

Vk refs

sh ⋅


=




sk ; shape factor



daymmC ref /10 21 =

115

( )

+⋅⋅=

0701

3.605.0't

kCtC T

( ) 21712593.081

77 ≤≤−⋅⋅⋅= CccwC

−=TTT

TkT50005000exp'

00



13908801210

+−=∞

z

sε ; 012'1

5.025.13

12

≥−

⋅

+⋅

⋅+⋅= cf

cw

cs

sg

caz







C.1.5. Bažant and Baweja’s - B3 Method

B3 model was proposed by Bažant and Baweja (1995) as a new improvement and an

update of previous models such as BP (Bažant and Panula, 1978) and BP-KX (Bažant,

Panula, Kim, Koo, and Xi, 1992). According the Bažant and Baweja (1995), B3 model is

more simple, better theoretically supported and more exact than the previous ones. The main

difference with the BP model is that the B3 model only takes into account basic and drying

creep portions.

116

Creep Model. The average compliance function incorporating instantaneous

deformation, basic and drying creep, is expressed in Equation C.18:

),',()',()',( 01 od tttCttCqttJ ++= (C.18)

where

0

6

1106.0

Eq ×

= instantaneous strain due to unit stress (1/ksi)





E0: asymptotic modulus elastic modulus (ksi) (age independent)

Basic Creep Model. Basic creep is given by Equation C.19, as follows:

( ) [ ]

+−+⋅+⋅=

'ln)'(1ln',)',( 4320 t

tqttqttQqttC n (C.19)

where


9.02 '1.451 −⋅= cfcq ; ageing viscoelastic compliance

fc’: compressive strength of concrete cylinders at 28 days (psi)

( ) ( ) ( )( )

( ) ( ) ( ) ( ) ( )[ ]( ) ( ) ( )[ ]( ) ( ) 8'7.1'

'1ln'','21.1'086.0'

;','

1'',12.0

19

49

2'

1'

+⋅=−+⋅=

⋅+⋅=

+⋅= −

−−

ttrtttttZ

tttQ

ttZtQ

tQttQ nmftrtr

ff

m = 0.5; n = 0.1



117

2

4

3 29.0 qcwq ⋅

⋅= ; non-ageing viscoelastic compliance

7.0

4 14.0−

⋅=

caq ; flow compliance




Drying Creep Model. Additional creep due to drying is given by Equation C.20

( ){ } ( ){ }[ ] 21

050 '8exp8exp),',( tHtHqtttCd ⋅−−⋅−⋅= (C.20)

where

6.05 '

757000 −∞⋅= sh

cfq ε


( ) ( )sh

tthtH

τ0tanh11

−⋅−−=





t0’: max(t′,t0) (days)

τsh: size factor as shown in Equation C.21

Drying Shrinkage Model. Drying shrinkage expression is given by Equation C.21, as

follows:

118

shhshsh

ttktt

τεε 0

0 tanh),(−

⋅⋅−= ∞ (C.21)

where

εsh: shrinkage strain

( )[ ]( )

( )2

1

0

0

21

28.01.221

85.04

60785.04607

270'02565.0

+⋅+

+

⋅+⋅+⋅⋅⋅⋅−= −∞

sh

sh

csh

tt

fw

ττ

ααε

=

cementIIItypeforcementIItypeforcementItypefor

,10.1,85.0,00.1

1α ; cement type factor

−=

−=

specimenssealedforspecimenscuredhorwaterfor

specimenscuredsteamfor

,20.100.1,00.1

,75.0

2α ; curing factor



≤≤=−≤−

=00.198.0forioninterpolatlinear

00.12.098.01 3

hhforhforh





( )225.0008.00 2'8.190 S

Vkft scsh ⋅⋅⋅⋅⋅= −−τ ; size-dependent factor

119

=




sk ; shape factor



C.1.6. Gardner and Lockman’s - GL Method

Gardner and Lockman (2001) proposed a more compact model for creep coefficient

depending only on relative humidity and member geometry. Equations C.22 and C.23

present GL model equations for creep and shrinkage.

Creep Model:

( ) ( ) 28

21

22

21

21

3.0

3.0

1

4.2515.0)'(

)'(086.115.2

7)'()'(7

14)'()'(2)',(

c

ocr

ES

Vtt

tth

tttt

tttttttc

⋅

⋅⋅+−

−⋅⋅−⋅+

+

+−

−⋅

+

+−−⋅

=

(C.22)

where

ccr: specific creep at age t loaded at t′ (µε/ksi)






120


Ec28: 28-day elastic modulus (ksi)

Drying Shrinkage Model:

( ) ( )2

1

2

0

040

4.2515.0)(

)(18.11),(

⋅⋅+−

−⋅⋅−⋅=

SVtt

tthtt shush εε (C.23)

where


62

1

10'

35.41000 −⋅

⋅⋅=

cshu f

Kε ; ultimate shrinkage strain

=

cement III Typefor 15.1cement II Typefor 70.0

cement I Typefor 00.1K ; cement factor







C.1.7. Sakata’s - SAK 93 Method

Sakata (1993) developed an exponential model for specific creep and drying

shrinkage. The models presented in Equations C.24 through C.26 are based on relative

humidity, member geometry, and water and cement content.

121

Creep Model. SAK method models specific creep based on two portions: basic creep

and drying creep. Equation C.24 proposes that both portions progress following an

exponential curve.

( ) ( ){ }( )6.0'09.0exp1'')',( tttt dcbccr −⋅−−⋅+= εεε (C.24)

where

εcr: specific creep at age “t” loaded at t′ (µε/ksi)



ε’bc: basic creep portion, parameter depending on water and cement content, water-to-cement

ratio, and age of loading

ε’dc: drying creep portion, parameter depending on water and cement content, water-to-

cement ratio, member volume-to-surface ratio, and relative humidity

Basic Creep Model. Basic creep is given by Equation C.25, as follows:

( ) ( ) [ ]( ) 67.04.22 'ln641.3' −⋅⋅+⋅= tcwwcbcε (C.25)

where

ε’bc: basic specific creep portion (µε/ksi)




Drying Creep Model. Drying creep is given by Equation C.26

( ) ( ) ( )[ ]( ) ( ) ( ) 3.00

36.02.22.44.1 14.25ln015.0' −−⋅−⋅⋅⋅⋅+⋅= thS

Vc

wwcdcε (C.26)

122

where

ε’dc: drying specific creep portion (µε/ksi)







Drying Shrinkage Model

( ){ }( ) 556.000 10108.0exp1),( −

∞ ×−⋅−−⋅= tttt shsh εε (C.27)

where




{ }( ) [ ] ( )[ ]( ) [ ]0

2ln444.25ln50593.0ln380exp1780600 tS

Vwhsh ⋅+⋅⋅−⋅⋅+−⋅+−=∞ε ; ultimate

shrinkage strain





123

C.2 Models for High Strength Concrete

C.2.1 CEB-FIP Method as modified by Yue and Taerwe (1993)

Han (1996) reported the changes suggested by Yue and Taerwe (1993) to CEB-FIP

creep equations in order to predict creep of high strength concrete. βH and ø0 from Equation

C.8 can be modified as shown in Equations C.28 and C.29

( )[ ] 15002508.50012.01'

85.18 18 ≤+

⋅⋅⋅+⋅= u

Ahf

c

cHβ (C.28)

where

βH: constant depending on member size and relative humidity





( )2.0

310 '1.0

1

145.1

'6.2

367.0

11tf

uA

h

cc+

⋅

−

⋅

⋅

−+=φ (C.29)

where

φ0: ; notional creep coefficient






124

C.2.2. Bažant and Panula’s - BP Method

Bažant and Panula (1984) proposed some modifications to drying creep portion of the

BP model to take into account high strength concrete. They found that the rest of the

expressions were still valid for HSC. Equation C.30 presents the new version of Equation

C.15 where the new parameters bd and ad are introduced.

ncshd

shh

mdd

d

ttb

ktE

tttC⋅−

∞−

−⋅

+⋅⋅⋅⋅='

1'''

),',( 2

00

τε

φ (C.30)

where

Cd: drying creep portion [specific creep - (µε)/ksi]




dshd

d att

φτ

φ ⋅

⋅−

+=− 2

1

0'1'

≥

≤=

psiffor

psiffora

c

c

d

10000'1

6000'10; linear interpolation between 6000 and 10000 psi

( )01

12

8.50150

600tC

CS

Vk refs

sh ⋅


=




sk ; shape factor


125


daymmC ref /10 21 =

( )

+⋅⋅=

0701

3.605.0't

kCtC T

( ) 21712593.081

77 ≤≤−⋅⋅⋅= CccwC

−=TTT

TkT50005000exp'

00



85.0'560000008.0

07.011027.0008.0 5.1

3.13.04.1

−

⋅

⋅

⋅⋅=

≤

>⋅+

⋅+

=∞

−

scd

cw

sgf

asr

rfor

rforr

εφ






f’c: compressive strength (ksi)

13908801210

+−=∞

z

sε ; 012'1

5.025.13

12

≥−

⋅

+⋅

⋅+⋅= cf

cw

cs

sg

caz


126

( )2'128.0cf

m += ; material parameter

5.15.10' hhkh −= humidity dependent parameter


≥

≤=

psiffor

psifforb

c

c

d

10000'100

6000'10; linear interpolation between 6000 and 10000 psi

ncd ⋅−= 5.78.2

( )( ) ( ) 4'1.01.2

412.0

45130

07.012.0

1

2.23

15.1

6

6

−⋅

⋅

⋅⋅+⋅=

≤

>+⋅

+

= aga

cwf

cs

ca

xxfor

xforx

x

n c

C.2.3. Sakata’s - SAK 01 Method

Sakata et al. (2001) derived new Equations for predicting creep and drying shrinkage

for a wide range of concrete strength. Equations C.31 and C.32 show the new specific creep

and drying shrinkage expressions:

( )( )( ) [ ] 8966.61'ln

''8966.6123501373.2)',( ×

+−⋅

⋅+⋅+−⋅⋅

= tttf

hwttc

crε (C.31)

where

εcr: specific creep at age “t” loaded at t′ (µε/ksi)





127

fc’(t′): compressive strength at the age of t′(psi)


( ) ( )( )0

00,

tttt

tt shsh −+

−⋅= ∞

βε

ε (C.32)

where




( )01

1

'5.72exp1501

5933.01t

f

wh

c

sh ⋅+⋅

−+

⋅⋅−=∞ ηα

ε ; ultimate shrinkage strain

=cementhardeningslowfor8cementportlandnormalfor10

α ; cement factor




( )( ) 4101483.0'0483.0exp15 −×⋅+⋅⋅= wfcη

07.0100

8.19

tS

Vw

⋅+

⋅=β



128

C.2.4. AFREM Method

Le Roy et al. (1996) described the AFREM model for modeling long-term

deformations of high strength concrete. AFREM method main expressions for modeling

creep and drying shrinkage are presented in Equations C.33 through C.36.

Creep Model. Equation C.33 presents AFREM creep prediction Equation which is

comprised of basic creep portion and drying creep portion.

( ) ( ))',()',(')',(28

ttttE

ttt dbcr φφσ

ε += (C.33)

where


σ(t′): applied stress at t′ (ksi)

E28: 28-day elastic modulus (ksi)



øb: basic creep coefficient at age “t” loaded at t′

ød: drying creep coefficient at age “t” loaded at t′

Basic Creep Model. Basic creep coefficient can be expressed as shown in Equation

C.34, as follows:

( )'

'', 0 tttttt

bcbb

−+−

⋅=β

φφ (C.34)

where

( )

=

concrete fume-silicanon for 4.1

concrete fume-silicafor ''

762.137.0

0tf c

bφ

129

f’c(t′): compressive strength at the age of t′ (ksi)

( )

( )

⋅⋅

⋅⋅

=

concrete fume-silicanon for '''

1.3exp40.0

concrete fume-silicafor '''

8.2exp37.0

c

c

c

c

bc

ftf

ftf

β

f’c: compressive strength of concrete cylinders at 28 days (ksi)

Drying Creep Model. Drying creep coefficient is given by Equation C.35

( ) ( ) ( )( )0000 ,',,', ttttttt shshdd εεφφ −⋅= (C.35)

where

=concrete fume-silicanon for 3200

concrete fume-silicafor 10000dφ

εsh: drying shrinkage as shown in Equation C.36

Drying Shrinkage Model. Drying creep expression is shown in Equation C.36, as

follows:

( ) { }( )

( )( ) 6

0

0

2

0

0 108.50

10075'3172.0exp72'),( −×−⋅

−+

⋅⋅

⋅−+⋅−⋅⋅= tt

ttuA

hffKtt

cds

ccsh

βε (C.36)

where




( )

≥⋅−

≤=

ksifforf

ksifforfK

cc

c

c

25.8''448.130

25.8'18' ; strength-dependent factor

130



=concrete fume-silicanon for 021.0

concrete fume-silicafor 007.00dsβ



C.2.5. AASHTO-LRFD as modified by Shams and Kahn (2000)

Shams and Kahn (2000), proposed some changes to AASHTO-LRFD creep and

shrinkage expression (see Section C.1.2) in order to better predict long-term strains of HPC.

Creep Model. Shams and Kahn method for estimating creep is presented in Equation

C.37.

( )( ) 6.0

6.0

' ''ttd

ttkkkkkk mtHfvst c −+−

⋅⋅⋅⋅⋅⋅⋅= ∞ σφφ (C.37)

where

øt: creep coefficient at “t” loaded at t′

−∆+

−⋅∆= ∑ 65.13)(273

4000exp

0TtT

tti

ndayuntil


−∆+

−⋅∆= ∑ 65.13)(273

4000exp'

0TtT

tti

loadinguntil



T0: 1 oC

131

73.2=∞φ : ultimate creep coefficient

{ } { }

⋅−⋅+⋅

+

+⋅⋅=

587.2

54.0exp77.180.1

45

36.0exp26 SV

tt

tSV

t

kvs ; size factor



'645.18.4

cf f

kc += ; concrete strength factor


hkH ⋅−= 83.058.1 ; ambient relative humidity factor


+

⋅=57.0'

7.0exp65.0' tkt ; maturity at loading factor

( ){ }

≤Γ

≤Γ≤−Γ⋅=

4.00.1

6.04.04.05.1exp

for

forkσ ; stress-to-strength ratio factor

Γ: stress-to-strength ratio at loading

{ }( ) 73.559.0exp165.01 mkm ⋅−−⋅+= : moist curing period factor

m: moist curing period (days)

'09.0356.0'

ttd

⋅+= : maturity for 50% of ultimate creep coefficient

Drying Shrinkage Model. Equation C.38 shows Shams and Kahn drying shrinkage

expression.

132

( ) ( )

5.0

'',

−+

−⋅⋅⋅⋅= ∞

o

otHvsshosh ttf

ttkkktto

εε (C.38)

where

=∞ concrete cured-moistfor560concrete cured-sfor510

µεµε

εteam

sh ; ultimate shrinkage strain

−∆+

−⋅∆= ∑ 65.13)(273

4000exp

0TtT

tti

ndayuntil


−∆+

−⋅∆= ∑ 65.13)(273

4000exp

0

0

TtT

tti

dryingbeginninguntil

i ; maturity of concrete at the beginning of

drying (days)


T0: 1 oC

( ){ } ( )( )( )

⋅−⋅

−+−

−+⋅⋅

−

=923

94.01064

45

36.0exp26

0

0

0

0

SV

tttt

ttSVtt

kvs ; size factor

≥⋅−<⋅−

=80.029.429.480.043.100.2

hforhhforh

kH ; ambient relative humidity factor


+⋅=

ot t

k45.9

2.4exp67.00

; factor for maturity at the beginning of drying

f: 23 (days)

133

C.3 Models for Lightweight Concrete

Even though there are not models specifically developed for lightweight concrete,

some of the models presented in Section C.1 consider some corrections when lightweight

aggregate are being used.

C.3.1. ACI-209 Method

Creep and shrinkage predicting equation proposed by the ACI-209 (Equation C.1 and

C.3) were based on research done in NWC and SLC, so they are entirely applicable to normal

weight, “sand-lightweight”, and “all-lightweight” concrete.

C.3.2. AASHTO-LRFD Method

Since AASHTO-LRFD method for estimating creep and shrinkage is an updated

version of ACI-209 method (see Section C.1.2), equations C.5 and C.6 are applicable to SLC.

In fact, AASHTO-LRFD creep and shrinkage equations are in the section “normal and

structural lightweight concrete” section of the code.

C.3.3. Gardner and Lockman’s - GL Method

Even though Gardner and Lockman’s (2001) method does to include lightweight

aggregate in its scope, the authors proposed a way to incorporate aggregate stiffness in their

creep and shrinkage prediction equations (Equations C.22 and C.23). Equation C.39 shows

the proposed relationship between concrete elastic modulus and compressive strength.

Equation C.39 is a compromise between ACI-209 and ACI-363 expressions.

'644.150028 cc fE ⋅+= (C.39)

where

134



According the Gardner and Lockman (2001) stiffness corrected compressive strength

and elastic modulus are used in creep and shrinkage equations (Equations C22 and C.23) as

input data. To modify the compressive strength and stiffness, Equations C.40 and C.41 are

used.

2644.1

500'2

28

−

+=

cc

Ecorrectedc

Eff (C.40)

Ecorrectedc

Ecorrectedc fE ⋅+= 644.150028 (C.41)

where

Ecorrectedcf : stiffness corrected compressive strength of concrete at 28 days (ksi)



EcorrectedcE 28 : stiffness corrected 28-day elastic modulus (ksi)

135

Appendix D. Prestress Losses - Background

D.1 Prestress Losses

D.1.1. Introduction to Prestress Losses

The prestressing force in a prestressed concrete member continuously decreases with

time (Zia et al., 1979). The Precast Prestressed Concrete Institute (PCI) Committee on

Prestress Losses, identified the factors influencing prestress losses as friction in post-

tensioning operations, movement of the prestressing steel at the end anchorage, elastic

shortening at transfer, effect due to connection of the prestressed member with other

structural member, and time dependent losses due to steel relaxation, creep and shrinkage of

the concrete (PCI Committee on Prestress Losses, 1975). The same committee pointed out

that the determination of stress losses in prestressed members is an extremely complicated

problem because the effect of one factor is continuously being altered by changes in stress

due to other factors. In describing the loss of prestress, ACI Committee 209 (1997) stated,

“Prestress losses due to steel relaxation and concrete creep and shrinkage are inter-dependent

and also time dependent.”

The contribution of each loss factor to the total losses depends on the following: the

structural design, material properties (concrete and steel), prestressing method (pretensioned

or posttensioned), concrete age at stressing, and the method of prestress computation (PCI,

1998).

136

D.1.2. Prestress Losses in Normal Weight Normal Strength Concrete

Bandyopadhyay and Sengupta (1986) concluded that for normal weight normal

strength concrete (NWNSC) deformations due to creep and shrinkage in concrete are several

times the elastic deformation. Figure D.1 shows a numerical example given by Nawy (2003)

where initial and long-term strains are estimated for a NWNSC subjected to 900 psi

compression stress. Figure D.1 shows how long-term prestress losses (shrinkage and creep)

of prestressed concrete members can be as large as five times the initial elastic strain.

Figure D.1. Example of initial and long-term strains in prestressed concrete

In summary, partial loss of prestress in a prestressed concrete member is affected by

friction (only post-tensioned members), anchorage seating, elastic shortening, shrinkage of

concrete, creep of concrete, and relaxation of prestressing steel. Anchorage setting and

elastic shortening are usually grouped as initial losses, and shrinkage, creep and relaxation

are grouped as long-term time dependent losses. According PCI (1998) total loss of prestress

in typical members will range from about 25,000 to 50,000 psi for NWNSC.

250

500

750

0100200300400500600700800900

1000

Initial elastic strain one-year shrinkagestrain

one-year creep strain

Stra

in (µ

ε)

250

500

750

0100200300400500600700800900

1000

Initial elastic strain one-year shrinkagestrain

one-year creep strain

Stra

in (µ

ε)

137

D.1.3. Prestress Losses in Special Concretes

Prestress losses in special concretes such as SLC, HPC and HPLC follow the same

principles and are affected by the same factors that NWNSC, but they are influenced by the

particular properties of each.

Prestress losses in HPC: As stated in Appendices A and B, HPC usually has higher

modulus of elasticity, a lower creep and a similar or lower shrinkage than a NSC. Based on

that, it is expected to obtain fewer losses due to elastic shortening, fewer losses due to creep

losses, similar or fewer losses due to shrinkage, and more losses due to steel relaxation. The

expected increase in steel relaxation losses is a consequence of a higher stress level in the

prestressing steel due to a decrease on concrete losses. Total losses are expected to be less

than NSC. According Roller et al. (1995), measured long-term prestress losses in HPC

prestressed girder were approximately 50% less than the expected value.

Prestress losses in SLC: As seen in Appendices A and B, properties of SLC may vary

in a wide range, so the prestress losses may also widely vary. In general SLC presents a

lower modulus of elasticity than a NWC of the same strength. It also has a higher ultimate

creep and ultimate shrinkage than the NWC counterparts. Therefore, elastic shortening, and

final creep and shrinkage losses are expected to be greater in SLC. Steel relaxation losses,

however, are going to decrease due to the increase in the others. ACI-213 (1999) concluded

that combined loss of prestress in a SLC member is about 110 to 115% of the total losses for

NWC when both are cured normally. If they are steam-cured, prestress losses in SLC are

expected to be 124% of the losses in NWC. PCI (1998) gave a range for total prestress

losses of “sand-lightweight” members of 30,000 to 55,000 psi which is about 15% higher

than the range given for NWC.

138

Prestress losses in HPLC: To the authors’ knowledge, there is no previous research

on prestress losses of HPLC; however, from the material properties some conclusions can be

drawn. Elastic shortening losses are expected to be similar or less than NWNSC but more

than HPC. Creep and shrinkage losses would be similar to the one of HPC. Steel relaxation

losses would tend to be higher than losses in NWNSC because the previous losses are lower.

D.2 Codes

Prestress losses methods can be classified into two groups: (1) final prestress losses

estimate and (2) losses estimated at any time. There are three methods for estimating final

prestress losses: Precast Prestressed Concrete Institute Method (PCI, 1999), refined estimate

and approximate lump sum estimate, both proposed by the American Association of State

Highway and Transportation Officials Method (AASHTO-LRFD, 1998). For losses at any

time, American Concrete Institute Committee 209 (ACI-209, 1997) proposed a prestress loss

estimate method based on creep and shrinkage estimates (Equations C.1 and C.3).

Even though anchorage seating losses and friction losses can be an important portion

of the total prestress losses, they are not considered here because such losses are related with

the manufacturing process rather than material properties.

D.2.1. PCI Method

The PCI method gives an estimate of the final prestress losses of a prestressed

concrete member based on four equations for each type of losses. They are applicable to

NWC and SLC. Total losses are given by Equation D.1

RESHCRESLT +++=.. (D.1)

where

139

T.L.: total prestress losses (ksi)

ES: elastic shortening loss (ksi)

CR: creep of concrete loss (ksi)

SH: shrinkage of concrete loss (ksi)

RE: steel relaxation loss (ksi)

Elastic Shortening. Caused by concrete shortening around tendons as the prestressing

force is transferred, elastic shortening can be estimated by Equation D.2.

ci

cirpses

EfEK

ES⋅⋅

= (D.2)

where


Kes: elastic shortening constant, 1.0 for pretensioned members

Eps: elastic modulus of prestressing steel (ksi)

Eci: elastic modulus of concrete at transfer (ksi)

g

g

g

i

g

icircir I

eMI

ePAP

Kf⋅

−

⋅+⋅=

2

: net compressive stress in the section at the center of

gravity of the prestressing force (cgs) immediately after

transfer (ksi)

where

Kcir: a constant, 0.9 for pretensioned members

Pi : initial prestressing force after anchorage seating loss (kip)

e: eccentricity of the cgs. with respect to the center of gravity of the section at the cross

section considered. Eccentricity is negative if below concrete section neutral axis (in)

140

Ag: gross area of the section (in2)

Ig: gross moment of inertia (in4)

Mg: the dead load gravity moment applied to the section at time of prestressing (kip-in)

Creep of concrete. The final loss of prestress due to creep is given by Equation D.3.

( )cdscirc

pscr ff

EE

KCR −⋅

⋅= (D.3)

where

CR: creep loss (ksi)

= SLCfor 6.1

NWCfor 0.2crK : creep constant

Ec: elastic modulus at design age (ksi)

Eps: elastic modulus of prestressing steel (ksi)

g

sdcds I

eMf = : stress in concrete at the cgs due to all superimposed dead loads (ksi)

Msd: Moment due to all superimposed permanent dead loads and sustained loads after

prestressing (kip-inches)


Shrinkage of concrete. The final prestress loss due to drying shrinkage is given by

member geometry and relative humidity at which member is exposed. Equation D.4 shows

PCI expression to estimate shrinkage loss.

141

( ) ( )RHSVEKSH pssh −⋅

−⋅⋅⋅×= − 10006.01102.8 6 (D.4)

where,

SH: shrinkage loss (ksi)

Ksh: 1.0 for pretensioned members



RH: relative humidity, %

Steel relaxation. defined as the loss of stress over a certain period of time, steel

relaxation depends on the type of prestressing steel (stress-relieved or lo relaxation) and the

other prestress losses. Equation D.5 gives the loss of prestress due to steel relaxation.

( ) ( )[ ] CRHESCRSHJKRE re ⋅−⋅++⋅−= 100 (D.5)

where


Kre: maximum relaxation stress, 5,000 psi for grade 270, low relaxation strands

J: parameter, 0.04 for grade 270, low relaxation strands,




C: parameter depending on the initial prestress to ultimate strand strength and strand type,

0.70 this case.

142

D.2.2. AASHTO-LRFD Refined Estimates of Time-Dependent Losses

According AASHTO-LRFD (1998), the total loss of prestress, not including

anchorage seating loss, is the sum of the elastic shortening, creep, shrinkage, and steel

relaxation losses, given by Equation D.6. Equation D.6 applies to prestressed members with

spans no greater than 250 ft., NWC and compressive strength above 3,500 psi.

21 pRpRpSHpCRpESpT ffffff ∆+∆+∆+∆+∆=∆ (D.6)

where

∆fpT: total prestress losses (ksi)

∆fpES: elastic shortening loss (ksi)

∆fpCR: creep of concrete loss (ksi)

∆fpSR: shrinkage of concrete loss (ksi)

∆fpR1: initial steel relaxation loss (ksi)

∆fpR2: after transfer steel relaxation loss (ksi)

Elastic Shortening. According to AASHTO-LRFD, the Elastic shortening loss is

given by Equation D.7.

cgpci

ppES f

EE

f ⋅=∆ (D.7)

where,


g

g

g

i

g

icgp I

eMI

ePAPf

⋅−

⋅+=

2

fcgp: sum of the stresses in the concrete at the cgs due to

prestress force at transfer and the maximum dead load moment (ksi)

143







Ep: elastic modulus of prestressing steel (ksi)

Eci: elastic modulus of concrete at transfer (ksi)

Creep of concrete. The final loss of prestress due to creep is given by Equation D.8.

cdpcgppCR fff ∆⋅−⋅=∆ 712 (D.8)

where,


g

g

g

i

g

icgp I

eMI

ePAPf

⋅−

⋅+=

2

fcgp: sum of the stresses in the concrete at the cgs due to

prestress force at transfer and the maximum dead load moment (ksi)







144

g

sdcds I

eMf =∆ : change in concrete stress at the center of gravity of prestressing strands due to

permanent loads, with the exception of the loads at the time the prestressing force is

applied. (ksi)

Shrinkage of concrete. The prestress loss due to drying shrinkage is given in

Equation D.9.

Hf pSR ⋅−=∆ 15.00.17 (D.9)

where,


H: relative humidity, %

Steel relaxation. Steel relaxation loss is considered to be comprised of two

components: relaxation at transfer and relaxation over the rest of the life of the girder. For

low relaxation strands, the two components are given by Equations D.10 and D.11.

pjpy

pjpR f

fftf ⋅

−⋅

⋅=∆ 55.0

40)24log(

1 (D.10)

where,

∆fpR1: initial steel relaxation loss (ksi)

t: time since prestressing (days)

fpj: initial prestress (ksi)

fpy: yield strength of the prestressing steel (ksi)

( )pCRpSRpESpR ffff ∆+∆⋅−∆⋅−=∆ 2.04.0202 (D.11)

145

where

∆fpR2: after transfer steel relaxation loss (ksi)




D.2.3. AASHTO-LRFD Lump Sum Estimate of Time-Dependent Losses

Lump sum method is based on data taken from a large number of prestressed

structures, and it gives an estimate of final prestress losses due to concrete creep and

shrinkage and steel relaxation. According AASHTO-LRFD (1998), Lump sum method is

applicable to members that are made from NWC, so it is not suitable for predicting losses in

SLC. Lump sum method proposes eleven equations depending on the type of beam section

and prestressing element (strands, bars). For I-shaped girders prestressed with 235, 250, or

270 ksi wires or strands, the time-dependent losses can be obtained from Equation D.12.

PPRf

f cpTD ⋅+

−

⋅−⋅=∆ 0.60.6

0.6'15.00.10.33 (D.12)

where

∆fpTD: time-dependent losses (ksi)


yspyps

pyps

fAfAfA

PPR⋅+⋅

⋅= : partial prestressing ratio

Aps: area of prestressing steel (in2)

fpy: yield stress of prestressing steel (ksi)

As: area of non-prestressing steel (in2)

146

fy: yield stress of non-prestressing steel (ksi)

D.2.4. ACI-209 Method

Based on creep and shrinkage equations presented in section C.1.1, ACI through its

committee 209, proposed a general expression for estimating loss of prestress in prestressed

concrete beams as shown in Equation D.13. As explained in Section C.3.1, ACI-209 creep

and shrinkage equations are applicable to SLC.

( )[ ]100×

+++=

si

tsrt f

fSHCRESλ (D.13)

where

λt: prestress losses in percent of the initial tensioning stress




(fsr)t: steel relaxation loss (ksi)

fsi: initial tensioning stress (ksi)

Elastic Shortening. Elastic shortening can be estimate by Equation D.14

cfnES ⋅= (D.14)

where


n: modular ratio at the time of prestressing

147

g

g

g

i

g

ic I

eMI

ePAP

f⋅

+⋅

+=2

: net compressive stress in the section at the center of gravity of

the prestressing force (cgs) immediately after transfer (ksi)







Creep of concrete. Equation D.15 shows the expression used for creep losses

estimate.

⋅

−⋅⋅=02

1F

FESCR t

tφ (D.15)

where



φt: creep coefficient as defined by ACI-209 (Equation C.1)

0FFt : Loss of prestress ratio given in Table D.1

148

Table D.1. Loss of prestress ratios for different concretes and time under loading conditions

Type of concrete Normal weight

concrete

Sand-lightweight

concrete

All-lightweight

concrete For three weeks to one month between prestressing and sustained load application

0.10 0.12 0.14

For two to three months between prestressing and sustained load application

0.14 0.16 0.18

Ultimate 0.18 0.21 0.23

Shrinkage of concrete. Prestress losses due to drying shrinkage are estimated by

Equation D.16. The denominator KSE represents the stiffening effect of the steel and the

effect of concrete creep. Without KSE the losses due to drying shrinkage are somewhat

overestimated.

( )SE

pstsh K

ESH ⋅= ε (D.16)

where


(εsh)t: shrinkage strain as defined by ACI-209 (Equation C.3)

Eps: Elastic modulus of prestressing steel

sSE nK ρξ⋅+= 1 =1.25 (design simplification)

n: modular ratio at the time of prestressing

ρ: non-prestressing reinforcement ratio

ξs: cross section shape coefficient

Steel relaxation. Steel relaxation losses depend on the steel of the strands (stress-

relieved or low relaxation), and time. For low relaxation strands, the relaxation losses are

given by Equation D.17.

149

[ ]tfRE pj 10log005.0 ⋅⋅= (D.17)

where


fpj: initial prestress (ksi)

t: time under load in hours (for t>105, pjfRE ⋅= 025.0 )

150


151

Appendix E. Concrete Properties – Experimental Program

E.1 Introduction

The main objective of Task 3 was to characterize the HPLC mixes obtained from

Task 2. This characterization included: slump, air content, and unit weight for the plastic

state, and compressive strength, elastic modulus, rupture modulus, chloride permeability,

creep and non-stress dependent strains such as shrinkage and coefficient of thermal

expansion.

E.2 Mix Design

Two HPLC mixes were suggested: (1) 8,000-psi compressive strength (8L made in

the laboratory and 8F made in the field) and (2) 10,000-psi compressive strength (10L made

in the laboratory and 10F made in the field). The actual mix proportions used on each case

are presented in Table E.1.

Table E.1. Actual mixes used in the laboratory specimens (8L and 10L) and used to cast the girders tested on Task 5 (8F and 10F)

Component Type 8L 8F 10L 10F cement, Type III (lb/yd3) / [kg/m3] 783 [464] 780 [463] 740 [439] 737 [437] Fly ash, class F (lb/yd3) / [kg/m3] 142 [84] 141 [84] 150 [89] 149 [88] Silica Fume, (lb/yd3) / [kg/m3] 19 [11] 19 [11] 100 [59] 100 [59]

Natural sand (lb/yd3) / [kg/m3] 1022 [606]

1018 [604]

1030 [611]

1025 [608]

1/2" Lightweight aggregate (lb/yd3) / [kg/m3] 947 [562] 944 [560] 955 [566] 956 [567]

Water (lb/yd3) / [kg/m3]: 268 [159] 284 [169] 227 [135] 260 [154] AEA, Daravair 1000 (oz/yd3) / [l/m3] 7.8 [0.3] 7.8 [0.3] 7.4 [0.3] 5.5 [0.2]

Water reducer, WRDA 35 (oz/yd3) / [l/m3] 47 [1.8] 46.8 [1.8] 44.4 [1.7] 44.2 [1.7]

HRWR, Adva 100 (oz/yd3) / [l/m3] 47.5 [1.8] 53.4 [2.1] 102 [3.9] 95.8 [3.7]

152

E.3 Test Procedures

All laboratory concrete specimens were taken from mixes made according to standard

procedures at the Georgia Tech Structural Engineering Laboratory. All field concrete

specimens were taken from actual field batches used in the girders at Tindall Corporation

precast plant at Jonesboro, GA. Testing of all specimens was done at the Georgia Tech

Structural Engineering Laboratory. All specimens were cured and removed from their forms

as required. The following tests were performed:

1. Compressive Strength. Compressive strength was determined by testing 4” x 8”

cylinders according to ASTM C 39.

