HYDRAULIC PROCESSES ON AllUVlAl...

HYDRAULIC PROCESSES ON AllUVlAl FANS

wood -- mostly pinyon pine and junipers -- brought to the apex of the alluvial fan by a debris flow in Busher Creek, east flank of the White Mountains, Fish Lake Valley, Nevada, on July 18, 1984. Photo by Chest B. Beaty, University of Lethbridge, Alberta. (Used with permission.)

HYDRAULIC PROCESSES ON ALLUVIAL FANS

R.H. FRENCH

Water Resources Centre, University of Nevada System, 2505 Chandler Avenue, Suite I, Las Vegas, N V 89120, U.S.A.

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French, P l c h t r d H. H y d r a u l i c processes on alluvlal fans.

(Developments i n wate r sc ience ; 31) B i b l i o g r a p h y : p. I n c l u d e s indexes. 1. Channels ( H y d r a d i c ecg inees ing ) 2. Alluvia l

fans. 3. Sef iment t r a n s p o r t . I. T i t l e . 11. Ser ies . ‘IC1;5.F77 19c7 ~27l.45 87-5409 ISBW 0-444-4‘27-1-3 (U.S . )

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VII

PREFACE

Alluvial fans are among the most prominent landscape features in

the American Southwest and throughout the semi-arid and arid regions

of the world. The importance of developing qualitative and

quantitativeunderstandings of hydraulic processes on these features

derivesprimarily fromthe rapidand significantdevelopment thathas

taken place on them in the American Southwest over the past four

decades - development that is continuing and whose pace may be accelerating. As development and unplanned urban sprawl moved from

valley floors onto alluvial fan s t heamount andseriousness of damage

incurred from infrequent flow events has dramatically increased.

Whetherthedevelopment onalluvial fans isplannedorhaphazardseems to make very little difference because we have an inadequate

understanding of both the size of the flood events that might be

expected and how they will behave when they occur.

From the viewpoint of traditional civil engineering, the study

of hydraulic processes on alluvial fans is an exciting endeavor

because so very little is known and because the behavior of flows on

alluvial fans is quite different from traditional open-channel

hydraulics. The development of an understanding of hydraulic

processes on alluvial fans must begin for the engineer with the

understanding and anappreciation ofthe pioneeringresearch that has

been performed by the geologists. Likewise our colleagues, the

geologists, must realize that to date much of the information they

have provided is very qualitative rather than quantitative. Thus,

geologist, as he examines alluvial fans, requires knowledge of

hydraulic engineeringand itsneed forquantitativedatatoassert and

verify hypotheses. On the other hand, the hydraulic engineer must

appreciate that he is dealing with an evolving land-form whose

development may be affected by a very limited number of large events

whose distribution in time is unknown.

Over the past seven years, I have observed flood damage

throughout the Southwest and situations in which unplanned or

inadequately planned developments or oversights by engineers and

agencies, and a poor understanding of the processes involved have

resulted in substantial damage and the loss of life. I have also

observed situations in which the taxpayers' dollars were wasted on

flood control plans that bore no relationship to the unique set of

hydrologic, geologic, andhydraulicconditionsthatexist onalluvial

fans. I have had the opportunity of collaborating with government

VIII

officials, engineering and geologic consultants, attorneys,

developers, and individual homeowners who are concerned with cost-

effective but adequate planning to control floods on alluvial fans.

During this same period of time, I have also had the honor of being a

member of the Graduate Faculty at both the University of Nevada, Las

Vegas through the Department of Geosciences and the University of

Nevada, Reno through the Department of Civil Engineering. In this

capacity, I have had the unique opportunity of working with

individuals having very diverse academic backgrounds and interests.

My practical and academicexperience has led meto concludethat ifwe

are to develop an accurate understanding of hydraulic processes on

alluvial fansthenthe engineeringand geologiccommunities mustwork

together sharing information and theories. This collaboration must

have as its basis an understanding that the theories of each

discipline have merit and/orapplication. It is theambitious goal of

this book to establish this common data base andunderstanding ofthe

basic concepts of both disciplines.

There have been many agencies, companies and individuals who

have given freely of their time t o m a k e t h i s b o o k p o s s i b l e a n d Ithank all of them. In particular, I wouldacknowledge my colleagues atthe DesertResearchInst i tutewhosawfi t torecommendmysabbat ical leave application, the Board of Regents of the University of Nevada System

who approved my sabbatical leave, and the Water Resources Center of the Desert Research Institute - my employer - who made available the equipment inwhichto producethis volume. In particular, I wouldlike

to thank my wife Darlene who did much of the typing, editorial

revision, and art layout.

IX

TABLE OF CONTENTS

1 INTRODUCTION

1.1 Scope and Importance of Problem, 1

1.2 Initial Concepts and Definitions, 17

1.3 Conclusion, 24

2 BASIC GEOLOGIC CONCEPTS

2.1 Introduction, 28

2.2 Competing Geologic Doctrines, 28

2.3 Alluvial Fan Systems: General

Morphometric Characteristics, 32

2.4 Conditions Favoring the Development and

Modification of Alluvial Fans, 43

2.4.1 Vegative Cover/Precipitation/

Sediment Yield, 43

2.5 Fanhead Entrenchment, 61

2.6 Conditions Favorable to the Formation of

Debris and Mud-Flows, 65

2.6.1 Precipitation, 69

2.6.2 Lithology, 72

2.6.3 Topography, 72

2.6.4 Land Use, 73

2.7 Characteristics of Flows in Ephemeral

Streams, 73

3 BASIC PRINCIPLES OF OPEN CHANNEL HYDRAULICS


3.2 Specific Energy, 82

3.3 Uniform/Normal Flow, 87

3.4 Alluvial Channel Stability, 90

3.5 Debris Flow Mechanics, 106

3.5.1 Fluid Types, 109

3.5.2 Analytic Results for

Debris Flows, 114

3.6 Hydraulic/Physical Models, 123

3.6.1 Froude Law Models, 124

3.6.2 Moveable Bed Models, 125

3.6.3 Theoretical Techniques, 126

3.6.4 Empirical, 130

3.7 Conclusion, 131

1

28

82

X

4 MODELS OF HYDRAULIC PROCESSES ON ALLWIAL FANS 136


4.2 Numerical Model, Geologic Time Scale:

Price (1972,1974) , 136 4.2.1 Initial and Boundary Conditions, 137

4.2.2 Co-ordinate System, 138

4.2.3 Input Variables and Parameters, 138

4.2.4 Process: Uplift/Relief Development, 139

4.2.5 Process: Weatherins and Accumulation

of Material in the "Drainage Basin, 143

4.2.6 Process: Flow, 144

4.2.7 Calibration/Verification/Validation, 152

4.2.8 Summary, 152

4.3 Physical Model, Geologic Time Scale: Hooke

(1965,1967,1968), 154

4.3.1 Experimental Apparatus, 154

4.3.2 Experimental Procedures, 155

4.3.3 Verification, 155

4.3.4 Results, 155

4.3.5 Summary, 158

Scale: Anon. (1981a), 159

4.4.1 Experimental Apparatus, 160

4.4.2 Theoretical Assumptions and

4.4.3 Results, 167

4.4.4 Summary, 173

4.5 Numerical Models of Debris Flows in Channels:

DeLeon and Jeppson (1982) and Jeppson and

Rodriguez (1983), 174

4.5.1 Debris Flow Relative to Water Flow

4.4 Numerical/Physical Model, Engineering Time

Development, 160

Depths, 175

4.5.2 Results, 178

4.5.3 Discussion, 178

4.6 Conclusion, 179

5 METHODS OF FLOOD HAZARD ASSESSMENT ON ALLWIAL

FANS 183


5.2 FEMA Methodology for Alluviai Fan

XI

Studies, 183

5.2.1 FEMA Assumptions Explicit

5.2.2 Implementation, 185


StUdie6, 195


Methodology, 199

5.4.1 Proposed Modifications to the FEMA


and Implicit, 183

5.3 Alternative Methodology for Alluvial Fan

5.4 Proposed Modification of the FEMA

Methodology, 201

5.5 Conclusion, 206

6 CONCLUSION


6.2 Socio-Economic and Institutional

Problems, 214

6.3.1 Prognosis, 219

6.3 Research Needs, 216

214

GLOSSARY

AUTHOR INDEX

INDEX

222

228

234

CHAPTER 1

INTRODUCTION

1.1 SCOPE AND IMPORTANCE OF PROBLEM

According to Stone (1967) , an alluvial fan is a "triangular or fanshapeddepos i tofboulders , gravel, sand, and fine sediment at the

base of desert mountain slopes deposited by intermittent streams as

they debouch onto the valley floor1t. There are many other

definitions of alluvial fans: see for example, Anstey (1965), Bull

(1977) , and Rachocki (1981) : and some might find reason to take issue withthedefinitiongiven by Stone: for example, alluvial fans occur

not only in desert environments but also in the southeastern portion

of the United States, Anstey (1965) and the recently glaciated areas

of Poland, Rachocki (1981). However, the definition given above is reasonable for this book because its focus is hydraulic processes on

alluvial fans in arid and semi-arid environments.

Besides the innate curiosity of the human race regarding the environment in which they live, there are at least three important

reasonswhyhydraul icprocessesonal luvia l fans inaridandsemi-ar id

environments are of interest to the engineering and scientific

community. First, and perhaps most important, is that some of the

fastest developing areas oftheunitedstates are located inthearid

andsemi-aridsouthwesternregions ofthe countrywhere alluvial fans

or bajadas occupy 31.4 percent of the area, Anstey (1965). Major

urbanareas suchas LosAngeles, SanDiego, Tucson, Phoenix, SaltLake

City, and Las Vegas have in the last fifty years grown from dusty

oblivion into important industrial, financial, and recreational

centers. Portions, a n d i n s o m e c a s e s a l l o f t h e s e c i t i e s , arelocated

on alluvial fans. Since 1980, Phoenix, Salt Lake City, and Las

Vegas have all experienced devastating floods or debris flows which

have resulted in both the loss of life and significant property

damage. Note, Table 1.l.la was abstracted from Anon. (1981b) and

additional details regarding the flood events summarized in this

table are available in this reference. Table 1.l.la summarizes

locations in the western United States whichhave experienced flood

damage inthe pasttwenty years, identifiesthe floodhazard type, the

geologic formation(s) on which the damaged areas were located, the

typeof development inthedamaged area, the floodcontrol measure sin

place at the time of flooding, and the estimated dollar amount of

damage. The dollar amount of damage done is not only a function of

2

flood magnitude but also the amount of development. Table 1.l.lb

summarizes flooddamage (not corrected for inflation) inthe LasVegas

area alongwith an estimate of metropolitan population. It is clear

that there is some

correlation between population (development) and flood damage from

thedata inthis table. Unfortunately, the floodcontrol measures in

placeat the t imeof theeventsnoted inthis table.are notdocumented.