2. Modulus of Elasticity. The chord modulus of elasticity was tested using 6” x 12”

cylinders loaded in compression according to ASTM C 469. Figure E.1 shows elastic

modulus test.

3. Modulus of Rupture. Modulus of rupture was determined by testing 4” x 4” x 14”

beams according to ASTM C 78. Figure E.2 shows modulus of rupture test.

4. Chloride Permeability. Chloride permeability was determined by testing 4” x 2”

cylinders according ASTM C 1202. Figure E.3 shows the test set up.

5. Creep, Drying Shrinkage and Coefficient of Thermal Expansion. The procedures

for testing creep, drying shrinkage and coefficient of thermal expansion are given in

sections E.4, E.5 and E.6, respectively.

153

Figure E.1. Elastic modulus test

Figure E.2. Rupture modulus test

Figure E.3. Chloride permeability test set up.

154

E.4 Creep Test Procedures

Creep was determined by testing 4” x 15” cylinders according the ASTM C 512

guidelines. However there were four differences with respect to the ASTM procedure.

The first difference is that the diameter of the cylinders was smaller than the

recommended in ASTM because bearing capacity of the creep frames was not enough for

applying the required stress levels to 6” x 12” cylinders. The other three deviations were the

age of loading (24 hours instead of 2 days or greater), the curing regime, and the stress-to-

strength ratio (up to 60% instead of 40%). The later changes were adopted in order to match

the actual conditions of the HPC bridge prestressed girders which were loaded at 60% of the

initial strength and at very early ages.

Figure E.4 shows a schematic and working principle of the creep frames used in the

experimental program. Figure E.5 shows creep specimens during the loading process and

under load.

155

Figure E.4. Creep frames components and working principle.

Figure E.5. Creep specimens during loading process and under load in creep frames

156

The 4” x 15” cylinders were instrumented with four sets of brass inserts located

diametrically opposite on the surface of the specimen. Each set was a 10”-long gage line for

measuring deformation with a detachable mechanical gage (DEMEC gage). Brass inserts

were bolted to the wall of the metal cylindrical forms (Figure E.6), and after initial set of the

concrete (4 to 6 hours); the screws holding them were removed allowing specimens to

expand freely during curing. The ends of the molds were 1/2”-thick and 4” diameter metal

plates which remained attached to the specimens permanently after striping the molds. The

end plates also had 1/4-inch deep center holes in order to assure a concentric loading by

pinning the specimens to the creep frames. Figure E.6 shows one of the molds used for

preparing creep specimens.

Figure E.6. Steel mold used in casting 4” X 15” cylinders

The specimens were removed from the molds 30 minutes before loading. After that

they were placed in an environment controlled room at 50 ± 3% of relative humidity and 70

± 3oF and kept there during the time of testing.

157

E.5 Shrinkage Test Procedures

Shrinkage specimens were identical to the creep specimens described in section E.4.

They were made following the same procedures that creep specimens, but they remained

unloaded for the time of testing. Figure E.7 shows some shrinkage specimens placed over

roller to allow free movement. Figure E.7 also shows four brass inserts labeled as “A” and

“B” in the specimens where DEMEC gage reader is inserted.

Figure E.7. Shrinkage and coefficient of thermal expansion specimens

As recommended in ASTM C512, shrinkage was measured at the same intervals that

creep. Creep was finally obtained by subtracting elastic strain and shrinkage from total strain

measured on creep specimens.

E.6 Coefficient of Thermal Expansion Test Procedures

Coefficient of thermal expansion was determined by testing 4” x 15” cylinders and

following the guidelines of the Army Corps of Engineers Specification CRD-C39.

Specimens were heated up to 140 oF and then cooled down to 40 oF. The difference between

158

the DEMEC gage readings at 140 and 40 oF is the thermal expansion of concrete for a

gradient of 100 oF. Figure E.8 shows the specimen and measurement procedure.

Figure E.8. DEMEC gage reader for creep, shrinkage and coefficient of thermal expansion.

159

Appendix F. Experimental Results and Analysis

8,000-psi and 10,000-psi compressive strength mixes were made in both laboratory

and field. The laboratory mixes were meant to characterize material properties while the

field mixes were made for casting AASHTO Type II girders. This section presents the

experimental properties measured on laboratory and field mixes.

F.1 Plastic Properties

Slump, unit weight, and air content (ASTM C173: volumetric method) were

measured in laboratory and field batches. Table F.1 presents the average results of those

tests.

Table F.1. Fresh concrete properties of HPLC mixes

8,000-psi HPLC 10,000-psi HPLC 8L 8F 10L 10F

Slump, in 5.0 8.0 4.0 4.5 Air Content, % 4.0 4.5 3.5 3.3

Plastic unit weight, lb/ft3 120 118 122 119 Temperature, oF 90 85 90 85

From the workability results shown above, 8,000-psi HPLC slump might be classified

as 6.5 ± 1.5 in. 10,000-psi mix had a slump 4.0 ± 0. 50 in. The air content, on the other

hand, averaged 4.25% for 8,000-psi mix and 3.8% for 10,000-psi mix.

F.2 Unit Weight

As shown in Table F.1, plastic unit weight varied from 114 to 122 lb/ft3 with most of

the values close to 120 lb/ft3. The 8,000-psi mix averaged a unit weight of 117 lb/ft3 while

the 10,000-psi HPLC an average unit weight of 119 lb/ft3. These values represent 78 and

79% of the weight of an HPC.

160

ACI-213 (1999) proposed the “air-dry” condition as a standard for measuring

hardened lightweight concrete unit weight. “Air-dry” unit weight was measured on two sets

of samples that had 8F and 10F 4”x8” cylinders cured according ASTM and accelerated

curing. The results obtained for hardened “air-dry” condition were compared with plastic

and hardened oven-dry conditions. Plastic unit weight was measured in fresh state before

casting, and hardened oven-dry condition was reached drying hardened samples in an oven at

230oF until constant weight.

An analysis of variance (ANOVA) determined that the difference between curing

conditions (accelerated vs. ASTM) was less than the variation within the same curing

method. Type of curing was not a statistically significant factor in determining unit weight

of the HPLC mixes. Therefore, the average between the cure methods can be used for each

mix. From ANOVA, the authors concluded the moisture content was statistically significant

in the HPLC unit weight. Air-dry and oven-dry unit weights were 0.45 and 1.2 lb/ft3 less

than plastic unit weight regardless the type of HPLC. Those differences were lower than the

variability obtained for plastic unit weight (see Table F.1). Figure F.1 presents measured

plastic unit weight and estimated9 air-dry and oven-dry unit weight unit weight for each mix.

9 Estimate made based on actual results for those properties

161

Figure F.1. Unit weight of HPLC under different moisture conditions.

F.3 Compressive Strength

Specimens used for testing mechanical properties were cured in two different ways:

ASTM C 39 (fog room and 73oF) and accelerated curing that simulates the condition within a

precast prestressed member. Compressive strength for laboratory mixes was measured in 4”

x 8” cylinders at 16, 20 and 24 hours, and then at, 7, 28, and 56 days. For field mixes

strength was measured at 1, 7, 28, 56, and more than 100 days after casting. Table F.2

presents the average strength values obtained for each curing method and mix type. Figure

F.2 to F.5 show individual and average strength of three specimens tested at each age and

curing procedure. They also show the strength limits for FHWA HPC Grade 2 and 3 concrete

(Goodspeed et al, 1996).

117 119

150

75

85

95

105

115

125

135

145

155

8F 10F HPC

Uni

t Wei

ght (

lb/ft

3 )


117 119

150

75

85

95

105

115

125

135

145

155

8F 10F HPC

Uni

t Wei

ght (

lb/ft

3 )


162

Table F.2. Compressive strength of HPLC mixes (psi)

8L 8F 10L 10F Accelerated Cure 7,324 9,838 16

hours ASTM Accelerated Cure 7,630 9,764 20

hours ASTM Accelerated Cure 7,730 7,465 11,101 8,439 1 day ASTM 6,300 5,735 6,889 7,312 Accelerated Cure 9,300 7,811 10,230 9,152 7

days ASTM 7,100 7,317 7,800 8,072 Accelerated Cure 9,632 8,711 10,588 9,344 28

days ASTM 9,928 8,835 10,604 9,807 Accelerated Cure 10,427 9,084 10,855 10,352 56

days ASTM 10,522 9,346 11,476 10,583 Accelerated Cure 9,418 103

days ASTM 10,229 Accelerated Cure 123

days ASTM Accelerated Cure 10,454 144

days ASTM 10,868

From the data presented in Table F.2 and Figures F.2 and F.3, it can be concluded,

that 8L and 8F mixes meet the specified strength, since the age of 28 days. At 56 days, 8L

mix overcame the 10,000 psi limit with an average strength close to 10,500 psi. At 103 days,

8F mix reached a compressive strength slightly above upper limit of FHWA HPC Grade 3.

Compressive strength of 10,000-psi mixes, laboratory (10L) and field (10F), is

presented in Figures F.4 and F.5. Figures F.4 and F.5 also show the minimum specified

strength at 56 days and the strength limits for FHWA HPC Grade 3 concrete.

163

Figure F.2. Compressive strength vs. time of 8L mix for accelerated and ASTM curing methods.

Figure F.3. Compressive strength vs. time of 8F mix for accelerated and ASTM curing methods.

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

0 7 14 21 28 35 42 49 56Age (days)

Com

pres

sive

Stre

ngth

(psi)

8L Accelerated Curing8L Average Accelerated Curing

8L ASTM Curing

8L Average ASTM Curing

Limit FHWA HPC Grade 2

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

0 7 14 21 28 35 42 49 56Age (days)

Com

pres

sive

Stre

ngth

(psi)

8L Accelerated Curing8L Average Accelerated Curing

8L ASTM Curing

8L Average ASTM Curing

Limit FHWA HPC Grade 2

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

0 7 14 21 28 35 42 49 56 63 70 77 84 91 98Age (days)

Com

pres

sive

Stre

ngth

(psi)

8F Accelerated Curing8F Average Accelerated Curing8F ASTM Curing

8F Average ASTM CuringLimit FHWA HPC Grade 2

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

0 7 14 21 28 35 42 49 56 63 70 77 84 91 98Age (days)

Com

pres

sive

Stre

ngth

(psi)

8F Accelerated Curing8F Average Accelerated Curing8F ASTM Curing

8F Average ASTM CuringLimit FHWA HPC Grade 2

164

Figure F.4. Compressive strength vs. time of 10L mix for accelerated and ASTM curing methods

Figure F.5. Compressive strength vs. time of 10F mixes for accelerated and ASTM curing methods compressive strength vs. time

0100020003000400050006000700080009000

100001100012000130001400015000

0 7 14 21 28 35 42 49 56Age (days)

Com

pres

sive

Stre

ngth

(psi)

10L Accelerated Curing10L Average Accelerated Curing10L ASTM Curing

10L Average ASTM CuringLimit FHWA HPC Grade 3

0100020003000400050006000700080009000

100001100012000130001400015000

0 7 14 21 28 35 42 49 56Age (days)

Com

pres

sive

Stre

ngth

(psi)

10L Accelerated Curing10L Average Accelerated Curing10L ASTM Curing

10L Average ASTM CuringLimit FHWA HPC Grade 3

0100020003000400050006000700080009000

100001100012000130001400015000

0 14 28 42 56 70 84 98 112 126 140 154Age (days)

Com

pres

sive

Stre

ngth

(psi)

10FB Accelerated Curing

10FB Average Accelerated Curing

10FB ASTM Curing

10FB Average ASTM CuringLimit FHWA HPC Grade 3

0100020003000400050006000700080009000

100001100012000130001400015000

0 14 28 42 56 70 84 98 112 126 140 154Age (days)

Com

pres

sive

Stre

ngth

(psi)

10FB Accelerated Curing

10FB Average Accelerated Curing

10FB ASTM Curing

10FB Average ASTM CuringLimit FHWA HPC Grade 3

165

From Figure F.4 it can be stated that 10L mix overcame the lower limit of the FHWA

HPC Grade 3 at 28 days with no single result below it. At 56 days average strength was

close to 11,500 psi. Field mixes, on the other hand reached the specified lower limit at 56

days. One out of 33 specimens had a compressive strength of 9,800 psi which was below

10,000-psi limit.

F.4 Modulus of Elasticity

Modulus of elasticity of concrete was measured on the 8,000 and 10,000-psi mixes

according ASTM C 469. Specimens with accelerated curing were tested at 16 hours, 24

hours, and 56 days while the ones under ASTM curing were tested only at 56 days. Figure

F.6 shows the elastic modulus obtained for all the tests. Even though there were no

requirements in the specifications for the concrete elastic modulus, experimental results were

lower than the ones given by FHWA of 6,000 and 7,500 ksi for Grade 2 and 3, respectively.

These results were expected since lightweight aggregate was used.

Analysis of variance (ANOVA) indicated that none of the considered factors

(strength, age, curing procedure, and lab or field) were statistically significant (at 90% level)

in explaining variability of Poisson’s ratio. Average 56-day Poisson’s ratio was 0.19 with

90% of the results in the range 0.188 and 0.192. Poisson’s ratio results were higher than the

range 0.142 to 0.152 obtained by Lopez and Kahn (2004) for an equivalent HPC of normal

weight.

166

Figure F.6. Elastic modulus of 8,000 and 10,000-psi HPLC mixes

F.5 Modulus of Rupture

Modulus of rupture was measured in 8,000 and 10,000-psi HPLC at the age of 56

days under accelerated and ASTM curing methods. Figure F.7 shows the modulus of rupture

grouped by HPLC mix and type of curing. The result can be compared with the compressive

strength as shown in Table F.3 where each value is an average of three tests.

For the mixes, accelerated-cured specimens presented higher rupture modulus than

ASTM-cured specimens. On average, 8,000-psi mixes had higher rupture modulus than

10,000-psi mixes.

3000

3200

3400

3600

3800

4000

4200

4400

0.1 1 10 100Age (days)

Mod

ulus

of E

last

icity

(ksi

)

8L Accelerated Curing 8L ASTM Curing8F Accelerated Curing 8F ASTM Curing10L Accelerated Curing 10L ASTM Curing10F Accelerated Curing 10F ASTM Curing8L Acc. curing average 8F Acc. curing average10L Acc. curing average 10F Acc. curing average

3000

3200

3400

3600

3800

4000

4200

4400

0.1 1 10 100Age (days)

Mod

ulus

of E

last

icity

(ksi

)

8L Accelerated Curing 8L ASTM Curing8F Accelerated Curing 8F ASTM Curing10L Accelerated Curing 10L ASTM Curing10F Accelerated Curing 10F ASTM Curing8L Acc. curing average 8F Acc. curing average10L Acc. curing average 10F Acc. curing average

167

Even though the ratio between rupture modulus and square root of compressive

strength (fifth column on Table F.3), was always higher than ACI-318 value of 7.5 as shown

in Figure F.7, the compressive strength affected the mentioned ratio. The 8,000-psi HPLC

yielded on average a higher ratio than 10,000-psi HPLC. From Table F.3, it can be said that

56-day modulus of rupture was increased when using accelerated curing method, while the

56-day compressive strength was decreased. As a result, the modulus of rupture-to-

compressive strength ratio was higher in the accelerated cured specimens than in the ASTM

cured specimens.

Figure F.7 also shows the value of 6.375 which is the 7.5 value times the lightweight

factor λ (0.85 for sand-lightweight concrete). It is concluded that the use of '5.7 cr ff ⋅= is

conservative for predicting modulus of rupture of HPLC.

Figure F.7. Rupture modulus of HPLC mixes and design values (ACI-318)

10.0 10.39.5

10.5 10.911.4

8.6 8.9

0

12

3

4

5

6

7

8

9

10

11

12



7.5: NWC


f r/(f c′)

0.5

10.0 10.39.5

10.5 10.911.4

8.6 8.9

0

12

3

4

5

6

7

8

9

10

11

12



7.5: NWC


f r/(f c′)

0.5

168

Table F.3. Rupture modulus of HPLC mixes

HPLC type

Curing Type

56-day average

strength-fc′ (psi)

56-day modulus of rupture - fr

(psi) 'c

r

ff

8L 10522 1030 10.0 8F 9346 992 10.3

10L 11476 918 8.6 10F

ASTM Curing 10664 981 9.5

8L 10427 1077 10.5 8F 9084 1042 10.9

10L 10855 926 8.9 10F

Accelerated Curing 10333 1161 11.4

F.6 Chloride Ion Permeability

Chloride ion permeability was measured at 56 days on 8L, 8F, 10L, and 10F

specimens. The results are presented in Figure F.8 including the limits given in ASTM

C1202 for each category.

Figure F.8. Chloride ion permeability of 8,000 and 10,000-psi HPLC mixes

1

10

100

1000

10000

8L 8F 10L 10F

HPLC Type

Cou

lum

bs

Negligible

Very low

LowModerateHigh

1

10

100

1000

10000

8L 8F 10L 10F

HPLC Type

Cou

lum

bs

Negligible

Very low

LowModerateHigh

169

All HPLC mixes had a chloride ion permeability classified as “very low”. 8,000-psi

HPLC results were in the range 615 - 900 coulombs while 10,000-psi mixes presented results

within the range of 100 - 350 coulombs.

F.7 Coefficient of Thermal Expansion

Coefficient of thermal expansion (CTE) was measured in 8F, 10L, 10F mixes at 56

days and 100% of relative humidity. The results of those tests are presented in Figure F.9.

This test was necessary to correct creep and shrinkage by temperature. Because those tests

began at 24 hours, specimens were not at room temperature, but at the temperature reached

during the hydration process. Therefore, total change in length included creep, shrinkage,

and thermal contraction.

Figure F.9. Coefficient of thermal expansion of 8,000 and 10,000-psi HPLC mixes

8F mix CTE averaged 5.14 µε/oF while 10L and 10FB mixes presented slightly

higher values of 5.32 and 5.17 µε/oF. All HPLC CTE results were higher than the one

reported by Lopez and Kahn (2004) for 10,000-psi HPC (4.9 µε/oF at 100%). All results

were lower than 6.0 µε/oF commonly used for concrete.

5.07 5.20 5.475.17 5.17 4.90

0.0

1.0

2.0

3.0

4.0

5.0

6.0

8F-1 8F-2 10F-1 10F-2 10L-1 HPCHPLC Type

Coe

ffic

ient

of T

herm

al

Expa

nsio

n (µε/

o F)

5.07 5.20 5.475.17 5.17 4.90

0.0

1.0

2.0

3.0

4.0

5.0

6.0

8F-1 8F-2 10F-1 10F-2 10L-1 HPCHPLC Type

Coe

ffic

ient

of T

herm

al

Expa

nsio

n (µε/

o F)

170

F.8 Creep

F.8.1. Creep of 8L and 10L HPLC

Eight creep specimens were cast from each laboratory mix (8L and 10L). Four of

them were loaded at 16 hours after casting (denoted by 16h). Among those, two specimens

were loaded at a stress-to-initial-strength ratio of 40% (denoted by 16h-40%) while the other

two were loaded at 60% (16h-60%). The same procedure was followed with the other four

specimens, but at 24 hours after casting (24h-40% and 24h-60%). Creep specimens were

cured with the accelerated method until 30 minutes before loading when they were stripped

and prepared for loading in the environment controlled room. As explained in Appendix E,

the deformation in creep and shrinkage specimens was measured with a DEMEC reader. The

deformation on each specimen was obtained by averaging four readings; two on each side.

The strain response (elastic strain, creep and shrinkage) of 8L is presented in linear and

logarithmic scale in Figures F.10a and F.10b, respectively.

As shown in Figure F.10a and F.10b, there was no appreciable difference in total

strain between the 16h-40% and 24h-40% specimens. 24h-60% specimens had a slightly

higher strain than 16h-60% specimens, but individual results were overlapped. The average

total strain after 620 days was 3,250 and 4,250 µε for a stress-to-initial strength ratio of 40%

and 60%, respectively. After 200 days the total strain was approximately 92% of the strain at

620 days. After time under load between 2 and 2.33 days, all the samples reached roughly

the 50% of the strain at 620 days. Instantaneous strain is shown by the initial strain in Figure

F.10b, and is in agreement with the strain predicted by using the initial modulus of elasticity

and the applied load. It must be pointed out that this strain includes the initial elastic portion

171

and not only delayed deformations. Figure F.10b, shows a fairly linear progression in

logarithmic scale.

Figure F.10. 8L HPLC Total strain (a) linear scale and (b) logarithmic scale.

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 100 200 300 400 500 600Age (days)

Mic

rost

rain

s (in

/in x

10-6

)

16h-40%16h-60%24h-40%24h-60%

0

500

1000

1500

2000

2500

3000

3500

4000

4500

1 10 100 1000Age (days)

Mic

rost

rain

s (in

/in x

10-6

)

16h-40%16h-60%24h-40%24h-60%

b

a

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 100 200 300 400 500 600Age (days)

Mic

rost

rain

s (in

/in x

10-6

)

16h-40%16h-60%24h-40%24h-60%

0

500

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Figure F.11. 10L HPLC Total strain (a) linear scale and (b) logarithmic scale.

The strain response (elastic strain, creep and shrinkage) of 10L is presented in linear

and logarithmic scale in Figures F.11a and F.11b, respectively. For 10L HPLC, the

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difference between strains when loaded at 16 and 24 hours was more noticeable. This

difference might be due to the fact that the specimens loaded at 16 and 24 hours were made

from different batches. For 16h-40% and 24h-40%, total strain was below and above 3,000

µε after 620 days, respectively. Total strain of 16h-60% and 24h-60% specimens was about

3500 and 4,000 µε after 620 days, respectively. At 200 days under load and drying, all

specimens reached approximately 92% of the strain obtained at 620 days. 50% of the total

strain at 620 days was reached only a few hours after loading.

Creep strain was obtained by subtracting instantaneous, shrinkage and thermal strains

from data in Figures F.10 and F.11. Creep of 16h-40%, 16h-60%, 24h-40%, and 24h-60%

specimens is presented in Figure F.12. Figure F.12a and 12b show the mentioned data for

8L and 10L HPLC, respectively.

Measured creep strain (basic and drying creep) of 8L mix at 620 days was

approximately 1,500 and 2,150 µε for a stress-to-initial strength ratio of 40% and 60%,

respectively regardless the age at the time of loading. At 620 days, the ratio between creep at

60% and 40% was 1.43, which is close to the actual ratio between stresses (1.5). This

demonstrates the approximately linear proportion between stress and creep for stress levels

up to 60% of the initial strength of HPLC. A complete analysis of variance (ANOVA) of

creep results is presented in Appendix G.

Creep of 10L HPLC varied with age at application of load. Measured creep after 620

days of 16h-40% and 16h-60% specimens was quite similar (1,500 and 1,620 µε,

respectively). This result was not expected since the applied stresses were considerably

different. The unexpected data comes probably from 16h-40% specimens which creep was

too high for virtually any age.

174

Figure F.12. Creep of HPLC loaded at 16 and 24 hours (a) 8L HPLC stress-to-strength ratio of 40% and 60% (b)10L HPLC for stress-to-strength ratio of 40% and 60%.

Creep of 24h-40% and 24h-60% specimens after 620 days of loading was 1,250 and

1,820 µε, respectively. As expected, the ratio between those creep strains after 620 days was

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1.46, which was very close to the ratio between the applied stresses (1.5). As mentioned

before, specimens loaded at 24 hours were made from a different batch from the specimens

loaded at 16 hours. In fact, specimens loaded at 24 hours made from the first batch broke

during the loading process which may indicate that the first 10L batch was not correctly

made. Therefore, the creep results from specimens made from the first batch (16h-40% and

16h-60%) should be carefully analyzed.

Figure F.13a and F.13b show specific creep for 8L and 10L HPLC, respectively.

Figure F.13 also shows the specific creep limits given by Goodspeed et al. (1996) for a

FHWA HPC Grade 2 and 3 (Table A.2).

From Figure F.13a, it can be concluded that specific creep measured in 8L specimens

after 180 days was in the range 0.425 to 0.525 µε/psi which was above the higher limit of

0.41 µε/psi given by Goodspeed et al. (1996) for HPC Grade 2. After 620 days under load

specific creep of 8L HPLC ranged from 0.470 to 0.563 µε/psi. After one year under load,

creep of 8L did not significantly change showing a fairly horizontal line over time.

Figure F.13b shows the anomalous creep response of the 16h-40% specimens. When

creep strains of those specimens was divided by the applied stress, the resulting specific

creep after 620 days ranged between 0.490 and 0.512 µε/psi while specific creep of all other

specimens ranged between 0.289 and 0.365 µε/psi. After 180 days under load, specimens

loaded at 24 hours had a specific creep of 0.255 µε/psi, which was within the range given by

Goodspeed et al (1996) for an HPC Grade 3. Specific creep for 16h-60% specimens was

close to the upper boundary given for HPC Grade 3. Finally, 16h-40% specimens presented

a much higher specific creep than the range proposed for HPC Grade 3.

176

Figure F.13. Specific creep of 8L HPLC (a) and 10L HPLC (b) and limits for FHWA HPC Grade 2 and 3.

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Figure F.14. Creep coefficient of 8L HPLC (a) and 10L HPLC (b).

Creep coefficient is the ratio between creep strain and elastic strain under a

determinate load. Creep coefficient is another common way to represent creep of concrete

independently from the magnitude of the applied load. Figure F.14a and F.14b present creep

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coefficient of the 8L and 10L HPLC, respectively. Even though Figure F.14 shows similar

tendencies to the ones analyzed from Figure F.12, creep coefficient might have advantage

over specific creep. When using specific creep, creep data are expressed in terms of applied

stress. When using creep coefficient, creep data are expressed not only in terms of applied

stress, but also in terms of concrete stiffness (which changes with age).

The fact that creep coefficient might be a better parameter for expressing creep can be

seen when compared the coefficient of variation (standard deviation divided by average)

obtained from Figure F.13a and F.14a. The 620-day coefficient of variation from creep

coefficient was 5% while the one obtained from specific creep was 7.5%.

Figure F.14b (creep coefficient of 10L HPLC) shows that creep measured in the 16h-

40% specimens was much higher than the all other 10L HPLC specimens.

Figures F.10a and F.11a clearly show an increasing creep strain at a decreasing creep

rate. Moreover, when the time is presented in logarithmic scale as done in Figures F.10b and

F.11b, the creep strain tends to change linearly with the log of time.

F.8.2. Creep of 8F and 10F HPLC

The same procedure of Section F.8.1 is followed here to present creep data of the

field mixes. Four creep specimens each were cast from each the 8,000-psi and 10,000-psi

field HPLC. Two specimens were loaded at 24 hours using a stress-to-initial strength ratio of

40% (denoted by 24h-40%), The other two specimens were loaded at the same age, but with

60 and 50% of the initial strength for 8,000-psi and 10,000-psi HPLC, respectively (denoted

by 24h-60% and 24h-50%). Creep specimens were cured with the accelerated method for

23.5 hours. At that time they were stripped and loaded at the age of 24 hours in the

environment controlled room. As explained in Section F.8.1, four individual readings were

179

taken from each specimen (two on each side). Later they were averaged in pairs obtaining

two strain measurements per specimen.

Figure F.15. 8F HPLC Total strain (a) linear scale and (b) logarithmic scale.

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The strain response (elastic strain, creep and shrinkage) of 8F is presented in Figure

F.15 in linear time scale (a), and logarithmic time scale (b).

After 680 days, total strain of 8F was 3,550 and 4,200 µε for 24h-40% and 24h-60%

specimens, respectively. Total strain did not change significantly since the measurement

done at 420 days. Total strain developed faster in the 24h-60% specimens than in the 24h-

40% specimens. 24h-60% specimens reached 50% and 90% of the 680-day strain after 1 and

150 days, respectively while 24h-40% specimens reached those levels after 5 and 250 days.

Figure F.16 presents the total strain measured in 10F HPLC for the two testing

conditions 24h-40% and 24h-50%. Average 680-day total strain was 2,800 and 3,100 µε for

the two stress levels. The last three measurements performed at 580, 610, and 680 days did

not change significantly which might indicate that long term strains have reached some sort

of stable condition. The small difference in total strain between the two stress levels might

be due to the actual stress levels of 40 and 50% used for 10F. Figure F.16 includes not only

creep, but also shrinkage and elastic strain; therefore, creep differences seem smaller.

Delayed strain rate was very similar for the 24h-40% and 24h-50% specimens. Both

reached 50% and 90% of the 680-day strain after 5 and 225 days.

In order to analyze creep, elastic strain and shrinkage was subtracted from data

presented in Figures F.15 and F.16, so only deformation due to creep (basic and drying) was

obtained. Figure F.17a presents creep and shrinkage of 8F HPLC, while Figure F.17b does it

for 10F HPLC.

When analyzing creep of 8F HPLC shown in Figure F.17a, it can be seen that 24h-

60% specimens reached a maximum after 325 days. 24h-40% specimens, on the other hand,

had some increase of creep strain after one year.

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Figure F.16. 10F HPLC Total strain (a) linear scale and (b) logarithmic scale.

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Figure F.17. Creep of HPLC loaded at 16 and 24 hours (a) 8F HPLC stress-to-strength ratio of 40% and 60% (b)10F HPLC for stress-to-strength ratio of 40% and 50%.

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Creep of 8F HPLC after 680 days was 1,750 and 1,880 µε for the two stress level

conditions. In general creep of 24h-60% specimens was developed faster than the one in 24h-

40% specimens. 50% and 90% of the 680-day creep was reached 21 and 50 days faster by

24h-60% specimens.

Creep of 10F specimens stored at 50% of relative humidity was approximately 1,100

and 1,225 µε for 24h-40% and 24h-50%, respectively. Creep results at 585, 607, and 680

days under load and drying were very similar indicating a possible steady condition. Creep

rate was very alike for the two stress conditions. After 22 days 24h-40% and 24h-50%

specimens had reached 50% of the 680-day creep, and after 335 days both had reached 90%

of 680-day creep.

Figure F.18 shows the specific creep measured on the two HPLC under study. Figure

F.18 also shows the limits proposed by FHWA for HPC Grade 2 and 3 (Goodspeed et al.,

1996). As shown in Figure F.18a, 8F specific creep was quite different for 24h-40% and

24h-60% specimens. It can be seen that creep of 8F specimens was not proportional to the

applied stress. 24h-40% specimens presented too much creep in comparison to the 24h-60%

specimens. The former specimens had a 680-day specific creep of 0.618 µε/psi compared

with only 0.442 µε/psi measured in the latter. When contrasted with the FHWA limits for an

HPC Grade 2, the same conclusion can be drawn: after 180 days under load, specific creep

for 40% and 60% stress level was 0.468 and 0.377 µε/psi which were higher and lower than

the upper boundary of 0.41 given by FHWA. It should be noticed that creep specimens were

neither cured for 7 days nor loaded at 28 days as recommended by ASTM C 512, so FHWA

limits are not entirely applicable. In fact, if specimens had been cured and loaded according

ASTM C 512, measured creep would have been lower.

184

Figure F.18. Specific creep of 8F HPLC (a) and 10F HPLC (b) and limits for FHWA HPC Grade 2 and 3

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185

Figure F.19. Creep coefficient of 8F HPLC (a) and 10F HPLC (b).

According Figure F.18b, 10F specific creep after 680 days was approximately 0.330

regardless of the stress level. This means that creep observed in 10F specimens was

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proportional to the applied stress. Specific creep after 180 days of loading and drying was on

average 0.218 µε/psi which is very close to the lower boundary proposed by FHWA for HPC

Grade 3 of 0.21 µε/psi.

When creep of 8F specimens is expressed as creep coefficient, as shown in Figure

F.19a, it can be seen that the creep presented by 8F specimens 24h-40% and 24h-60% is still

quite different. After 680 days creep coefficient of those specimens was 2.05 and 1.37,

respectively. This means that the proportionally high creep observed in 24h-40% specimens

cannot be explained based on the stiffness of those specimens. Moreover, the creep

difference observed in Figure F.19a (creep coefficient) was proportionally larger than the one

observed in Figure F.18a (specific creep).

With respect to creep coefficient, 10F HPLC presented similar findings to the ones

obtained using the specific creep (see Figure F.18b). That is, creep coefficient after 680 days

was approximately the same for the two stress levels (0.126). Creep of 10F HPLC is not

only proportional to the stress, but also proportional to the elastic strain obtained under the

same load.

F.9. Shrinkage

As recommended in ASTM C 512, companion shrinkage specimens were kept at

same conditions as the creep specimens, that is, accelerated cured for either 15.5 or 23.5

hours and then placed in the environment controlled room for testing.

Shrinkage specimens were still warm at the beginning of drying period, so the

shortening obtained from the DEMEC reading (“total contraction”) corresponded to

shrinkage and thermal contraction. Total contraction readings were corrected for temperature

in order to obtain the shrinkage portion.

187

Figure F.20. Shrinkage of 8L HPLC (a) and 10L HPLC (b) and limits for FHWA HPC Grade 2 and 3.

Shrin

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188

The same correction was applied to the readings taken after 230 and 260 days after

the beginning of drying because the temperature in the environment controlled room raised

above 80 oF. Although creep specimens were also under change in temperature, creep data

did not need temperature correction because it was obtained by subtracting “total

contraction” from readings from creep specimens. Therefore, the computed creep values

already include temperature strain correction.

F.9.1. Shrinkage of 8L and 10L HPLC

Figure F.20 presents “total contraction”, temperature movement and shrinkage of the

8L and 10L HPLC. Figure F.20 also shows the drying shrinkage limits proposed by

Goodspeed et al. (1996) for FHWA HPC Grades 2 and 3 (Table A.2).

The 180-day shrinkage measured in 8L HPLC specimens at 50% relative humidity

was higher than the upper FHWA limit for HPC Grade 2 as shown in Figure F.20a.

However, the difference was less than 10%. In fact, average shrinkage after 180 days of

drying was approximately 650 µε while the upper boundary of HPC Grade 2 is 600 µε. As

stated for creep results, since shrinkage was not measured following the curing procedures of

ASTM C 157 (28-day moist curing), FHWA limits are not entirely applicable. FHWA limits

might be too severe for shrinkage measured after only one day of curing in HPLC mixes

because the specimens probably included important autogenous shrinkage as well as drying

shrinkage.

Figure F.18b shows that 180-day shrinkage of 10L HPLC was about 330 µε which is

below the upper boundary given for HPC Grade 3 of 400 µε. Figure F.20 also shows the

experimental variation of drying shrinkage by comparing individual readings with average

189

reading. From the experimental variation it can be concluded that even though 8L HPLC

presented much higher shrinkage than 10L HPLC, it had lower variance.

Differences among individual shrinkage results ranged between 33 and 50 µε and

between 56 and 77 µε for 8L and 10L HPLC, respectively. In spite of the higher variance of

10L HPLC shrinkage results, there were no individual values above 400 µε at 180 days.

As shown in Figure F.20a, 620-day shrinkage of 8L HPLC was 760 µε. 50% and 90%

of the 620-day shrinkage was reached approximately after 20 and 100 days of drying,

respectively. Figure F.20b shows that 620-day shrinkage of 10L HPLC was on average 427

µε. The 90% of the 620-day shrinkage was reached after one year of drying while the 50%

was reached after approximately 20 days.

F.9.2. Shrinkage of 8F and 10F HPLC

Figure F.21a presents detailed information about shrinkage of 8F HPLC which

includes individual results, average shrinkage, thermal correction and average shrinkage

before thermal correction. Figure F.19b gives the same information of Figure F.21a, but for

10F HPLC. Figure F.21 also includes the limits proposed by FHWA for HPC Grade 2 and 3.

8F HPLC had average 680-day shrinkage of 855 µε. However the variance around

the average value ranged between 700 to 1,000 µε. When analyzing shrinkage rate, two

portions can be distinguished: first, a fairly high and constant rate until 150 days of drying,

and secondly a flat portion with shrinkage around 860 µε between 150 and 680 days. All

individual readings of shrinkage after 180 days of drying were higher than FHWA upper

limit of 600 µε. Based on shrinkage change with time, it can be stated that the increase in

total strain of 8F HPLC (see Figure F.15) after 150 days was mostly due to creep since

shrinkage average did not change importantly.

190

Figure F.21. Shrinkage of 8F HPLC (a) and 10F HPLC (b) and limits for FHWA HPC Grade 2 and 3.

a

b

Shrin

kage

(µε)

Shrin

kage

(µε)

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0 100 200 300 400 500 600 700Time under Drying (days)

8F Individual Reading8F Average Shrinkage8F Total Contraction8F Temp CorrectionFHWA HPC Grade 2 Limits

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10F Individual Reading10F Average Shrinkage10F Total Contraction10F Temp CorrectionFHWA HPC Grade 3 Limit

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8F Individual Reading8F Average Shrinkage8F Total Contraction8F Temp CorrectionFHWA HPC Grade 2 Limits

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10F Individual Reading10F Average Shrinkage10F Total Contraction10F Temp CorrectionFHWA HPC Grade 3 Limit

191

10F HPLC had an average shrinkage after 680 days of drying of 788 µε. Individual

readings ranged from 712 to 868 µε which was considerably less than the variance seen in

Figure F.21a for 8F HPLC. Measured shrinkage after 180 days of drying was much higher

than the 400 µε limit proposed by FHWA.

In Figure F.21b, it can be also distinguished two main portions in shrinkage rate: one

from the beginning of drying to approximately 170 days and one from 170 to 680 days. The

first portion presents an accelerated and fairly constant rate while the second portion shows a

very slight change with time. As seen in Figure F.21b, shrinkage at 50% of relative humidity

developed very fast, but after six month stabilized. The change in length observed on the

creep specimens after 170 days was mainly due to creep since the change in shrinkage was

not important.

192


193

Appendix G. Analysis of Creep and Shrinkage

G.1 Comparison of Creep Performance of Laboratory HPLC with Field HPLC

As explained, 8,000 and 10,000-psi HPLC mixes were made in laboratory (8L/10L)

and field (8F/10F) using the same mix design. In Appendix F their mechanical properties

including creep and shrinkage are analyzed separately. In this section the performance of the

laboratory mixes is compared with the one of the field mixes. Creep is not compared directly

because the applied stress was not the same for laboratory and field mixes. Even though the

mixes were loaded to the same stress-to-initial strength ratio, they did not have the same

initial strength at 24 hours, so the applied stress was different. Nevertheless, specific creep

and creep coefficient can be compared regardless the applied stress because they are

expressed in terms of it.

An analysis of variance (ANOVA) of specific creep (sc) and creep coefficient (øc)

was performed. The considered factors were: time under load, stress level, and whether the

mix was prepared in laboratory or field. The tables presented with the ANOVA results (see

Tables G.1, G.2, and G.3) show in their first column the factors that are tested against the

variance of sc and øc. Second and fourth columns present the contribution of each factor to

the total mean squared error (MSE). It is a number below 1.0; the closer to 1.0, the higher the

portion of the mean squared error explained by the factor. The third and fifth columns give

the P-value obtained for each factor. P-value represents the probability that the considered

factor is not significant in explaining the variance. A P-value less than 0.05 (generally

adopted as confidence limit) means that there is more than a 95% chance that the factor is

significant and should be included.

194

G.1.1. Comparison of Creep Performance of 8L HPLC with 8F HPLC

An analysis of variance was carried out between 8,000-psi mixes made in laboratory

(8L) and field (8F). The 8L HPLC was loaded at 16 and 24 hours while 8F was loaded only

at 24 hour. Hence, the comparison was performed for creep of specimens loaded at 24 hour

with a stress of 40% and 60% of initial strength. Table G.1 presents the most relevant results

from the ANOVA.

Table G.1. ANOVA results for creep of 8,000-psi HPLC

Factors Specific Creep Creep Coefficient Rel MSE P-value Rel MSE P-value

Time 0.436 0.000 0.447 0.000 Stress Level 0.020 0.000 0.027 0.000

Lab/Field -0.001 0.746 0.001 0.145

Form Table G.1 it can be concluded that the factor Lab/Field is not a significant

factor for any of the creep parameters (sc or øc). The relative MSE were less than 0.1% and

the P-values much greater than 0.05. Even though stress level had P-values below 0.05, the

portion of MSE explained by stress level was only 2.0 and 2.7% for sc and øc, respectively.

The low contribution of stress level to the variability of sc and øc was expected because the

creep deformation was divided by applied stress and elastic strain, respectively. Time was a

significant factor and explained 43.6 and 44.7% of variance. The fact that the relative MSE

of time was far from 1.0 is due to ANOVA model which considers a linear effect of the

factors. As it is shown in Section F.8, creep was not linear with time, but approximately

logarithmic.

Figure G.1 presents a comparison between average creep coefficient of 8L and 8F

HPLC. As concluded in section F.8, creep coefficient at 40% of initial strength was

195

somehow higher than the one for 60% stress level. That was also seen in ANOVA (see Table

G.1) where stress level is still significant for creep coefficient.

Figure G.1. Creep coefficient of 8L and 8F HPLC (a) linear time scale and (b) logarithmic time scale.

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

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Cre

ep C

oeffi

cien

t

8L 24h-40%

8F 24h-40%

8L 24h-60%

8F 24h-60%

Cre

ep C

oeffi

cien

t

a

b

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0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

0.01 0.1 1 10 100 1000Time (days)

8L 24h-40%

8F 24h-40%

8L 24h-60%

8F 24h-60%

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

0 100 200 300 400 500 600Time (days)

Cre

ep C

oeffi

cien

t

8L 24h-40%

8F 24h-40%

8L 24h-60%

8F 24h-60%

Cre

ep C

oeffi

cien

t

a

b

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

0.01 0.1 1 10 100 1000Time (days)

8L 24h-40%

8F 24h-40%

8L 24h-60%

8F 24h-60%

196

It also can be noticed in Figure G.1a that field mix had an average higher long-term

creep for 40% of stress level, but lower long-term creep for 60% stress level. From Figure

G.1b it can be seen that creep coefficient curves intercept each other several times during the

testing period.

Results for less than one day show that field mix had more early creep than the

laboratory mix. However, after 100 days under load the opposite conclusion can be drawn.

The multiple intersections between creep curves from laboratory and field indicates that even

though the averages show visible differences there are overlaps in the results.

From ANOVA it can be concluded that the place of casting (laboratory or field) was

not a significant factor; therefore, 8L and 8F HPLC are the same HPLC and from now on

they might be referred as 8,000-psi HPLC.

G.1.2. Comparison of Creep Performance of 10L HPLC with 10F HPLC

Four specimens of the 10L HPLC were loaded at 16 hours and four more at 24 hours.

Field mix (10F) specimens were loaded only at 24 hours. Therefore, the comparison was

performed for creep of specimens loaded at 24 hours with two stress levels: 40% and 60% of

initial strength for laboratory mix and 40% and 50% for field mix. Table G.2 presents the

most relevant results from the analysis of variance (ANOVA) and Figure G.2 shows the

average specific creep and creep coefficient for each type of mix.

Table G.2. ANOVA results for creep of 10,000-psi HPLC


Time 0.364 0.000 0.365 0.000 Stress Level 0.002 0.072 0.000 0.412

Lab/Field 0.003 0.024 0.000 0.492

197

Figure G.2. Creep coefficient of 10L and 10F HPLC (a) linear time scale and (b) logarithmic time scale.

0.00

0.25

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0.75

1.00

1.25

0 100 200 300 400 500 600Time (days)

Cre

ep C

oeffi

cien

t

10L 24h-40%

10F 24h-40%

10L 24h-60%

10F 24h-50%

0.00

0.25

0.50

0.75

1.00

1.25

0.01 0.10 1.00 10.0 100 1000Time (days)

Cre

ep C

oeffi

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t

10L 24h-40%

10F 24h-40%

10L 24h-60%

10F 24h-50%

a

b

0.00

0.25

0.50

0.75

1.00

1.25

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Cre

ep C

oeffi

cien

t

10L 24h-40%

10F 24h-40%

10L 24h-60%

10F 24h-50%

0.00

0.25

0.50

0.75

1.00

1.25

0.01 0.10 1.00 10.0 100 1000Time (days)

Cre

ep C

oeffi

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t

10L 24h-40%

10F 24h-40%

10L 24h-60%

10F 24h-50%

a

b

198

From Table G.2 it can be concluded that the factor Lab/Field was significant for sc,

but it explained only 0.3% of the mean squared error (Rel MSE=0.003). Lab/Field factor was

not significant for creep coefficient (it has a P-value of 0.492 and Relative MSE of 0.%).

Stress level was not significant for any of the creep parameters; P-values were greater than

0.05 and relative MSE was 0.2% and 0% for sc and øc, respectively.

Figure G.2 presents a comparison between creep coefficient of 10L and 10F HPLC.

From ANOVA results it was concluded that stress level was not a significant factor for creep

coefficient.

The same conclusion can be observed from Figure G.2a and G.2b. It also can be

noticed in Figure G.2a that field mix had an average higher long-term creep coefficient than

laboratory mix. However, Figure G.2b shows that creep coefficient curves are not parallel

and constantly intercept each other during the testing period.

From ANOVA and Figure G.2, it can be stated that the place of casting (laboratory or

field) and stress level were not significant factors for creep of 10,000-psi HPLC. As a

conclusion 10L and 10F are the same HPLC and from now on they might be referred as

10,000-psi HPLC.

G.2 Comparison of Creep of 8,000-psi HPLC with 10,000-psi HPLC

Following the same procedure described in Section G.1, creep performance of 8,000-

psi and 10,000-psi HPLC was compared. The factors considered were time under load, stress

level (40% or 60% of initial strength), compressive strength (8,000 psi or 10,000 psi), and

time of application of load (16 hours or 24 hours). Table G.3 presents the most relevant

results from the analysis of variance (ANOVA). Data used in this comparison came from the

199

laboratory mixes because they included two ages of loading. However, as it was concluded in

last section they are representative of 8,000 and 10,000-psi mixes.

Table G.3. ANOVA results for creep of HPLC


Time 0.610 0.000 0.587 0.000 Compressive Strength 0.099 0.000 0.068 0.000

Age at loading 0.040 0.000 0.025 0.000 Stress Level 0.024 0.000 0.015 0.000

From Table G.3 it can be concluded that all the four factors were statistically

significant since none of the P-values were above 0.05. Stress level was the least important

factor. It explained 2.4 and 1.5% of the mean squared error (MSE) of sc and øc, respectively.

Age of loading was more important than stress level, but explained only 4 and 2.5% of the

mean squared error (MSE) of sc and øc, respectively. As a result, if age of loading and stress

level are dropped from creep coefficient as factors, the mean squared error decreases only

4%. Compressive strength was more important than the two previous factors explaining 9.9

and 6.8% of mean squared error. Therefore, if strength of mix is not considered as a factor,

the mean squared error would increase more importantly. Finally, time under load was, as

expected, the most important factor explaining variance of sc and øc.

Figure G.3 presents a comparison between creep coefficient of 8L and 10L HPLC.

Figure G.3a shows creep coefficient at different age of loading; stress levels are also

presented. From the data it was concluded that, besides from the series “10L 16h-40%”, age

at application of load and stress level did not importantly change creep of 8,000-psi and

10,000-psi HPLC. After 620 days under load and drying, 8,000-psi creep coefficient ranged

between 1.59 and 1.74. 10,000-psi HPLC had a 620-day creep coefficient between 1.03 and

1.25.

200

Figure G.3. Creep coefficient of 8L and 10L HPLC (a) linear time scale and (b) logarithmic time scale.

Cre

ep C

oeffi

cien

t

a

b

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1.50

1.75

0 100 200 300 400 500 600Time (days)

8L 16h-40% 8L 24h-40%

10L 16h-40% 10L 24h-40%

8L 16h-60% 8L 24h-60%

10L 16h-60% 10L 24h-60%

Cre

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1.50

1.75

0.01 0.10 1.00 10.0 100 1000Time (days)

8L 16h-40% 8L 24h-40%

10L 16h-40% 10L 24h-40%

8L 16h-60% 8L 24h-60%

10L 16h-60% 10L 24h-60%

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a

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8L 16h-40% 8L 24h-40%

10L 16h-40% 10L 24h-40%

8L 16h-60% 8L 24h-60%

10L 16h-60% 10L 24h-60%

Cre

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0.01 0.10 1.00 10.0 100 1000Time (days)

8L 16h-40% 8L 24h-40%

10L 16h-40% 10L 24h-40%

8L 16h-60% 8L 24h-60%

10L 16h-60% 10L 24h-60%

201

Figure G.3b shows that creep coefficient curves are fairly parallel showing that creep

of 10,000-psi (excluding10L 16h-40%) was lower for almost any time under load.

From ANOVA and Figure G.3, it can be concluded that age at application of load (16

or 24 hours) and stress level were not important factors for creep of HPLC, and 10,000-psi

HPLC had on average lower creep than 8,000-psi HPLC.

Figure G.4 presents the average creep coefficient obtained from 8,000-psi and

10,000-psi mixes in logarithmic time scale.

Figure G.4 shows that 620-day creep coefficient was 1.684 and 1.143 for 8,000-psi

and 10,000-psi HPLC, respectively. The 50% and 90% of 620-day creep coefficient were

reached after 16 and 250 days regardless the type of HPLC.

Figure G.4. Average creep coefficient of 8,000-psi and 10,000-psi HPLC in logarithmic time scale.

0.0

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Cre

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8,000-psi HPLC

10,000-psi HPLC

0.10 1.00 10.0 100 1000Time (days)

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8,000-psi HPLC

10,000-psi HPLC

0.10 1.00 10.0 100 1000Time (days)

202

G.3 Comparison of Shrinkage of 8,000-psi HPLC with 10,000-psi HPLC

Following the same procedure described in Section G.1, shrinkage performance of

8,000-psi and 10,000-psi HPLC was compared. The factors considered were time under

drying, compressive strength (8,000 psi or 10,000 psi), age at the beginning of drying (16

hours or 24 hours). Table G.4 presents the most relevant ANOVA output from four different

comparisons: (1) Place of mixing for 8,000-psi HPLC (8L vs. 8F); (2) Compressive strength

for laboratory mixes (8L vs. 10L); (3) Compressive strength for field mixes (8F vs. 10F);

and (4) Place of mixing for 10,000-psi HPLC (10L vs. 10F).

Since relative mean squared error (MSE) was negative and P-value was greater than

0.05 for the first comparison (8L vs. 8F), it can be concluded that the place of mixing was not

a significant factor for shrinkage of 8,000-psi HPLC.

Table G.4 ANOVA results for shrinkage of HPLC

Factors Shrinkage 8L vs. 8F

Shrinkage 8L vs. 10L

Shrinkage 8F vs. 10F

Shrinkage 10L vs. 10F

Rel MSE

P-value

Rel MSE

P-value

Rel MSE

P-value

Rel MSE

P-value

Time under drying 0.472 0.000 0.851 0.001 0.618 0.000 1.028 0.000 Compressive Strength 0.021 0.000 0.000 0.303

Age at drying -0.001 0.588 Laboratory/Field -0.002 0.675 0.028 0.007

Age at the beginning of drying (16 or 24 hours) was also analyzed for the laboratory

mixes (8L and 10L). ANOVA results showed that it was not a statistically significant factor.

10L HPLC had considerable less shrinkage than 8L mix. ANOVA demonstrated that

compressive strength of the mix was a significant factor affecting shrinkage (P-value less

than 0.001). On the contrary, shrinkage was not clearly different within the field mixes (8F

203

vs. 10F). Therefore, compressive strength was not significant (P-value above 0.05) for field

mixes.

In addition, a significant difference was detected when comparing shrinkage of 10L

and 10F HPLC; P-value was less than 0.05 and relative MSE was 2.8%. Therefore, place of

mixing (laboratory or field) affected shrinkage of 10,000-psi HPLC.

Figure G.5 presents the shrinkage results obtained for each HPLC. As concluded

from ANOVA, there is a clear difference between 8L and 10L HPLC at any time of drying

(Figure G.5a). 8L and 8F mixes had a similar average value though the variance of the 8F

shrinkage result was higher than the one of 8L HPLC.

Figure G.6 presents the average shrinkage obtained from 8,000-psi and 10,000-psi

mixes in logarithmic time scale.

Figure G.6 shows that 620-day shrinkage was 818 and 610 µε for 8,000-psi and

10,000-psi HPLC, respectively. At very early ages (less than one day) shrinkage of 10,000-

psi mix was considerably greater than 8,000-psi mix. After one day, shrinkage rate of the

10,000-psi mix slowed down, and measured shrinkage was much lower for that HPLC. 50%

and 90% of 620-day shrinkage was reached after 27 and 170 days for 8,000-psi HPLC and

after 55 and 170 days for 10,000-psi mix.

204

Figure G.5. Shrinkage of 8,000-psi and 10,000-psi HPLC (a) laboratory mixes and (b) field mixes.

0

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8L16 8L24

10L16 10L24


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b

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10L16 10L24


a

b

205

Figure G.6. Average shrinkage of 8,000-psi and 10,000-psi HPLC in logarithmic time scale

G.4 Comparison of Creep and Shrinkage Test Results with Code Models

G.4.1. Creep and Shrinkage Models Results

Models presented in section C.1 for normal strength concrete and models presented in

section C.2 for high strength concrete were used to predict creep of 8,000-psi and 10,000-psi

HPLC. The parameters used in the models are presented in Table G.5.

Since the last experimental results were taken after 620 days of drying and loading,

Table G.6 presents measured and predicted shrinkage and specific creep at that age. Table

G.6 also presents the predicted values at 40 years which represents the ultimate creep and

shrinkage values.

0

100

200

300

400

500

600

700

800

0.01 0.10 1.00 10.0 100 1000Time (days)

Shrin

kage

(µε)

8,000-psi HPLC

10,000-psi HPLC

0

100

200

300

400

500

600

700

800

0.01 0.10 1.00 10.0 100 1000Time (days)

Shrin

kage

(µε)

8,000-psi HPLC

10,000-psi HPLC

206

Table G.5. Parameters used in creep prediction equations

Parameter Mix Parameter Mix 8,000 10,000 8,000 10,000

t′: age of concrete at loading 1 day V: specimen volume 188.5 in3 t0: age of concrete at drying 1 day Steam curing 1 day

S: specimen surface area

188.5 in2

fci′: initial compressive strength (psi) 7,730 11,100 fc′: 56-day compressive strength (psi) 10,000 11,475

V/S: volume-to-surface ratio

1 in

Ec: 56-day elastic modulus (ksi) 4,020 4,240 Mix design (lb/yd3) σc (40%): stress at 40% fci’ (psi) 2,845 3,517 c: cement 944 990 Elastic strain at σc (40%) µε 890 1,059 w: water 268 227 σc (60%): stress at 60% fci’(psi) 4,273 5,276 a: total aggregate 2,764 2,787 Elastic strain at σc (60%) µε 1,307 1,470 s: sand content 1022 1030 Slump (in) 4.5 4.0 g: lightweight agg1 1724 1757 Air Content (%) 3.75 3.50 h: relative humidity 50% 1 weight occupied by the same volume of normal weight aggregate.

Table G.6. Long-term shrinkage and specific creep

Parameter 620-day shrinkage

µε

40-year shrinkage

µε

620-day creep coefficient

40-year creep coefficient

8,000 10,000 8,000 10,000 8,000 10,000 8,000 10,000 Measured 763 610 1.66 1.29 ACI-209 644 640 698 694 1.739 1.639 2.305 2.173

AASHTO-LRFD 725 725 755 755 1.965 1.852 1.529 1.439 CEB-FIP 381 313 407 334 3.727 3.564 4.202 4.019

BP 322 298 330 310 3.928 3.807 4.746 4.65 B3 385 329 390 334 4.465 4.511 5.325 5.392 GL 555 530 594 568 5.112 5.111 5.585 5.585

SAK-93 291 230 297 234 4.464 2.815 4.528 2.856 Shams & Kahn 590 585 604 599 1.479 1.373 1.634 1.523 CEB-FIP - HSC 381 313 407 334 2.896 2.707 3.279 3.058

BP - HSC 322 298 330 310 3.357 3.254 4.649 4.519 SAK-2001 - HSC 512 357 553 382 1.451 1.027 2.164 1.531 AFREM - HSC 396 350 408 359 1.137 0.941 1.215 1.051

In order to establish a better comparison, Figure G.7 presents the predicted-to-

measured ratio creep coefficient and shrinkage after 620 days of drying and loading. The

computed ratio was greater and lower than one for overestimates and underestimates,

respectively.

207

Figure G.7. Predicted-to-measured ratio of 620-day specific creep and shrinkage of HPLC

Figure G.7 shows that the best shrinkage estimate is given by AASHTO LRFD and

Shams and Kahn’s model, for 8,000-psi and 10,000-psi HPLC, respectively. Those models

underestimated shrinkage by only 5 and 4%, respectively. Creep coefficient of 8,000-psi

HPLC was best predicted by AASHTO LRFD model with an underestimate of 8% while

creep coefficient of 10,000-psi HPLC was best predicted by Shams and Kahn with 6%

overestimate. If it is assumed that such models are the most adequate for predicting HPLC

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

ACI-209

AASHTO-LRFD

CEB-FIP

BP

B3

GL

SAK-93

SHAMS & KAHN

CEB-FIP - HSC

BP - HSC

SAK-2001 - HSC

AFREM - HSC

Predicted-to-measured value

8,000-psi 620-day Shrinkage8,000-psi 620-day Creep Coefficient10,000-psi 620-day Shrinkage10,000-psi 620-day Creep Coefficient

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

ACI-209

AASHTO-LRFD

CEB-FIP

BP

B3

GL

SAK-93

SHAMS & KAHN

CEB-FIP - HSC

BP - HSC

SAK-2001 - HSC

AFREM - HSC

Predicted-to-measured value

8,000-psi 620-day Shrinkage8,000-psi 620-day Creep Coefficient10,000-psi 620-day Shrinkage10,000-psi 620-day Creep Coefficient

208

long-term performance and that the 620-day predicted-to-measured ratio is maintained at

ultimate, the ultimate shrinkage would be 795 and 625 µε for 8,000-psi and 10,000-psi

HPLC, respectively. In addition, ultimate creep coefficient would be 1.925 and 1.431 for

8,000-psi and 10,000-psi HPLC, respectively.

Hence, at 50% of relative humidity, ultimate total strain of 8,000-psi HPLC (elastic,

shrinkage and creep) would be approximately 3,400 and 4,620 µε, for stress-to-strength ratio

of 0.4 and 0.6, respectively. Under the same conditions 10,000-psi HPLC would have a total

strain of 3,200 and 4,200 µε when stressed at 40 and 60% of it initial strength.

G.4.2. Creep Models Performance Comparison

Figure G.8 presents a comparison between measured creep coefficient versus time

and predicted values using normal strength concrete models (section C.1). Figure G.8a

shows results for 8,000-psi HPLC and Figure G.8b does it for 10,000-psi HPC. A more

detailed comparison for each model is presented in Appendix L.

When comparing model performance from Figure G.8a, it can be concluded that ACI-

209 model had the best overall performance closely followed by AASHTO-LRFD model.

Even though ACI-209 model under estimated creep for time under load less than 10 days and

overestimated creep for times greater than 100 days, it was the one with best agreement with

the experimental data. The second best model was AASHTO-LRFD model which followed

the same tendency as ACI-209 at early ages, but continued underestimating creep at all ages.

209

Figure G.8. Comparison between measured creep coefficient and estimated from models for normal strength concrete: (a) 8,000-psi HPLC, (b) 10,000-psi HPLC.

The good performance presented by ACI-209 model might be due to that model is

explicitly including SLC in its data base. However, because the model was largely based on


a

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Cre

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oeffi

cien

tGardner Lockman

AASHTO LRFD

ACI-209

CEB-FIP

Bažant Panula

Bažant Baweja

Sakata 93

8,000-psi Measured


b

0.0

0.5

1.0

1.5

2.0

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Cre

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oeffi

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Gardner Lockman

AASHTO LRFD

ACI-209

CEB-FIP

Bažant Panula

Bažant Baweja

Sakata 93

10,000-psi Measured


a

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tGardner Lockman

AASHTO LRFD

ACI-209

CEB-FIP

Bažant Panula

Bažant Baweja

Sakata 93

8,000-psi Measured


a

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Cre

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oeffi

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tGardner Lockman

AASHTO LRFD

ACI-209

CEB-FIP

Bažant Panula

Bažant Baweja

Sakata 93

8,000-psi Measured


b

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Gardner Lockman

AASHTO LRFD

ACI-209

CEB-FIP

Bažant Panula

Bažant Baweja

Sakata 93

10,000-psi Measured


b

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Gardner Lockman

AASHTO LRFD

ACI-209

CEB-FIP

Bažant Panula

Bažant Baweja

Sakata 93

10,000-psi Measured

210

work done between 1957 and 1970 it can be assumed that high strength concrete and

supplementary cementing materials were not part of the database.

All the other models greatly overestimated creep of 8,000-psi HPLC especially after

10 days under load. Figure G.8b shows the same general tendencies of Figure G.8a. The best

model among the models for normal strength concrete was AASHTO-LRFD. For 10,000-psi

HPLC that model was in great agreement with experimental data for any time under load

between 1 and 600 days. ACI-209 model, the second best, tended to overestimate creep

coefficient for times under load greater than 30 days.

Figure G.9 shows a comparison between experimental creep coefficient and estimated

creep coefficient using high strength concrete models (section C.2). Again, part (a) of Figure

G.9 compares data from 8,000-psi HPLC and part (b) compares 10,000-psi HPLC data (for

more details see Appendix L).

In Figure G.9 it can be seen that the performance of creep models for HSC was in

general better than the ones for normal strength concrete. Even though BP and CEB-FIP

were modified for HSC, they still greatly overestimated creep of 8,000-psi and 10,000-psi

HPLC. BP modified for HSC overestimated creep at all ages while CEB-FIP Modified for

HSC did it for ages greater than 20 days.

The AFREM model, on the other hand, tended to underestimate creep. As shown on

Table G.6 and Figure G.9, 620-day specific creep predicted by AFREM was approximately

68 and 73% of the measured value for 8,000-psi and 10,000-psi HPLC, respectively. Shams

and Kahn’s model (2000) and Sakata’s model (2001) gave the best estimates of the 620-day

creep coefficient of 8,000-psi HPLC.

211

Figure G.9. Comparison between measured creep coefficient and estimated from models for high strength concrete: (a) 8,000-psi HPLC, (b) 10,000-psi HPLC.

0.0

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BPMOD-HSC

CEB-FIP MOD-HSC

AFREM

Sakata 2001

Shams&Kahn

a

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10,000-psi Measured

BPMOD-HSC

CEB-FIP MOD-HSC

AFREM

Sakata 2001

Shams&Kahn

b

8,000-psi Measured

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CEB-FIP MOD-HSC

AFREM

Sakata 2001

Shams&Kahn

a

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10,000-psi Measured

BPMOD-HSC

CEB-FIP MOD-HSC

AFREM

Sakata 2001

Shams&Kahn

b

8,000-psi Measured

212

Despite the fact that the two models gave a very similar 620-day estimate, from

Figure G.9a Sakata’s model underestimated creep for time under load less than 300 days.

The best model among the models for HSC was Shams and Kahn model which not

only gave a good 620-day estimate, but also followed the shape of the experimental data as

well.

Figure G.9b presents a similar scenario as Figure G.9a, Sakata’s model and

AASHTO-LRFD as modified by Shams and Kahn gave the two best estimates after 620-day

under load. The AFREM model also gave reasonable estimations for 10,000-psi HPLC.

However, the best model, including early and late ages, was AASHTO-LRFD model as

modified by Shams and Kahn.

Overall, the model with the best performance for estimating creep of 8,000-psi and

10,000-psi HPLC, including models for NSC and HSC, was AASHTO-LRFD model as

modified by Shams and Kahn.

Table G.7 presents the sum of squared error (SSE) and coefficient of determination

(R2) between experimental data and creep models for 8,000-psi and 10,000-psi HPLC.

Models are presented ordered by performance (best performance model at the top).

As shown in Table G.7 the best model for estimating creep was AASHTO-LRFD

model as modified by Shams and Kahn, which presented the lowest SSE for 8,000-psi and

10,000-psi (0.9 and 0.3, respectively) and consequently the largest R2 (0.922 and 0.945,

respectively). AASHTO-LRFD model presented the overall second best performance with

an average10 SSE of 0.95 and the second largest average10 R2 (0.899). In third place, but far

10 Average of the parameter obtained for 8,000-psi and 10,000-psi HPLC

213

away from the first two was ACI-209 model with average10 SSE and R2 of 2.55 and 0.608,

respectively.

Bažant and Baweja’s model (B3) and Gardner and Lockman’s model (GL) gave the

least good performance for HPLC. Negative values in Table G.7 indicate that SSE between

model estimate and data were greater than the variance in the data itself. The latter means

that the model estimates were so deviated from data that using only the average of data

(average includes results at any time regardless the time under drying) gives a lower SSE

than the model.

Table G.7. Sum of squared error and coefficient of determination of creep coefficient models

8,000-psi HPLC 10,000-psi HPLC Model SSE R2 Model SSE R2

Shams & Kahn 0.9 0.922 Shams & Kahn 0.3 0.946 ACI-209 1.2 0.895 AASHTO 0.4 0.927

AASHTO 1.5 0.871 AFREM 2.2 0.606 AFREM 5.0 0.561 ACI-209 3.9 0.295

SAK2001 6.0 0.467 SAK2001 4.2 0.292 CEB HSC 17.3 <0.0 CEB HSC 26.3 <0.0 BP HSC 46.0 <0.0 SAK1993 33.4 <0.0 CEB-FIP 53.9 <0.0 BP HSC 64.0 <0.0

BP 89.4 <0.0 CEB-FIP 70.4 <0.0 SAK1993 108.2 <0.0 BP 107.8 <0.0

B3 138.9 <0.0 B3 186.4 <0.0 GL 304.4 <0.0 GL 365.5 <0.0

AASHTO-LRFD as modified by Shams and Kahn and AASHTO-LRFD, the two

models that better estimate creep of HPLC, utilized the maturity of concrete at loading rather

than age. As shown in Section B.2, age of loading is an important factor in determining

creep. For precast prestressed concrete members the age of application of load can be as low

as 16 hours, so creep becomes very dependant of concrete mechanical properties at the

moment of loading. HPC usually includes high contents of cementitious materials which

generate more heat of hydration than normal strength concrete. This heat of hydration is

214

responsible for raising concrete temperature at levels as high as 145 oF which accelerates the

hydration process. This self feeding reaction increases concrete mechanical properties above

the expected values. Because maturity includes temperature history, it leads to more accurate

estimate of concrete performance. Shams and Kahn’s and AASHTO-LRFD models were

able to better estimate creep because 8,000-psi and 10,000-psi HPLC had a maturity at 24

hours equivalent to 147 and 158 hours (6.1 and 6.6 days).

G.4.3. Shrinkage Models Performance Comparison

8,000-psi HPLC

Figure G.10 presents a comparison between measured shrinkage in 8L HPLC and

predicted values using normal strength concrete and HSC models (section C.1 and C.2). A

more detailed comparison for each model is presented in Appendix L.

As shown in Table G.4, AASHTO-LRFD model gave the best shrinkage estimate at

620 days after the starting of drying. The same conclusion was also true for anytime greater

than 30 days. For drying times less than 5 days AASHTO-LRFD model underestimated

shrinkage. AASHTO-LRFD model as modified by Shams and Kahn also presented good

performance in the range 5 to 100 days of drying. After 100 days, however, the latter model

tended to underestimate shrinkage of 8,000-psi HPLC. ACI-209 shrinkage model

underestimated shrinkage at any age, but the shape of the shrinkage curve was very similar to

the experimental data.

The other five models for normal strength concrete behaved similarly and

underestimated shrinkage at anytime after drying started. Sakata’s (1993) and BP models

presented the two lowest estimates on this group. They estimated shrinkage at 620 days as

215

300 and 330 µε, respectively. Models that include HSC in its scope (AFREM and Sakata

2001) did not behave better, and their estimates were in the range given by NSC ranges.

All considered models (for NSC and HSC) greatly underestimated shrinkage at early

ages (less than 3 days). Early age experimental shrinkage was between 100 and 170 µε while

all the estimates were in the range 0 to 100 µε.

A possible explanation of this poor performance at early ages might be due to

autogenous shrinkage. As explained in Section B.4.2, autogenous shrinkage might be

included on shrinkage measurements when testing started early ages such as 24 hours.

216

Figure G.10. Comparison between measured shrinkage of 8L HPLC and estimated from models for normal and high strength concrete.

10,000-psi HPLC

Figure G.11 presents a comparison between shrinkage of 10,000-psi and the values

predicted using the models presented in the literature.