Although Tables 1.l.la and 1.l.lb quantify the material damage

that floods in the desert can cause, in many cases the actual cost can

be much more easily visualized and indelibly printed in the

consciousness ofthe disinterested technical person or manager with

photographs.

Fig. 1.l.la is a photograph of the Caesars Palace (Las Vegas,

Nevada) parking lot which was, at the time of the photograph, located

in Flamingo Wash, a primary drainage channel. In the photograph,

note both the sign warning of flash flood hazard and the box culvert

structure in the background which was intended to carry flood flows

under Las Vegas Boulevard. Fig. 1.l.lb shows this same parking lot

during the flood that occurred on July 3 , 1975. The Caesars Palace

hotel-casino complex is in the background. Inthis photograph, note

the truck in the right-center foreground of the photograph. Fig.

1.1.1~ shows the aftermath of the July 3 , 1975 flood. In the

3

FIG. 1.l.la Flash flood warning sign in the Caesars Palace parking

lot, Las Vegas, Nevada. This parking lot was built in the bottom of

Flamingo Wash. Note in the background of the photograph the box

culvert structure intended to carry flood flows under Las Vegas

Boulevard. Photograph by E. N. Cooper.

4

FIG. 1.l.lb Flash floodofJuly 3, 1975 passingthrough theparking

lot of Caesars Palace, Las Vegas, Nevada. The building in the

background of this photograph is the hotel-casino complex.

Photograph by E. N. Cooper.

F I G . 1.1.1~ The af te rmath of t h e J u l y 3 , 1975 f lood i n t h e Caesars Pa lacepa rk ing l o t , LasVegas, Nevada. Note i n t h e b a c k g r o u n d t h e b o x c u l v e r t s t r u c t u r e a l s o shown i n Figure 1.1. l a which was intended t o convey f lood f lows under Las Vegas Boulevard. Photograph by E . N .

Cooper.

6

background of this photograph is the box culvert structure shown in

Fig. 1.l.la. During the flood, this structure became blocked with

TABLE 1.l.lb Summary of flood damage (not corrected for inflation) as a function of population for the LasVegas, Nevada metropolitan area, after Randerson (1976). ________________________________________---_-__-________-__--_ -_______________________________________------------------_---

Date IEstimated I Estimated 1 Comment I Damage I Population I I (dollars) I I

I I I 23 July 19231 20,000 I 5,000 I 50.3mm (1.98 inches)

I I I of rain

I 10,000 I I

_________________________________________--------------------- ____________---__________________________---------------------

.............................................................. 10 July 19321 -1,000- I 9,000 1 .............................................................. 9 August I -1,000- I 10,000 I 40.1 mm (1.58 inches)

13 June 195512,000,000 I 50,000 I

24 July 19551 200,000 I 50,000 I

21 August I 500,000 I 70,000 I 65.3 mm (2.57 inches)

4 September 11,000,000 I 150,000 I 27.2 nun (1.07 inches)

12 September1 250,000 I 250,000 I

3 July 1975 14,500,000 I 350,000 I

1942 I 10,000 I I of rain .............................................................. .............................................................. ..............................................................

1957 I I I of rain .............................................................. 1963 I I I

1969 I I I

..............................................................

..............................................................

..............................................................

debris, such as the truck in Fig. l.l.lb, and did not perform its

intended function. In Fig. 1.1.2 a houseconstructed ina channel on

an alluvial fan in Henderson, Nevada is shown after a flood that

occurred inthesummer of1984. Figs. 1.1.3 document thedestructive

nature of debris flows. The material in this photograph was

transported in a debris flow in Ophir Creek (Washoe Valley between

Reno and Carson City, Nevada). In Figs. 1.1.4 and 1.1.5 the

relative minor but very inconvenient flood damage to urban areas

built on alluvial fans is shown.

Propertydamageis, of course, inmanyways onlythe most obvious

and easily quantifiable type of loss that is sustained during flood

events in arid and semi-arid regions. In many floods, there is an

accompanyinglossof life. Forexample, onSeptember14, 1974 aflash

flood swept through Eldorado Canyon on the west side of Lake Mojave

(Arizona and Nevada) killing at least nine people; destroying five

FIG. 1.1.2 House constructed in the bottom of a channel on an

alluvial fan in Henderson, Nevada aftera flash flood inthe summerof

1984. Photograph by R. H. French.

FIG. 1 .1.3a Debris f low d e s t r u c t i o n o f a b u i l d i n g i n t h e v i c i n i t y o f Ophir Creek, Nevada. Note, t h e boulders i n t h e foreground t r anspor t ed by t h i s f low. Photograph cour tesy of P. Glancy, U . S .

Geological Survey, Carson C i ty , Nevada.

9

FIG. 1.1.2.b Ophir Creek debris flow destruction of a school bus.

Washoe Lake, Nevada is in the background. Photograph courtesy of P.

Glancy, U.S. Geological Survey, Carson City, Nevada.

10

FIG. 1.1.4 Minor flash flood during the summer of 1984. The street

shown is Tropicana Avenue in the vicinity of Boulder Highway, Las

Vegas, Nevada. Photograph by R. H. French.

11

FIG. 1 . 1 . 5 Minor flood damage i n Boulder City, Nevada. The white

pipe inthisphotograph is irrigationpipethathasbeenuncoveredbya 1984 flood. Note a l s o the erosion i n the background and the

destruction of the sidewalk. Photograph by D . Zimmerman.

12

mobile homes, 38 vehicles, 19 boat trailers, and 23 boats:

obliterating a restaurant: and destroying half of the extensive boat

docking facilties on the lake. The peak flow from the 59 km2 (22.9

mi') drainage basin was estimated to be 2,200 m3/s (76,000 ft3/s) , Glancy and Harmsen (19751. The flood event pictured in Fig. 1.1. lb

resulted in the following account in the Las Vegas Review Journal:

##One City employee in North L a s Vegas was confirmed dead and his companion believed dead. --- The men were swept away from their vehicle --- when they were hit by a wall of water ---.@I

OnJuly26, 1981adis tantthunderstormresul tedinasmal l f lash flood in Tanque Verde Creek, a popular summer recreation area near Tucson,

Arizona, and swept eight people to their deaths over Tanque Verde

Falls, Hjalmarson (1984). Because of the fatalities, this small

flood received a great deal of media attention while much larger

floods which occurred one day earlier and four days later receivedno

mediaattention. Asnotedby Imhoffand Shanahan (1980), flooding in

arid and semi-arid areas is less related totheabsolutemagnitudeof

the flood than is the case with flooding of perennial rivers and more

related to the quickness and ferocity of the event. Floods on alluvial fans also have the troublesome characteristic that the

channels in which they occur are not stable. As discussed by Scott

(1973), channels on alluvial fans canrapidlymigratebybankerosion

and often appear to 'jump' from an old channel to a completely new

channel radiating from the apex of the fan.

Thephysical impact of floodwaters onhumans canbe estimatedas

follows. Ifthehumanbody is approximatedas acircular cylinder 0.30

m (1.0 ft) in diameter, then the drag or force exerted on this body by

flood waters of variousdepths andvelocities canbe estimated, Table

1.1.2. Inthistable, thevelocityof flowranges from0.50to5.0m/s

(1.6-16 ft/s) ; and the depth of flow ranges from0.25 to 1.50 m (0.82-

4.9 ft) . Anon. (1980) asserted that a healthy human adult might be

able to stand in water approximately 1.5 m (5 ft) deep and moving at a

velocity of 0.61 m/s (2 ft/s) while resisting a drag force of

approximately89 N (201b). However, th isanalys isneglectsbuoyancy

forces which would reduce the effective weight of the individual.

Anon. (1980) further asserted that at a velocity of 0.91 m/s (3 ft/s)

an adult could withstand depths of 0.91 m (3 ft) : and at a velocity of 1.5 m/s (5 ft/s) a depth of 0.61 m (2 ft). At greater depths or

velocities, the chances of survival rapidlydecrease as indicated in

1 3

Table 1 . 1 . 2 . A ‘rough rule of thumb’ is t h a t a heal thy a d u l t would probably survive i n flows i n which t h e product of t h e veloci ty and depthof flow, i n t h e S I s y s t e m o f u n i t s , is less than 1 ( i n theEnglish

Depth of I I I I I I I 2 Immersion,ml 0.25 I 0.50 I 0.75 I 1-00 I 1-25

2.00

2.50

3.00

3.50

4.00

4.50

5.00

150. 300. I 450. 600. 750.

234. I 469. 703. 938. 1170.

338. 1 675.

I

1:::: -----------

1010. 1350. 1690. 2020. I

I

I

I

0 459. I 919. ld

600. 11200. 1800. 2400. 3000. 3600. C D

759. 11520. 2280. 3040. 3800. 4560.

938. 1880. 2810. 3750. 4690. 5620.

‘1380. 1840. 2300. 2760. ICI

----------

system of u n i t s t h e product of t h e depth of flow and t h e ve loc i ty should no t exceed 1 0 ) . Children and handicapped persons have a much smaller chance of survival i n any flooding s i t u a t i o n .

The power and f e r o c i t y of floods on a l l u v i a l fans i n a r i d and semi-arid regions should never be underestimated. For example, Chawner (1935) r e p o r t e d t h e followingdata r ega rd ing the t r anspor to f boulders during t h e 1934 flooding a t Montrose ( a suburb t o the northeast of Los Angeles, Ca l i fo rn ia ) :

!‘The weights and d i s t ances fromthecanyonmouthof t h e g r e a t e s t boulderswere: 32tonsat7,OOO f e e t ( 2 . 8 x 1 0 ’ N a t2 ,100 m ) ; 2 3

t ons a t 7,900 f e e t ( 2 . 0 x 10’ N a t 2 , 4 0 0 rn) ; 11 tons a t 8,400 f e e t (9.8 x l o 4 N a t 2 , 6 0 0 m ) ; 5.5 tons a t 9,400 f e e t ( 4 . 9 x l o 4 N a t 2,900m); 5 t o n s a t 9 , 8 0 0 f e e t ( 4 . 4 ~ 1 0 ~ Nat3,OOOm); 1 . 6 t o n s a t 9,600 f e e t ( 1 . 4 x l o 4 N a t 2,900 m ) ; and 1 . 2 tons a t 11,800 f e e t (1.1 x l o 4 N a t 3 ,600 , ) . * I

14

Inthe above quotation, thecurrent authorhas addedthe conversionto

SI units shown in parentheses. Chawner (1935) further noted that

during this single flood event approximately 535,000 m3 (700,000 yd3)

of sediment were deposited in the study area. This amount of

deposition indicates that 0.064 m (2.5 in) of material had been

removed from the total contributing watershed, Chawner (1935).

rational to believe that as development in the arid

and semi-arid regions ofthe Unitedstates continuesthat floodingon

alluvial fans will either cease or become less serious. In fact,

unless abetterunderstanding of hydraulic processeson alluvial fans

is developed and rational, equitable, andcost-effective floodplain

management schemes are implemented, there is every reason to believe

thatfloodingondevelopedalluvialfanswillbecomebothmore serious

and costly.

In addition to technical considerations, there are also socio-

economic and legal issues which cannot be ignored. As discussed by

Edwards and Thielmann (1984) technically justified flood plain

management regulations can also be viewed by the owners of the

property affected as de facto appropriation of property without just

compensation. In some heavily urbanized areas such as Los Angeles,

only areas near the apices of alluvial fans are available for

development, Scott (1973). Such areas without proper structural

protection are subject toboth waterand debris floods, Rantz (1970).

Compounding these problems are the long dry periods which

characterize arid and semi-arid areas. During these periods,

memoriesofprevious floodingare forgottenandproperty inthealmost

unrecognizable flood plains becomes almost irresistible to

developers and home buyers, see forexample Fig. 1.1.2, rScott(1973) and Santarcangelo (1984)l. Also during the dry periods, the

t axpayersbecomeunwi l l ing to fund flood control thatwill protectthe urban sprawl that grows year by year. Rantz (1970, p. B1)

appropriately defined urban sprawl "as the rapid expansion of

suburban development without complete planning for the optimum

control and development of water and associated land resources.Il

Rantz (1970) continued to note that the greatest economic damage and

loss of life during the disastrous floods that occurred in Southern

California during 1969 were incurred in areas where either the

potential hazards of water and debris floods had not been taken into

account or where flood control facilities had not kept pace with

urbanization.

It is not

15

A further socio-economic problem hindering the development of

both effective and cost-effective flood control in the American

environment are the conflicting responsibilities of various

governmental units. This situation results from the fact that in

general there is no central or regional authority charged and

responsible for flood control planning in heavily urbanized areas.

Rather, local jurisdiction over planning for development and flood

control resides with the many incorporatedcommunities that together

comprise the urban area. For example, the number of incorporated

areas in L o s Angeles County increased by 75 percent between 1935 and

1969,Rantz (1970). Suchrap idgrowthwi thconf l i c t ingzon ingcodes , land use policies, and community goals essentially precludes the

development on a regional scale of fair - both actual and perceived - flood control policies and plans.

A second important reason for examining hydraulic processes on

alluvial fansderives fromthe fact that arid andsemi-arid regionsof

the Unitedstates are considered bymany tobe ideal locations forthe

storage and/or disposal of hazardous and radioactive wastes. In

Nevada alone, there is a low level radioactive waste burial site for

commerciallygeneratedwastenearBeattyandasimilarburialsite for defense related low level radioactive waste on the Nevada Test Site.

Further, at thetimeofthiswriting, YuccaMountainnorthof LasVegas

isbeinggivenserious considerationasa site forthedisposal ofhigh

level radioactive waste produced by the nuclear power industry.

Thick, unsaturated alluvial zones in arid and semi-arid regions have

also been proposed andconsidered aspossible disposal sites forhigh

level radioactive waste, Winograd (1981). The low level waste

management sites are locatedonalluvial fans, and themethod ofwaste

disposal is termed shallow land burial. At both of the sites in

Nevada, flooding, erosion, and deposition are important

considerations. In all cases, the wastemust be transported to the

disposal sites by road and rail networks which by necessity cross

alluvial fans. The damage floods can cause to vehicular

transportation systems built on alluvial fans has been discussedby

Anstey (1965) and Beaty (1968). In addition to vehicular systems,

there are other types of vital transportation systems which cross

alluvial fans such as the San Luis Canal which conveys water from

Northern to Southern California. This canal crosses many alluvial

fans in the San Joaquin Valley and on each fan provisions were made to

pass flood flows either under or over the canal.

The design of safe waste disposal sites and transportation and

I

16

conveyance systems i n t h e a r id and semi-arid environment r equ i r e s an understandingofhydraulicprocesses, b o t h o n a l l u v i a l fansand i n t h e upstream watersheds.

The t h i r d reason f o r examining hydraulic processes on a l l u v i a l fans i s t h a t inmany a r i d a n d semi-ar idregionstheprimary sourcesof potablewaterareaquiferswhichare a subsurface p a r t of t h e a l l u v i a l fan. For example, Tucson, Arizona is c u r r e n t l y t o t a l l y dependent on groundwater f o r its potable water supply, and much of t h e groundwater ava i l ab le t o Tucsonderives from an a l l u v i a l fan deposi t of l a te Cenozoic age, Bull ( 1 9 7 7 ) . As noted by Babcock and Cushing ( 1 9 4 1 ) , t h e primary sourceof recharge f o r m a n y a l l u v i a l f a n a q u i f e r s is t h e occasional f lood which i n f i l t r a t e s through t h e channel bed where t h e flood crosses t h e fan. I n attempting t o i n t e r p r e t hydrogeologicdata f o r w a t e r resourcesdevelopment, anunderstanding o f t h e hydraulic processes which formedthese landscape f ea tu res can be very important. A s groundwater is withdrawn from a l l u v i a l fan aqu i f e r s , s i g n i f i c a n t subsidence of t h e ground su r face may be experienced. For example, more than 2 m (6.6 f t ) of subsidence has been measured i n Arizona and 8 m ( 2 6 f t ) i n c e n t r a l Ca l i fo rn ia where groundwater has been withdrawn from fan aqu i f e r s , Bull (1977) . The reverse problem is a l s o important. I n some areas; f o r example, Las Vegas, a r t i f i c i a l recharge of a l l u v i a l aqu i f e r s is being considered asaviablemethodofutil izingotherwisewastedrunoffandrecharging

depleted groundwater resources. One p o t e n t i a l problem is t h a t old spr ings on t h e a l l u v i a l fans which ceased flowing many years agomay, a s a r e s u l t of a r t i f i c i a l recharge, begin t o flow again i n inconvenient locat ions, such a s under foundations. A second p o t e n t i a l problem is t h a t clayey a l l u v i a l fan depositsmay be subject tosubsidencewhenwetted. Forexample, Bull (1964) n o t e d t h a t i n t h e w e s t c e n t r a l SanJoaquinValley of Cal i fornia seve ra l hundred square kilometers of land subsided a f t e r t h e c l ay binding t h e fan depos i t s was wetted by i r r i g a t i o n water f o r t h e f i r s t t i m e s ince drying i n t h e Quaternary period.

An understanding of t h e hydraul ic processes which formed and continue t o form and modify a l l u v i a l fan a q u i f e r s could a i d i n developing e f f e c t i v e and acceptable plans f o r water resources development and u t i l i z a t i o n .

Thus, formany reasons o t h e r t h a n c u r i o s i t y , an understandingof hydraulic processes on a l l u v i a l fans is important. Further, t h e importance of understanding and quantifying these processes is not only important t o engineers and s c i e n t i s t s i n t h e United States, but

alsototheircolleagueslivinginsimilarareasthroughouttheworld.

Unfortunately, the state-of-the-art in this field is primitive in

comparison to our understanding of the hydrogeology, hydrology, and

hydraulics of systems in humid areas.

1.2 INITIAL CONCEPTS AND DEFINITIONS The study of hydraulic processes on alluvial fans requires an

understanding of geomorphology, watershed hydrology, and hydraulic

engineering. Although with the exception of watershed hydrology,

theseareaswillbediscussedin somedetail insubsequent chaptersof

thisbook, this sec t ionwi l lbr ie f ly in troduce someoftheterminology and discuss the importance and relevance of these topics to the

sub] ect at hand.

In examining hydraulic processes on alluvial fans, it becomes

apparent that consideration must be given to the two distinct time

scales that are involved. Fansdevelop ona geologictime scale, and

the available evidence indicatesthat theiraverage rateof growth is

relativelyslow. InTable1.2.ltheestimatedageandaveragerateof

vertical accretion of several alluvial fans is given. The data in

this table indicate that alluvial fans have developed their

characteristic shape over millenia rather than years. It must be

emphasized that only average rates of vertical accretion for the

18

entire fan surface can be estimated. It is appropriate to note that

Beaty (1963, 1970, 1974) has concludedtha tnomore than10-15% ofthe material composing the alluvial fans of the White Mountains,

California and Nevada is the result of normal fluvial depositional

processes - 85-90% of the deposition on these fans is the result of successiveandoverlappingdebris flows. BellandKatzer (1986) have

a s s e r t e d t h a t i n D i x i e V a l l e y , Nevada debris flow depositionis oneof

the primary sediment transport mechanisms currently active and that

debris flow transport quantities are commonly measured in thousands

of cubic meters. Consideration of deposition by cataclysmic events

such as debris flows would certainly significantly modify the

vertical accretion rates noted in Table 1.2.1.

In contrast to the geologic time scale is the engineering or

human time scale which is measured in years or decades rather than

millenia. Table 1.2.2 summarizes the design or useful life of a few

engineered structures and facilities that might commonly be

constructed on alluvial fans. Relative to the age of the fan, the

lifespan of the engineered works of man is insignificant. On a

geologic time scale, flow paths across a fan surface are erratic and

TABLE 1.2.2 Estimated avera e lives qf various structures and components in years, Anon. (1264) and Linsley and Franzini (1979).