0

100

200

300

400

500

600

700


Shrin

kage

(µε)

Gardner Lockman

AASHTO LRFD

ACI-209

CEB-FIP

Shams&Kahn

Bažant Panula

Bažant Baweja

Sakata 93

8,000-psi Measured

AFREM Sakata 2001

0

100

200

300

400

500

600

700


Shrin

kage

(µε)

Gardner Lockman

AASHTO LRFD

ACI-209

CEB-FIP

Shams&Kahn

Bažant Panula

Bažant Baweja

Sakata 93

8,000-psi Measured

AFREM Sakata 2001

217

As seen in Figure G.11, ACI-209, Shams and Kahn’s and Gardner and Lockman’s

(GL) models gave fairly good estimated of shrinkage for any time except for the first 24

hours. AASHTO-LRFD model overestimated shrinkage for drying periods longer than 10

days.

Figure G.11. Comparison between measured shrinkage of 8L HPLC and estimated from models for normal and high strength concrete.

All the rest of the models greatly underestimated shrinkage for times greater than 100

days of drying regardless whether they were meant for HSC or not. Experimental shrinkage

of 10,000-psi HPLC was generally bounded by the estimates of Gardner and Lockman’s

(GL) and ACI-209 models. After 620 days experimental shrinkage was 610 µε while GL and

0

100

200

300

400

500

600

700


Shrin

kage

(µε)

Gardner Lockman

AASHTO LRFD

ACI-209

CEB-FIP

Shams&Kahn

Bažant Panula

Bažant Baweja

Sakata 93

10,000-psi Measured

Sakata 2001

AFREM

0

100

200

300

400

500

600

700


Shrin

kage

(µε)

Gardner Lockman

AASHTO LRFD

ACI-209

CEB-FIP

Shams&Kahn

Bažant Panula

Bažant Baweja

Sakata 93

10,000-psi Measured

Sakata 2001

AFREM

218

ACI-209 estimated 530 and 640 µε, respectively. If it is assumed that GL and ACI-209 are

good bounds for ultimate shrinkage, it can be stated that ultimate shrinkage would be less

than 694 µε (ACI-209 estimate).

Table G.8 presents the sum of squared error (SSE) and coefficient of determination

(R2) between experimental shrinkage and of models.

Table G.8 Sum of squared error and coefficient of determination of shrinkage models

8,000-psi HPLC 10,000-psi HPLC Model SSE R2 Model SSE R2

AASHTO 159118 0.929 GL 74390 0.931 Shams and Kahn 406485 0.820 ACI209 121631 0.887

ACI-209 598791 0.734 Shams and Kahn 172596 0.840 GL 745030 0.669 AASHTO 412376 0.617

SAK2001 1348516 0.401 AFREM 516334 0.521 AFREM 1869585 0.170 SAK2001 640493 0.406

B3 2211313 0.019 B3 666277 0.382 CEB-FIP 2247762 0.002 CEB-FIP 759697 0.295

BP 2629329 <0.0 BP 770986 0.284 SAK1993 3396498 <0.0 SAK1993 1290219 <0.0

As shown in Table G.8, the highest R2 values were very similar for 8,000-psi and

10,000-psi HPLC and were obtained by AASHTO-LRFD and GL model, respectively.

AASHTO-LRFD model as modified by Shams and Kahn, which had the second best

performance for 8,000-psi mix, had the third best for 10,000-psi mix. It must be noted that

the same four models obtained the four best performances for the two types of HPLC. When

R2 values from each mix were averaged in order to obtain an overall performance,

AASHTO-LRFD as modified by Shams and Kahn and ACI-209 models had the two highest

R2 average values with 0.830 and 0.811, respectively.

219

G.5 Comparison of Creep and Shrinkage of HPLC with HPC

Since 1998, Georgia Institute of Technology and Georgia Department of

Transportation have been developing and investigating High Performance Concrete of

normal weight with locally available materials in Georgia. During Task 3: “Use of High

Strength/High Performance Concrete for Precast Prestressed Concrete Bridge Girders”, time-

dependent behavior of high performance concrete (HPC) was investigated. Six HPC mixes

were developed, and creep and shrinkage of each were measured for 480 days after loading

and drying. In Task 6 “Evaluation of Georgia’s High Performance Concrete Bridge” creep

performance of an HPC Grade 3 mix was measured and evaluated for 650 days.

This section presents a comparison between creep and shrinkage of 10,000-psi HPLC

and HPC mixes from Task 3 and Task 6 of HPC project. Testing parameters and mechanical

properties of mix “G2/27 mix” (from Task 3) and “2S mix” (from Task 6) were adequately

similar for comparison with HPLC. Table G.9 presents mix design, mechanical properties

and some fresh properties of HPC-3 (G2/27 mix), HPC-6, and the 10,000-psi HPLC11 mixes.

HPC-3 and HPC-6 might be classified as an HPC Grade 3 according to the FHWA

designation. They are a 10,000-psi compressive strength mix with most of its properties

equivalent to the one obtained for HPLC. The HPC-6 mix had about the same paste volume

and total cementitious content as the HPLC mix; therefore it was regarded as most similar.

From Table G.9 it can be seen that HPLC and the two HPC had similar water-to-

cementitious material ratio and similar compressive strength at 24 hours. At 56 days HPC-3

and HPC-6 had a compressive strength higher than the average value measured on HPLC.

11 In this section 10,000-psi HPLC is referred as HPLC because there is no other HPLC being

compared

220

The 24-hour elastic modulus of HPC-3 was similar to the maximum obtained for its HPLC

counterpart. HPC-6 had a 24-hour modulus of elasticity lower than HPLC mix. HPC-6 and

HPLC had very similar cement paste content (0.443 yd3 and 0.458 yd3, respectively), but that

was considerably higher than that of HPC-3 (0.381 yd3). As explained in Section B.2.3,

creep and shrinkage of concrete increase as the relative amount of cement paste increases.

Table G.9. Mix design and properties of HPLC and HPC, for one cubic yard

Amount 10,000-psi HPLC

HPC-3 HPC-6

Cement, Type I (lbs) 675 796 Cement, Type III (lbs) 740 Fly ash, class F (lbs) 150 100 98 Silica Fume, Force 10,000 (lbs) 100 33 70 Brown Brothers #2 sand (lbs) 1030 1,000 965 Coarse Aggregate (lbs) 955 1,750 1837 Water (lbs) 227.3 208 237 Water-to-cementitious ratio 0.230 0.257 0.246 Cement paste volume (yd3) 0.458 0.381 0.443 Air entrainer (oz) 9.5 16 7 Retarder (oz) 0 21 0 Water reducer (oz) 57 0 35 High-range water reducer (oz) 132 188 169

ASTM-cured 56-day compressive strength (psi) 10,250-11,500

11,619 13,618

Accelerated-cured 24-hour compressive strength (psi) 8,300-11,100

7,957 8,455

ASTM-cured 56-day elastic modulus (ksi) 4,050-4,330

4,748 4,973

Accelerated-cured 24-hour elastic modulus (ksi) 3,550-4,250

4,244 3,410

Slump (in) 4-6 7 4.6 Air content (%) 3.5-4.5 5 4.2 Unit weight (lb/ft3) 114-122 144 147

G.5.1. Creep Comparison

Figure G.12 presents a comparison of creep expressed as specific creep of each mix.

Figure G.12 (a) and (b) show the same data, but the time after loading is in linear and

221

logarithmic time scale, respectively. From Figure G.12a and G.12b it can be concluded that

average specific creep of HPLC was much lower than the specific creep of HPC-6 and

slightly lower than the specific creep of HPC-3. This was true for at any time after 20 days

under load.

At early times after loading (less than 10 days) HPC-3 and HPLC had equivalent

specific creep. Figure G.12b shows that after 3 days, the creep curves of HPC-3 and HPLC

are not parallel which implies that creep rate of HPLC was lower than the one of HPC.

Figure G.13 presents creep coefficient of the mixes presented in Table G.9. Creep

coefficient represents creep as a function of the elastic strain obtained under the same load.

The HPLC had a lower average elastic modulus than the normal weight counterpart of the

same strength.

From Figure G.13 it can be seen that the difference between HPC-3 and HPLC was

slightly greater than the one obtained using specific creep. On the contrary, the difference

between HPC-6 and HPLC was slightly lower due to the lower 24-hour modulus of elasticity

of HPC-6. Figure G.13 demonstrates that HPLC had the lowest 620-day creep in relation to

the elastic strain. The first hours of measurements creep of HPLC was significantly lower

than that of HPC-6, but the difference decreased as the time under load increased. The ratio

between HPC-6 and HPLC creep coefficients was 2.03, 1.86, and 1.53 for 40, 100 and 500

days. After 40 days the creep coefficient of HPLC started to be noticeably lower than that of

HPC-3. After 40 days the ratio between HPC-3 and HPLC creep coefficients remained fairly

steady around 1.13.

222

Figure G.12. Comparison between specific creep of HPC and HPLC mixes (a) linear time scale and (b) logarithmic time scale

b

a

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0 100 200 300 400 500 600Time (days)

Spec

ific

Cre

ep

HPLC

HPC-3

HPC-6

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.01 0.10 1.00 10.0 100 1000Time (days)

Spec

ific

Cre

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HPLC

HPC-3

HPC-6

b

a

0.00

0.10

0.20

0.30

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0.60

0 100 200 300 400 500 600Time (days)

Spec

ific

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HPLC

HPC-3

HPC-6

0.00

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0.30

0.40

0.50

0.60

0.01 0.10 1.00 10.0 100 1000Time (days)

Spec

ific

Cre

ep

HPLC

HPC-3

HPC-6

223

Figure G.13. Comparison between creep coefficient of HPC and HPLC mixes (a) linear time scale and (b) logarithmic time scale.

b

0.01 0.10 1.00 10.0 100 1000Time (days)

a

0.0

0.5

1.0

1.5

2.0

0 100 200 300 400 500 600Time (days)

Cre

ep C

oeffi

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t

HPLC

HPC-3

HPC-6

0.0

0.5

1.0

1.5

2.0

Cre

ep C

oeffi

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t

HPLC

HPC-3

HPC-6

b

0.01 0.10 1.00 10.0 100 1000Time (days)

a

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0 100 200 300 400 500 600Time (days)

Cre

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oeffi

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t

HPLC

HPC-3

HPC-6

0.0

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1.5

2.0

Cre

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HPLC

HPC-3

HPC-6

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Cre

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t

HPLC

HPC-3

HPC-6

224

G.5.2. Shrinkage Comparison

Figure G.14 compares shrinkage of HPLC and the two HPC mixes. Figure G.14 is

comprised of a linear time scale plot (G.14a) and a logarithmic time scale plot (G.14b) for

highlighting long-term and early-age behavior, respectively.

Average shrinkage of HPC-3, HPC-6 and HPLC was of the same magnitude for any

time up to 480 days of drying. After 480 days only HPC-6 and HPLC experimental results

are available, and they show an increasing difference as time increases. Shrinkage of HPC-6

did not increase significantly after one year while HPLC shrinkage went from 550 to 600 µε

during the 365-to-600-day period.

Before one year of drying, there were some periods in which one of the mixes had

more shrinkage than the others. For instance, before 10 days under drying, HPC-6 had the

least shrinkage, and HPC-3 had the most. Between 10 and 100 days after the beginning of

dying the experimental results overlapped. After 250 days shrinkage of HPLC was higher

than shrinkage of the other two normal weight mixes. HPC-3 and HPLC presented very

similar shrinkage rate. Figure G.14b, shows that the two shrinkage curves were fairly

parallel. HPC-6, on the other hand, showed a much faster shrinkage rate until 100 days of

drying, and after that it showed almost no increase in shrinkage.

From creep comparison it was concluded that creep of HPLC was either lower or very

similar to creep of the HPC of the same strength. On the other hand, from shrinkage

comparison it seems that shrinkage of HPLC was higher than HPC counterparts after one

year.

225

Figure G.14. Comparison between shrinkage of HPC and HPLC mixes (a) linear time scale and (b) logarithmic time scale.

a

0

100

200

300

400

500

600

0 100 200 300 400 500 600Time (days)

Shrin

kage

(µε)

HPLC

HPC-3

HPC-6

b

0

100

200

300

400

500

600

0.01 0.10 1.00 10.0 100 1000Time (days)

Shrin

kage

(µε)

HPLC

HPC-3

HPC-6

a

0

100

200

300

400

500

600

0 100 200 300 400 500 600Time (days)

Shrin

kage

(µε)

HPLC

HPC-3

HPC-6

a

0

100

200

300

400

500

600

0 100 200 300 400 500 600Time (days)

Shrin

kage

(µε)

HPLC

HPC-3

HPC-6

b

0

100

200

300

400

500

600

0.01 0.10 1.00 10.0 100 1000Time (days)

Shrin

kage

(µε)

HPLC

HPC-3

HPC-6

b

0

100

200

300

400

500

600

0.01 0.10 1.00 10.0 100 1000Time (days)

Shrin

kage

(µε)

HPLC

HPC-3

HPC-6

226

G.5.3. Total Strain Projection

Various mathematical models (logarithmic, hyperbolic, and exponential) were fitted

to specific creep and shrinkage of HPLC and the two HPC mixes. Exponential model (based

on Sakata’s model, 1993) gave good12 fits for specific creep for the three mixes. On the

other hand, hyperbolic tangent model (based on B3 model) gave good3 fits for shrinkage of

HPLC and HPC mixes. Figure G.15a shows specific creep of the mixes and its respective

exponential regressions. Figure G.15b shows shrinkage data and the hyperbolic tangent

regressions.

With the best fit curves, values at ultimate (40 years) can be estimated for specific

creep and shrinkage of HPLC and HPC’s. Once ultimate specific creep and ultimate

shrinkage were estimated; the total strain at 40 years (elastic strain, creep and shrinkage) was

calculated. Table G.10 presents the obtained estimates.

Table G.10. Ultimate strain estimates for HPLC and HPC loaded at 40 and 60% of its initial strength.

HPLC HPC-3 HPC-6 Stress

level 40%

Stress level 60%

Stress level 40%

Stress level 60%

Stress level 40%

Stress level 60%

Elastic Modulus1 3,663 3,949 3,350 stress (psi) 4,000 6,000 4,000 6,000 4,000 6,000

Elastic Strain2 (µε) 1,092 1,638 1,013 1,519 1,191 1,786 Shrinkage3 (µε) 607 504 539

Specific creep3 (µε/psi) 0.371 0.367 0.650 Creep strain4 (µε) 1,484 2,227 1,467 2,200 2,599 3,898 Total strain (µε) 3,184 4,472 2,984 4,224 4,328 6,226

Note: 1 measured from creep specimens; 2 elastic modulus times applied stress; 3 estimated from best fit; 4 specific creep times applied stress

12 Exponential fit was not the best mathematical model for each mix, but it gave the overall best

performance if only one model was to be used in the three mixes

227

Figure G.15. Best fit regressions for HPC and HPLC mixes (a) specific creep and (b) shrinkage.

0.01 0.10 1.00 10.0 100 1000 10000 100000

Time (days)

a

0.00

0.10

0.20

0.30

0.40

0.50

0.60Sp

ecifi

c Cr

eep

HPLCHPC-3HPC-6Best fit HPLCBest fit HPC-3Best fit HPC-6

0.01 0.10 1.00 10.0 100 1000 10000 100000

Time (days)

b

0

100

200

300

400

500

600

Shrin

kage

(µε)


0.01 0.10 1.00 10.0 100 1000 10000 100000

Time (days)

a

0.00

0.10

0.20

0.30

0.40

0.50

0.60Sp

ecifi

c Cr

eep



0.01 0.10 1.00 10.0 100 1000 10000 100000

Time (days)

b

0

100

200

300

400

500

600

Shrin

kage

(µε)



228

Total strain of HPLC at 40 years stressed with 40% and 60% of its ultimate strength

was estimated to be 3,184 and 4,472 µε, respectively. On the other hand, the strains under

the same condition for HPC-3 were slightly lower: 2,984 µε and 4,224 µε for 40% and 60%

stress level, respectively. Finally, total strain after 40 years of HPC-6 was estimated to be

4,328 µε and 6,226 µε, respectively.

The difference of about 6% between HPC-3 and HPLC was due in first place to the

higher elastic strain obtained in HPLC, and secondly, due to shrinkage. As seen in Figure

G.15a, there is virtually no difference between 40-year creep strain of HPLC and HPC. The

40% higher total strain predicted for HPC-6 were mainly due to the 75% higher specific

creep predicted on that concrete.

229

Appendix H. Comparison of Estimated Prestress Losses with

Experimental Results

H.1. Experimental Results

Actual losses were computed from experimental strains of concrete. The

experimental data did not include steel relaxation losses. Experimental strains were

projected to ultimate condition in order to compare with the estimates from the codes. Six

AASHTO Type II girders were cast using HPLC: three each with 8,000-psi and 10,000-psi

mixes. Four were 39-ft long and two were 43-ft long. Each was reinforced with ten 0.6-inch

diameter 270 ksi low relaxation strands. Approximately two month after girder fabrication, a

normal weight. 3,500-psi, composite deck slab was cast atop of each girder. The girders

were tested to determine flexure, shear and strand development strength about six month

after initial construction. Each girder was instrumented to measure internal and external

strains (Meyer et al., 2002). Figure H.1 shows the 6-inch embedded vibrating wire gage used

to measure strains at the center of gravity of the strands. Figure H.2 shows the six AASHTO

Type II girders at the laboratory before the deck placement.

Figure H.1. Vibrating wire strain gage used to measure internal strains in the girders.

230

Figure H.2 Measuring strains in the AASHTO Type II precast prestressed HPLC girders.

Strain measurements of the girders over time provided experimental data for actual

prestress computations. Table H.1 present the strain data obtained from the girders.

Table H.1 Experimental strains of 39-ft long girders (µε)

8,000-psi 10,000-psi DAYS G1A G1B DAYS G2A G2B Init1 0 0 Init1 0 0 Init2 0 0 Init2 0 0

Release -583 -609 Release -426 -417 2 -661 -695 1 -475 -471 3 -696 -731 3 -482 -479 7 -768 -811 7 -506 -496

14 -822 -870 14 -506 -506 106 -865 125 -531 113 -945 140 -520

231

Experimental strains are also shown in Figure H.3 for the 8,000-psi and 10,000-psi

HPLC 39-ft girders. Elastic strain of the 8,000-psi HPLC girders was about 600 µε while

total strain after 110 days was approximately 900 µε. The 10,000-psi HPLC girders, on the

other hand, had an elastic strain of 400 µε and total strain after 130 days of 530 µε.

Figure H.3 Experimental strains over time for the 8,000-psi and 10,000-psi HPLC 39-ft girders

Creep and shrinkage strains of the girders were computed as the difference between

total strain and initial elastic strain. After approximately 110 days, creep and shrinkage

strains were 309 µε for the 8,000-psi HPLC girders, and after 130 days they were 104 µε for

the 10,000-psi HPLC girders. Figure H.4 presents creep and shrinkage strains for individual

girders and the exponential regression obtained for each. Figure H.4(a) presents the data in a

linear time scale until the time of the last measurement, and Figure H.4(b) presents the data

in a logarithmic time scale projected until 10,000 days (27.4 years).

-1000

-800

-600

-400

-200

00 20 40 60 80 100 120 140

Age (Days)

Mic

rost

rain

s (in

/in x

10-6

)


Deck pouring

-1000

-800

-600

-400

-200

00 20 40 60 80 100 120 140

Age (Days)

Mic

rost

rain

s (in

/in x

10-6

)


Deck pouring

232

Figure H.4 Experimental creep and shrinkage and exponential regression for the 8,000-psi and 10,000-psi HPLC 39-ft girders (a) linear time scale (b) logarithmic time scale.

After 100 days under load and drying, creep and shrinkage of the 8,000-psi and

10,000-psi HPLC girders were approximately 300 and 100 µε, respectively. The regression

predicts that after 100 days creep and shrinkage are not going to increase significantly.

Based on the regressions shown in Figure H.4b, the creep and shrinkage strains at ultimate

would be 309 and 104 µε for the 8,000-psi and 10,000-psi HPLC girders, respectively.

-400

-300

-200

-100

00 20 40 60 80 100 120 140

Age (Days)

Mic

rost

rain

s (in

/in x

10-6

) 8,000-psi Individual Girder Result 8,000-psi Regression

10,000-psi Individual Girder Result 10,000-psi Regression

-400

-300

-200

-100

00.01 0.10 1.00 10.0 100 1000 10000

Age (Days)

Mic

rost

rain

s (in

/in x

10-6

) a

b

-400

-300

-200

-100

00 20 40 60 80 100 120 140

Age (Days)

Mic

rost

rain

s (in

/in x

10-6

) 8,000-psi Individual Girder Result 8,000-psi Regression

10,000-psi Individual Girder Result 10,000-psi Regression

-400

-300

-200

-100

00.01 0.10 1.00 10.0 100 1000 10000

Age (Days)

Mic

rost

rain

s (in

/in x

10-6

) a

b

233

H.2. Prestress Losses Calculations from Standards

Prestress losses for AASHTO Type II girders were computed by using the models

presented in section D.3. Table H.2 presents a comparison among the four models and the

actual losses in the 8,000-psi and 10,000-psi HPLC prestressed girders.

Table H.2 Comparison between experimental and estimated prestress losses of 8,000-psi HPLC prestressed girders




Stress After Jacking 202.5 100.0 202.5 100.0 202.5 100.0 202.5 100.0 202.5 100.0 Elastic Shortening -17.0 -8.4 -11.2 -5.5 -10.4 -5.2 -10.5 -5.2 -12.0 -5.9

Creep -16.4 -8.1 -14.1 -7.0 -14.8 -7.3 Shrinkage


CR+SH -8.8 -4.3 -22.9 -11.3 -19.2 -9.5 -26.1 -12.9

Relaxation -

11.513 -5.74 -18.7 -9.2


-3.8 -1.9 -5.6 -2.8 Total Time-dependent -20.2 -10.0 -41.5 -20.5 -24.2 -12.0 -23.0 -11.3 -31.7 -15.7

Total Losses -37.2 -18.4 -52.8 -26.1 -34.7 -17.1 -33.5 -16.5 -43.7 -21.6




Stress After Jacking 202.5 100.0 202.5 100.0 202.5 100.0 202.5 100.0 202.5 100.0 Elastic Shortening -12.0 -5.9 -10.1 -5.0 -9.8 -4.8 -9.0 -4.4 -10.9 -5.4

Creep -16.1 -7.9 -13.0 -6.4 -12.7 -6.3 Shrinkage


CR+SH -3.0 -1.5 -22.6 -11.2 -18.1 -8.9 -24.0 -11.8 Relaxation -14.64 -7.24 -19.2 -9.5


-3.9 -1.9 -5.6 -2.8 Total Losses -29.6 -14.6 -51.9 -25.6 -33.3 -16.4 -31.0 -15.3 -40.5 -20.0

The PCI and the two AASHTO models estimate final prestress losses while ACI-209

model estimates losses at any time after prestressing. For comparison purposes, ACI-209

estimates were computed for 40 years after prestressing assuming that as the final state of

13 Relaxation was determinate with Equation D.11 and experimental ES, CR and SH.

234

losses. Actual losses were computed from experimental strains of concrete at the center of

gravity of the strands. The AASHTO lump sum model gives a single time-dependent losses

estimate, so comparison of creep, shrinkage and relaxation is not possible for that model.

The experimental data, on the other hand, included only losses associated with

concrete: elastic shortening (ES), creep (CR) and shrinkage (SH). Steel relaxation was not

measured. Rather the “experimental” relaxation was computed using the AASHTO-LRFD

refined technique, considering the measured elastic, creep and shrinkage losses.

Experimental strains were projected to ultimate condition for comparison with the estimates

from the standards as shown in Figure H.4.

Figure H.5 (a) and (b) shows a comparison of estimated prestress losses with

experimental prestress losses, for the 8,000-psi and 10,000-psi ASSHTO Type II girders.

Figure H.5 presents elastic, creep and shrinkage, total time-dependent and total losses.

Experimental “total losses” for 8,000-psi HPLC girders was 37.2 ksi. The AASHTO-

LRFD refined and ACI-209 method overestimated losses by 15.6 and 6.5 ksi, respectively.

The AASHTO-LRFD lump sum and PCI methods were close to experimental data, but they

underestimated total losses by 2.5 and 3.7 ksi, respectively. Those differences expressed as

percentage of the initial stress before losses are: 7.7, 3.2, -1.2, and -1.8%, for the AASHTO-

LRFD refined, ACI-209, AASHTO-LRFD lump sum and PCI techniques, respectively.

The experimental prestress losses in the 10,000-psi girders were 29.6 ksi which was

lower than that of 8,000-psi girders by 7.6 ksi. The four methods shown in Figure H.5b

overestimated the experimental data. AASHTO-LRFD refined and lump sum methods

overestimated total losses by 22.3 and 3.7 ksi, respectively. When compared with initial

235

stress those differences are: 75.3, 12.5, 4.7, and 36.8%, for the AASHTO-LRFD refined,

AASHTO-LRFD lump sum, PCI, and ACI-209 techniques, respectively.

Figure H.5. Comparison between estimated prestress losses from AASHTO-LRFD, PCI, and ACI-209 methods (a) 8,000-psi HPLC girders, (b) 10,000-psi HPLC girders

Figure H.5 also shows that the four methods underestimated elastic shortening losses

regardless the type of HPLC. The AASHTO-LRFD refined, PCI and ACI-209 overestimated

creep and shrinkage losses by at least 100%. The underestimate in steel relaxation losses

given by the PCI and ACI-209 methods is probably due to the much higher creep and

Pres

tress

Los

ses (

ksi)

-55-50-45-40-35-30-25-20-15-10-50

ES CR+SH RE Total TimeDependent

Total Losses

Experimental 8,000-psi girders AASHTO RefinedAASHTO Lump sumPCIACI 209

a

b

Pres

tress

Los

ses (

ksi)

-55-50-45-40-35-30-25-20-15-10-50


Total Losses

Experimental 10,000-psi girdersAASHTO RefinedAASHTO Lump sumPCIACI 209

Pres

tress

Los

ses (

ksi)

-55-50-45-40-35-30-25-20-15-10-50


Total Losses



a

b

Pres

tress

Los

ses (

ksi)

-55-50-45-40-35-30-25-20-15-10-50


Total Losses



236

shrinkage losses that they predicted which decreases relaxation in the steel. AASHTO-

LRFD refined method also predicted a much lower relaxation after transfer (see Equation

D.11), but the losses before transfer (see Equation D.10) are still greatly overestimated. This

overestimate leads to a total relaxation loss higher than the computed from the experimental

data.

In Figure H.6, the predicted-to-measured ratio is shown. Losses are grouped in

elastic shortening, creep and shrinkage, total time dependent and total losses. Overestimates

appear as a predicted-to measured ratio greater than one, and the underestimates as lower

than one.

Figure H.6. Predicted-to-measured ratio of prestress losses from AASHTO-LRFD, PCI, and ACI-209 models

The fact that all methods underestimated elastic shortening was probably a

consequence of the procedures for measuring elastic shortening. The strain measurement

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

8,000-psiHPLC

10,000-psiHPLC

8,000-psiHPLC

10,000-psiHPLC

8,000-psiHPLC

10,000-psiHPLC

8,000-psiHPLC

10,000-psiHPLC


Pred

icte

d-to

-mea

sure

d ra


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

8,000-psiHPLC

10,000-psiHPLC

8,000-psiHPLC

10,000-psiHPLC

8,000-psiHPLC

10,000-psiHPLC

8,000-psiHPLC

10,000-psiHPLC


Pred

icte

d-to

-mea

sure

d ra


237

was taken after prestress transfer, which took approximately one hour. Therefore, the first

reading after transfer included not only instantaneous elastic strain, but also early creep plus

autogenous and drying shrinkage. The AASHTO-LRFD refined, PCI and ACI methods

greatly overestimated creep and shrinkage losses. The closest estimate was almost 120%

higher than experimental data. The same argument used to explain the underestimate of

elastic shortening can be used to explain overestimate of creep and shrinkage. Hence, the first

measurement after transfer probably included some creep and shrinkage which makes

experimental creep and shrinkage seem lower. All four methods overestimated total time-

dependent losses, which means that they are conservative for estimating those losses.

However, for the AASHTO-LRFD lump sum and PCI methods (8,000-psi HPLC girders),

the overestimate of time-dependent losses did not overcome the underestimate in elastic

losses, so the total predicted losses were lower than experimentally determined losses.

Nevertheless, the differences were small.

H.3. Estimates vs. Experimental Laboratory Results

As described in Appendix F, creep and shrinkage tests were conducted on HPLC

mixes. Therefore, estimates for such strains using prestress losses models can be compared

with experimental results to evaluate the performance of the models.

Code estimates for creep and shrinkage strains can be obtained by dividing the

equations given in Section D.2 by elastic modulus of prestressing steel. Figure H.7 presents

those estimates for 8,000-psi HPLC specimens by PCI, AASHTO refined and ACI-209

standards. It should be noted that actual conditions of creep and shrinkage testing were used

on Figure H.2 results. Actual conditions were 50% of relative humidity and a volume-to-

238

surface ratio of 1 inch, so the magnitudes obtained were higher than the ones discussed in

Section H.2.

Figure H.7 Comparison between 8,000-psi HPLC experimental strains and those estimated by AASHTO-LRFD refined, PCI, and ACI-209 models.

The AASHTO-LRFD refined, PCI and ACI-209 models gave a good estimate of

elastic shortening. The 10% difference was probably caused by the fact that model used

experimental elastic modulus measured on 6”x12” cylinders while creep specimens were

4”x15” cylinders. A higher slenderness might have led to higher elastic strain. As seen

before, the largest differences were obtained on the shrinkage portion where PCI and

AASHTO refined methods underestimated shrinkage by more than 70%. The PCI method

was the least accurate method for estimating creep; it underestimated it by slightly less than

1307

2616

828

1192

1791

228

1127

1599

231

1192

2459

698

0 500 1000 1500 2000 2500 3000

Elastic Strain

Creep

Shrinkage

Microstrains (in/inx10-6)

MeasuredAASHTO refinedPCIACI 209

1307

2616

828

1192

1791

228

1127

1599

231

1192

2459

698

0 500 1000 1500 2000 2500 3000

Elastic Strain

Creep

Shrinkage



239

40%. The AASHTO refined method also underestimated creep losses, but by 30%. The

ACI-209 method gave the best creep estimate with only 4.4% underestimate. The fact that

the PCI and AASHTO refined methods underestimated creep strains in such proportion is

probably because those design methods are estimating what happens on a prestressed

concrete member rather than for test specimens. On a prestressed member, creep of concrete

occurs at a decreasing stress because creep, shrinkage and steel relaxation decrease the

effective stress on concrete. In creep testing, creep develops at a constant stress, so no

decrease in such stress occurs over time, and the resulting creep is larger. The ACI-209

prestress losses method is based on ACI-209 creep and shrinkage models which were derived

from material testing at constant stress. The ACI-209 model also uses many more factors in

modeling creep and shrinkage.

Figure H.8 compares the measured strains in 10,000-psi HPLC cylinders specimens

and the values obtained from standard estimates.

As occurred with 8,000-psi HPLC, elastic shortening was underestimated due to the

slenderness of the creep specimens that have an apparent lower modulus of elasticity. Creep

was overestimated by 13 and 35% by the AASHTO refined and ACI-209 methods,

respectively. The PCI method again gave the least accurate estimate of creep. The PCI creep

loss expression (Equation D.3) estimates creep of concrete as a factor (Kcr) times long-term

stresses on concrete. As presented in Sections B.2, C.1 and C.2, creep of concrete is a

complex phenomenon that depends on many factors. The PCI expression oversimplifies

creep leading to large differences with other more sophisticated methods such as ACI-209.

Shrinkage was underestimated by more than 60% by the PCI and AASHTO refined

methods, and it was overestimated by the ACI-209 method.

240

Figure H.8 Comparison between 10,000-psi HPLC experimental strains and those estimated by AASHTO-LRFD refined, PCI, and ACI-209 models.

All the analyzed methods for estimating prestress losses overestimated the actual

losses measured in 8,000-psi and 10,000-psi HPLC AASHTO Type II prestressed girders. In

particular, AASHTO refined and lump sum methods were conservative in predicting strains

in HPLC. As explained in Section D.2, the AASHTO methods do not consider lightweight

concrete, so they estimate losses for a normal weight HPC.

1470

1850

610

1275

2099

228

1148

1773

231

1275

2481

694

0 500 1000 1500 2000 2500 3000

Elastic Strain

Creep

Shrinkage



1470

1850

610

1275

2099

228

1148

1773

231

1275

2481

694

0 500 1000 1500 2000 2500 3000

Elastic Strain

Creep

Shrinkage



241

Appendix I. Creep and Drying Shrinkage Models S.I. units

I.1 Models for Normal Strength Concrete

I.1.1. ACI-209 Method

Creep Model:

ut ttdtt φφ ψ

ψ

⋅−+

−=

)'()'(

(I.1)

where

øt: creep coefficient at age “t” loaded at t′



ψ: constant depending on member shape and size

d: constant depending on member shape and size


αψλ γγγγγγφ ⋅⋅⋅⋅⋅⋅= svslau 35.2 (I.2)

where


⋅⋅

=−

−

curingsteamfortcuringmoistfort

la 094.0

118.0

'13.1'25.1

γ ; age of loading factor


242

≥⋅−

=otherwise

hforh00.1

40.067.027.1λγ ; ambient relative humidity factor


{ }( )SV

VS ⋅−⋅+= 0213.0exp13.1132γ ; volume-to-surface ratio factor

V: specimen volume (mm3)

S: specimen surface area (mm2)


s: slump (mm)

ψλψ ⋅+= 24.088.0 ; fine aggregate content factor



α: air content (%)


ushtsh ttftt )(

)()()(

0

0 εε α

α

⋅−+

−= (I.3)

where



(εsh)t: shrinkage strain after “t-t0” days under drying (mm/mm)

α: constant depending on member shape and size

f: constant depending on member shape and size

243

(εsh)u: ultimate shrinkage strain (mm/mm)

αψλ γγγγγγε ⋅⋅⋅⋅⋅⋅= csvsush 780)( (I.4)

where


>⋅−≤≤⋅−

=80.00.300.3

80.040.00.140.1hforh

hforhλγ ; ambient relative humidity factor


{ }SV

VS ⋅−⋅= 00472.0exp2.1γ ; volume-to-surface ratio factor




s: slump (mm)

>⋅−≤⋅−

=50.02.090.050.04.130.0

ψψψψ

γψ forfor

; fine aggregate content factor


cc ⋅+= 00061.075.0γ ; cement content factor

c: cement content (kg/m3)


α: air content (%)

244

I.1.2. AASHTO-LRFD Method

Creep Model:

fchlau kkkk ⋅⋅⋅⋅= 50.3φ (I.5)

where


curingmoistfortkla118.0'00.1 −⋅= ; age of loading factor

−∆+

−⋅∆= ∑ 65.13)(273

4000exp

0TtT

tti

ndayuntil


−∆+

−⋅∆= ∑ 65.13)(273

4000exp'

0TtT

tti

loadinguntil


∆ti: period of time (days) at temperature T(∆ti) (oC)

T0: 1 oC

hkh ⋅−= 83.058.1 ; ambient relative humidity factor


{ } { }

⋅−⋅+⋅

+

+⋅⋅=

587.2

0216.0exp77.180.1

45

0142.0exp26 SV

tt

tSV

t

kc ; size factor



245

9'

67.0

1c

f fk

+= ; concrete strength factor

fc’: compressive strength at 28 days (ksi)

Shrinkage Model:

hsush kkK ⋅⋅=)(ε (I.6)

where


=curingsteamforcuringmoistfor

Kµεµε

560510

; ultimate shrinkage base value

( ){ } ( )

( )( )

⋅−⋅

−+−

−+⋅⋅

−

=923

037.01064

45

0142.0exp26

0

0

0

0

SV

tttt

ttSV

tt

ks ; size factor





≥⋅−<⋅−

=80.029.429.480.043.100.2

hforhhforh

kh ; ambient relative humidity factor


246

I.1.3. CEB-FIP Method

Creep Model:

)',()'(

)',( 2828

ttE

ttt c

cr φσ

ε = (I.7)

3.0

028 )'()'(

−+

−⋅=

tttt

Hβφφ (I.8)

where




σc(t′): applied stress (MPa)

E28: 28-day elastic modulus (MPa)

ø28: creep coefficient at age “t” loaded at t′

( )2.0

310 '1.0

1

10'

3.5

100

246.0

11tf

uA

h

cc+

⋅⋅

⋅⋅

−+=φ ; notional creep coefficient


Ac: cross sectional area (mm2)

u: exposed perimeter (mm)

fc’: compressive strength at 28 days (MPa)

247

( )[ ] 1500250100

22.11150 18 ≤+

⋅⋅⋅+⋅= u

Ah

c

Hβ ; constant depending on member size and

relative humidity

When cement different from normal hardening is used and/or special curing regime is

followed, t′ is modified following Equations I.9 and I.10 which incorporate the maturity

concept.

dayst

ttT

T 5.01)'(2

9'' 2.1 ≥

+

+=

α

(I.9)

−

∆+−⋅∆= ∑ 65.13

)(273

4000exp'

TotT

tti

iT (I.10)

where

+

−=



1/0

1α ; cement type parameter

t′T: adjusted age of concrete at loading


T0: 1 oC

When stresses between 40 and 60% of compressive strength are applied, CEB-FIP

recommends using a high stress correction to the notional creep “ø0” as shown in Equation

I.11.

( ){ }4.05.1exp0,0 −⋅⋅= σφφ kk (I.11)

248

where

kσ: stress-to-strength ratio at time of application of load.


)(),( 00 tttt ssos −⋅⋅= βεε (I.12)

where



RHc

scsf

ββε ⋅

−⋅⋅+=

10'

9101600 ; notional shrinkage coefficient

=



sc

8/5

4β ; cement type parameter

[ ]

≥

≤≤−⋅−

99.025.0

99.040.0155.1:

3

hfor

hforhRHβ


fc’: compressive strength of concrete cylinders at 28 days (MPa)

( ) ( )( )

5.0

0

00,

−+

−=

tttt

ttsH

s ββ ; shrinkage function

2

100

2350

⋅⋅= u

Ac

sHβ


249


When temperatures above 30oC (86oF) are applied, CEB-FIP recommends using an

elevated temperature correction for βsH and βRH as shown below.

( ){ }2006.0exp, −⋅−⋅= TsHTsH ββ

−⋅

−+⋅=

4020

03.108.01,

ThRHTRH ββ

TsH ,β : geometric factor corrected by temperature

TRH ,β ; relative humidity factor corrected by temperature

T: ambient temperature (oC)


I.1.4. Bažant and Panula’s - BP Method

Creep Model:

),',(),',()',(1)',( 0000

tttCtttCttCE

ttJ pd −++= (I.13)

where


E0: Modulus of elasticity at the age of loading (MPa)

C0: basic creep portion [specific creep - (mm/mm)/MPa]

Cd: drying creep portion [specific creep - (mm/mm)/MPa]

Cp: creep decrease after drying [specific creep - (mm/mm)/MPa]




250

Basic Creep Model:

( ) ( )nm tttE

ttC '')',(0

10 −⋅+⋅= − α

φ (I.14)

where



( )αφ+⋅

= −

⋅

m

n

282103

1 material parameter



( ) 4'145.01.01.2412.0

45130

07.012.0

1

2.23

15.1

6

6

−⋅

⋅

⋅⋅⋅+⋅=

≤

>+⋅

+

= aga

cwf

cs

ca

xxfor

xforx

x

n c


w: water content (kg/m3)

a: aggregate content (kg/m3)

s: sand content (kg/m3)

g: coarse aggregate content (kg/m3)





05.193.000.1

251

( )2'145.0128.0

cfm

⋅+= ; ( )c

w⋅=


Drying Creep Model:

According to Bažant and Panula (1978c and 1984) drying creep can be modeled by

Equation I.15:

ncsh

shh

mdd

d

ttkt

EtttC

⋅−

∞−

−⋅

+⋅⋅⋅⋅='

101''

'),',( 2

00

τε

φ (I.15)

where



dsh

dtt

φτ

φ ⋅

⋅−

+=− 2

1

0

10'

1'

85.0'145.0560000008.0

07.011027.0008.0 5.1

3.13.04.1

−

⋅

⋅

⋅⋅⋅=

≤

>⋅+

⋅+

=∞

−

scd

cw

sgf

asr

rfor

rforr

εφ







252

( )01

12

2150

600tC

CS

Vk refs

sh ⋅

⋅⋅⋅=τ size-dependent parameter

=

cubeaforsphereafor

prismsquaredfiniteinforcylinderfiniteinfor

slabfiniteinfor

ks

55.130.125.115.10.1

; shape factor



daymmC ref /6451 21 =

( )

+⋅⋅=

0701

3.605.0't

kCtC T

2171281

77 ≤≤−⋅⋅= CccwC

−=TTT

TkT50005000exp'

00

T0: 296.15 K (reference temperature)

T: ambient temperature K

( )2'145.0128.0

cfm

⋅+= ; material parameters

( ) 4'145.01.01.2412.0

45130

07.012.0

1

2.23

15.1

6

6

−⋅

⋅

⋅⋅⋅+⋅=

≤

>+⋅

+

= aga

cwf

cs

ca

xxfor

xforx

x

n c




05.193.000.1

253



h0: 0.98 to 1.0

ncd ⋅−= 5.78.2

εs∞: final shrinkage in µε as in Equation I.17

Creep Decrease after Drying

( )',100

1''),',( 00

0 ttCtt

kctttCn

shhpp ⋅

−⋅

+⋅⋅=−

τ (I.16)

where

Cp: creep decrease after drying portion (specific creep)




83.0=pc

220'' hhkh −= humidity dependent parameter


h0: 0.98 to 1.0

( )01

12

2150

600tC

CS

Vk refs

sh ⋅


254

=

cubeaforsphereafor


slabfiniteinfor

ks

55.130.125.115.10.1

; shape factor




( )

+⋅⋅=

0701

3.605.0't

kCtC T

2171281

77 ≤≤−⋅⋅= CccwC

( ) 4'145.01.01.2412.0

45130

07.012.0

1

2.23

15.1

6

6

−⋅

⋅

⋅⋅⋅+⋅=

≤

>+⋅

+

= aga

cwf

cs

ca

xxfor

xforx

x

n c




05.193.000.1







255


0

00 ),(

tttt

kttsh

hshsh −+−

⋅⋅= ∞ τεε (I.17)

where

εsh∞: ultimate shrinkage stain µε

≤≤=−≤−

=00.198.0int

00.12.098.01 3






( )01

12

2150

600tC

CS

Vk refs

sh ⋅


=

cubeaforsphereafor


slabfiniteinfor

ks

55.130.125.115.10.1

; shape factor




( )

+⋅⋅=

0701

3.605.0't

kCtC T ; 2171281

77 ≤≤−⋅⋅= CccwC

−=TTT

TkT50005000exp'

00

256

T0: 296.15 K (reference temperature)

T: ambient temperature K

13908801210

+−=∞

z

sε ; 012'145.01

5.025.13

12

≥−

⋅⋅

+⋅

⋅+⋅= cf

cw

cs

sg

caz







I.1.5. Bažant and Baweja’s - B3 Method

Creep Model:

),',()',()',( 01 od tttCttCqttJ ++= (I.18)

where


0

6

1106.0

Eq ×

= instantaneous strain due to unit stress





257


E0: asymptotic modulus elastic modulus (MPa) (age independent)

Basic Creep Model

Basic creep is given by Equation I.19, as follows:

( ) [ ]

+−+⋅+⋅=

'ln)'(1ln',)',( 4320 t

tqttqttQqttC n (I.19)

where

( ) 9.02 '1456856.11.451 −⋅⋅⋅= cfcq ; ageing viscoelastic compliance



( ) ( ) ( )( )

( ) ( ) ( ) ( ) ( )[ ]( ) ( ) ( )[ ]( ) ( ) 8'7.1'

'1ln'','21.1'086.0'

;','

1'',12.0

19

49

2'

1'

+⋅=−+⋅=

⋅+⋅=

+⋅= −

−−

ttrtttttZ

tttQ

ttZtQ

tQttQ nmftrtr

ff

m = 0.5; n = 0.1



2

4

3 29.0 qcwq ⋅

⋅= ; non-ageing viscoelastic compliance

7.0

4 14.0−

⋅=

caq ; flow compliance




258

Drying Creep Model

Additional creep due to drying is given by Equation I.20

( ){ } ( ){ }[ ] 21

050 '8exp8exp),',( tHtHqtttCd ⋅−−⋅−⋅= (I.20)

where

6.05 '

7.5220 −∞⋅= sh

cfq ε


εsh∞: ultimate shrinkage as shown in Equation I.21

( ) ( )sh

tthtH

τ0tanh11

−⋅−−=





t0’: max(t′,t0) (days)

τsh: size factor as shown in Equation I.21


shhshsh

ttktt

τεε 0

0 tanh),(−

⋅⋅−= ∞ (I.21)

where




259

( )[ ]( )

( )2

1

0

0

21

28.01.221

85.04

60785.04607

270'14500856.0

+⋅+

+

⋅+⋅+⋅⋅⋅⋅⋅−= −∞

sh

sh

csh

tt

fw

ττ

ααε

=

cementIIItypeforcementIItypeforcementItypefor

,10.1,85.0,00.1

1α ; cement type factor

−=

−=

specimenssealedforspecimenscuredhorwaterfor

specimenscuredsteamfor

,20.100.1,00.1

,75.0

2α ; curing factor



≤≤=−≤−

=00.198.0int

00.12.098.01 3




( ) ( )225.0008.00 0787.0'1458.190 S

Vkft scsh ⋅⋅⋅⋅⋅⋅= −−τ ; size-dependent factor

=

cubeaforsphereafor


slabfiniteinfor

ks

55.130.125.115.10.1

; shape factor



260

I.1.6. Gardner and Lockman’s - GL Method

Creep Model:

( ) ( ) 28

21

22

21

21

3.0

3.0

1

15.0)'(

)'(086.115.2

7)'()'(7

14)'()'(2)',(

c

ocr

ES

Vtt

tth

tttt

tttttttc

⋅

⋅+−

−⋅⋅−⋅+

+

+−

−⋅

+

+−−⋅

=

(I.22)

where

ccr: creep coefficient at age “t” loaded at t′ (µε/MPa)







Ec28: 28-day elastic modulus (MPa)


( ) ( )2

1

2

0

040

15.0)(

)(18.11),(

⋅+−

−⋅⋅−⋅=

SVtt

tthtt shush εε (I.23)

where


261

62

1

10'

301000 −⋅

⋅⋅=

cshu f

Kε ; ultimate shrinkage strain

=

cementIIITypeforcementIITypefor

cementITypeforK

15.170.000.1

; cement factor







I.1.7. Sakata’s - SAK Method

Creep Model:

( ) ( ){ }( )6.0'09.0exp1'')',( tttt dcbccr −⋅−−⋅+= εεε (I.24)

where

εcr: specific creep at age “t” loaded at t′ (µε/MPa)



ε’bc: basic creep portion, parameter depending on water and cement content, water-to-cement

ratio, and age of loading

ε’dc: drying creep portion, parameter depending on water and cement content, water-to-

cement ratio, member volume-to-surface ratio, and relative humidity

Basic Creep Model

262

Basic creep is given by Equation I.25, as follows:

( ) ( ) [ ]( ) 67.04.22 'ln5.1' −⋅⋅+⋅= tcwwcbcε (I.25)

where

ε’bc: basic specific creep portion (µε/MPa)




Drying Creep Model

Drying creep is given by Equation I.26

( ) ( ) [ ]( ) ( ) ( ) 3.00

36.02.22.44.1 1ln0045.0' −−⋅−⋅⋅⋅+⋅= thS

Vc

wwcdcε (I.26)

where

ε’dc: drying specific creep portion (µε/MPa)






( ){ }( ) 556.000 10108.0exp1),( −

∞ ×−⋅−−⋅= tttt shsh εε (I.27)

where


263



{ }( ) [ ] [ ]( ) [ ]0

2ln44ln50ln380exp1780600 tS

Vwhsh ⋅+⋅−⋅+−⋅+−=∞ε ; ultimate shrinkage

strain





I.2 Models for High Strength Concrete

I.2.1. CEB-FIP Method as modified by Yue and Taerwe (1993)

( )[ ] 15002502012.01'

130 18 ≤+

⋅⋅⋅+⋅= u

Ahf

c

cHβ (I.28)

where

βH: constant depending on member size and relative humidity




( )2.0

310 '1.0

1

110

'6.2

100

246.0

11tf

uA

h

cc+

⋅

−

⋅

⋅⋅

−+=φ (I.29)

264

where

φ0: ; notional creep coefficient






I.2.2. Bažant and Panula’s - BP Method

ncshd

shh

mdd

d

ttb

ktE

tttC⋅−

∞−

−⋅

+⋅⋅⋅⋅='

1'''

),',( 2

00

τε

φ (I.30)

where

Cd: drying creep portion [specific creep - (µε)/MPa]


dshd

d att

φτ

φ ⋅

⋅−

+=− 2

1

0'1'

≥

≤=

MPaffor

MPaffora

c

c

d

0.69'1

4.41'10; linear interpolation between 41.4 and 69.0 MPa

( )01

12

2150

600tC

CS

Vk refs

sh ⋅


=

cubeaforsphereafor


slabfiniteinfor

ks

55.130.125.115.10.1

; shape factor

265




( )

+⋅⋅=

0701

3.605.0't

kCtC T

2171281

77 ≤≤−⋅⋅= CccwC

−=TTT

TkT50005000exp'

00

T: ambient temperature oK


85.0'560000008.0

07.011027.0008.0 5.1

3.13.04.1

−

⋅

⋅

⋅⋅=

≤

>⋅+

⋅+

=∞

−

scd

cw

sgf

asr

rfor

rforr

εφ







13908801210

+−=∞

z

sε ; 012'145.01

5.025.13

12

≥−

⋅⋅

+⋅

⋅+⋅= cf

cw

cs

sg

caz :

final shrinkage in µε

266

( )2'145.0128.0

cfm

⋅+=



h0: 0.98 to 1.0

≥

≤=

MPaffor

MPafforb

c

c

d

0.69'100

4.41'10; linear interpolation between 41.4 and 69.0 MPa

ncd ⋅−= 5.78.2

( ) 4'145.01.01.2412.0

45130

07.012.0

1

2.23

15.1

6

6

−⋅

⋅

⋅⋅⋅+⋅=

≤

>+⋅

+

= aga

cwf

cs

ca

xxfor

xforx

x

n c




05.193.000.1

I.2.3. Sakata’s - SAK Method

( )( ) [ ]1'ln

''1235014)',( +−⋅

+⋅+−⋅⋅

= tttf

hwttc

crε (I.31)

where

εcr: specific creep at age “t” loaded at t′ (µε/MPa)



267

fc’(t′): compressive strength at the age of t′(MPa)




( ) ( )( )0

00,

tttt

tt shsh −+

−⋅= ∞

βε

ε (I.32)

where




( )01

1

'500exp1501

1t

f

wh

c

sh ⋅+⋅

−+

⋅−=∞ η

αε ; ultimate shrinkage strain

=cementhardeningslowfor8cementportlandnormalfor10

α ; cement factor




( )( ) 41025.0'007.0exp15 −×⋅+⋅⋅= wfcη

07.0100

4

tS

Vw

⋅+

⋅=β



268

I.2.4. AFREM Method

Creep Model:

( ) ( ))',()',(')',(28

ttttE

ttt dbcr φφσε += (I.33)

where


σ (t′): applied stress at t′ (MPa)

E28: 28-day elastic modulus (MPa)



øb: basic creep coefficient at age “t” loaded at t′

ød: drying creep coefficient at age “t” loaded at t′

Basic Creep Model

( )'

'', 0 tttttt

bcbb

−+−

⋅=β

φφ (I.34)

where

( )

−

−=

concretefumesilicanonfor

concretefumesilicafortfc

b

4.1

''6.3

37.0

0φ

( )

( )

−

⋅⋅

−

⋅⋅

=

concretefumesilicanonforf

tf

concretefumesilicaforf

tf

c

c

c

c

bc

'''

1.3exp40.0

'''

8.2exp37.0

β

f’c(t′): compressive strength at the age of t′ (MPa)

269

f’c: compressive strength at 28 days (MPa)

Drying Creep Model

( ) ( ) ( )( )0000 ,',,', ttttttt shshdd εεφφ −⋅= (I.35)

where

−

−=


concretefumesilicaford

3200

10000φ

εsh: drying shrinkage as shown in Equation I.36


( ) { }( )

( )( ) 6

0

0

2

0

0 102

10075'046.0exp72'),( −×−⋅

−+

⋅⋅

⋅−+⋅−⋅⋅= tt

ttuA

hffKtt

cds

ccsh

βε (I.36)

where


( )

≥⋅−

≤=

MPafforf

MPafforfK

cc

c

c

57''21.030

57'18' ; strength-dependent factor





−

−=


concretefumesilicafords

021.0

007.00β



270

I.2.5. AASHTO-LRFD method as modified by Shams and Kahn (2000)

Shams and Kahn (2000), proposed some changes to AASHTO-LRFD creep

expression (see Section I.1.2) in order to better predict creep of HPC. Shams and Kahn

method for estimating creep is presented in Equation I.37.

( )( ) 6.0

6.0

' ''ttd

ttkkkkkk mtHfvst c −+−

⋅⋅⋅⋅⋅⋅⋅= ∞ σφφ (I.37)

where

øt: creep coefficient at “t” loaded at t′

−∆+

−⋅∆= ∑ 65.13)(273

4000exp

0TtT

tti

ndayuntil


−∆+

−⋅∆= ∑ 65.13)(273

4000exp'

0TtT

tti

loadinguntil



T0: 1 oC

73.2=∞φ : ultimate creep coefficient

{ } { }

⋅−⋅+⋅

+

+⋅⋅=

587.2

0216.0exp77.180.1

45

0142.0exp26 SV

tt

tSV

t

kvs ; size factor



271

'145645.18.4

cf f

kc ⋅+= ; concrete strength factor

fc’: compressive strength of concrete cylinders at 28 days (MPa)

hkH ⋅−= 83.058.1 ; ambient relative humidity factor


+

⋅=57.0'

7.0exp65.0' tkt ; maturity at loading factor

( ){ }

≤Γ

≤Γ≤−Γ⋅=

4.00.1

6.04.04.05.1exp

for

forkσ ; stress-to-strength ratio factor

Γ: stress-to-strength ratio at loading

{ }( ) 73.559.0exp165.01 mkm ⋅−−⋅+= : moist curing period factor

m: moist curing period (days)

'09.0356.0'

ttd

⋅+= : maturity for 50% of ultimate creep coefficient

Drying Shrinkage Model: Equation I.37 shows Shams and Kahn drying shrinkage

expression.

( ) ( )

5.0

'',

−+

−⋅⋅⋅⋅= ∞

o

otHvsshosh ttf

ttkkktto

εε (I.38)

where

=∞ concrete cured-moistfor560concrete cured-sfor510

µεµε

εteam

sh ; ultimate shrinkage strain

−∆+

−⋅∆= ∑ 65.13)(273

4000exp

0TtT

tti

ndayuntil


272

−∆+

−⋅∆= ∑ 65.13)(273

4000exp

0

0

TtT

tti

dryingbeginninguntil

i ; maturity of concrete at the beginning of

drying (days)


T0: 1 oC

{ } { }

⋅−⋅+⋅

+

+⋅⋅=

587.2

0216.0exp77.180.1

45

0142.0exp26 SV

tt

tSV

t

kvs ; size factor



≥⋅−<⋅−

=80.029.429.480.043.100.2

hforhhforh

kH ; ambient relative humidity factor


+⋅=

ot t

k45.9

2.4exp67.00

; factor for maturity at the beginning of drying

f: 23 (days)

273

Appendix J. Analysis of Variance - ANOVA

Analysis of Variance (ANOVA) was performed using JMP 5.01 statistical software.

The same analysis was performed using creep deformation, creep coefficient, specific creep

and shrinkage.

Note: α=0.05 was adopted through the analysis of variance presented in this section.

Therefore, when it is concluded that a certain factor is statistically significant, it means that

P-value is smaller than 0.05.

J.1. Three-Factor ANOVA: Creep of 8L HPLC

Levels Age at Loading 16 hours 24 hours

Stress Level 40% initial strength 60% initial strength

Fact

ors

Time under Load 34 levels (see Appendix K)

CreepParameter Estimate df SS Fratio Prob Alpha 0.05Intercept -239.403 1 0 0 1Log(time) 212.40439 1 208333836 13501.1329 0.00E+00 Significant at alpha levelStress Leve16.000189 1 13517120 875.980769 6.67E-114 Significant at alpha levelAge Loadin 0.2940341 1 7.30E+02 0.04733253 0.82785633 Not signigicant at alpha level

Step Parameter Action DF error Sgg pro Seq SS MSE Rel MSE Rsquared Cp p527 229937447 436313.9412 1.000 0.000

1 Log(time) Entered 526 2.75E-272 208333836 41072 0.094 0.906 876.0281 22 Stress LeveEntered 525 4.14E-114 13517120 15403 0.035 0.965 2.0473325 33 Age LoadinEntered 524 0.82785633 730.380682 15431 0.035 0.965 4 4

Specific CreepParameter Estimate df SS Fratio Prob Alpha 0.05Intercept 0.3838421 1 0 0 1Log(time) 0.0606254 1 16.9723559 21681.3996 0.00E+00 Significant at alpha levelStress Leve -0.00245 1 0.31703001 404.99117 3.69E-67 Significant at alpha levelAge Loadin -0.004954 1 2.07E-01 264.813848 1.72E-48 Significant at alpha level

Step Parameter Action DF error Sgg pro Seq SS MSE Rel MSE Rsquared Cp p527 17.906875 0.03397889 1.000 0.000

1 Log(time) Entered 526 0.00E+00 16.9723559 0.001777 0.052 0.948 669.80502 22 Stress LeveEntered 525 3.43E-49 0.31703001 0.001176 0.035 0.966 266.81385 33 Age LoadinEntered 524 1.72E-48 0.20729819 0.000783 0.023 0.977 4 4

Creep CoefficientParameter Estimate df SS Fratio Prob Alpha 0.05Intercept 0.9296568 1 0 0 1Log(time) 0.1955531 1 176.588379 22692.4061 0.00E+00 Significant at alpha levelStress Leve -0.00663 1 2.32113648 298.276545 3.10E-53 Significant at alpha levelAge Loadin -0.003821 1 1.23E-01 15.8500842 0.00007824 Significant at alpha level


1 Log(time) Entered 526 0.00E+00 176.588379 0.012400 0.036 0.964 314.12663 22 Stress LeveEntered 525 4.14E-52 2.32113648 0.008002 0.023 0.977 17.850084 33 Age LoadinEntered 524 0.00007824 0.12334261 0.007782 0.022 0.978 4 4

274

J.2. Three-Factor ANOVA: Creep of 10L HPLC

Levels Age at Loading 16 hours 24 hours


Fact

ors


CreepParameter Estimate df SS Fratio Prob Alpha 0.05Intercept 279.3054 1 0 0 1Log(time) 154.1747 1 117219528 6561.9803 1.66E-298 Significant at alpha levelStress Leve 10.76042 1 6113530.7 342.23707 3.52E-59 Significant at alpha levelAge loading -15.0251 1 1.91E+06 106.76362 6.66E-23 Significant at alpha level


1 Log(time) Entered 526 5.92E-236 117219528 33044 0.129 0.871 449.00069 22 Stress LeveEntered 525 2.25E-51 6113530.7 21462 0.084 0.916 108.76362 33 Age LoadinEntered 524 6.66E-23 1907165.3 17863 0.070 0.930 4 4

Specific CreepParameter Estimate df SS Fratio Prob Alpha 0.05Intercept 0.502678 1 0 0 1Log(time) 0.036619 1 6.6129225 4109.7526 3.62E-250 Significant at alpha levelStress Leve -0.002436 1 0.3133651 194.74794 7.33E-38 Significant at alpha levelAge loading -0.012822 1 1.39E+00 863.21249 7.38E-113 Significant at alpha level


1 Log(time) Entered 526 2.35E-148 6.6129225 0.004839 0.278 0.722 1057.9604 22 Stress LeveEntered 525 1.03E-16 0.3133651 0.004252 0.245 0.756 865.21249 33 Age LoadinEntered 524 7.38E-113 1.3889783 0.001609 0.093 0.908 4 4

Creep CoefficientParameter Estimate df SS Fratio Prob Alpha 0.05Intercept 1.586833 1 0 0 1Log(time) 0.126168 1 78.50038 3621.6345 1.69E-237 Significant at alpha levelStress Leve -0.006031 1 1.9207722 88.615302 1.51E-19 Significant at alpha levelAge loading -0.042806 1 1.55E+01 714.15659 6.59E-100 Significant at alpha level


1 Log(time) Entered 526 1.82E-152 78.50038 0.054674 0.269 0.732 802.77189 22 Stress LeveEntered 525 1.73E-09 1.9207722 0.051119 0.251 0.750 716.15659 33 Age LoadinEntered 524 6.59E-100 15.47963 0.021675 0.106 0.894 4 4

275

J.3. Two-Factor ANOVA: Creep of 8F HPLC

Levels Stress Level 40% initial strength 60% initial strength

Fact

ors


CreepParameter Estimate df SS Fratio Prob Alpha 0.05Intercept -301.6422 1 0 0 1Log(time) 164.5522 1 84123632 1104.162 2.17E-101 Significant at alpha levelStress Leve 34.24291 1 34708267 455.56223 1.25E-61 Significant at alpha levelAge Loadin 0 0 0.00E+00 . . Not signigicant at alpha level


1 Log(time) Entered 294 8.36E-60 84123632 193984 0.405 0.596 456.5622 22 Stress LeveEntered 293 1.25E-61 34708267 76188 0.159 0.842 3 3

Specific CreepParameter Estimate df SS Fratio Prob Alpha 0.05Intercept 0.414483 1 0 0 1Log(time) 0.046714 1 6.7795888 819.09765 7.42E-87 Significant at alpha levelStress Leve -0.000388 1 0.0044524 0.5379283 4.64E-01 Not signigicant at alpha levelAge Loadin 0 0 0.00E+00 . . Not signigicant at alpha level


1 Log(time) Entered 294 4.64E-87 6.7795888 0.008264 0.265 0.736 1.537928 22 Stress LeveEntered 293 0.463879 0.0044524 0.008277 0.265 0.737 3 3

Creep CoefficientParameter Estimate df SS Fratio Prob Alpha 0.05Intercept 3.036545 1 0 0 1Log(time) 0.216522 1 145.6516 640.48268 1.06E-75 Significant at alpha levelStress Leve -0.024359 1 17.563658 77.233742 1.31E-16 Significant at alpha levelAge Loadin 0 0 0.00E+00 . . Not signigicant at alpha level


1 Log(time) Entered 294 4.48E-66 145.6516 0.286376 0.368 0.634 78.23374 22 Stress LeveEntered 293 1.31E-16 17.563658 0.227409 0.292 0.710 3 3

276

J.4. Two-Factor ANOVA: Creep of 10F HPLC

Levels Stress Level 40% initial strength 60% initial strength

Fact

ors


CreepParameter Estimate df SS Fratio Prob Alpha 0.05Intercept 118.77542 1 0 0 1Log(time) 112.8567 1 37001430 2687.763 1.30E-144 Significant at alpha levelStress Level 3.7102679 1 246688.29 17.9193 3.14E-05 Significant at alpha levelAge loading 0 0 0.00E+00 . . Not signigicant at alpha level


1 Time under l Entered 278 1.05E-141 37001430 14604 0.099 0.901 18.9193 22 Stress Level Entered 277 3.14E-05 246688.3 13767 0.094 0.907 3 3

Specific CreepParameter Estimate df SS Fratio Prob Alpha 0.05Intercept 0.147995 1 0 0 1Log(time) 0.0318249 1 2.9423712 2677.352 2.12E-144 Significant at alpha levelStress Level -0.001329 1 0.0316519 28.80101 1.70E-07 Significant at alpha levelAge loading 0 0 0.00E+00 . . Not signigicant at alpha level


1 Log(time) Entered 278 1.58E-139 2.942371 0.001209 0.103 0.897 29.80101 22 Stress Level Entered 277 1.70E-07 0.031652 0.001099 0.094 0.907 3 3

Creep CoefficientParameter Estimate df SS Fratio Prob Alpha 0.05Intercept 0.4562763 1 0 0 1Log(time) 0.1222933 1 43.447929 2759.688 4.70E-146 Significant at alpha levelStress Level -0.002772 1 0.1376846 8.74533 3.37E-03 Significant at alpha levelAge loading 0 0 0.00E+00 . . Not signigicant at alpha level


1 Log(time) Entered 278 7.16E-145 43.44793 0.016182 0.094 0.906 9.74533 22 Stress Level Entered 277 3.37E-03 0.137685 0.015744 0.092 0.909 3 3

277

J.5. Four-Factor ANOVA: Creep of Laboratory HPLC (8L & 10L)

Levels Compressive

Strength 8,000-psi 10,000-psi

Age at Loading 16 hours 24 hours Stress Level 40% initial strength 60% initial strength Fa

ctor

s

Time under Load 29 levels (see Appendix K) Creep

Parameter Estimate df SS Fratio Prob Alpha 0.05Intercept 1055.015 1 0 0 1Time Load 1.957662 1 1.33E+08 895.564439 4.45E-138 Significant at alpha levelStress leve 1314.5 1 16034703 107.895964 5.59E-24 Significant at alpha levelStrength -93.6476 1 8138447 54.7628234 3.06E-13 Significant at alpha levelAge at load -3.78604 1 2.13E+05 1.43206139 0.2317356 Not signigicant at alpha level


1 Time Load Entered 926 5.90E-123 133057904 174449 0.549 0.452 162.9857 22 Stress leveEntered 925 8.71E-23 16019079.3 157320 0.495 0.506 57.19488 33 Strength Entered 924 3.09E-13 8138447.23 148682 0.468 0.534 4.432061 44 Age at loadEntered 923 0.231736 212822.411 148613 0.468 0.534 5 5

Specific CreepParameter Estimate df SS Fratio Prob Alpha 0.05Intercept 0.942578 1 0 0 1Time Load 0.000513 1 9.147475 812.666873 1.02E-128 Significant at alpha levelStress leve -0.24545 1 0.559065 49.6676202 3.56E-12 Significant at alpha levelStrength -0.05004 1 2.323902 206.45673 2.13E-42 Significant at alpha levelAge at load -0.00796 1 9.40E-01 83.5543196 3.85E-19 Significant at alpha level


1 Time Load Entered 926 8.15E-102 9.12786482 0.01536 0.610 0.391 339.2365 22 Strength Entered 925 9.24E-38 2.32390164 0.01286 0.511 0.491 134.7798 33 Age at loadEntered 924 2.10E-18 0.94677652 0.01185 0.470 0.531 52.66762 44 Stress leveEntered 923 3.56E-12 0.55906467 0.01126 0.447 0.555 5 5

Creep CoefficientParameter Estimate df SS Fratio Prob Alpha 0.05Intercept 2.63176 1 0 0 1Time Load 0.001702 1 100.5712 801.887559 1.82E-127 Significant at alpha levelStress leve -0.63576 1 3.750795 29.9063224 5.84E-08 Significant at alpha levelStrength -0.13428 1 16.73319 133.419226 6.39E-29 Significant at alpha levelAge at load -0.02042 1 6.19E+00 49.3489226 4.16E-12 Significant at alpha level


1 Time Load Entered 926 2.27E-109 100.404664 0.15386 0.587 0.413 212.0071 22 Strength Entered 925 6.11E-27 16.7331894 0.13594 0.519 0.482 80.58791 33 Age at loadEntered 924 7.34E-12 6.23097134 0.12934 0.494 0.508 32.90632 44 Stress leveEntered 923 5.84E-08 3.75079495 0.12542 0.479 0.523 5 5

278

J.6. Three-Factor ANOVA: Shrinkage of Laboratory HPLC (8L & 10L)

Levels Compressive


Age at Loading 16 hours 24 hours

Fact

ors

Time under Load 29 levels (see Appendix K) Shrinkage

Parameter Estimate df SS Fratio Prob Alpha 0.05Intercept 4724.043 1 0 0 1Time Load 0.789139 1 10186141 11.9895374 5.87E-04 Significant at alpha levelStrength -448.483 1 68848089 81.0372355 6.72E-18 Significant at alpha levelAge at load -5.94504 1 250207 0.29450468 5.88E-01 Not signigicant at alpha level