Buildings Apartments ............................ 40 Banks ................................. 50 Factories ............................. 45 Offices ............................... 45 Warehouses ............................ 60 Individual dwellings ................... 50

Canals and ditches .................... 75 Dams .................................. 25 - 150 Power plants

Fossil ........................... 28 Nuclear .......................... 20

Pipes Cast-iron ........................ 50 - 100 Concrete ......................... 20 Steel ............................ 30 - 40

Reservoirs ............................ 7 5 Standpipes ............................ 50 Wells ................................. 40 - 5 0

Elements of Water Resources Systems

unstable. On an engineering time scale flow paths across a fan

surface may be stable if they are not changed by development. Thus,

inexaminingthepotential for flooddamageonanalluvial fan, itmust

first be determined whether stable or unstable flow paths exist.

19

In the arid or semi-arid environment, three types of alluvial

landscape features are found which although similar in appearancemay

have quite different hydraulic characteristics. These three

features - alluvial fans, alluvial aprons, and washes - exhibit important hydraulic process differences because of when and where

they were formed on a geologic time scale. All three of these

features are found where rock-walled canyons debouch from steep

mountain fronts. At the mountain fronts, the water spreads out and

the sediment carrying capacity of the flow is significantly

decreased. Over geologic time, a cone shaped deposit of alluvium is

formed with its apex at the mountain front. Such a formation is

termed an alluvial fan. The term wash has been defined; see for

example, Anon. (1981a) , as a channel which is confined by rock walls. Washes can be found in the canyonareas abovethe apexofthealluvial

deposit at the mountain front and on alluvial fans. The crucial

characteristic of a wash is that it is a confined channel with stable

banks. In a wash, flood flows may attain high velocities and

significant depths of flow; but since the channel isstable, the flow

path of the water is predictable. The standard techniques of

hydraul icengineer ingcanbeappl iedtothesechannels and flood flows

occurring in them.

As a series of alluvial fans form along a mountain front and as

theresultofuntoldrunoffeventsthroughgeologictimegrow out into

the valley, the downgradient edges of these fans coalesce into a

landscape feature usually termed an alluvial apron. Fig. 1.2.1 is a

schematic of two alluvial fans which have joined to form an alluvial

apron. In the fan areas, the maximum slopes radiate away from the

apex of the fan. Apron areas are characterized by reasonably linear

contour lines and parallel channels whichdrain theapron. Flooding

in fan areas is characterized by erratic channel locations while on

the apron the flow may be confined to the channels.

Anon. (1981a) identified the following types of flood hazard as

being common on alluvial fans:

inundation,

sediment deposition,

foundation scour and undermining,

impact forces,

hydrostatic and buoyant forces,

high flow velocities, and

unpredictable flow paths.

2 0

FIG. 1.2.1 Schematicdrawingoftwoalluvialfanswhichhavejoined to form an alluvial apron.

Anon. (1981a) also identified three zones of different hydraulic

processes on alluvial fans. With reference to Figs. 1.2.2:

1. A channelized zone near and above the apex of the fan where

there is a single definable, active channel.

Abraided zone downstreamof the fan apexwhere channelsare

unstable and there may be multiple flow paths.

3 . A sheet flow zone found far down the fan where the flow

spreads laterally and is very shallow.

2 .

The above material describes the situation that exists in the

natural, unaltered environment. Often the action of humans in the

process of development obstructs or channelizes the flow on a fan

either without understanding the potential results of these actions

or without caring.

A third consideration in discussing hydraulic processes on

alluvial fans is the upstreamwatershed where excess precipitation is

collected. Some of the key characteristics of watersheds which

influence the magnitude ofthe peak flood flows deliveredtotheapex

of a fan are:

21

Channelized Braided Flow .5 - -- _ _ -

Plan

I I

F I G . 1.2.2a Planview of an idealized alluvial fan withthe zonesof flow indicated.

drainage area

watershed slope

watershed soil and vegetative type,

fire frequency,

precipitation intensity and duration,

storm path over the watershed, and

time between consecutive precipitation events.

Unfortunately in arid and semi-arid regions, the traditional methods

of f loodf requencyes t ima t ion : see for example, Anon. (1977a, 1 9 8 1 ~ ) ~ are usually not applicable. Precipitation records in such areas are

usuallyrare- if availableatall-andunreliable. Although frontal

weather system scancause floodingon alluvial fans, serious flooding

on alluvial fans is usuallythe result of convectivethunderstorms.

2 2

P r o f iLe

r Mountain

Fan Apex Canyon Bed

Channel Bed

I ' Braided or Tributary System o f Channels

F I G . l,.2.,2b flow ind ica t ed .

P r o f i l e v i e w of an i d e a l i z e d a l l u v i a l f a n w i t h zones of

Thunderstormsmayvary i n a r e a l e x t e n t f roma squa rek i lome te r tomore than 70 km2. Combinations of thunderstorm cel ls may cause i n t e n s e p r e c i p i t a t i o n over r e l a t i v e l y l a r g e a r e a s , and cel ls may e i ther remain s t a t i o n a r y o r d r i f t wi th t h e p r e v a i l i n g winds. The i n t e n s i t y and du ra t ion of p r e c i p i t a t i o n and t h e movement of p r e c i p i t a t i o n events overthewatershedallhaveacriticaleffectonboththevolume of water discharged from a watershed and the t iming and magnitude of t h e peak f lood d ischarge . Fur ther , it is a mistake t o assume t h a t f lood even t s on a l l u v i a l f ans only occur dur ing t h e summer months. Fig. 1 .2 .3 summarizes i n t e r m s of f r equency the reco rded f l o o d e v e n t s f o r Clark County, Nevada on a monthly b a s i s f o r t h e per iod 1905-1975, Anon. (197713). W i t h r e g a r d t o t h i s f i g u r e , n o t e t h a t t h e f requencyor p r o b a b i l i t y of f looding is non-zero i n every month; however, f lood frequency i n Clark County, Nevada is h ighly c o r r e l a t e d w i t h t h e frequency o r p r o b a b i l i t y of thunderstorm a c t i v i t y ; see f o r example, Sakamoto ( 1 9 7 2 ) . Fur ther , Fig. 1 . 2 . 3 is b ia sed s i n c e f o r t h e per iod 1905-1946 newspaper accounts f o r each month of t h e yea r were scanned t o t a b u l a t e t h e number of observed f lood events . However, f o r t h e per iod 1947-1975, newspaper accounts f o r only t h e months of March, Apr i l , J u n e , J u l y , August, Septemberand o n e o t h e r month f o r eachyea r were scanned. F i n a l l y , t h e s e a r e o n l y t h e o b s e r v e d f l o o d e v e n t s . In a governmental u n i t as l a r g e a s Clark County - l a r g e governmental u n i t s arecommon i n a r i d a n d s e m i - a r i d a r e a s - thenumber of unrecorded f lood even t s may have exceeded those recorded.

2 3

MONTH

January

February

March

A p r i l

May

June

Ju ly

August

September

October

November

December b 0 0.1 0.2 0.3 0 . 4

FLOOD FREQUENCY

F I G . 1.2.3 Monthly frequency of flood events for Clark County, Nevada based on the record from 1905-1975.

There are a variety of methods available for the estimation of

peak flood flows when the traditional methods of flood frequency

estimation cannot beused. In general, these alternative techniques

are based on one of the following approaches?

1. All of the streamflow records available in a hydrologic

region can be combined using statistical methods to yield

regional equations for peak flood flow estimates. A

complete discussion of this approach is available inRiggs

(1973) and for an example of its use, the reader is referred

to Roeske (1978). A second technique that should be

2 4

mentionedwithinthis category is the flood envelopecurve;

see for example, Crippen (1982) or Crippen and Bue (1977).

2. If precipitation characteristics for the area of interest

are either known or can be assumed, then watershed modeling

can be performed. This methodology is overviewed by

Viessman et al. (1977).

3. In situations where the lack of sufficient, reliable

streamflow and precipitation data preclude the use of the

above techniques, paleohydraulic reconstruction of flash

flood peaks may be appropriate. Although this methodology

maybeunfamiliartotheengineeringcommunity, ithas along

history inthegeosciencescommunity; see forexample, Bretz

(1925), Pardee (1942), Birkeland (1968), Malde (1968),

Williams (1971), Baker (1973, 1974), Gupta (1975), and

Bradley and Mears (1980). Costa (1983) has asserted that

the paleohydraulic reconstruction of flash flood peaks can

be used in conjunction with the slope-area technique; see

for example, French (1985) , Glancy and Harmsen (1975) , and Dalrymple and Benson (1976), to estimate historical peak

flood flows.

1.3 CONCLUSION

From the foregoing discussion, it is concluded that a

comprehensive understanding of hydraulic processes on alluvial fans

requires some knowledge and expertise in the academic disciplines of

geomorphology, hydrometeorology, hydrology, hydrogeology, and

hydraulic engineering. This book will only discuss the geologic and

hydraulic engineering aspects of the subject because the other

aspects are adequately treated in existing books; see for example,

Viessmanetal. (1977). Tothisend, thebook isarranged as follows.

In Chapter 2, the relevant geologic aspects of alluvial fans are

discussed. This is a summary chapter intended to familiarize the

readerwiththeaspectsofgeologyimportanttothe subject. Fromthe

viewpoint of geology, this is by no means a comprehensive chapter.

Chapter3 summarizesthebasicprinciplesofopen-channelhydraulics,

sediment transport, and debris flows. Again, this is a summary

chapter. In Chapter 4, the information and data presented in

Chapters 2 and 3 are combinedto discuss the models, both physical and

numericalandonbothgeologicandengineeringtimescales,whichhave

2 5

been used to study hydraulic processes on alluvial fans. Chapter 5

discusses various analytic methodologies which can beusedto assess

flood hazard on alluvial fans. Chapter 6, the concluding chapter,

discusses where we are and where we should be going for safe

development of urban areason alluvial fans. Given that this book is

intended to be interdisciplinary between geologyand engineering, it

concludes with a glossary of the relevant geologic and hydrologic

engineering terms.

REFERENCES

Anon., 1964. Depreciation guidelines and rules. Publication No. 456. U.S. Treasury Department, Internal Revenue Service, Washington.

Anon. 1977a. Guidelines for determinin flood, flow frequency. Bulletin 17A, U.S. Water Resources Counci?, Washington.

Anon., 197733. Floodhazardanal sis LasVe asWashandTrjbutaries Clark County Nevada S ecial Sepokt- his%.or- of flooding, Clark County Nev6da 1906-1875. Prepared B - .S. Department of Agriculture, Soil Conservation Service, #;no, Nevada.

Anon., 1980. Potential flood hazards at Willow Beach Lake Mead National Recreation Area. Prepared By: Lineley, Kraeger hssociates , Aptos, Ca. For: U.S. National Park Service.

Anon., 1981a. Flood lainmanagement tools foralluvial fans, study fin?ings. Pre ared gy: Anderson-Nichols, Inc.,, Palo Alto, Ca. For.

Anon., 1981b. Floodplainmana ementtools foralluvial fans study documentation. Prepared By: Inderson-Nichols , Inc,. , Palo’ Alto, Ca. For: Federal Emergency Management Agency, Washington.

Anon. 1981c. Guidelines for determining flood flow frequency. Bullefin 17b. U.S. Water Resources Council , Washington.

ederal Emergency Management Agency, Washington.

Anstey R.L., 1965. Physical characteristics of alJuvia1 f ns. Technibal Report ES-20. U.S. Army Natick Laboratories, NatTck, Massachusetts.

BabcocK H.M. andCushin E.M., 1941. Rechargetoground-water from floods Yn a tyR’ca-1 dese&wash, Pinal count Arizona. Transaction, American Geop ysical Union, 23 (1) : 49-52:

Bqker V.R., 973. Paleohydrolo y and sedimentolo o,f Lake Missoha floodtn in eastern Was%ington: Geologicalqociety of American Special gaper 144. 79 p.

Baker V.R., 1974. Paleohydraulic interpretation of-Quaternary alluvium near Golden, Colorado: Quaternary Research, 4. 94-112.

C,.B., 1963. Origin of alluvial fans White Mountajns, %f$&rnia and Nevada. Annals of the Association of American Geographers, 53: 516-535.

Beat C.B., 1968. Sequential stud ofdeser$ flooding in the White M o u n h n s of California nd Nevadla. TechnicaJ Re ort 68-31-ES. U.S. Army Natick Earth Scfence Laboratory, Natick, Sassachusetts.

Beaty C.B., 1970. A e and es imated rate of accumulation of alluv‘al fan, White Moun%ains, Calffornia, U.S.A.. American Journal of science, 268: 50-77.

Beaty C.B., 1974. Debris flows, alluvial fans and a revitalized catasfrophism. Z. Geomorph. N.F. , Suppl. Bd. 2f:39-51.

2 6

Bell, J.W. and Katzer, T., 1986. Surficialgeology hydrolo and Quaterpary tectonic histor of the IXL canyon area, ds relatezk the 1954 Dixie Valley earthquaze, Nevada Bureau of Mines and Geology, in press.

Birkeland, P.W., 1968. Meanvelocities a q d b o u l d e r t r a n s p o r t d u r i n g Tahoe-age floods of the Truckee River California-Nevada: Geological Society of America Bulletin, 79: 137-141.

Bradley W.C. andMears+.I., 1980. Calculations of flows neededto transpok coarse fraction of Boulder Creek alluvium at Boulder , Colorado: Geological Societyof AmericanBulletin, Part 11, 91: 1057- 1090.

Bretz, J.H., 1925. TheSpokane floodbe ondthechanneledscablands, Journal of Geology, 33: 97-115, 236-229.

Bull, W.B., 1964. Alluvial "fans and near-surface su]7sidence in western Fresno county. U.S. Geological Survey Professional Paper 437-A, Washington.

Bull W.B., 1977. The alluvial-fan environment. In: Progress in Physical Geography, 1: 222-270.

Chawner, W.D., 1935. Alluvial fan flooding: the Montrose, California flood of 1934. Geographical Review, 25: 255-263.

Costa, J.E., 1983. Paleohydraulic reconstruction of flash-flood Geological

gociety of America Bulletin, 94: eaks from boulder deposits in thecolorado Front Range.

986-1004.

Cri pen J.R. gnd Bue, C.D. 1977. Maximum floodflows in the conFenninous United States. 6. S. Geological Survey Water Supply Paper 1887, Washington.

Cri pen J.R., 1982. Envelope cyrye$ for extreme Tlood events. ASCE, Jburnal of the Hydraulics Division, 108 (HY10) . 1208-1212. Dalr ple, T. and Benson M.A., 1?76. Measurementof peakdischarge by &?q sl,ope-area medhod. In. Techniyes of Water-Resources Investigations of the United States Geo,ogical Survey, Book 3, Chapter A2. U.S. Geological Survey, Washington.

Edwards, K.L. and Thjelmann J. , 1.984. challenge. ASCE , Civil Enhineering, Alluvial fans:

54 (11) : 66-68. novel flood

French, R.H 1985. Open-Channel Hydraulics. McGraw-Hill Book Company, Inc'.', New York, 705 pp.

French R.H. gndLombardo, W.S.,198+. &wsessmentofflood hazardat the radioactive waste management site in area 5 of the Nevada Test Site Prepared By: Water Resources Center Desert Research Institute, Las Vegas, Nv. For. U.S. Departmek of Energy.

Glancy P.A. and Hamsen,, L. , 1975. A hydrologic assessment of the Septeder 14 , 1974 flood in Eldorado Cgnyon, Nevada. U. S. Geological Survey Professional Paper 930, Washington.

Gupta, A., 1975. Stream characteristics in eastern Jamaica, an enyironment of seasonal flow and large floods, American Journal of Science, 275: 825-847.

Hjalmarson H., 1984. Flash flood,in Tanque Verde creek Tucson, Arizona. ASCE, Journal of Hydraulic Engineering, 110 (15) : 1841- 1852.

Imhoff, J.C.. and Shanahan E.W., 1980. Floodplainmanagementtools for alluvial fans: dtate-of-the-art report. Prepared By: Anderson-Nichols Inc. Palo Alto, Ca. For: Federal Emergency Management Agency, Washington.

Lin$ley, R.K. and Franzini, J.B., 1979. Water Resources Engineering. McGraw-Hi11 Book Company, Inc., New York.

Malde H.E., 1968. The catast ophic late Pleistocene Bonneville flood' in the Snake River plafn, Idaho, U.S. Geological Survey Professional Paper 596, 52 p.

Pardee, J.T. 1942. U usual currents in gla,cial e k e Missoula, Montana, Geol!ogical Society of America Bulletin, 53. 1569-1599. Rachocki, A., 1981. Alluvial Fans, An Attempt at an Empirical

2 7

Approach. John Wiley and Sons, Inc., New York.

Randerson D., 1976. Meteorolo ical analysis for the Las-Ve as, Nevada fldod of 3 July 1975. 419- 727.

Monzhly Weather Review, 104 (6).

Rantz S.E., 1970. Urbansprawl and floodin InSouthernCalifornia. U. S. keological Survey Circular 601-B, Was%ington.

Rig s, H.C., 1973. Regionalanalysisgf streamflowcharapteristics. Tec%niques of Water-Resources Investigations of the United States Geological Survey, Washington.

Roeske, R.H., 1978. Methods for estimating the magnitude and frequenc 0.f floods in Arizona. ADOT-RS-15(121). Pre ared By: U.S. GeologicaA Survey T,ucson,, Arizona. For: Arizona Apartment of Transportation, Phohix, Arizona.

Sakamoto, C.M., 1972. Thunderstorms and hail days robabilities in Nevada. Western Region Technical Memorandum so. , 74 U.S. De artment of Commerce, NOAA, National Weather Service, Sakt Lake CiFy, Utah.

Santarcan elo S.A., 1984. Flood pl in management techniques for alluvial Pans ,I arid, and semi-arid envfronments. Nevada Division of Emergency Management, Carson City, NV.

Scott K.M. 1973. Scour and fill in Ti'un a Wash - a faphead valley in &ban gouthern California - 1963. %.S. Geological Survey Professional Paper 732-B, Washington.

Stone R.O. 1967. A desertglossary. In: Earth Science Reviews, Elsevier Publishing Company, Amsterdam, 3 : 211-268.

Viessman W., Knap J.W., Lewis, G.L., and Harbaugh, T.E., 1977. Introduction to Hygf-ology. Harper and ROW, New York.

Williams G.E., 1971. Flood de gsits of the sand-bed ephemeral streams bf central Australia, Segimentology, 17: 1-40.

Winograd I,., 1981. Radioactivewaste disposal in thickunsaturated zones. bcience, 212 (4502) : 1457-1464.

2 8

CHAPTER 2

BASIC GEOLOGIC CONCEPTS

2.1 INTRODUCTION

Thepr imarygoalof th ischapter is to introducethe engineer and planner tothe fundamentalgeologicandgeomorphologic conceptswhich

should be considered when hydraulic processes on alluvial fans are

examined.

Indiscussinghydraulicprocesses onalluvial fans, it shouldbe

first stated that in the past there have been a number of serious but

artificial problems which seem to have precluded productive

discussions between talented and knowledgeable geoscience,

engineering, and planning professionals of different academic

disciplines. For example, geologists and geomorphologists have

typically concentrated their efforts on either developing or

justifying hypotheses of erosional and depositional processes which

form landscape features on a geologic time scale or on the detailed

identification and classification of landscape features. In

contrast, engineers and planners have focused their attention on

designing short-term solutions which will allow for the safe

development of continuously evolving landscape features with little

or no consideration being given to long-term trends or understanding

how these features develop and evolve on a geologic time scale. The

result on the one hand is a very qualitative description of processes

and f ea tu reswhichmayormayno thaveapp l i edapp l i ca t ions ; andonthe other hand very quantitative and specific problem solutions based on

traditional engineering practice in humid areas which may or may not

be effective in thearid environment. Theproblems of arid andsemi-

aridregionsare inmanyways unique, and thedevelopment of rational,

cost-effective, and acceptable solutions to these problems require

effective communication among professionals of all disciplines.

Further, the engineer and planner must constantly remind themselves

that their primary responsibility is not the development of studies

and plans which satisfy rather arbitrary rules and laws, but a

commitment to protect public health, safety, and welfare.