Step Parameter Action DF error Sgg pro Seq SS MSE Rel MSE Rsquared Cp p443 452607454 1021687 1.000 0.000

1 Drying TimEntered 442 1.83E-17 68380396 869292 0.851 0.151 12.25219 22 Strength Entered 441 5.91E-04 10159076.6 848227 0.830 0.174 2.294505 33 Loading @ Entered 440 0.587623 250207.008 849586 0.832 0.174 4 4

279

J.7. Three-Factor ANOVA: Creep of 8,000-psi HPLC (8L & 8F)

Levels Place of Mixing Laboratory Field


Fact

ors


Parameter Estimate df SS Fratio Prob Alpha 0.05Intercept 234.3627 1 0 0 1Time Load 2.627139 1 93920489 603.63518 8.63E-84 Significant at alpha levelStress leve 1164.236 1 5855526 37.633974 1.94E-09 Significant at alpha levelLab:1 Field -81.09722 1 710290 4.565096 0.03319634 Significant at alpha level


1 Time Load Entered 430 3.97E-79 93920489 170137 0.439 0.562 42.19907 22 Stress leveEntered 429 2.25E-09 5855525.5 156884 0.405 0.597 6.565096 33 Lab:1 FieldEntered 428 3.32E-02 710290.02 155591 0.401 0.601 4 4

Specific CreepParameter Estimate df SS Fratio Prob Alpha 0.05Intercept 0.323232 1 0 0 1Time Load 0.000736 1 7.365558 584.12772 5.17E-82 Significant at alpha levelStress leve -0.25 1 0.27 21.412428 4.92E-06 Significant at alpha levelLab:1 Field -0.003509 1 1.33E-03 0.1054768 7.46E-01 Not signigicant at alpha level


1 Time Load Entered 430 9.10E-80 7.3655581 0.01318 0.436 0.565 21.51791 22 Stress leveEntered 429 4.80E-06 0.27 0.01258 0.416 0.586 2.105477 33 Lab:1 FieldEntered 428 7.46E-01 0.00133 0.01261 0.417 0.586 4 4

Creep CoefficientParameter Estimate df SS Fratio Prob Alpha 0.05Intercept 1.194014 1 0 0 1Time Load 0.002425 1 80.02417 568.32986 1.51E-80 Significant at alpha levelStress leve -0.958542 1 3.969225 28.189349 1.77E-07 Significant at alpha levelLab:1 Field -0.052708 1 3.00E-01 2.130893 0.14509021 Not signigicant at alpha level


1 Time Load Entered 430 2.56E-77 80.024167 0.15008 0.447 0.554 30.32024 22 Stress leveEntered 429 1.83E-07 3.9692252 0.14118 0.421 0.581 4.130893 33 Lab:1 FieldEntered 428 0.14509 0.3000422 0.14081 0.420 0.583 4 4

280

J.8. Two-Factor ANOVA: Shrinkage of 8,000-psi HPLC (8L & 8F)


Fact

ors


Parameter Estimate df SS Fratio Prob Alpha 0.05Intercept 221.1937 1 0 0 1Time Load 1.342174 1 12256931 240.204 8.92E-37 Not signigicant at alpha levelLab:1 Field 12.92593 1 9022.296 0.176814 6.75E-01 Significant at alpha level


1 Drying TImEntered 214 6.40E-37 12256931 50831 0.472 0.530 1.176814 22 Lab:1 & FIeEntered 213 0.67455 9022.296 51027 0.474 0.530 3 3

281

J.9. Three-Factor ANOVA: Creep of 10,000-psi HPLC (10L & 10F)



Fact

ors


Parameter Estimate df SS Fratio Prob Alpha 0.05Intercept 427.689 1 0 0 1Time Load 1.918871 1 49982264 670.8149 8.47E-91 Significant at alpha levelStress leve 1039.219 1 4838291 64.93498 7.22E-15 Significant at alpha levelLab:1 Field -305.183 1 10431309 139.9992 2.89E-28 Significant at alpha level


1 Time Load Entered 446 9.42E-71 49982264 108412 0.493 0.508 204.9342 22 Stress leveEntered 445 2.66E-25 10431309 85215 0.387 0.614 66.93498 33 Lab:1 FieldEntered 444 7.22E-15 4838291 74510 0.339 0.664 4 4

Specific CreepParameter Estimate df SS Fratio Prob Alpha 0.05Intercept 0.156805 1 0 0 1Time Load 0.000455 1 2.807139 791.8002 9.56E-101 Significant at alpha levelStress leve -0.05065 1 0.011492 3.241475 7.25E-02 Not signigicant at alpha levelLab:1 Field -0.01274 1 1.82E-02 5.124803 2.41E-02 Significant at alpha level


1 Time Load Entered 446 4.91E-100 2.81E+00 0.003596 0.364 0.636 8.366278 22 Stress leveEntered 445 7.38E-02 0.011492 0.003578 0.363 0.639 7.124803 33 Lab:1 FieldEntered 444 2.41E-02 0.018169 0.003545 0.359 0.643 4 4

Creep CoefficientParameter Estimate df SS Fratio Prob Alpha 0.05Intercept 0.34536 1 0 0 1Time Load 0.001668 1 37.75847 777.5278 1.26E-99 Significant at alpha levelStress leve 0.085558 1 0.032794 0.675307 4.12E-01 Not signigicant at alpha levelLab:1 Field 0.014335 1 2.30E-02 0.473919 0.491549 Not signigicant at alpha level


1 Time Load Entered 446 6.62E-100 37.75847 0.048470 0.365 0.636 1.149226 22 Stress leveEntered 445 4.11E-01 0.032794 0.048505 0.365 0.636 2.473919 33 Lab:1 FieldEntered 444 0.491549 0.023015 0.048562 0.366 0.637 4 4

282

J.10. Three-Factor ANOVA: Shrinkage of 10,000-psi HPLC (10L & 10F)



Fact

ors


Parameter Estimate df SS Fratio Prob Alpha 0.05Intercept 115.3497 1 0 0 1Time Load 0.824243 1 4655163 101.029 7.16E-20 Significant at alpha levelLab:1 Field 76.98464 1 337664.1 7.32818 7.31E-03 Significant at alpha level


1 Time Load Entered 226 2.27E-19 4625348 47368 1.028 0.302 8.32818 22 Lab:1 FieldEntered 225 0.007309 337664.1 46077 1.000 0.324 3 3

283

J.11. Three-Factor ANOVA: Creep of Field HPLC (8F & 10F)

Levels Compressive



Fact

ors


Parameter Estimate df SS Fratio Prob Alpha 0.05Intercept -13.3363 1 0 0 1Time Load 2.092374 1 89525212 916.14116 2.08E-118 Significant at alpha levelStress leve 1408.417 1 9189872 94.043008 1.32E-20 Significant at alpha levelStrength -2.38051 1 20454109 209.31367 2.50E-40 Significant at alpha level


1 Time Load Entered 542 2.46E-91 85341224 138699 0.469 0.532 229.2908 22 Stress leveEntered 541 1.57E-24 13216401 114526 0.387 0.614 96.04301 33 Strength Entered 540 1.32E-20 9189872.3 97720 0.331 0.671 4 4

Specific CreepParameter Estimate df SS Fratio Prob Alpha 0.05Intercept 0.201499 1 0 0 1Time Load 0.000602 1 7.42199 745.74811 8.46E-104 Significant at alpha levelStress leve -0.01973 1 0.001803 0.1811516 6.71E-01 Not signigicant at alpha levelStrength -0.00061 1 1.33E+00 133.43002 9.80E-28 Significant at alpha level


1 Time Load Entered 542 9.01E-85 7.1168985 0.012878 0.496 0.505 161.3373 22 Stress leveEntered 541 2.80E-06 0.277745 0.012389 0.477 0.525 135.43 33 Strength Entered 540 9.80E-28 1.3279501 0.009952 0.383 0.619 4 4

Creep CoefficientParameter Estimate df SS Fratio Prob Alpha 0.05Intercept 0.795909 1 0 0 1Time Load 0.002071 1 87.70273 815.34215 5.48E-110 Significant at alpha levelStress leve -0.3948 1 0.722102 6.7131348 9.83E-03 Significant at alpha levelStrength -0.00127 1 5.84E+00 54.255951 6.62E-13 Significant at alpha level


1 Time Load Entered 542 2.65E-98 85.587631 0.124803 0.442 0.559 88.85592 22 Stress leveEntered 541 3.37E-18 8.8357343 0.108701 0.385 0.616 8.713135 33 Strength Entered 540 0.009829 0.7221021 0.107566 0.381 0.621 4 4

284

J.12. Two-Factor ANOVA: Shrinkage of Field HPLC (8F & 10F)

Levels Compressive


Fact

ors


Parameter Estimate df SS Fratio Prob Alpha 0.05Intercept 217.5329 1 0 0 1Time Load 1.076373 1 14487633 200.826 7.88E-36 Significant at alpha levelStrength 0.360069 1 76713.95 1.0634 3.03E-01 Not signigicant at alpha level


1 Time Load Entered 326 3.27E-36 14683624 72154 0.618 0.384 2.0634 22 Strength Entered 325 0.303208 76713.95 72140 0.617 0.386 3 3

285

Appendix K. Experimental Results

K.1. Compressive Strength Accelerated-Cured ASTM-Cured

Age 8L 10L 8F 10F Age 8L 10L 8F 10F(days) Single test Single test Single test Single test (days) Single test Single test Single test Single test16 hours 7278.951 9375.818 1 6570.712 6764.085 5619.761 6686.89516 hours 6992.472 9980.606 1 6168.05 7013.958 5611.008 6825.3616 hours 7699.916 10157.27 1 6162.479 6888.226 5973.085 6147.3620 hours 8004.698 9609.775 7 7323.515 8332.55720 hours 7672.064 9896.254 7 7109.451 8206.02920 hours 7212.106 9786.437 7 7519.275 7676.043

1 6996 11388 7314 8540 28 9945.592 10678.5 8826.733 9964.6911 8259 11265 6753 7983 28 10060.98 10375.31 8712.142 9593.0641 7935 10651 7212 8415 28 9776.092 10758.87 8966.789 9862.0361 7340 8534 56 10699.19 11494.97 9328.867 10574.251 7772 8062 56 10751.71 11345.36 9070.24 10325.971 7577 8480 56 10115.09 11588.07 9656.726 9832.5921 8401 8331 56 9347.966 10758.081 7783 8738 56 9718.001 10694.421 8689 8266 56 9659.113 11175.861 7268 8028 56 9305.79 10389.631 7292 8015 56 9938.43 10364.171 7171 7737 56 10259.13 10459.661 6959 0 56 8716.916 10496.271 7183 0 56 8873.684 10723.861 7259 0 56 8552.987 10349.857 8915 10123 8130 9472 56 9212.6847 9460 9955 7717 8812 56 9072.6287 9524 10612 7586 9174 56 9470.51528 9689 10739 8641 9193 103 10229 1086828 9651 10722 8742 9295 144 10229 1086828 9556 10303 8750 954556 10375 10625 9036 1037156 10503 10970 9038 1011556 10402 10971 9178 10261

103 9418144 10454

286

K.2. Modulus of Elasticity

Time (days)

Accelerated Curing

ASTM Curing

Accelerated Curing

ASTM Curing

Accelerated Curing

ASTM Curing

Accelerated Curing

ASTM Curing

0.67 3460 40600.67 3660 40200.67 3470 4170

1 3750 4220 3670 38751 3690 4260 3520 38101 3560 4260 3510 350056 4030 4380 4210 4430 3810 3880 4060 413056 4040 4460 4210 4300 3900 3770 4025 392056 3990 4320 4300 4260 3880 4100 3960 413056 359056 3820

Values in ksi

8L 10L 8F 10F

K.3. Modulus of Rupture

Time (days)

Accelerated Curing

ASTM Curing

Accelerated Curing

ASTM Curing

Accelerated Curing

ASTM Curing

Accelerated Curing

ASTM Curing

1 649 761 645 67856 1077 1,030 926 918 1042 992 1161 981

Values in psi

8L 10L 8F 10F

287

K.4. Chloride Ion Permeability 8L 10L 8F 10F

Time (days)

Accelerated Curing

Accelerated Curing

Accelerated Curing

Accelerated Curing

630 342 903 193618 106 888 298618 105 767 230616 764 186

Values in coulombs

56

K.5. Coefficient of Thermal Expansion 8F 10F

Time (days)

Accelerated Curing

Accelerated Curing

5.07 1935.20 186

Values in µε/oF

56

288

K.6. 8L Creep and Shrinkage

Shrinkage Shrinkage Shrinkage Shrinkage Shrinkage Shrinkage Shrinkage Shrinkage Shrinkage ShrinkageDrying Time 1 top 1 bottom 2 top 2 bottom Average 1 top 1 bottom 2 top 2 bottom Average SH

0.00 0 0 0 0 0 0 0 0 0 00.04 25 60 135 165 96 100 135 135 165 1340.08 109 104 175 180 142 200 195 175 180 1870.13 144 149 105 65 116 240 245 105 65 1640.17 136 141 117 107 125 240 245 120 110 1790.21 146 146 115 115 130 250 250 115 115 1820.43 175 175 144 154 162 250 250 155 165 2050.83 164 145 134 149 148 250 230 155 170 2011.88 136 126 141 151 138 240 230 165 175 2023.00 146 131 120 140 134 250 235 155 175 2045.04 228 219 173 198 205 330 320 200 225 2697.19 244 249 204 234 232 340 345 225 255 2918.98 241 241 221 226 232 340 340 245 250 294

16.17 325 316 293 328 316 430 420 320 355 38123.02 344 340 329 369 346 430 425 340 380 39427.09 348 349 333 378 352 449 450 360 405 41637.06 486 472 456 501 479 579 565 475 520 53555.68 569 554 549 579 563 659 645 565 595 61668.97 579 564 574 609 581 669 655 590 625 63583.06 608 569 579 599 589 699 660 595 615 642

111.04 636 617 631 651 634 729 710 650 670 690138.83 650 621 636 661 642 749 720 660 685 704167.19 640 641 638 658 645 739 740 665 685 707195.23 644 640 668 693 662 759 755 695 720 732224.94 662 648 677 687 669 779 765 720 730 749258.23 657 653 668 688 666 729 725 665 685 701282.93 672 663 667 687 672 789 780 710 730 752336.81 709 700 720 730 715 829 820 765 775 797363.78 700 696 703 723 705 769 765 740 760 759504.86 728 734 761 766 748 859 865 820 825 842532.77 749 750 772 782 763 869 870 820 830 847567.98 735 751 761 776 756 879 895 830 845 862600.73 738 744 752 777 753 879 885 795 820 845621.93 766 752 761 771 763 899 885 820 830 859

Corrected by Temperature NOT corrected by temperature

289

16h-40% 16h-40% 16h-40% 16h-40% 1 1 1 1 16h-60% 16h-60% 16h-60% 16h-60% 1 1 1 1Time Load3 top 3 bottom 4 top 4 bottom 3 top 3 bottom 4 top 4 bottom Average C 5 top 5 bottom 6 top 6 bottom 5 top 5 bottom 6 top 6 bottom Average C

0 0 0 0 0 0 0 00.00 850 855 885 950 0 0 0 0 0 1230 1220 1360 1294 0 0 0 0 00.02 1019 1020 1050 1130 36 31 31 46 36 1540 1385 1560 1459 176 31 66 31 760.06 1124 1125 1150 1230 87 83 77 93 85 1460 1455 1679 1529 43 48 132 47 670.10 1189 1180 1215 1285 176 161 166 171 169 1575 1590 1839 1673 181 206 316 216 2300.14 1249 1235 1280 1355 221 201 216 226 216 1625 1640 1899 1728 216 241 361 256 2690.18 1269 1260 1300 1385 237 223 232 253 236 1635 1700 1989 1818 223 298 447 342 3270.41 1404 1395 1420 1515 350 335 330 360 344 1800 1871 2079 1963 365 445 515 464 4470.93 1449 1430 1479 1560 399 374 394 409 394 1885 1931 2159 2038 454 509 599 543 5261.84 1549 1540 1584 1655 497 483 497 503 495 2050 2081 2319 2208 618 658 757 712 6863.17 1689 1680 1719 1805 636 621 631 651 635 2220 2246 2489 2368 786 822 926 870 8515.16 1789 1760 1824 1900 671 636 671 681 665 2380 2406 2659 2543 881 917 1031 980 9527.31 1904 1875 1919 2005 763 729 743 764 750 2485 2516 2729 2658 964 1004 1078 1073 10309.10 1944 1925 1974 2045 801 776 796 801 794 2560 2571 2789 2703 1036 1057 1136 1115 1086

16.31 2134 2115 2174 2260 903 879 908 929 905 2745 2801 2999 2957 1134 1199 1258 1282 121823.15 2319 2300 2344 2430 1076 1052 1066 1086 1070 2905 2981 3199 3152 1281 1367 1446 1465 139027.22 2359 2340 2399 2475 1093 1069 1098 1109 1092 2980 3061 3239 3222 1334 1424 1463 1512 143337.17 2539 2495 2529 2620 1154 1105 1110 1135 1126 3175 3251 3439 3432 1410 1496 1544 1603 151355.81 2679 2640 2689 2775 1213 1169 1188 1209 1195 3335 3411 3579 3577 1489 1575 1603 1667 158369.10 2769 2710 2769 2840 1284 1220 1250 1255 1252 3415 3481 3679 3677 1550 1626 1684 1748 165283.19 2809 2760 2809 2875 1317 1263 1282 1283 1286 3480 3541 3769 3747 1608 1678 1767 1810 1716

111.17 2904 2850 2904 2975 1364 1305 1329 1335 1334 3580 3631 3829 3807 1660 1721 1779 1823 1746138.95 2968 2910 2959 3040 1415 1352 1371 1387 1381 3640 3686 3889 3861 1706 1762 1826 1864 1790167.32 3003 2945 2984 3065 1447 1383 1392 1408 1407 3690 3711 3929 3886 1753 1783 1862 1885 1821195.36 3028 2960 3024 3100 1447 1373 1407 1418 1411 3925 3711 3929 3916 1963 1758 1837 1890 1862225.08 3053 3005 3049 3120 1455 1402 1416 1422 1424 3945 3756 3969 3951 1967 1787 1861 1909 1881258.36 3073 3020 3034 3105 1523 1464 1448 1454 1472 3935 3766 3949 3916 2004 1845 1888 1921 1915283.06 3118 3060 3094 3165 1517 1453 1457 1463 1472 4005 3821 4039 3971 2023 1848 1927 1925 1931336.94 3158 3095 3164 3250 1511 1443 1482 1503 1485 4025 3851 4059 4016 1998 1833 1902 1925 1915363.90 3143 3075 3099 3170 1535 1462 1456 1462 1479 3845 3796 4039 3976 1856 1817 1921 1924 1880504.99 3238 3185 3239 3315 1546 1488 1512 1523 1517 4165 3926 4159 4141 2093 1863 1957 2005 1980532.89 3233 3170 3224 3300 1536 1468 1492 1503 1500 4130 3911 4129 4081 2053 1843 1922 1940 1940568.11 3298 3240 3289 3365 1586 1523 1542 1553 1551 4185 3966 4189 4156 2093 1883 1967 2000 1986600.83 3263 3200 3279 3355 1569 1500 1549 1560 1545 4200 3971 4149 4156 2125 1906 1944 2018 1998621.84 3258 3195 3239 3315 1550 1482 1496 1507 1509 4225 4006 4189 4181 2137 1927 1971 2029 2016

Total strains CreepTotal strains Creep

290

24h-40% 24h-40% 24h-40% 24h-40% 1 1 1 1 24h-60% 24h-60% 24h-60% 24h-60% 1 1 1 1Time Load 7 top 7 bottom 8 top 8 bottom 7 top 7 bottom 8 top 8 bottom Average C9 top 9 bottom 10 top 10 bottom 9 top 9 bottom 10 top 10 bottom Average C

0 0 0 0 0 0 0 00.00 989 824 835 935 0 0 0 0 0 1325 1370 1347 1309 0 0 0 0 00.02 1149 959 1000 1090 26 1 31 21 20 1490 1555 1492 1474 31 51 11 31 310.06 1214 1044 1070 1150 37 32 48 27 36 1620 1650 1586 1583 108 92 52 86 850.10 1264 1094 1130 1195 111 106 131 96 111 1755 1790 1721 1698 266 256 211 225 2390.14 1259 1079 1090 1190 91 76 76 76 80 1750 1775 1706 1693 246 226 181 205 2150.18 1234 1074 1115 1185 62 67 98 68 74 1810 1825 1771 1742 303 272 242 251 2670.41 1329 1164 1215 1295 135 135 175 155 150 1891 1910 1826 1807 360 335 274 293 3150.93 1379 1214 1240 1330 189 189 204 194 194 1991 2005 1951 1912 464 434 402 401 4251.84 1764 1604 1630 1720 572 577 593 582 581 2146 2174 2095 2051 618 602 546 539 5763.17 1904 1759 1785 1880 711 731 746 741 732 2271 2294 2195 2175 742 721 644 662 6925.16 2049 1894 1920 2020 791 801 817 816 806 2471 2499 2404 2409 877 861 789 831 8397.31 2094 1934 1945 2070 813 818 819 844 823 2551 2564 2479 2474 934 904 841 874 8889.10 2134 1964 2010 2095 851 846 882 866 861 2646 2674 2584 2564 1027 1011 944 961 986

16.31 2309 2153 2220 2300 938 948 1004 984 968 2856 2859 2734 2704 1149 1108 1006 1013 106923.15 2458 2288 2365 2439 1075 1070 1137 1111 1098 3111 3134 2993 3017 1392 1371 1253 1314 133227.22 2508 2343 2415 2499 1103 1103 1164 1149 1130 3246 3274 3123 3106 1504 1488 1360 1381 143337.17 2628 2473 2565 2629 1104 1114 1195 1160 1143 3431 3469 3307 3315 1571 1565 1426 1471 150855.81 2808 2643 2716 2794 1203 1203 1264 1243 1228 3631 3679 3492 3484 1689 1693 1529 1559 161869.10 2868 2713 2816 2869 1244 1254 1346 1300 1286 3716 3739 3592 3579 1756 1735 1610 1634 168483.19 2888 2738 2846 2889 1256 1271 1368 1312 1302 3781 3804 3637 3633 1813 1792 1647 1682 1734

111.17 2973 2818 2921 2979 1294 1304 1396 1355 1337 3921 3944 3766 3743 1906 1884 1729 1744 1816138.95 3013 2853 2936 3019 1320 1325 1397 1381 1356 3966 4014 3821 3793 1937 1941 1771 1780 1857167.32 3093 2933 3006 3089 1396 1401 1463 1447 1427 4041 4069 3891 3863 2008 1992 1837 1846 1921195.36 3078 2923 3011 3094 1356 1366 1443 1427 1398 4046 4084 3886 3882 1988 1982 1807 1841 1904225.08 3118 2978 3066 3144 1380 1405 1482 1461 1432 4061 4099 3911 3877 1987 1981 1815 1820 1901258.36 3108 2968 3056 3139 1417 1442 1519 1503 1471 4051 4104 3951 3907 2025 2033 1903 1897 1964283.06 3163 3028 3121 3194 1421 1451 1533 1507 1478 4146 4214 3981 3962 2068 2092 1882 1900 1986336.94 3248 3088 3161 3224 1461 1466 1528 1492 1487 4216 4294 4051 4142 2093 2127 1906 2035 2040363.90 3218 3063 3141 3204 1470 1480 1547 1511 1502 4231 4294 4061 4091 2147 2166 1955 2024 2073504.99 3358 3213 3256 3324 1526 1546 1578 1547 1549 4316 4369 4170 4151 2148 2157 1981 1999 2071532.89 3313 3158 3236 3289 1476 1486 1553 1507 1506 4311 4374 4155 4146 2138 2157 1961 1989 2061568.11 3363 3193 3271 3334 1511 1506 1573 1537 1532 4366 4439 4190 4176 2178 2207 1981 2004 2093600.83 3358 3208 3306 3379 1523 1538 1626 1600 1572 4356 4439 4220 4201 2186 2224 2028 2047 2121621.84 3343 3233 3291 3384 1495 1550 1597 1591 1558 4396 4464 4215 4206 2212 2236 2010 2038 2124


291

K.7. 8F Creep and Shrinkage

Shrinkage Shrinkage Shrinkage Shrinkage Shrinkage Shrinkage Shrinkage Shrinkage Shrinkage ShrinkageDrying Tim1 top 1 bottom 2 top 2 bottom Average S1 top 1 bottom 2 top 2 bottom Average S

0.00 0 0 0 0 0 0 0 0 0 00.04 -248 -258 -497 32 -243 -225 -235 -474 55 -2200.06 -218 -237 -262 47 -168 -190 -210 -235 75 -1400.08 -212 -372 -167 -42 -198 -180 -340 -135 -10 -1660.13 -111 -331 -156 74 -131 -70 -290 -115 115 -900.17 -228 -172 -213 97 -129 -190 -135 -165 145 -860.21 -92 -247 -118 117 -85 -55 -210 -70 165 -420.42 -12 -177 -88 177 -25 25 -140 -40 225 180.63 143 -217 -48 147 6 180 -180 0 195 490.83 248 -162 152 187 106 285 -125 200 235 1491.00 268 73 137 302 195 305 110 185 350 2372.00 378 -42 346 282 241 415 -5 394 330 2843.00 403 -12 351 312 263 440 25 400 360 3065.00 443 33 396 312 296 480 70 444 360 3397.00 448 18 361 362 297 486 55 410 410 3409.00 508 207 466 432 403 545 245 514 480 446

16.00 583 157 451 457 412 620 195 499 505 45523.00 588 217 456 497 440 625 255 504 545 48227.00 613 222 486 502 456 650 260 534 550 49837.00 673 282 441 512 477 710 320 489 560 52055.00 658 322 481 532 498 695 359 529 580 54179.00 648 332 466 637 521 685 369 514 685 563

107.00 768 482 631 797 669 805 519 679 845 712149.00 958 662 816 976 853 995 699 864 1024 896167.14 978 662 812 967 854 1015 699 849 1004 892194.82 980 669 799 959 851 1025 714 844 1004 897223.34 977 666 801 947 848 1020 709 844 989 891251.36 964 648 748 908 817 1025 709 809 969 878279.27 946 630 740 910 807 1010 694 804 974 871307.44 946 630 740 905 805 1010 694 804 969 869336.45 922 606 731 886 786 935 619 744 899 799364.22 929 603 723 878 783 945 619 739 895 799393.47 958 632 752 907 812 1035 709 829 984 889422.03 986 670 760 920 834 1055 739 829 989 903588.01 1028 702 822 967 880 1100 774 894 1039 952615.93 1009 703 819 959 873 1095 789 904 1044 958679.93 984 678 813 944 855 1075 769 904 1034 946


292

24h-40% 24h-40% 24h-40% 24h-40% 1 1 1 1 24h-60% 24h-60% 24h-60% 24h-60% 1 1 1 1Time Load1 top 1 bottom 2 top 2 bottom 1 top 1 bottom 2 top 2 bottom Average C3 top 3 bottom 4 top 4 bottom 3 top 3 bottom 4 top 4 bottom Average C

0.00 822 832 857 908 0 0 0 0 0 1337 1332 1411 1411 0 0 0 0 00.04 921 851 1041 192 319 239 404 -497 117 1427 1472 1501 1660 309 359 309 469 3620.06 856 871 1051 1058 175 180 335 290 245 1517 1377 1311 1600 320 185 40 329 2180.08 792 662 1057 934 137 -3 367 192 173 1473 1408 1497 1836 302 242 252 591 3460.13 868 933 1098 384 136 191 331 -434 56 1798 1824 2082 1911 551 581 761 591 6210.17 956 1411 1181 1083 221 665 411 261 389 1537 1592 1821 1984 286 346 495 660 4470.21 1046 1446 1301 1153 267 656 487 287 424 1667 1617 1970 1890 372 327 602 521 4560.42 1091 1666 1466 1218 252 816 592 292 488 1692 1682 2000 1974 337 332 572 546 4470.63 1096 1636 1555 1183 226 755 650 226 464 1857 1712 2065 2079 471 331 605 620 5070.83 1131 1835 1650 1303 161 855 645 246 477 1926 1777 2290 2149 441 296 730 590 5141.00 1191 1785 1595 1308 132 716 501 162 378 1996 1957 2295 2299 422 387 646 651 5272.00 1276 1940 1925 1383 171 825 785 191 493 2086 2112 2725 2409 466 496 1030 715 6773.00 1346 2010 1860 1513 218 872 698 299 522 2136 2132 2570 2454 493 493 853 737 6445.00 1406 1860 1790 1483 245 690 595 236 442 2086 2017 2345 2399 411 346 595 650 5007.00 1606 2310 1825 1738 444 1138 629 490 675 2326 2327 2650 2574 649 654 899 823 7569.00 1650 2225 1885 1718 383 947 583 364 569 2401 2392 2835 2694 618 613 978 837 762

16.00 1860 2380 2165 1923 584 1093 854 561 773 2591 2587 2995 2878 800 800 1129 1013 93523.00 1910 2410 2220 1963 606 1096 881 573 789 2626 2632 3050 2938 807 817 1156 1046 95627.00 1890 2430 2260 1963 570 1100 905 557 783 2681 2677 3170 2958 846 846 1260 1049 100037.00 1970 2470 2300 2059 629 1118 924 631 825 2726 2716 3110 3043 870 865 1179 1113 100655.00 2070 2575 2405 2149 708 1202 1007 700 904 2911 2896 3274 3273 1033 1023 1322 1321 117579.00 2315 2795 2624 2394 930 1400 1205 922 1114 3176 3156 3509 3448 1276 1261 1535 1474 1386

107.00 2565 2984 2904 2649 1031 1441 1336 1029 1209 3446 3381 3784 3588 1397 1337 1661 1465 1465149.00 2785 3184 3114 2864 1067 1457 1362 1061 1237 3646 3586 4004 3807 1413 1359 1697 1501 1493166.88 2830 3255 3180 2930 1117 1531 1431 1130 1302 3712 3702 4085 3893 1483 1478 1781 1590 1583194.56 2892 3322 3232 2962 1174 1593 1478 1157 1351 3754 3734 4137 3950 1520 1505 1828 1642 1624223.08 2955 3369 3249 2985 1243 1647 1502 1186 1394 3756 3757 4134 4012 1529 1534 1832 1711 1652251.10 2961 3431 3285 3031 1261 1721 1551 1245 1445 3773 3788 4210 4099 1558 1578 1921 1810 1717279.01 3033 3503 3348 3088 1341 1801 1621 1310 1518 3760 3785 4218 4106 1552 1583 1936 1825 1724307.18 3058 3553 3403 3073 1367 1852 1677 1296 1548 3780 3795 4228 4121 1574 1594 1947 1841 1739335.70 3079 3594 3468 3099 1458 1962 1812 1391 1656 3776 3881 4228 4112 1639 1749 2018 1902 1827363.96 3111 3631 3471 3101 1490 2000 1815 1394 1675 3823 3908 4321 4254 1687 1777 2110 2044 1904393.22 3155 3660 3564 3155 1444 1939 1818 1358 1640 3837 3912 4354 4272 1610 1690 2054 1973 1832421.77 3198 3718 3592 3183 1473 1983 1833 1372 1665 3870 3950 4397 4305 1630 1715 2083 1992 1855587.74 3375 3800 3729 3326 1602 2016 1921 1466 1751 4012 4092 4495 4388 1723 1808 2132 2025 1922615.66 3327 3851 3731 3327 1547 2062 1916 1461 1747 3964 4034 4471 4344 1669 1744 2102 1976 1873679.69 3321 3846 3726 3322 1554 2069 1924 1468 1754 3958 4029 4466 4339 1676 1751 2109 1983 1880


293

K.8. 10L Creep and Shrinkage

Shrinkage Shrinkage ShrinkageShrinkage Shrinkage Shrinkage Shrinkage Shrinkage ShrinkageShrinkage Shrinkage ShrinkageDrying Tim1 top 1 bottom Average S1 top 1 bottom Average SDrying Tim2 top 2 bottom Average S2 top 2 bottom Average S

0.00 0 0 0 0 0 0 0.00 0 0 0 0 0 00.02 58 43 50 95 80 87 0.03 21 76 48 50 105 780.05 65 60 62 110 105 107 0.07 5 75 40 50 120 850.09 86 76 81 150 140 145 0.11 -40 45 2 5 90 470.13 61 46 53 135 120 127 0.15 32 92 62 80 140 1100.17 68 43 55 145 120 132 0.20 47 92 70 95 140 1180.38 83 68 76 155 140 147 0.24 117 127 122 165 175 1700.79 96 71 83 165 140 152 0.49 147 167 157 195 215 2051.81 76 56 66 150 130 140 1.19 150 165 157 200 215 2083.17 51 31 41 120 100 110 2.12 96 126 111 125 155 1404.82 76 41 58 145 110 127 3.44 121 146 133 150 175 1637.04 108 88 98 180 160 170 5.03 148 153 150 185 190 1889.10 84 54 69 145 115 130 7.57 156 161 159 180 185 183

15.93 171 151 161 235 215 225 9.44 146 155 151 180 190 18523.18 186 161 173 255 230 242 16.38 155 165 160 195 205 20028.22 246 216 231 310 280 295 23.17 235 260 247 280 305 29336.95 273 264 269 340 330 335 27.03 230 260 245 280 310 29555.25 293 279 286 360 345 352 37.16 288 298 293 325 335 33069.81 296 271 284 360 335 347 55.31 293 303 298 330 340 33582.87 350 316 333 430 395 412 68.99 298 318 308 335 355 345

111.02 321 296 309 385 360 372 83.33 309 339 324 365 395 380139.31 331 316 324 395 380 387 111.02 322 342 332 370 390 380167.36 305 280 293 390 365 377 139.45 323 358 340 365 400 383194.93 320 295 307 410 385 397 167.41 344 359 352 405 420 413225.23 324 300 312 415 390 402 196.38 349 349 349 405 405 405251.25 310 275 292 355 320 337 223.52 350 345 347 395 390 393279.31 336 312 324 395 370 382 252.56 319 338 329 345 365 355306.49 346 307 326 450 410 430 307.72 407 391 399 470 455 463335.00 367 322 344 465 420 442 335.03 416 390 403 495 470 483371.98 378 339 358 490 450 470 365.19 395 405 400 480 490 485495.95 394 354 374 500 460 480 489.13 441 450 446 520 530 525523.87 367 333 350 455 420 437 517.05 424 419 422 485 480 483559.06 431 391 411 545 505 525 552.23 485 465 475 575 555 565591.89 406 381 393 520 495 507 591.20 461 455 458 540 535 538620.72 421 377 399 525 480 502 619.97 466 446 456 540 520 530