2.2 COMPETING GEOLOGIC DOCTRINES

At the present time, there are three doctrines competing to be

adapted as the favored conceptual foundation on which all

geomorphologicalhypotheses canbe based. Thesedoctrines are known

2 9

as catastrophism, uniformitarianism, and thresholds.

Thedoctrineofcatastrophismwas or ig inal lydevelopedagainsta

background of scientific ignorance, at least relative to our present

knowledge, and a belief that the earth was developedand continuesto

bemodif iedbyaseriesofcatacl ismicevents . Forexample, TheBible

asserts that the earth was created over a period of six days and that

our heritage extends back only approximately6,OOO years. TheBible

is also repletewith detaileddescriptions of such cataclismicevents

as Noah's flood, the parting of the Red Sea, and the destruction of

total cities such as Sodom and Gomorrah. Preceding eventhe Bibleare

m y t h i c a l d e s c r i p t i o n s o f t h e d e s t r u c t i o n o f c o n t i n e n t s , Atlantis, and cataclismic battles of the gods. Since western civilization

developed in areas around the Mediterranean Sea where volcanic

eruptions, earthquakes, tsunamis, and landslides were and still are

commonplace, it is not unusual that early western civilizations

developed a doctrine which asserted that catastrophes were the

primary element in modifyingthe landscape. Althoughthe doctrine of

catastrophism has fallen into disrepute, there are those in the 20th

century who have noted the important role of the 'rare' event in

geology, Gretetner (1967) , and those who have asserted that

catastrophism is the only concept that can be used to explain the

landscape in arid or semi-arid areas, Beaty (1974).

In the latter partofthe18th century, various scientistsbegan

to hypothesize that erosion and depositionwere continuous processes

which took place so slowly it was virtually impossible for the

significant effects of these processes to be noted by man who has, at

least relative to the geologic time scale, a very limited lifespan.

W i t h t h i s h y p o t h e s i s , t h e d o c t r i n e o f u n i f o r m i t a r i a n i s m w a s b o r n . At

approximately the same time, attacks on the Biblical accountswhich

werethe foundationof catastrophismbegan. In the 20th century, the

doctrine of uniformitarianism has been effectively explained and

championed by Wolman and Miller (1960) and Leopold et a1 (1964).

These authors explained that while the spectacular catastrophe

captures the attention of man, it is events of much more moderate

intensity which are also much more frequent that accomplish a

preponderance of the work required to modify the landscape.

Also during the 19th and 20th centuries there was substantial

interest in what might be termed steady-state or equilibrium

geomorphic systems; see for example, Leopold and Langbein (1962) and

Langbein and Leopold (1964). Thus, over the past four decades as

scientific knowledge anddata have rapidly expanded, the emphasis in

30

geomorphic studies has been on the identification and proof of

hypotheses asserting that landscape is rather stable and changing

only very slowly.

Catastrophism and uniformitarianism are antithetical

doctrines. According to Coates and Vitek (1980), the element that

hasbeenpreviouslymissing ingeomorphic studies is a consideration of unbalanced systems or systems which are on the verge of becoming

unstable. The study of suchsystems hasevolved intothe doctrineof

thresholds. Recall, a thresh,old is the point at which an effect

begins to be produced in response to a stimulus. To the hydraulic

engineer , the doctrine of thresholds is appealing because he is familiar with threshold concepts: for example, the critical Reynolds

number for differentiating laminar fromturbulentflow, thecritical

Froude number for differentiating subcritical from supercritical

flow, and the Shield's diagram defining the threshold of sediment

movement. In arid and semi-arid climates, above average amounts of

precipitation could be considered a threshold producing event under

some circumstances. For example, over a period of years or decades

weatheredmaterialmay accumulateonthe slopes and inthe channels of

a drainage basin. The frequent precipitation events of moderate

intensity do not produce sufficient runoff to transport this

accumulated material great distances. However, the rare

precipitation event may produce sufficient runoff to transport the

detritus which has accumulated over a long period of time to a new

environment in a matter of minutes or hours.

Regardless of which geomorphologic doctrine is correct, the

geologist, engineer, and planner cannot ignorethe fact that overthe

last100 years a number of significant flow eventshave beenobserved

to occur on the alluvial fans in the southwestern United States: see

for example, Beaty (1968, 1974), Anstey (1965), and Pack (1923).

Without doubt many more significant flow events have occurred than

have been observed given the very sparse population of this area.

Thus, as asserted by Beaty (1974), catastrophic flows in arid and

semi-arid regions arenotathingofthe past and willundoubtedly bea

significant consideration in the present and future. The engineer

familiarwith flood frequency analysis: see forexample Anon. (1977), must realize that even though an event may be unlikely that is

significantly different from an event being impossible. As notedby

Gretetner (1967), the improbable is bound to occur if the number of

trials is sufficiently large. When an improbable event does occur,

it appears to even the experienced observer as a catastrophe.

31

Asanexampleoftheprobabilityofarareeventonanengineering

t i m e s c a l e occurring, consider t h e s i t u a t i o n i n which a person l i v e s f o r 70yea r s besidea r i v e r . It can b e e a s i l y shown; see forexample, Viessman e t a1 (1977), t h a t t h e p robab i l i t y t h a t t h i s person w i l l observe a flood event w i t h a r e tu rn period of T, years is given by

1 ' O R = 1 - [ 1 - --I ( 2 . 2 . 1 )

I n F i g . 2 . 2 . 1 , R is p l o t t e d ds a funct ion of T,. From t h i s f i gu re , it

R Probabtllty o f Event Betng

Observed by Hpothetlcol Person P 5 E;

m < ; a

F I G . 2 . 2 . 1 Probabi l i ty R of a hypothet ical person l i v i n g 70 years beside a r i v e r observing a flow event w i t h a r e tu rn period T,.

can be concluded t h a t t h e p robab i l i t y of t h i s hypothet ical person observingthe f l o w e v e n t w i t h a r e t u r n p e r i o d of100 y e a r s i s 0 . 5 0 ; t h e flow event of a r e tu rn period of 200 years is 0.30; and t h e flow event with a r e tu rn period of 500 years is 0.13. Thus, it is l i k e l y t h a t

32

t h i s hypothetical person w i l l observe a t l e a s t one ' c a t a s t roph ic ' flow event i n h i s l i f e t ime .

2.3 ALLUVIAL FAN SYSTEMS: GENERAL MORPHOMETRIC CHARACTERISTICS

Asnoted i n t h e p r e v i o u s c h a p t e r , a l l u v i a l f a n s a r e d e p o s i t s w i t h surfaces t h a t approximate a cone r ad ia t ing downslope from a point where a stream debouches from a mountain f ron t : and t h e sediment carrying capacity of t h e stream is reduced by t h e increase i n flow area. Although a l l u v i a l fans a r e found i n both a r i d and humid a reas throughout t h e world, t h i s discussion w i l l focus only on t h e development of fans i n t h e a r id and semi-arid environment.

Cooke and Warren (1973) noted tha t a l l u v i a l fans seem t o occur pr imari ly i n regions wherethe r a t i o o f depos i t i ona la rea tomountain area is small. A t y p i c a l d e s e r t p r o f i l e , Fig. 2.3.1, c o n s i s t s of a

F I G . 2.3.1 Charac te r i s t i c desert p r o f i l e .

mountainmasswithadownstreampiedimentplain. Thepiedimentplain iscomposedofapedimentandanalluvialplainwiththelatter insome c a s e s b e i n g a n a l l u v i a l fan. I n t h i s andsubsequent discussions, the following d e f i n i t i o n s w i l l be used.

Alluvial Fan: IITriangular o r fan-shaped deposi t of boulders, gravel , sand and f i n e r sediment a t t h e base of d e s e r t mountain s lopes deposited by in t e rmi t t en t streams as they debouch onto t h e va l l ey f loor , 'g Stone (1967, p. 215).

3 3

Alluvial Plain: "A p l a i n formed by t h e deposi t ion of water t ransported sediments," Stone (1967, p. 215).

Arroyo: "Spanishtermused in thesouthwes ternUni tedSta tes to designate t h e channel of temporary stream. The channel usually has v e r t i c a l wal ls of unconsolidated mater ia l 2 f t ( 0 . 6 1 m ) o r more high," Stone (1967, p. 215).

Bajada: "Blanket deposi t of alluvium a t t h e base of dese r t mountain s lopes formed by t h e coalescing of a l l u v i a l fans o r cones,1t Stone (1967, p. 2 1 5 ) .

Pediment: IlSlightly incl ined rock p l a i n t h i n l y veneered w i t h f l u v i a l gravels: a rock-carved p l a i n formedas desertmountains r e t r e a t under t h e influence of p l an ta t ionby streams, sheetwash and r i l lwash and backweathering," Stone (1967, p. 2 3 6 ) .

Piedmont Plain: IIExtensive and ccntinuous p l a i n developed alongthemarginsofamountainrangeortableland,l* Stone (1967,

p. 2 3 9 ) .

Theprimary, funct ional d i f f e rence betweena pediment and a n a l l u v i a l fan is t h a t a pediment is an erosional surface while a fan is a deposi t ional surface. I n i ts s implest form, an a l l u v i a l fan is a discrete f e a t u r e formedatthebaseofamountain f r o n t . Sucha fan is termed an unsegmented fan, Fig. 2.3.2a. A much more common type of fan is formedovert imeas several unsegmented fans coalesceand forma segmented fan, Figs. 2 . 3 . 2 b and 2 . 3 . 2 ~ .

I n t h e case of unsegmented a l l u v i a l fans , t h r e e morphometric p rope r t i e s have been considered: shape, area, and slope. A s

suggested, an a l l u v i a l fan is t y p i c a l l y fan-shaped i n t h e plan view; and given t h i s c h a r a c t e r i s t i c , Troeh (1965) , among o the r s , attempted t o describe t h e fan shape quan t i t a t ive ly o r

Z = P + SR + LRz (2 .3 .1)

whereZ = e l e v a t i o n o f anypoint o n t h e fan, P = e l e v a t i o n a t t h e a p e x o f t h e fan, S = slope of t h e fan a t t h e apex, R = r a d i a l d i s t ance from the apex t o t h e point where Z is t o be estimated, and L = ha l f t h e r a t e of change of s lope along a radial l i n e . Bull (1968) applied Equation ( 2 . 3 . 1 ) t o one a l l u v i a l fan and found t h a t it provided a reasonable

34

~

Mountain F r o n t

Fans

Ynl lNG

(a)

\

OLD

2.3.2 Plan view showing the development of alluvial fans, X f i a r to Denny (1967).

35

approximation. Lustig (1969) hypothesized that it should be

possible to find a solution of Equation (2.3.1) on a regional basis,

but to date this has not been done.