Corrected by Temperature NO corrected by Temperature Corrected by Temperature NO corrected by Temperature

294

16h-40% 16h-40% 16h-40% 16h-40% 1 1 1 1 16h-60% 16h-60% 16h-60% 16h-60% 1 1 1 1Drying Tim3 top 3 bottom 4 top 4 bottom 3 top 3 bottom 4 top 4 bottom Average C5 top 5 bottom 6 top 6 bottom 5 top 5 bottom 6 top 6 bottom Average C

0 0 0 0 0 0 0 00.00 865 850 875 950 0 0 0 0 0 1320 1300 1323 1294 0 0 0 0 00.02 1070 1015 1105 1140 118 78 142 102 110 1510 1490 1522 1479 103 103 112 97 1040.05 1165 1130 1205 1245 193 173 222 187 194 1575 1550 1627 1563 148 143 197 161 1620.09 1260 1240 1305 1340 250 245 285 245 256 1705 1665 1702 1648 240 220 234 208 2260.13 1305 1290 1325 1385 313 313 322 307 314 1720 1670 1687 1658 273 243 237 236 2470.17 1320 1305 1335 1385 323 323 327 302 319 1755 1715 1726 1692 303 283 271 266 2810.38 1340 1380 1414 1455 328 383 392 357 365 1835 1790 1796 1767 368 343 326 325 3400.79 1466 1465 1469 1530 448 463 442 427 445 1890 1860 1866 1817 418 408 391 370 3961.81 1561 1555 1549 1605 555 565 535 515 543 2005 1955 1955 1936 545 515 493 502 5143.17 1641 1635 1619 1670 665 675 635 610 646 2080 2065 2040 2001 650 655 607 596 6274.82 1756 1705 1704 1780 763 728 702 702 724 2195 2165 2159 2125 748 738 709 703 7247.04 1781 1730 1734 1825 745 710 690 705 713 2255 2220 2224 2185 765 750 731 720 7429.10 1931 1870 1884 1920 935 890 880 840 886 2376 2340 2333 2304 925 910 881 880 899

15.93 2106 2045 2069 2120 1015 970 970 945 975 2586 2555 2562 2533 1040 1030 1014 1014 102523.18 2206 2180 2179 2240 1098 1088 1062 1047 1074 2686 2640 2642 2608 1123 1098 1076 1071 109228.22 2296 2260 2269 2320 1136 1115 1100 1075 1106 2791 2750 2766 2727 1175 1155 1148 1138 115436.95 2346 2315 2319 2365 1146 1130 1110 1080 1116 2856 2830 2840 2787 1200 1195 1183 1157 118455.25 2436 2410 2414 2475 1218 1208 1187 1172 1196 2961 2915 2925 2876 1288 1263 1250 1229 125769.81 2491 2445 2469 2535 1278 1248 1247 1237 1253 3006 2960 2975 2931 1338 1313 1305 1289 131182.87 2556 2520 2529 2605 1278 1258 1242 1243 1255 3116 3055 3074 3020 1383 1343 1339 1314 1345

111.02 2581 2565 2564 2585 1343 1343 1317 1263 1316 3136 3085 3099 3040 1443 1413 1404 1374 1408139.31 2571 2540 2564 2595 1318 1303 1302 1258 1295 3131 3070 3094 3045 1423 1383 1384 1364 1388167.36 2601 2590 2614 2655 1358 1363 1362 1328 1353 3171 3125 3154 3100 1473 1448 1454 1428 1451194.93 2651 2625 2644 2680 1388 1378 1372 1333 1368 3231 3160 3198 3145 1513 1463 1478 1453 1477225.23 2651 2635 2679 2710 1383 1383 1402 1357 1381 3231 3170 3193 3135 1508 1468 1468 1438 1471251.25 2616 2605 2589 2635 1413 1418 1377 1348 1389 3221 3115 3173 3110 1563 1478 1514 1478 1508279.31 2656 2625 2674 2725 1408 1393 1417 1392 1403 3246 3185 3238 3170 1543 1503 1533 1493 1518306.49 2736 2730 2729 2780 1441 1450 1424 1400 1429 3296 3225 3278 3199 1545 1495 1525 1475 1510335.00 2766 2745 2759 2790 1458 1453 1442 1397 1438 3386 3335 3367 3284 1623 1593 1602 1547 1591371.98 2781 2750 2769 2805 1446 1430 1424 1385 1421 3356 3285 3343 3254 1565 1515 1550 1490 1530495.95 2846 2815 2839 2870 1501 1485 1484 1440 1478 3436 3375 3417 3344 1636 1595 1615 1570 1604523.87 2851 2805 2849 2875 1548 1518 1537 1487 1523 3431 3365 3422 3344 1673 1628 1662 1612 1644559.06 2916 2865 2899 2920 1526 1490 1499 1445 1490 3491 3435 3487 3414 1646 1610 1640 1594 1622591.89 2926 2900 2904 2925 1553 1543 1522 1468 1521 3471 3425 3477 3409 1643 1618 1647 1607 1629620.72 2911 2875 2894 2930 1543 1523 1517 1478 1515 3471 3425 3477 3409 1648 1623 1652 1612 1634

Total strains Creep Total strains Creep

295

24h-40% 24h-40% 24h-40% 24h-40% 1 1 1 1 24h-60% 24h-60% 24h-60% 24h-60% 1 1 1 1Drying Tim7 top 7 bottom 8 top 8 bottom 7 top 7 bottom 8 top 8 bottom Average C9 top 9 bottom 10 top 10 bottom 9 top 9 bottom 10 top 10 bottom Average C

0 0 0 0 0 0 0 00.00 1339 1565 1008 1020 0 0 0 0 0 1824 1598 1525 1576 0 0 0 0 00.03 1469 1655 1103 1114 52 13 17 17 25 1979 1748 1660 1831 77 72 57 178 960.07 1539 1730 1173 1169 115 80 80 64 85 2089 1863 1760 1916 180 180 150 255 1910.11 1539 1745 1193 1209 152 133 137 141 141 2209 1983 1875 1986 337 337 303 363 3350.15 1624 1820 1283 1263 175 145 164 134 154 2239 2003 1905 2006 305 295 270 320 2970.20 1654 1830 1312 1278 197 147 187 141 168 2334 2118 2000 2081 392 402 357 388 3850.24 1654 1835 1312 1293 145 100 134 103 121 2354 2148 2025 2106 360 379 330 360 3570.49 1799 1965 1477 1452 255 195 264 227 235 2519 2323 2190 2251 490 519 460 470 4851.19 1839 2035 1547 1512 292 262 331 285 293 2524 2323 2205 2286 492 517 472 503 4962.12 1889 2050 1567 1552 410 345 419 392 391 2644 2432 2300 2377 680 694 635 660 6673.44 1959 2115 1662 1642 457 387 491 459 449 2679 2467 2325 2412 692 707 637 673 6775.03 1984 2140 1697 1672 457 387 501 464 452 2759 2547 2420 2487 747 761 707 723 7357.57 2124 2290 1851 1826 602 542 661 623 607 2839 2657 2540 2597 832 876 832 838 8459.44 2119 2285 1846 1826 595 535 653 621 601 2934 2722 2575 2647 924 939 865 886 903

16.38 2229 2390 1971 1950 690 625 763 730 702 3059 2842 2715 2832 1034 1044 990 1056 103123.17 2354 2495 2091 2060 722 637 790 747 724 3194 2992 2845 2962 1077 1101 1027 1093 107527.03 2349 2505 2091 2065 715 645 788 750 724 3204 2997 2855 2962 1084 1103 1035 1091 107837.16 2449 2595 2201 2174 779 700 863 824 792 3328 3107 2995 3092 1174 1178 1140 1186 117055.31 2524 2650 2251 2224 849 750 908 869 844 3453 3227 3090 3197 1294 1293 1230 1286 127668.99 2624 2760 2346 2323 939 850 992 958 935 3518 3297 3175 3272 1349 1353 1305 1351 134083.33 2649 2800 2395 2363 929 855 1007 963 939 3613 3391 3270 3372 1409 1413 1365 1416 1401

111.02 2659 2800 2405 2378 939 855 1017 978 947 3643 3431 3325 3427 1439 1453 1420 1471 1446139.45 2729 2845 2475 2438 1007 897 1085 1035 1006 3728 3531 3410 3522 1522 1550 1502 1564 1535167.41 2769 2890 2505 2467 1017 912 1084 1035 1012 3768 3566 3435 3533 1531 1555 1497 1544 1532196.38 2794 2915 2535 2477 1049 945 1122 1052 1042 3793 3591 3465 3563 1564 1588 1535 1581 1567223.52 2819 2920 2560 2517 1087 962 1159 1105 1078 3813 3626 3490 3578 1596 1635 1572 1609 1603252.56 2799 2925 2555 2502 1104 1005 1192 1127 1107 3868 3681 3520 3638 1689 1728 1640 1706 1691307.72 2959 3050 2685 2642 1157 1022 1214 1159 1138 3953 3816 3610 3733 1666 1755 1622 1694 1684335.03 2994 3090 2710 2661 1172 1042 1219 1159 1148 3998 3791 3625 3738 1691 1710 1617 1679 1674365.19 3004 3100 2760 2691 1179 1050 1267 1186 1171 4013 3811 3675 3803 1704 1728 1665 1742 1710489.13 3054 3155 2810 2756 1189 1065 1276 1211 1185 4098 3866 3725 3858 1749 1743 1675 1757 1731517.05 3069 3174 2805 2741 1247 1127 1314 1239 1232 4103 3901 3755 3888 1796 1820 1747 1829 1798552.23 3134 3239 2845 2806 1229 1110 1271 1221 1208 4178 3966 3845 3983 1789 1802 1755 1842 1797591.20 3149 3259 2875 2836 1272 1157 1329 1278 1259 4173 3966 3840 3988 1811 1830 1777 1874 1823619.97 3154 3254 2885 2841 1284 1160 1346 1291 1270 4183 3981 3830 3968 1829 1852 1775 1862 1829

Total strains Creep Total strains Creep

296

K.9. 10F Creep and Shrinkage

Shrinkage Shrinkage Shrinkage Shrinkage Shrinkage Shrinkage Shrinkage Shrinkage Shrinkage ShrinkageDrying Tim1 top 1 bottom 2 top 2 bottom Average S1 top 1 bottom 2 top 2 bottom Average S

0.00 0 0 0 0 0 0 0 0 0 00.02 40 10 7 0 14 45 15 12 5 190.04 125 -20 -13 -25 17 135 -10 -2 -15 270.06 -44 -34 23 1 -14 -30 -20 37 15 10.08 52 7 29 -3 21 75 30 52 20 440.13 165 180 157 55 139 195 210 187 85 1690.17 234 165 27 5 108 265 195 57 35 1380.24 140 335 82 60 154 170 365 112 90 1840.42 170 275 107 70 155 200 305 137 100 1860.83 175 115 127 95 128 205 145 157 125 1581.00 175 115 127 95 128 205 145 157 125 1581.92 155 122 127 90 123 185 152 157 120 1542.92 135 130 132 85 120 165 160 162 115 1504.92 240 145 227 120 183 270 175 257 150 2136.92 244 214 262 180 225 275 245 292 210 2558.92 264 214 287 200 241 295 245 317 230 272

15.92 175 194 252 145 191 205 225 282 175 22222.92 200 234 312 190 234 230 265 342 220 26426.92 150 184 297 140 193 180 215 327 170 22336.92 259 279 382 250 293 290 310 412 280 32354.92 254 274 387 314 308 285 305 417 345 33878.92 329 354 467 364 379 360 385 497 395 409

106.92 469 504 617 539 532 500 534 647 570 563147.92 676 731 789 697 723 709 764 822 729 756167.03 695 750 832 745 780 714 769 852 764 813194.74 657 702 774 692 837 684 729 802 719 870223.13 659 718 781 714 718 699 759 822 754 759253.00 676 711 808 721 729 719 754 852 764 772278.92 663 713 791 703 718 709 759 837 749 764306.96 716 765 863 786 782 719 769 867 789 786335.71 676 731 799 726 733 674 729 797 724 731364.96 640 670 743 675 682 699 729 802 734 741418.56 680 730 823 740 743 734 784 877 794 797584.70 705 740 828 745 755 759 794 882 799 809607.65 742 776 864 787 792 814 849 937 859 865680.08 747 787 885 807 807 809 849 947 869 869


297

24h-40% 24h-40% 24h-40% 24h-40% 1 1 1 1 24h-60% 24h-60% 24h-60% 24h-60% 1 1 1 1Time Load7 top 7 bottom 8 top 8 bottom 7 top 7 bottom 8 top 8 bottom Average C9 top 9 bottom 10 top 10 bottom 9 top 9 bottom 10 top 10 bottom Average C

0 0 0 00.00 902 895 815 765 0 0 0 0 0 1055 1031 965 966 0 0 0 0 00.02 972 985 910 855 51 71 76 71 67 1155 1161 1115 1076 81 111 131 91 1030.04 992 975 930 880 63 53 88 88 73 1210 1151 1125 1111 128 93 133 118 1180.06 1012 960 975 860 110 64 159 94 107 1280 1236 1220 1191 224 204 254 225 2270.08 1022 985 945 885 76 46 86 76 71 1285 1296 1205 1196 186 221 196 186 1970.13 1132 1125 1065 935 61 61 81 1 51 1295 1161 1195 1161 71 -39 61 26 300.17 1012 1155 1020 945 -28 122 67 42 51 1225 1211 1185 1161 32 42 82 57 530.22 1142 1140 1030 915 56 61 31 -34 28 1210 1201 1135 1106 -29 -14 -14 -44 -260.42 1233 1245 1120 985 145 164 119 34 116 1263 1241 1195 1151 23 25 44 0 230.83 1303 1324 1190 1040 243 272 217 117 212 1370 1321 1315 1241 157 132 192 117 1501.00 1333 1374 1230 1075 273 322 257 152 251 1459 1391 1405 1351 247 202 282 227 2401.92 1333 1384 1275 1150 277 336 306 231 288 1464 1446 1420 1436 256 262 301 317 2842.92 1333 1444 1350 1260 280 399 384 344 352 1554 1591 1685 1491 349 410 570 375 4264.92 1363 1439 1355 1285 248 332 327 307 303 1539 1611 1735 1526 272 367 557 347 3866.92 1473 1639 1510 1360 316 489 439 340 396 1689 1701 1780 1671 379 415 560 450 4518.92 1653 1729 1565 1420 480 563 478 383 476 1754 1716 1810 1696 428 414 573 459 469

15.92 1583 1684 1545 1450 460 568 508 463 500 1779 1736 1785 1736 503 484 598 549 53322.92 1734 1709 1659 1570 568 551 581 541 560 1849 1801 1865 1841 531 506 636 612 57126.92 1744 1764 1709 1565 619 647 672 577 629 1879 1816 1920 1856 602 562 732 668 64136.92 1864 1924 1739 1640 639 707 602 552 625 2039 1926 1990 1947 662 572 702 658 64954.92 1954 1919 1874 1720 714 687 722 617 685 2064 2086 2090 2007 672 717 787 703 72078.92 2054 1994 1969 1780 743 691 746 606 696 2149 2141 2175 2127 686 701 801 752 735

106.92 2325 2169 2149 2000 860 712 772 672 754 2384 2371 2430 2367 767 778 902 838 821147.92 2405 2319 2339 2155 747 668 768 633 704 2594 2581 2660 2567 783 794 939 845 840167.02 2485 2439 2394 2210 770 731 766 632 725 2644 2626 2720 2632 776 782 942 853 838194.73 2525 2489 2424 2240 753 724 739 605 705 2669 2721 2750 2647 744 821 915 811 823223.12 2605 2549 2499 2360 945 896 926 836 901 2769 2826 2810 2737 956 1037 1086 1013 1023252.99 2636 2594 2524 2370 961 927 937 832 914 2799 2866 2815 2747 972 1063 1078 1009 1030278.92 2676 2609 2529 2395 1010 951 951 866 944 2814 2886 2825 2742 996 1092 1096 1013 1049306.95 2706 2614 2534 2410 1018 933 933 859 936 2819 2896 2835 2737 978 1080 1084 985 1032335.70 2736 2629 2549 2440 1103 1003 1003 944 1013 2854 2901 2855 2742 1068 1140 1159 1045 1103364.94 2696 2654 2559 2425 1053 1018 1003 918 998 2874 2916 2865 2762 1078 1145 1159 1055 1109418.54 2716 2654 2594 2450 1016 962 982 887 962 2964 2976 2955 2847 1112 1148 1193 1084 1134584.67 2846 2804 2744 2605 1135 1101 1121 1031 1097 3059 3096 3090 2972 1196 1257 1316 1198 1242612.60 2846 2804 2774 2620 1079 1044 1094 990 1052 3069 3091 3075 2957 1149 1196 1245 1127 1179680.09 2916 2849 2839 2675 1146 1086 1156 1041 1107 3099 3106 3135 3042 1176 1207 1301 1208 1223


298

K.10. 8,000-psi HPLC girders Experimental Strains

G1A (8F)Date Cast 7/10/0111:30 ∆CTE 2.76

DAYS Defl CL ∆Defl CL Ohms Temp oC ∆temp Hz Strain7/10/01 0.48 0.00 Init1 1.703 0.00 2128 33.2 0.0 924.84 07/10/01 0.51 0.03 Init2 1.703 0.00 2128 33.2 0.0 924.84 07/10/01 0.63 0.15 Release 2.063 0.36 2128 33.2 0.0 822.05 -5837/11/01 0.32 0.84 1 2.078 0.387/12/01 0.32 1.84 2 2.094 0.39 2470 29.6 -3.5 809.31 -6617/13/01 0.30 2.82 3 2.094 0.39 2515 29.2 -3.9 802.8 -6967/17/01 0.27 6.79 7 2.109 0.41 2884 26.0 -7.1 790.57 -7687/24/01 0.29 13.81 14 2.125 0.42 2568 28.7 -4.4 778.42 -82210/24/01 0.50 106.02 106 3780 20.0 -13.2 774.77 -86510/29/01 0.50 111.02 111 3131 24.2 -9.0 763.93 -908

G1B (8F)Date Cast 7/10/0111:30 ∆CTE 2.76

DAYS Defl CL ∆Defl CL Ohms Temp oC ∆temp Hz Strain7/10/01 0.48 0.00 Init1 0.00 2009 34.5 0.0 929.61 07/10/01 0.51 0.03 Init2 0.00 2009 34.5 0.0 929.61 07/10/01 0.64 0.16 Release 0.00 2009 34.5 0.0 822.64 -6097/11/01 0.33 0.85 1 0.007/12/01 0.33 1.85 2 0.00 2448 29.8 -4.7 808.81 -6957/13/01 0.32 2.84 3 0.00 2534 29.0 -5.5 802.4 -7317/17/01 0.31 6.83 7 0.00 2905 25.9 -8.7 788.66 -8117/24/01 0.29 13.81 14 0.00 2499 29.4 -5.2 775.01 -87011/2/01 0.50 115.02 113 3035 24.9 -9.7 762.59 -94511/4/01 0.50 117.02 115 3770 20.0 -14.5 754.38 -999

8 ksi Shrinkage 1T1A 39 ft beam24 hours


299

K.11. 10,000-psi HPLC girders Experimental Strains

G2A 10FDate Cast 7/13/0110:15 ∆CTE 2.43

DAYS Defl CL ∆Defl CL Ohms Temp oC ∆temp Hz Strain7/13/01 0.43 0.00 Init1 2.047 0.00 1377 43.9 0.0 920.4 07/13/01 0.43 0.00 Init2 2.047 0.00 1377 43.9 0.0 920.4 07/13/01 0.65 0.22 Release 2.359 0.31 1410 43.3 -0.6 846.4 -4267/14/01 0.31 0.88 1 2.313 0.27 2771 27.0 -16.9 844.75 -475

7/16/01 0.28 2.85 3 2.32 0.27 2813 26.6 -17.3 843.64 -4827/20/01 0.33 6.90 7 2.344 0.30 2556 28.8 -15.0 838.23 -5067/27/01 0.29 13.86 14 2.344 0.30 2759 27.1 -16.8 839.09 -50611/16/01 0.27 125.84 125 3450 22.0 -21.9 836.69 -53111/21/01 0.27 130.84 130 3450 22.0 -21.9 836.12 -534

G2B 10FDate Cast 7/13/0112:40 ∆CTE 2.43

DAYS Defl CL ∆Defl CL Ohms Temp oC ∆temp Hz Strain7/13/01 0.53 0.00 Init1 1.875 0.00 1363 44.1 0.0 900.40 07/13/01 0.54 0.01 Init2 1.875 0.00 1363 44.1 0.0 900.40 07/13/01 0.63 0.10 Release 2.172 0.30 1396 43.5 -0.6 826.40 -4177/14/01 0.29 0.76 1 2.094 0.22 2653 28.0 -16.2 823.30 -471

7/16/01 0.28 2.76 3 2.117 0.24 2789 26.8 -17.3 822.40 -4797/20/01 0.30 6.77 7 2.148 0.27 2614 28.3 -15.8 818.38 -4967/27/01 0.27 13.74 14 2.164 0.29 2797 26.7 -17.4 817.30 -50611/28/01 0.27 137.74 140 3760 20.1 -24.1 817.63 -52012/5/01 0.27 144.74 142 3550 21.3 -22.8 813.30 -540



300


301

Appendix L. Model Comparison

L.1. Normal Strength Concrete Creep Models for 8,000-psi HPLC 8L ACI-209 AASHTO-L CEB-FIP GL2001 SAK1993

Time undecreep coeffcreep coeffcreep coeffcreep coeffbasic creepdrying creeafter dryingcreep coeffcreep coeffcreep coeffcreep coeffcreep coeffcreep coeffψ 0.6 0.6 0.3 coeff coeff coeff basic creepdrying cree total creepd 10 10 326.2Øu 2.378599 1.662089 4.229596

0.00 0.00 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0000.02 0.04 0.024 0.027 0.239 0.555 0.166 -0.037 0.683 1.182 0.081 1.263 0.853 0.0420.06 0.06 0.041 0.045 0.313 0.656 0.210 -0.052 0.814 1.283 0.102 1.385 1.240 0.0710.10 0.17 0.057 0.060 0.370 0.729 0.243 -0.064 0.907 1.349 0.118 1.467 1.520 0.1000.14 0.18 0.071 0.073 0.412 0.779 0.267 -0.073 0.972 1.393 0.130 1.523 1.708 0.1230.18 0.20 0.082 0.085 0.446 0.818 0.286 -0.081 1.022 1.426 0.139 1.565 1.848 0.1440.41 0.29 0.132 0.133 0.571 0.954 0.354 -0.110 1.198 1.535 0.173 1.708 2.286 0.2330.93 0.35 0.208 0.208 0.729 1.111 0.438 -0.149 1.400 1.650 0.216 1.866 2.727 0.3741.84 0.55 0.300 0.296 0.893 1.262 0.523 -0.193 1.592 1.752 0.263 2.014 3.116 0.5513.17 0.68 0.396 0.382 1.050 1.396 0.603 -0.236 1.763 1.836 0.309 2.145 3.440 0.7455.16 0.76 0.502 0.471 1.213 1.529 0.683 -0.283 1.929 1.915 0.360 2.275 3.728 0.9697.31 0.81 0.590 0.544 1.344 1.632 0.747 -0.322 2.057 1.974 0.403 2.377 3.923 1.1639.10 0.87 0.650 0.593 1.433 1.700 0.790 -0.350 2.141 2.011 0.433 2.445 4.039 1.300

16.31 0.97 0.828 0.735 1.697 1.896 0.916 -0.435 2.377 2.114 0.531 2.645 4.309 1.72723.15 1.14 0.945 0.824 1.874 2.024 0.998 -0.496 2.527 2.178 0.604 2.782 4.444 2.02527.22 1.18 1.001 0.865 1.960 2.086 1.039 -0.526 2.598 2.208 0.642 2.850 4.499 2.17237.17 1.22 1.110 0.944 2.134 2.211 1.119 -0.591 2.739 2.266 0.723 2.990 4.594 2.46855.81 1.30 1.255 1.045 2.375 2.385 1.229 -0.687 2.927 2.345 0.847 3.192 4.698 2.87169.10 1.36 1.331 1.097 2.506 2.482 1.288 -0.744 3.027 2.387 0.919 3.306 4.746 3.08383.19 1.39 1.395 1.140 2.622 2.570 1.340 -0.796 3.114 2.424 0.986 3.411 4.785 3.265

111.17 1.44 1.494 1.206 2.804 2.713 1.422 -0.886 3.249 2.483 1.096 3.579 4.840 3.537138.95 1.47 1.567 1.254 2.944 2.828 1.484 -0.962 3.350 2.529 1.183 3.712 4.880 3.731167.32 1.52 1.625 1.293 3.058 2.928 1.534 -1.029 3.433 2.568 1.254 3.822 4.911 3.879195.36 1.52 1.673 1.324 3.150 3.014 1.576 -1.089 3.501 2.601 1.312 3.913 4.936 3.990225.08 1.53 1.714 1.352 3.233 3.095 1.612 -1.146 3.561 2.632 1.362 3.994 4.959 4.083258.36 1.58 1.753 1.378 3.311 3.176 1.646 -1.205 3.617 2.661 1.408 4.070 4.980 4.164283.06 1.59 1.778 1.394 3.361 3.230 1.668 -1.245 3.654 2.681 1.437 4.118 4.994 4.212336.94 1.60 1.823 1.425 3.452 3.337 1.709 -1.325 3.721 2.720 1.487 4.206 5.020 4.292363.90 1.60 1.843 1.438 3.491 3.385 1.726 -1.362 3.749 2.737 1.507 4.243 5.032 4.323504.99 1.64 1.920 1.491 3.642 3.599 1.793 -1.529 3.863 2.810 1.576 4.386 5.081 4.423532.89 1.62 1.932 1.499 3.665 3.635 1.803 -1.558 3.880 2.822 1.585 4.407 5.089 4.435568.11 1.66 1.946 1.508 3.691 3.679 1.814 -1.593 3.900 2.837 1.595 4.432 5.098 4.448600.83 1.67 1.957 1.516 3.714 3.718 1.824 -1.624 3.918 2.850 1.603 4.453 5.106 4.458621.84 1.66 1.965 1.521 3.727 3.741 1.830 -1.643 3.928 2.858 1.607 4.465 5.112 4.464

5000 2.243 1.718 4.150 5.522 2.016 -3.119 4.418 3.369 1.667 5.036 5.423 4.52814600 2.305 1.764 4.202 6.745 2.039 -4.037 4.746 3.658 1.667 5.325 5.585 4.528

creep coefficientBažant Panula - BP Bažant Baweja - B3

302

ACI 209 CoeficientsBasic Input assumption steam cured for 1 day AASHTO-LRFD CEB-FIP

0.4 0.6 Creep t' (maturity) 6.1 day t' 1.0 dayeelast @24 890 1307 d 10 Creep MPA psistress 2845 4273 f MPA psi f'@24h 53.3 7730elast/stress 0.313 0.306 Øu f'@24h 53.3 7730 f'c 72.4 10500t' 1.0 day Base 2.35 f'c 72.4 10500 σc (40%) 19.6 2845t0 1.0 day Loading Age γla 1.130 t' 1.0 d 10 σc (60%) 29.5 4273f'@24h 7730 psi Differential Shrink 1 ψ 0.6 E28 27724 4020000f'c 10500 psi Inicial Mois Curing 1 Øu RH 50 %E28 4020000 psi Ambient Relative Hum 0.935 RH 50 % Base 3.5 h 50.8 mm2RH 50 % Volume Surface Ratio 1.106 v/s 1 in Loading Age 0.807594 βH 326.2v 188.50 in3 Temperature other tha 1 Strength factor kf 0.544465 øRH 2.362252s 188.50 in2 Slump γs 1.122 slump: 4.5 in Ambient Relative Hum 1.08 50 β(fm) 1.969542c 944 lb/yd3 Fine Aggregate % γψ 0.969 fa% 37.0 % Ultimate value 1.662089 β(t') 0.909091g 1742 lb/yd3 Cement Content γc 1 v 188.5 1 in øo 4.229596s 1022 lb/yd3 Air Content γα 0.7975 air% 3.75 % s 188.5w 267.8 lb/yd3 Ultimate value 2.378599 not used for creep ø28

ut tdt ?? ??

? 6.0

6.0)'()',(

28Etttcr φ

σε =

028 )'()'(

−+

−⋅=

tttt

Hβφφ

250100100

2.1115018

+⋅

⋅+⋅=

hRHHβ

303

Bažant Panula Bažant Baweja Gardner Lockman Sakatat' 1 day t' 1.0 day t' 1.0 day t' 1.1 dayto 1 day to 1.0 day to 1.0 day to 1.0 dayf'@24h 7730 f'@24h 7730 f'@24h 7730.0 f'@24h 7730 psif'c 10500 f'c 10500 E28 f'c 10500.0 f'c 10500 psi1/E0 8.28E-08 1/E0 0.104535 eelast @24RH 0.5

40% 60% 40% v 188.5 RH 50eelast @24 890 1307 Basic Creep 890 s 188.5 v 3088889 25.4 mmstress 2845 4273 ψ 0.3 60% v/s 1 in s 121609.8Estat 3195107 3269815 m 0.5 1307 40% 60%Estat bar 3232461 n 0.1 eelast @24 890 1307 a 1639.8 kg/m3Basic Creep α 0.001 stress 2845 4273 c 560.1 kg/m3ø1 3.865 q0 1.9518 g 1033.5 kg/m3m 0.289 Drying Creep s 606.3 kg/m3x 6.857 RH 50 % w 158.9 kg/m3a1 0.93 H(t') 1 e'bc 182.1n 0.187 q5 0.571429 e'dc 20.6α 0.088 Kh'Drying Creep v 188.5 1RH 50 s 188.5cd 1.400 τsh 128cp 0.830ø'd 0.031ød 0.031Kh' 0.646 cylinderKh'' 0.75C1 122.4Ks 1.15v 188.5s 188.5τsh 34.1εs? 356.2εsh? 377.9r 2.932a 2764c 944g 1742s 1022w 267.8

304

L.2. High Strength Concrete Creep Models for 8,000-psi HPLC 8F-8L Shams&KaB-FIP modif Sakata 2001

Time unde creep coeffSpecific CrSpecific Crbasic creepdrying creeafter dryingcreep coef creep coef creep coef creep coefψ 0.6 0.3 coeff coeff coeff basic creepdrying creepd 6.747 341.2Øu 2.73 1.019259

0.00 0.00 0.000 0.000 0.000 0.000 0.000 0.000 0.00 0.00 0.000 00.02 0.04 0.036 0.184 0.555 0.091 -0.037 0.608 0.04 0.00 0.041 -0.8550.06 0.06 0.060 0.241 0.656 0.115 -0.052 0.719 0.06 0.00 0.063 -0.6520.10 0.17 0.081 0.285 0.729 0.133 -0.064 0.797 0.08 0.00 0.082 -0.5260.14 0.18 0.098 0.317 0.779 0.146 -0.073 0.851 0.09 0.00 0.097 -0.4450.18 0.20 0.113 0.343 0.818 0.157 -0.081 0.893 0.11 0.00 0.109 -0.3860.41 0.29 0.176 0.440 0.954 0.194 -0.110 1.038 0.15 0.01 0.159 -0.2000.93 0.35 0.270 0.561 1.111 0.240 -0.149 1.202 0.21 0.02 0.226 -0.0161.84 0.55 0.378 0.688 1.262 0.287 -0.193 1.356 0.26 0.04 0.301 0.1383.17 0.68 0.479 0.809 1.396 0.331 -0.236 1.491 0.31 0.06 0.375 0.2605.16 0.76 0.579 0.935 1.529 0.376 -0.283 1.622 0.36 0.09 0.453 0.3707.31 0.81 0.659 1.036 1.632 0.412 -0.322 1.721 0.40 0.12 0.516 0.4499.10 0.87 0.711 1.104 1.700 0.436 -0.350 1.786 0.42 0.14 0.558 0.498

16.31 0.97 0.854 1.308 1.896 0.507 -0.435 1.968 0.48 0.19 0.674 0.63023.15 1.14 0.939 1.444 2.024 0.556 -0.496 2.084 0.52 0.23 0.745 0.70927.22 1.18 0.977 1.511 2.086 0.579 -0.526 2.139 0.53 0.25 0.776 0.74537.17 1.22 1.047 1.646 2.211 0.628 -0.591 2.248 0.56 0.27 0.834 0.81655.81 1.30 1.132 1.833 2.385 0.697 -0.687 2.396 0.60 0.31 0.903 0.90769.10 1.36 1.174 1.935 2.482 0.737 -0.744 2.476 0.61 0.32 0.936 0.95683.19 1.39 1.208 2.025 2.570 0.773 -0.796 2.546 0.63 0.34 0.962 0.998

111.17 1.44 1.258 2.167 2.713 0.832 -0.886 2.658 0.65 0.35 0.999 1.063138.95 1.47 1.294 2.276 2.828 0.880 -0.962 2.746 0.66 0.36 1.024 1.113167.32 1.52 1.322 2.366 2.928 0.922 -1.029 2.820 0.68 0.37 1.043 1.155195.36 1.52 1.344 2.439 3.014 0.958 -1.089 2.883 0.68 0.37 1.058 1.190225.08 1.53 1.364 2.504 3.095 0.992 -1.146 2.940 0.69 0.38 1.070 1.222258.36 1.58 1.382 2.565 3.176 1.026 -1.205 2.996 0.70 0.38 1.081 1.253283.06 1.59 1.393 2.604 3.230 1.048 -1.245 3.034 0.70 0.38 1.088 1.274336.94 1.60 1.414 2.677 3.337 1.093 -1.325 3.105 0.71 0.39 1.101 1.313363.90 1.60 1.423 2.708 3.385 1.113 -1.362 3.137 0.72 0.39 1.106 1.331504.99 1.64 1.459 2.828 3.599 1.201 -1.529 3.271 0.73 0.39 1.126 1.404532.89 1.62 1.464 2.846 3.635 1.216 -1.558 3.294 0.73 0.39 1.129 1.417568.11 1.66 1.470 2.867 3.679 1.234 -1.593 3.320 0.74 0.40 1.132 1.431600.83 1.67 1.476 2.885 3.718 1.249 -1.624 3.343 0.74 0.40 1.135 1.444621.84 1.66 1.479 2.896 3.741 1.259 -1.643 3.357 0.74 0.40 1.137 1.451