The second property of unsegmented alluvial fansthat has been

examined is surface area. Bull (1964~) and Hooke (1968) both

hypothesized that fan area and the contributing drainage basin area

should on the average exhibit a functional relationship. Hooke

(1968) suggested the following functional form

(2.3.2)

where A, = fan area, Ad = drainage basin area, and c and n are an

empirical coefficient and exponent, respectively. The

justification of Equation (2.3.2) relies primarilyon laboratoryand

field observations made byHooke (1968) and Bull (1964~) that suggest

insimilarenvironmentscoalescing fansmustapproachastheymaturea

steady-state area. Note, there are significant differences between

the steady-state hypothesis of Hooke (1968) and the fan area

equilibrium hypothesis of Denny (1965, 1967). Data presented by

Hooke (1968) regardingvaluesof cand nare summarizedin Table2.3.1

0.20

0.16

0.24

0.44

0.63

0.81

1.3

2.3

-------- --------

0.75

0.90

1.01

0.94

0.62

0.98

0.76

0.91

Deep Springs Valley, California, quartzite source area

Death Valley, California, east side

Cactus Flats, California

Owens Valley, California

Deep Springs Valley, California quartzite and dolomite source area

Data from Bull ( 1 9 6 4 ~ ) ~ sandstone source area (California)

Death Valley, California, west side

Data from Bull ( 1 9 6 4 ~ ) ~ shale source area (California)

36

where t h e values of c have been converted from t h e English system of u n i t s t o t h e SI system. I n t h i s table, a preponderance of t h e da t a was derived from a l l u v i a l fans i n t h e v i c i n i t y of t h e Owens and Death Valleys, Cal i fornia . T h e v a l u e o f n i s i n a l l c a s e s , except one, less thanl.O. Themathematicalimplicationisthatlargedrainagebasins

y i e l d proport ionately lower volumes of sediment t o t he fan area. Hooke (1968) suggested seve ra l reasons why such a r e l a t i o n s h i p might be reasonable. F i r s t , l a rge drainage basins are less l i k e l y t o be completelycoveredbya s i n g l e p r e c i p i t a t i o n event than s m a l l basins. Thus, o n l y a p o r t i o n o f a l a rgedra inage basinmay a c t i v e l y c o n t r i b u t e sediment t o the fan. Second, l a rge drainage basins tend t o have s l o p e s t h a t are small r e l a t i v e t o t h o s e found i n s m a l l e r basinswhich r e s u l t s i n reduced sediment t r anspor t capacity. Third, i n l a rge drainage basins more sediment maybe s to red o n h i l l s i d e s l o p e s a n d i n t h e channels. The e f f e c t of t h i s s torage is t h a t less sediment is t ransported t o t h e fan.

Valuesofthecoefficientcvarymuchmore w i d e l y t h a n t h e v a l u e s of n. Several important f a c t o r s whichmay a f f e c t t h e v a l u e o f c a r e : 1) t h e r a t i o of deposi t ional area to drainage basin area: 2 ) t h e type and e r o d i b i l i t y of t h e mater ia l i n the drainage basin; 3) tectonics: 4 ) regional climate: and 5) t h e amount of space ava i l ab le f o r deposit ion.

Final ly , Anstey's (1965) data d o n o t suppor t the hypo thes i s tha t there is a funct ional relationshipbetween A F and A,. However, Cooke and Warren (1973) suggest t h a t t h i s is because therewas a d i f f e r e n c e between t h e methods used by Hooke and Anstey to d e l i n e a t e t h e fan and drainage areas .

The t h i r d property of unsegmented a l l u v i a l fans t h a t has been widely discussed and examined is surface slope. Althoughthe s lopes of fan surfaces r a r e l y exceed t en degrees, they a r e i n general r a t h e r s teep. The longi tudinal p r o f i l e of unsegmented a l l u v i a l fan can o f t en be approximated a s a smooth exponential curve. Bull (1968)

found tha t f o r t h e f a n s h e e x a m i n e d i n t h e c e n t r a l v a l l e y of Cal i fornia tha t the longi tudinal p r o f i l e s of fans w i t h source a reas having high r a t e s of sediment productionwere s t e e p e r t h a n f answi th sou rcea reas having lower r a t e s of sediment production. Fan s lope is also

general ly inversely proportional t o fan s u r f a c e a r e a , drainagebasin area, and drainage basin discharge.

Melton (1965) hypothesized

37

(2.3.3)

where S = longitudinal slope of the upper fan surface in degrees, A =

drainage basin area, H = vertical relief of the drainage basin above

the fan apex, and the dimensionless number H/A is a characterization

of the ruggedness of the sediment source area of the fan. In

particular, Melton (1965) proposed that

(2.3.4)

where a and n are an undetermined coefficient and exponent,

respectively. Melton (1965) presented four groups of data to support

the validity of Equation (2.3.4) and calibrate the values of a and n.

Group 1 consisted of fifteen fans in southern Arizona and did not

include any modern or active fans. For this group, the functional

-a & PI VI PI c 1.0 lo i Group 1 Fans

yo do

0 om;, / byl I ,

0.10 I I I I I I

0.01 OJO H

L O O

38

10.

VI 01 01

PI -a b 1.0

us

0,lO 0,Ol 0.10 1.00

H

77

0.10 1 I I I I I I 1 1 I 1 I I I I I L

0.01 O J O H

1.00

39

10.

VI 01 aJ

01 71

1,o

tz

0,lO I 1 I I 1 1 1 1 I I I I 1 1 1 1

0.01 0.10 H

LOO

FIGS. 2.3.. 3 of fans in the western United States.

Upper fan s1op.e as a function of (H/A' 1 2 , for four groups

relationshipbetweenupper fan slope andtheparameter (H/A) was found

to be

(2.3.5a)

Group 2 consisted of four currently active fans emanating from the

Black Mountains on the east side of Death Valley, California. The

functional relationship for this group was found to be

(2.3.5b)

Group 3 consistedoftwo fans emanating fromthesan JacintoMountains

southwest of Palm Springs, California; a fan on the south side of

Pyramid Peak east of Death Valley, California; and seven fans

emanating from the Panamint Mountains on the west side of Death

Valley, California. The functional relationship for this group is

4 0

s = 4A2[ (2.3.5~)

Group 4 consisted of four fans emanating fromtheBig MariaMountains

north of Blythe, California. The functional relationship for this

group is

(2.3.5d)

The results of this analysis are plotted inFigs. 2.3.3. The primary

reasonsaccordingtoMelton (1965) for dividingthe thirty-three fans

s tudiedintofourgroupsare: 1)the fans in Groups2-4 are, relative

to the fans in Group 1, geologically young and 2) each group yields a

consistent relationship between S and the parameter (H/A) as

evidenced by Figs. 2.3.3. Although Melton (1965) attempted to

explpinthedi f ferenceamongthegroupsonthebas isofc l imate , hewas

not able to do this. Perhaps, the differences among the groups

includesnotonlyclimatic effectsbut also sediment availabilityand

other hydrologic and geologic differences.

It is conceptually very attractive to believe that simple

equations can be developed to quantitatively describe unsegmented

alluvial fanshape, area, and slope. However, giventhecomplexities

and interrelationships of the processes involved in building and

modifying alluvial fans, it is perhaps unrealistic to believe that

simple regressionrelationships forthesevariablescanbedeveloped.

Also, in attempting to develop simple regression relationshipsbased

on very limited data, the problem of spurious correlations must also

be considered; see for example, Benson (1965).

As noted previously, the terminology segmentedalluvial fans is

usedto refer to fans which have coalesced andusually haveundergone

long periods of development. The discussion of fan shape, area, and

slope becomes much more complex in the case of segmented fans; and

there are, at the present time, no results available.

Finally, Anstey (1965) surveyedthephysical characteristicsof

alluvial fans in both the United States and Pakistan. Some of the

resultsofthisstudyaresummarized inFigs. 2.3.4. In these figures,

41

Per Cent Incidence 4 8 12 16 20 24 0

i i i i 1

P <0.5 (<0.0087)

1 0.5-0.9 (0.0087-0.0157)

1.0-1.4 (0.0175-0.0244) 1

1.5-1.9 (0.0282-0.0332)

2.0-2.4 (0.0349-0.04 19) 1

2.5-2.9 (0.0437-0.0507) 1

3.0-3.4 (0.0524-0.0594) 1

3.5-3.9 (0.0612-0.0682)

4.0-4.4 (0.0899-0.0789)

4.5-4.9 (0.0787-0.0857)

5.0-5.4 (0.0875-0.0945)

5.5-5.9 (0.0963-0.1033)

6.0-6.4 (0.1051-0.1 122)

6.5-6.9 (0.1 139-0.1210)

P 7.0-7.4 (0.1228-0.1299)

P 7.5-7.9 (0.1317-0.1388)

P >8.0 (>0.1405) Paklatan (n =3 17) USA ( n - 5 8 8 )

F I G . 2.3.4a fans ‘n Pakistan and tLe wes ern United States from the vieyoint ox Jon ftudinal slope. Note, the slope is estimated as the di ference in t%e elevation of the a ex and the apron divided by the radius of the apex to the apron. DaFa from Anstey (1965) .