5000 1.606 3.237 5.522 1.791 -3.119 4.193 0.79 0.41 1.201 1.92214600 1.634 3.279 6.745 1.942 -4.037 4.649 0.81 0.41 1.215 2.164

Bažant Panula for HSC AFREM

305

Basic Input Shams&Kahn CEB-FIP modified by Yue and Taerwe (1993)0.4 0.6 assumption steam cured for 1 day t' 1.0 day

eelast @24 890 1307 MPA psistress 2845 4273 f'@24h 53.3 7730elast/stress 0.313 0.306 f'c 72.4 10500t' 1.0 day σc (40%) 19.6 2845t0 1.0 day σc (60%) 29.5 4273f'@24h 7730 psi E28 27724 4020000f'c 10500 psi d 6.747479 6.12 days RH 50 %E28 4020000 psi Ø? 2.73 m tm h 50.8 mmRH 50 % Kfc 0.395224 f'c 10500 psi βH 341.2v 188.50 in3 Kh 1.083333 øRH 2.362252s 188.50 in2 Kt' 0.721737 tm' (loading 6.12 days β(fm) 1.537569c 944 lb/yd3 Ks 1.161834 stress/strength 0.5 β(t') 0.909091g 1742 lb/yd3 Km 1.555365 RH 50 % øo 3.301933s 1022 lb/yd3 v 188.4956w 267.8 lb/yd3 s 188.4956 ø28

306

Bažant Panula for HSC AFREM model Sakatat' 1.0 day t' 1.0 day t' 1 dayto 1.0 day to 1.0 day to 1.0 dayf'@24h 7730 f'@24h 53.3 f'@24h 7730 psif'c 10500 f'c 72.4 E28 f'c 10500 psi1/E0 8.28E-09 1/E0 95.45147 eelast @241/E0 0.105

0.4 0.6 0.4 0.6 RH 0.5eelast @24 890 1307 eelast @24 890 1307 v 3088889 25.4 mmstress 2845 4273 stress 2845 4273 s 121609.8Estat 31951074 32698152 Estat 31951074 32698152Estat bar 32324613 Estat bar 32324613 a 1639.8 kg/m3Basic Creep SF? yes c 560 kg/m3ø1 3.865 Basic Creep g 1033 kg/m3m 0.289 øbo 0.827 s 606 kg/m3x 6.857 βbc 2.907 w 159 kg/m3a1 0.93 Drying Creep e'bcn 0.187 RH 50 % e'dc 26.4α 0.088Drying Creep ødo 1.0RH 50 % K(fmc) 14.793cd 1.399684 A(fmc,H) 27.574cp 0.83 βds0 0.007ø'd 0.031 h 50.8 mmød 0.031ad 1.000Kh' 0.646 cylinderKh'' 0.75C1 122.4 1Ks 1.15v 188.5s 188.5bd 100.0τsh 34.1εs? 356.2εsh? 377.9r 2.932a 2764c 944g 1742s 1022w 267.8

307

L.3. Shrinkage Models for 8,000-psi HPLC

Measured ACI209 AASHTO CEB BP B3 GL SAK-93 SAK-2001 AFREM Shams and

0.00 0 0 0 0 0 0 0 0 0 0 00.04 96 1 1 9 12 8 12 5 0 1 10.08 142 1 2 12 16 11 17 8 1 2 30.13 116 2 3 15 20 14 21 10 1 3 40.17 125 2 4 18 23 16 25 12 2 4 50.21 130 3 5 20 26 18 28 13 2 5 70.43 162 5 11 28 37 26 40 19 5 10 130.83 148 10 21 39 51 36 55 28 9 18 251.88 138 23 46 58 76 53 82 42 19 38 553.00 134 36 71 73 94 67 103 54 30 58 835.04 205 59 113 94 119 86 133 70 49 89 1297.19 232 81 151 111 138 102 157 82 67 116 1698.98 232 98 180 123 151 114 174 92 81 135 198

16.17 316 159 274 159 188 149 226 119 130 193 28623.02 346 207 339 184 210 174 261 138 169 229 34127.09 352 231 370 196 220 187 279 147 189 245 36637.06 479 282 430 220 239 212 314 165 229 274 41255.68 563 353 503 252 260 247 360 190 286 308 46468.97 581 390 538 268 271 266 385 203 315 323 48683.06 589 422 567 282 278 282 405 214 340 335 504

111.04 634 469 605 303 289 306 436 231 377 351 527138.83 642 502 631 317 296 323 458 243 403 361 542167.19 645 528 649 329 301 336 474 252 422 368 552195.23 662 547 663 337 305 346 487 259 438 373 559224.94 669 563 674 344 308 354 499 265 450 378 565258.23 666 578 684 351 311 360 508 270 461 381 570282.93 672 587 690 355 312 364 515 273 468 384 573336.81 715 603 700 362 315 371 525 279 480 387 578363.78 705 609 704 365 316 374 530 281 485 389 580504.86 748 632 718 376 320 382 546 288 503 394 587532.77 763 635 720 377 321 383 548 289 506 395 588567.98 756 639 722 379 321 384 551 290 508 395 589600.73 753 642 724 380 322 385 553 290 511 396 589621.93 763 644 725 381 322 385 555 291 512 396 590

5000 693 753 404 330 390 590 297 550 407 60314500 698 755 407 330 390 594 297 553 408 604

308

Basic Input ACI 209 Coeficients AASHTO CEB-FIP BP model0.4 0.6 assumpyion steam cured for 1 day Cure steam H 50 % to 1.0

eelast @24h 890 1307 Shrink K 560 βsRH 0.875 t' 1.0stress 2845 4273 d h 50 % βRH -1.356 f'c 10500elast/stress 0.313 0.306 f 55 Kh 1.286 βSC 8 a 2764t' 1.0 day (εsh)u v 188.5 in3 f'c 10500 c 944t0 1.0 day Base 780 s 188.5 in2 εso 407.8 g 1742f'@24h 7730 psi Loading Ag 1 v/s 1 in βsH 90.3224 s 1022f'c 10500 psi Differential 1 Ac 12.57 in2 w 267.8E28 4020000 psi Inicial Mois 1 u 12.57 in to 1RH 50 % Ambient R 0.900 0.5 @50% Ac/u 1 in RH 50v 188.50 in3 VS Ratio γ 1.064 1.0 Kh 0.875s 188.50 in2 Temperatu 1 C1 26.71904 k'tc 944 lb/yd3 Slump γs 1.075 slump: 4.5 in K't 1.327905 Ksg 1742 lb/yd3 Fine Agg % 0.818 fa% 37.0 % v 188.5 1s 1022 lb/yd3 Cement Co 1.08984 c 944 lb/yd3 s 188.5w 267.8 lb/yd3 Air Content 0.98 air% 3.75 % τsh 34.06 D

Ultimate va 701 not used for shrinkage z 10.619y 0.970εs8 356.2E(28) 4020000E(7+600) 4343498 607E(7+τsh) 4094197 35.1εsh? 378fc' 10.5

309

B3 model GL SAK-93 SAK-2000 AFREM Best Shams and Kahnto 1.0 drying startH 0.5 to 1.0 drying startto 1.0 drying startfc' 10.500 exponentia tm' (start of 6.12t' 1.0 loading sta Khum 0.926 H 0.5 H 0.5 K(fc') 14.80 ksi 514.0376 Cure member-cuf'c 10500 psi K 1 w 267.8 w 267.8 SF? yes 0.014329 eshu 510a 2764 lb/yd3 f'c 10500 εsh8 296.5 f'c 10.5 ksi βds 0.007 1.214075 h 50c 944 lb/yd3 εshu 644 V 188.5 in3 α 10 H 0.5 KH 1.286g 1742 lb/yd3 V 188.5 in3 S 188.5 in2 β 52.7 72 exp 27.58 v 188.5s 1022 lb/yd3 S 188.5 in2 η 0.243 Ac 12.57 in2 s 188.5w 267.8 lb/yd3 Kvs 96.8 εsh8 556 u 12.57 in v/s 1to 1 V 188.5 in3 2xAc/u 2 in kt0 0.87751RH 0.5 S 188.5 in2Kh 0.875Ks 1.15τsh 99.7v 188.5s 188.5α1 1α2 0.75E(607) 1.080 607E(to+τsh) 1.060εsh8 390

310

L.4. Normal Strength Concrete Creep Models for 10,000-psi HPLC 10L ACI-209 AASHTO-L CEB-FIP GL2001 SAK1993

Time undecreep coeffcreep coeffcreep coeffcreep coeffbasic creepdrying creeafter dryingcreep coeffcreep coeffcreep coeffcreep coeffcreep coeffcreep coeffψ 0.6 0.6 0.3 coeff coeff coeff basic creepdrying cree total creepd 10 10 326.2Øu 2.242345 1.555625 4.045742

0.00 0.00 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0000.02 0.07 0.022 0.024 0.223 0.542 0.130 -0.032 0.640 1.204 0.078 1.283 0.824 0.0250.05 0.13 0.035 0.038 0.284 0.630 0.160 -0.044 0.746 1.295 0.096 1.391 1.154 0.0400.09 0.20 0.051 0.053 0.344 0.710 0.189 -0.056 0.844 1.373 0.113 1.486 1.469 0.0590.13 0.21 0.064 0.066 0.386 0.764 0.210 -0.064 0.909 1.421 0.125 1.546 1.671 0.0740.17 0.24 0.076 0.077 0.421 0.807 0.226 -0.072 0.962 1.459 0.135 1.594 1.827 0.0880.38 0.25 0.119 0.119 0.533 0.935 0.278 -0.096 1.116 1.565 0.166 1.731 2.243 0.1400.79 0.33 0.179 0.178 0.664 1.073 0.336 -0.127 1.282 1.670 0.203 1.873 2.638 0.2151.81 0.39 0.280 0.275 0.850 1.254 0.417 -0.173 1.498 1.796 0.257 2.052 3.107 0.3443.17 0.49 0.374 0.357 1.005 1.393 0.483 -0.214 1.662 1.885 0.304 2.189 3.441 0.4704.82 0.54 0.458 0.428 1.137 1.506 0.538 -0.250 1.794 1.955 0.346 2.300 3.688 0.5897.04 0.55 0.547 0.501 1.272 1.617 0.593 -0.288 1.923 2.020 0.391 2.410 3.903 0.7199.10 0.68 0.613 0.555 1.371 1.697 0.634 -0.317 2.014 2.065 0.426 2.490 4.039 0.820

15.93 0.74 0.773 0.682 1.612 1.885 0.732 -0.391 2.225 2.166 0.517 2.683 4.300 1.07823.18 0.82 0.891 0.771 1.793 2.023 0.804 -0.450 2.377 2.236 0.593 2.829 4.444 1.27828.22 0.85 0.955 0.818 1.894 2.099 0.845 -0.485 2.459 2.273 0.639 2.912 4.510 1.39136.95 0.86 1.045 0.882 2.038 2.208 0.903 -0.536 2.574 2.325 0.708 3.034 4.592 1.55355.25 0.93 1.180 0.976 2.266 2.381 0.995 -0.623 2.753 2.405 0.828 3.233 4.696 1.80469.81 0.98 1.258 1.029 2.404 2.488 1.051 -0.680 2.859 2.453 0.906 3.359 4.748 1.95182.87 1.02 1.314 1.066 2.506 2.569 1.093 -0.725 2.937 2.488 0.967 3.455 4.784 2.057

111.02 1.05 1.408 1.128 2.682 2.714 1.167 -0.809 3.072 2.549 1.076 3.625 4.840 2.230139.31 1.05 1.478 1.174 2.817 2.832 1.225 -0.880 3.177 2.597 1.162 3.759 4.880 2.355167.36 1.11 1.532 1.210 2.925 2.932 1.272 -0.942 3.262 2.636 1.232 3.868 4.911 2.446194.93 1.12 1.576 1.239 3.012 3.017 1.310 -0.996 3.331 2.670 1.287 3.957 4.936 2.516225.23 1.13 1.616 1.265 3.093 3.100 1.347 -1.051 3.396 2.701 1.338 4.039 4.959 2.575251.25 1.15 1.645 1.285 3.152 3.164 1.374 -1.094 3.444 2.726 1.374 4.100 4.976 2.616279.31 1.18 1.673 1.303 3.208 3.228 1.400 -1.137 3.490 2.749 1.407 4.156 4.992 2.652306.49 1.19 1.696 1.318 3.255 3.284 1.422 -1.177 3.530 2.770 1.434 4.204 5.006 2.681335.00 1.21 1.718 1.333 3.299 3.340 1.443 -1.215 3.567 2.790 1.459 4.249 5.020 2.706371.98 1.20 1.742 1.349 3.349 3.406 1.467 -1.263 3.611 2.814 1.485 4.299 5.035 2.732495.95 1.24 1.806 1.392 3.477 3.595 1.531 -1.401 3.725 2.880 1.544 4.425 5.078 2.787523.87 1.28 1.818 1.400 3.499 3.632 1.542 -1.429 3.745 2.893 1.554 4.447 5.086 2.795559.06 1.26 1.831 1.409 3.525 3.677 1.555 -1.463 3.769 2.908 1.564 4.472 5.096 2.804591.89 1.29 1.842 1.417 3.547 3.716 1.567 -1.493 3.790 2.922 1.572 4.494 5.104 2.810620.72 1.29 1.852 1.423 3.564 3.750 1.576 -1.518 3.807 2.933 1.578 4.511 5.111 2.815

5000 2.115 1.608 3.970 5.547 1.811 -3.004 4.354 3.459 1.637 5.095 5.423 2.85614600 2.173 1.651 4.019 6.783 1.843 -3.976 4.650 3.755 1.637 5.392 5.585 2.856

creep coefficientBažant Panula - BP Bažant Baweja - B3

311

ACI 209 Coeficients

Basic Input assumption steam cured for 1 day AASHTO-LRFD CEB-FIP0.4 0.6 Creep t' (maturity) 6.6 day t' 1.0 day

eelast @24 1059 1470 d 10 Creep MPA psistress 3517 5276 f MPA psi f'@24h 76.6 11101elast/stress 0.301 0.279 Øu f'@24h 76.6 11101 f'c 79.1 11476t' 1.0 day Base 2.35 f'c 79.1 11476 σc (40%) 24.3 3517t0 1.0 day Loading Age γla 1.130 t' 1.0 day d 10 σc (60%) 36.4 5276f'@24h 11101 psi Differential Shrink 1 ψ 0.6 E28 2924 424000f'c 11476 psi Inicial Mois Curing 1 Øu RH 50 %E28 424000 psi Ambient Relative Hum 0.935 RH 50 % Base 3.5 h 50.8 mm2RH 50 % Volume Surface Ratio 1.106 v/s 1 in Loading Age 0.800493 βH 326.2v 188.50 in3 Temperature other tha 1 Strength factor kf 0.514109 øRH 2.362252s 188.50 in2 Slump γs 1.088 slump: 4 in Ambient Relative Hum 1.08 50 β(fm) 1.883929c 990 lb/yd3 Fine Aggregate % γψ 0.969 fa% 37.0 % Ultimate value 1.555625 β(t') 0.909091g 1757 lb/yd3 Cement Content γc 1 v 188.5 1 in øo 4.045742s 1030 lb/yd3 Air Content γα 0.775 air% 3.5 % s 188.5w 227.3 lb/yd3 Ultimate value 2.242345 not used for creep ø28

ut tdt ?? ??

? 6.0

6.0)'()',(

28Etttcr φ

σε =

028 )'()'(

−+

−⋅=

tttt

Hβφφ

250100100

2.1115018

+⋅

⋅+⋅=

hRHHβ

312

Bažant Panula Bažant Baweja Gardner Lockman Sakatat' 1 day t' 1.0 day t' 1.0 day t' 1.1 dayto 1 day to 1.0 day to 1.0 day to 1.0 dayf'@24h 11101 f'@24h 11101 f'@24h 11101.0 f'@24h 11101 psif'c 11476 f'c 11476 E28 f'c 11476.0 f'c 11476 psi1/E0 7.88E-08 1/E0 0.103797 eelast @24RH 0.5

40% 60% 40% v 188.5 RH 50eelast @24 1059 1470 Basic Creep 1059 s 188.5 v 3088889 25.4 mmstress 3517 5276 ψ 0.3 60% v/s 1 in s 121609.8Estat 3321119 3588648 m 0.5 1470 40% 60%Estat bar 3454883 n 0.1 eelast @24 1059 1470 a 1653.5 kg/m3Basic Creep α 0.001 stress 3517 5276 c 587.3 kg/m3ø1 3.714 q0 1.866959 g 1042.4 kg/m3m 0.288 Drying Creep s 611.1 kg/m3x 7.310 RH 50 % w 134.9 kg/m3a1 0.93 H(t') 1 e'bc 110.6n 0.188 q5 0.52283 e'dc 8.5α 0.109 Kh'Drying Creep v 188.5 1RH 50 s 188.5cd 1.392 τsh 128cp 0.830ø'd 0.030ød 0.030Kh' 0.646 cylinderKh'' 0.75C1 122.4Ks 1.15v 188.5s 188.5τsh 55.1εs? 342.1εsh? 354.8r 2.157a 2787c 990g 1757s 1030w 227.3

313

L.5. High Strength Concrete Creep Models for 10,000-psi HPLC 8F-8L Shams&KaB-FIP modif Sakata 2001

Time unde creep coeffSpecific CrSpecific Crbasic creepdrying creeafter dryingcreep coef creep coef creep coef creep coefψ 0.6 0.3 coeff coeff coeff basic creepdrying creepd 6.944 333.5Øu 2.73 0.8857

0.00 0.00 0.000 0.000 0.000 0.000 0.000 0.000 0.00 0.00 0.000 00.02 0.07 0.032 0.169 0.542 0.071 -0.032 0.581 0.02 0.00 0.019 -0.6180.05 0.13 0.049 0.214 0.630 0.088 -0.044 0.674 0.03 0.00 0.028 -0.4910.09 0.20 0.069 0.260 0.710 0.104 -0.056 0.759 0.04 0.00 0.038 -0.3880.13 0.21 0.085 0.292 0.764 0.115 -0.064 0.815 0.04 0.00 0.047 -0.3260.17 0.24 0.100 0.319 0.807 0.124 -0.072 0.859 0.05 0.00 0.054 -0.2800.38 0.25 0.153 0.403 0.935 0.152 -0.096 0.991 0.07 0.01 0.080 -0.1550.79 0.33 0.226 0.502 1.073 0.184 -0.127 1.131 0.10 0.02 0.115 -0.0371.81 0.39 0.342 0.643 1.254 0.229 -0.173 1.309 0.14 0.03 0.174 0.0953.17 0.49 0.437 0.760 1.393 0.265 -0.214 1.444 0.18 0.05 0.229 0.1844.82 0.54 0.515 0.860 1.506 0.295 -0.250 1.552 0.20 0.08 0.281 0.2517.04 0.55 0.594 0.962 1.617 0.326 -0.288 1.655 0.23 0.10 0.335 0.3129.10 0.68 0.651 1.037 1.697 0.349 -0.317 1.728 0.25 0.12 0.375 0.353

15.93 0.74 0.778 1.219 1.885 0.403 -0.391 1.897 0.30 0.17 0.471 0.44223.18 0.82 0.863 1.356 2.023 0.445 -0.450 2.017 0.34 0.20 0.538 0.50228.22 0.85 0.906 1.433 2.099 0.468 -0.485 2.082 0.35 0.22 0.573 0.53336.95 0.86 0.963 1.542 2.208 0.502 -0.536 2.174 0.38 0.24 0.620 0.57655.25 0.93 1.042 1.715 2.381 0.557 -0.623 2.315 0.41 0.27 0.685 0.64169.81 0.98 1.085 1.819 2.488 0.592 -0.680 2.400 0.43 0.29 0.720 0.67882.87 1.02 1.115 1.897 2.569 0.619 -0.725 2.463 0.45 0.30 0.745 0.705

111.02 1.05 1.163 2.031 2.714 0.667 -0.809 2.573 0.47 0.31 0.783 0.752139.31 1.05 1.197 2.134 2.832 0.707 -0.880 2.660 0.49 0.32 0.810 0.788167.36 1.11 1.224 2.216 2.932 0.741 -0.942 2.731 0.51 0.32 0.831 0.818194.93 1.12 1.245 2.283 3.017 0.770 -0.996 2.791 0.52 0.33 0.847 0.842225.23 1.13 1.264 2.345 3.100 0.798 -1.051 2.848 0.53 0.33 0.861 0.865251.25 1.15 1.277 2.390 3.164 0.821 -1.094 2.891 0.54 0.34 0.871 0.883279.31 1.18 1.290 2.433 3.228 0.843 -1.137 2.933 0.54 0.34 0.881 0.899306.49 1.19 1.301 2.469 3.284 0.862 -1.177 2.970 0.55 0.34 0.889 0.914335.00 1.21 1.311 2.503 3.340 0.881 -1.215 3.006 0.55 0.34 0.896 0.929371.98 1.20 1.323 2.541 3.406 0.904 -1.263 3.048 0.56 0.34 0.905 0.945495.95 1.24 1.352 2.639 3.595 0.970 -1.401 3.164 0.58 0.35 0.926 0.991523.87 1.28 1.358 2.656 3.632 0.982 -1.429 3.186 0.58 0.35 0.930 1.000559.06 1.26 1.364 2.676 3.677 0.998 -1.463 3.212 0.59 0.35 0.934 1.010591.89 1.29 1.369 2.693 3.716 1.011 -1.493 3.235 0.59 0.35 0.938 1.019620.72 1.29 1.373 2.707 3.750 1.023 -1.518 3.254 0.59 0.35 0.941 1.027

5000 1.495 3.020 5.547 1.532 -3.004 4.076 0.67 0.36 1.029 1.36014600 1.523 3.058 6.783 1.711 -3.976 4.519 0.69 0.36 1.051 1.531

Bažant Panula for HSC AFREM

314

Basic Input Shams&Kahn CEB-FIP modified by Yue and Taerwe (1993)

0.4 0.6 assumption steam cured for 1 day t' 1.0 dayeelast @24 1059 1470 MPA psistress 3517 5276 f'@24h 76.6 11101elast/stress 0.301 0.279 f'c 79.1 11476t' 1.0 day σc (40%) 24.3 3517t0 1.0 day σc (60%) 36.4 5276f'@24h 11101 psi E28 2924 424000f'c 11476 psi d 6.944136 6.59 days RH 50 %E28 424000 psi Ø? 2.73 m tm h 50.8 mmRH 50 % Kfc 0.365826 f'c 11476 psi βH 333.5v 188.50 in3 Kh 1.083333 øRH 2.362252s 188.50 in2 Kt' 0.71674 tm' (loading 6.59 days β(fm) 1.433874c 990 lb/yd3 Ks 1.161834 stress/strength 0.5 β(t') 0.909091g 1757 lb/yd3 Km 1.577384 RH 50 % øo 3.079248s 1030 lb/yd3 v 188.4956w 227.3 lb/yd3 s 188.4956 ø28

315

Bažant Panula for HSC AFREM model Sakatat' 1.0 day t' 1.0 day t' 1 dayto 1.0 day to 1.0 day to 1.0 dayf'@24h 11101 f'@24h 76.6 f'@24h 11101 psif'c 11476 f'c 79.1 E28 f'c 11476 psi1/E0 7.88E-09 1/E0 79.92243 eelast @241/E0 0.104

0.4 0.6 0.4 0.6 RH 0.5eelast @24 1059 1470 eelast @24 1059 1470 v 3088889 25.4 mmstress 3517 5276 stress 3517 5276 s 121609.8Estat 33211192 35886477 Estat 33211192 35886477Estat bar 34548834 Estat bar 34548834 a 1653.5 kg/m3Basic Creep SF? yes c 587 kg/m3ø1 3.714 Basic Creep g 1042 kg/m3m 0.288 øbo 0.723 s 611 kg/m3x 7.310 βbc 5.553 w 135 kg/m3a1 0.93 Drying Creep e'bc #DIV/0!n 0.188 RH 50 % e'dc 10.9α 0.109Drying Creep ødo 1.0RH 50 % K(fmc) 13.380cd 1.392073 A(fmc,H) 26.889cp 0.83 βds0 0.007ø'd 0.030 h 50.8 mmød 0.030ad 1.000Kh' 0.646 cylinderKh'' 0.75C1 122.4 1Ks 1.15v 188.5s 188.5bd 100.0τsh 55.1εs? 342.1εsh? 354.8r 2.157a 2787c 990g 1757s 1030w 227.3

316

L.6. Shrinkage Models for 10,000-psi HPLC

Measured ACI209 AASHTO CEB BP B3 GL SAK-93 SAK-2001 AFREM Shams and

0.03 32 0 1 6 7 6 10 3 0 1 10.07 19 1 2 9 11 9 15 5 1 1 20.12 90 1 3 12 14 12 20 8 1 2 40.16 83 2 4 14 17 13 23 9 1 3 50.24 127 3 6 17 20 17 28 11 2 5 70.45 138 6 12 24 28 23 39 16 4 9 141.10 120 14 28 37 43 35 60 25 9 21 332.02 100 25 49 49 58 48 81 35 17 36 583.18 108 38 75 62 72 60 102 44 25 54 874.97 154 58 111 76 89 74 126 55 38 78 1267.24 169 81 152 91 106 89 150 65 53 103 1699.18 199 100 183 102 117 99 168 73 65 121 200

16.15 179 158 273 130 148 129 216 94 102 170 28323.04 237 206 339 151 169 151 250 109 130 202 33926.97 225 229 369 161 178 161 266 116 144 216 36337.04 291 280 430 181 197 183 300 131 173 242 40955.11 299 349 502 206 220 212 344 150 211 271 45977.54 344 407 556 228 237 238 380 166 243 292 494

108.97 430 463 603 248 253 262 415 182 271 309 522167.22 542 524 649 270 269 288 454 199 302 325 547195.56 518 544 663 277 274 297 466 205 312 329 555223.33 519 559 674 282 278 303 476 209 319 333 560252.78 528 572 682 287 281 308 485 213 325 336 565307.34 573 591 695 294 286 315 497 218 334 340 571335.37 553 598 699 297 288 318 502 220 338 341 573365.07 531 605 704 300 289 320 507 222 341 343 575587.95 590 637 723 312 297 329 528 229 356 349 584613.81 610 639 724 313 297 329 530 230 357 350 585

5000 689 753 332 309 334 565 234 379 359 59814500 694 755 334 310 334 568 234 382 359 599

317

Basic Input ACI 209 Coeficients AASHTO CEB-FIP BP model0.4 0.6 assumpyion steam cured for 1 day Cure steam H 50 % to 1.0

eelast @24h 1059 1470 Shrink K 560 βsRH 0.875 t' 1.0stress 3517 5276 d h 50 % βRH -1.356 f'c 11476elast/stress 0.301 0.279 f 55 Kh 1.286 βSC 8 a 2787t' 1.0 day (εsh)u v 188.5 in3 f'c 11476 c 990t0 1.0 day Base 780 s 188.5 in2 εso 334.8 g 1757f'@24h 11101 psi Loading Ag 1 v/s 1 in βsH 90.3224 s 1030f'c 11476 psi Differential 1 Ac 12.57 in2 w 227.3E28 424000 psi Inicial Mois 1 u 12.57 in to 1RH 50 % Ambient R 0.900 0.5 @50% Ac/u 1 in RH 50v 188.50 in3 VS Ratio γ 1.064 1.0 Kh 0.875s 188.50 in2 Temperatu 1 C1 16.50905 k'tc 990 lb/yd3 Slump γs 1.054 slump: 4 in K't 1.327905 Ksg 1757 lb/yd3 Fine Agg % 0.817 fa% 37.0 % v 188.5 1s 1030 lb/yd3 Cement Co 1.1064 c 990 lb/yd3 s 188.5w 227.3 lb/yd3 Air Content 0.978 air% 3.5 % τsh 55.13 D

Ultimate va 697 not used for shrinkage z 12.926y 0.986εs8 342.1E(28) 424000E(7+600) 458120.2 607E(7+τsh) 441746.7 56.1εsh? 355fc' 11.476

ushtsh tft )()( εε ⋅+

=

318

B3 model GL SAK-93 SAK-2000 AFREM Best Shams and Kahnto 1.0 drying startH 0.5 to 1.0 drying startto 1.0 drying startfc' 11.476 exponentia tm' (start of 6.59t' 1.0 loading sta Khum 0.926 H 0.5 H 0.5 K(fc') 13.38 ksi 514.0376 Cure member-cuf'c 11476 psi K 1 w 227.3 w 227.3 SF? yes 0.014329 eshu 510a 2787 lb/yd3 f'c 11476 εsh8 234.2 f'c 11.476 ksi βds 0.007 1.214075 h 50c 990 lb/yd3 εshu 616 V 188.5 in3 α 10 H 0.5 KH 1.286g 1757 lb/yd3 V 188.5 in3 S 188.5 in2 β 44.7 72 exp 26.89 v 188.5s 1030 lb/yd3 S 188.5 in2 η 0.387 Ac 12.57 in2 s 188.5w 227.3 lb/yd3 Kvs 96.8 εsh8 383 u 12.57 in v/s 1to 1 V 188.5 in3 2xAc/u 2 in kt0 0.870522RH 0.5 S 188.5 in2Kh 0.875Ks 1.15τsh 97.5v 188.5s 188.5α1 1α2 0.75E(607) 1.080 607E(to+τsh) 1.060εsh8 334

319

Appendix M. Comparison between HPC and HPLC

M.1. Creep and Shrinkage Results HPC-3 and HPC-6

Shrinkage Creep Shrinkage Shrinkage Creep CreepTime 24h-40% Time 24h-40% 24h-60%

0.01 0 0 0.06 -182 -135 246 3320.05 20 92 0.09 -204 -136 284 3970.09 30 120 0.18 -232 -182 374 4900.14 30 199 0.27 -227 -190 402 5350.26 50 195 0.38 -205 -155 412 5810.41 60 167 0.92 -168 -93 739 9950.89 90 297 2.00 -13 50 710 9891.02 100 310 2.85 40 102 705 10471.41 110 363 4.85 5 80 855 11931.89 130 387 6.85 67 142 862 12552.45 120 363 8.85 105 202 913 13282.89 150 335 15.85 130 215 1047 14534.91 170 410 22.85 193 299 999 14355.36 210 517 26.85 200 332 1081 15255.86 180 513 36.85 278 378 1275 17236.09 170 504 54.84 416 1215 17246.41 200 497 83.26 501 1394 19246.93 200 522 110.88 530 1370 19227.93 220 557 139.01 522 1413 19549.01 220 572 167.32 512 1463 20209.99 190 635 195.36 519 1462 2032

11.14 240 675 222.93 511 1502 205711.94 190 659 253.24 511 1477 205113.99 150 715 279.24 510 1524 214815.93 220 745 307.32 486 1668 227318.91 210 724 334.49 482 1613 227021.99 210 799 363.88 479 1705 240525.91 230 832 619.95 493 1664 234228.99 260 874 648.91 488 1682 235931.99 250 895 stress 2857 428634.91 340 914 elastic strain 829 131039.99 330 942 E (ksi) 3446 327242.91 270 95946.91 300 97251.97 340 98961.91 290 106269.9 360 1062

84.92 430 106699.86 480 1124112.9 400 1193136.9 410 1231

152.96 450 1263179.92 450 1301221.95 470 1373262.91 510 1424308.91 470 1413361.02 460 1456423.84 490 1496461.23 513 1516

stress 4774elastic strain 1209E (ksi) 3949

HPC-6HPC-3

320

M.2. Best Creep and Shrinkage Fits for HPC-3, HPC-6, and HPLC

Best fits 0.373 0.367 0.655 607.452 503.859 538.5130.208 0.174 0.356 132.077 70.629 86.4550.333 0.397 0.271

time under Best fit Best fit Best fit time under Best fit Best fit Best fitload HPLC HPC-3 HPC-6 drying HPLC HPC-3 HPC-6

0.03 0.024 0.016 0.086 0.03 9.5 10.8 10.40.07 0.031 0.021 0.104 0.07 13.9 15.8 15.20.11 0.035 0.026 0.117 0.11 17.6 20.0 19.30.15 0.039 0.029 0.126 0.15 20.7 23.4 22.60.19 0.042 0.032 0.134 0.19 23.3 26.4 25.50.41 0.054 0.042 0.160 0.41 34.0 38.5 37.20.88 0.067 0.056 0.191 0.88 49.5 56.1 54.21.92 0.085 0.074 0.227 1.92 72.9 82.3 79.73.08 0.097 0.087 0.251 3.08 92.1 103.8 100.55.08 0.112 0.104 0.278 5.08 117.6 132.0 128.07.15 0.123 0.116 0.298 7.15 138.9 155.2 150.89.05 0.131 0.125 0.312 9.05 155.5 173.0 168.4

16.15 0.153 0.150 0.347 16.15 204.2 224.1 219.323.07 0.167 0.167 0.370 23.07 240.1 260.3 255.827.11 0.173 0.175 0.380 27.11 257.8 277.5 273.537.09 0.187 0.190 0.401 37.09 294.8 312.3 309.655.40 0.204 0.211 0.427 55.40 346.3 357.4 357.877.57 0.220 0.229 0.449 77.57 391.7 393.5 397.7

167.10 0.255 0.270 0.497 167.10 491.6 459.4 475.6194.96 0.262 0.278 0.506 194.96 509.1 468.8 487.6224.08 0.268 0.285 0.515 224.08 523.9 476.1 497.1254.73 0.273 0.291 0.522 254.73 536.3 481.8 504.8281.03 0.278 0.295 0.528 281.03 545.1 485.5 510.0336.32 0.285 0.303 0.538 336.32 559.5 491.2 518.1363.93 0.289 0.307 0.542 363.93 565.1 493.2 521.0594.29 0.308 0.326 0.567 594.29 590.2 500.8 532.9618.75 0.310 0.328 0.569 618.75 591.6 501.2 533.4

5000.00 0.363 0.365 0.637 5000.00 607.4 503.9 538.514600.00 0.371 0.367 0.650 14600.00 607.5 503.9 538.5

Creep Shrinkage and Prestress Losses

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