Comparison gf alluvia

a random sample of 100 fans in each geographical area are summarized,

and in general it would seem that the alluvial fans of Pakistan are

42

Per Cent Incidence 0 4 8 12 16 20

t- <0.5 (g0.31)

0.5-0.9 (0.31-0.56) - 1.0-1.4 (0.62-0.87)

1.5-1.9 (0.93-1.2)

2.0-2.4 (1.2-1.51

2.5-2.9 (1.6-1.8)

3.0-3.4 (1.9-2.11

3.5-3.9 (2.2-2.41

4.0-4.4 (2.5-2.7)

4.5-4.9 (2.6-3.01

5.0-5.4 (3.1-3.3)

5.5-5.9 (3.4-3.7)

8.0-6.4 (3.7-4.0)

6.5-6.9 (4.0-4.3)

7.0-7.4 (4.3-4.6)

7.5-7.9 (4.7-4.9)

8.0-8.4 (5.0-5.2)

8.5-8.9 (5.3-5.5)

>9.0 (>5.6) PmkIstan (n =346) USA (n '588)

FIG. 2.3.4b Comparison o f alluvial fans in Pakistan and the western United States from the viewpoint of radius.

reasonably similar to those found in the American West from the

viewpoints of radius and longitudinal slope.

43

2 . 4 C O N D I T I O N S FAVORING THE DEVELOPMENT AND MODIFICATION O F

ALLUVIAL FANS Thereareanumberof c l imat icandtopographic featureswhichcan

be i d e n t i f i e d a s e i t h e r f a v o r i n g t h e formation o r t h e preservat ionof a l l u v i a l fans. Among t h e f a c t o r s which w i l l be considered i n t h i s s ec t ion a r e vegetat ive cover and p r e c i p i t a t i o n , topographic r e l i e f , and tec ton ic s . It shouldbe n o t e d t h a t t h e i d e n t i f i c a t i o n of f ac to r s and t h e i r e f f e c t s on t h e formation of a l l u v i a l fans is a subject of continuing.discussion anddisagreement. The l i n k s between cause and e f f e c t a r e tenuous and a r e supported by l imi t ed , q u a l i t a t i v e evidence. T h i s author w i l l attempt t o discuss each of t hese f ac to r s from t h e viewpoint of hydraulic processes on a l l u v i a l fans.

2 . 4 . 1 Vegetative Cover/Precipitation/Sediment Yield T h e formation and growth of an a l l u v i a l fan requires both a

source of sediment and a means f o r t r anspor t ing t h e sediment t o the depos i t i ona la rea . Givenawatershed, theamount of sediment t h a t is produceddepends o n b o t h t h e v e g e t a t i v e cover i n thewatershed and the amount of e f f e c t i v e p r e c i p i t a t i o n received by t h e watershed. I n t h e context o f t h i s d i s c u s s i o n , e f f e c t i v e p r e c i p i t a t i o n i s d e f i n e d a s t h e amount of p r e c i p i t a t i o n r e q u i r e d t o producea knownamount of runoff: see f o r example, Langbein ( 1 9 4 9 ) . Further, i n t h e mater ia l which follows, e f f e c t i v e p r e c i p i t a t i o n is normalized t o a reference temperature of 1 0 degrees Centigrade (50 degrees Fahrenhei t ) . T h i s normalization process r e s u l t s i n some d i s t o r t i o n of t h e data a s w i l l be subsequently discussed. Another f a c t o r which w i l l be discussed t h a t can have a s i g n i f i c a n t e f f e c t on sediment y i e l d is land use.

Langbein and Schumm (1958) discussed t h e r e l a t ionsh ip of

4 4

Desert- Grassland - *Shrub - -

-Forest - - P

200.

100.

300.

0. 400. 800. 1200. 1600. 2000.

E f f ectlve Annual Preclpltatlon (nm)

F I G . 2 . 4 . l a Annual sediment yiqld a s a function of e f f e c t i v e annual p r e c i p i t a t i o n f o r sediment a ing s t a t i o n s i n t h e United S t a t e s , a f t e r Langbein and Schumm ,138). sediment yieldtomeanannual e f f e c t i v e p r e c i p i t a t i o n i n t e r m s o f b o t h streamsedimentgagingdataandreservoirsedimentdata f o r t h e u n i t e d S ta t e s . I n Table 2.4.la t h e annual average e f f e c t i v e p r e c i p i t a t i o n andsediment y i e l d d a t a forstreamsedimentstationsare summarized i n t abu la r form, and these same da ta a r e summarized i n g r a p h i c a l formin Fig. 2 . 4 . l a . I t is appropriate t o mention t h a t these da ta were derived from approximately 100 stream sediment s t a t i o n s across the UnitedStateswithpreferencebeinggiventosmal lerdrainagebas ins - Langbein and Schumm (1958) did not de f ine q u a n t i t a t i v e l y what they meant by t h e terminology smaller drainage basins. Langbein and Schumm (1958) cautioned t h a t these data may be biased due t o t h e f a c t t h a t r e l a t i v e l y f e w records w e r e ava i l ab le , t h e i r geographic d i s t r i b u t i o n was not uniform, and only suspended sediment data were avai lable . Note, apparently no consideration was given t o t h e bed load which may be s i g n i f i c a n t . I n an attempt t o o f f s e t t hese data biases i n t h e stream sediment da t a , Langbein and Schumm (1958) a l s o summarizedthe data regarding r e se rvo i r sedimentation f o r r e se rvo i r s s i t u a t e d below small drainage areas , Table 2 . 4 . l b and Fig. 2 . 4 . l b .

The shapes of t h e curves i n Figs. 2 . 4 . l a and 2 . 4 . l b a r e q u i t e s imi l a r w i t h the primary d i f f e rence between t h e m being t h a t the r e se rvo i r sediment y i e l d is approximately t w i c e t h a t of t h e stream sediment y i e ld .

-

4 5

I

I I I I

I I I I I

I

I I I I I

I

I

I

203 - 2291 31

254 I 38

279 I 12

356 - 6351 18

635 - 7621 10

762 - 9651 20

965 - 10161 11 1016 - 13971 18 1397 - 25401 5

216

2 54

279

483

698

902

991

1143

1854

I

I I I I

I I I I I

I I 397 I

I I I I

I

I I

I 491

I 414

I 526

1 502

I 277

I 197

I 165

I 154

15 reservoirs in San Rafael Swell, Utah and 16 in Badger Wash, Colorado

26 reservoirs in Twenty-Mile Creek basin, Wyoming; 7 in Cornfield Wash, New Mexico and 5 general

General

General

General including debris basins in ,

Southern California as one observation

General

General

General

General --_-________________________________________ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ________ The salient point of the data in Figs. 2.4.1 is that maximum

sediment yield occurs when the effective annual precipitation is

approximately 305 mm (12 in). Recall, an arid region is one which

receives 152mm (6 in) ofannual precipitationor lessand asemi-arid

region is one that receives 254-508 mm (10-20 in) of annual

precipitation, Stone (1967). Althoughthere is a differencebetween

annual precipitation and annual effective precipitation, the Figs.

2.4.1 indicate that maximum sediment yield occurs in semi-arid

regions. LangbeinandSchumm (1958) n o t e d t h a t t h e p a u c i t y o f d a t a i n arid and semi-arid climatesmakes it difficult todetermine thepoint

of maximumsediment yield accurately;however, other studies citedby

these authors also indicate that maximum sediment yield is in the

vicinity of 305 mm (12 in) of effective annual precipitation.

4 6

600.

Desert- _Grassland ~ Forest Shrub - -- w

-

400.

200.

0.

0. 400. 800. 1200. 1600. 2000.

E f f ectlve Annual Preclpltatlon <nm)

Annual sediment yield as a function of effective annual

Langbein and Schumm (1958) explained the variation of sediment yield with effective annual precipitation shown in Figs. 2.4.1 by

examining the effect of increasedprecipitation onboth erosionand

vegetative cover. Although increased precipitation increases

erosion, this effect is counteracted by the accompanying increase

vegetative cover which inhibits erosion. As noted by Antevs (1952)

inhis discussion of arroyo cuttingand filling,vegetation andplant

litter have a remarkable ability to bind soil and retain water that

would otherwise be lost to runoff and erosion. The discussion of

Croft (1962) regarding mudflows also concludes that when the

vegetation, litter, roots, and top soil of an area are damaged or

destroyedrunoff increasesdramatically. In contrast, a bareground

surface in arid and semi-arid areas may become almost impervious as

raindrops compact the surface layer andcolloidal mud fillsthe cracks

and pores. Langbein and Schumm (1958) attempted to functionally

relate these opposing factorsand theireffect onsediment yieldwith

the following equation

1

FIG. 2.4.lb precipitation for reservoirs, after Langbein and Schumm (1958).

s = apm[ ] (2.4.1)

where S = annual sediment yield; p = effective annual precipitation;

1 + bp"

47

and a, b, m, and n are undetermined coefficients and exponents. In

this equation, the factor ap’ quantifies the erosive effect of

precipitation while the factor1/(1 +bp ) ” quantifies theprotective

effect ofvegetativecover. [Note, forEnglish units; that is inches

of effective precipitation and tons of sediment per square mile,

LangbeinandSchumm (1958) found fortheirdatathatm= 2.3;n=3.33;

b = 0.0007; a = 10 for stream sediment station and a = 20 for the

reservoir data].

The question of sediment production has also been addressed in

empirical and theoreticaldiscussions byothers. Croft (1962) using

field data estimated annual sedimentation rates for four drainage

basins along the WasatchMountain Front, Utah, which have in thepast

produced mudflows. These results are summarized in Table 2.4.2.

Sedimentation rates can also be estimated from the data presented by

Croft (1962)

Croft (1962)

Croft (1962)

Croft (1962)

Price (1972)

Bairs Wasatck Mountain Front, Utah

Farmington Wasatch Mountain Front, Utah

Parrish Wasatch Mountain Front, Utah

Morris Wasatch Mountain Front, Utah

Basin above Arroyo Ciervo fan San Joaquin Valley California

0.533

1.14

2.97

0.00119

0.610

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

36

25

18

24

8

Drainage basin seriously damaged by fire or overgrazing on less than 10% of the area

See comments regarding Bairs Basin,

See comments regarding Bairs Basin

Undamaged, near- natural drainage basin

Estimated from deposition data given by Bull (196433) for the Arroyo Ciervo fan. The total basin area was used for this estimate

4 8

Bull (1964b) and analyzed by Price (1972) are noted in Table 2.4.2.

Modelsofdrainagebasin sedimentationhave beendeveloped by Flaxman

(1972), Weber & (1976) and Szidarovszky and Krzysztofowicz

(1976) . The foregoing discussion provides the basis for asserting that

in arid and semi-arid climatesthe supply and potential for sediment

transport was and in many cases remains sufficient to form and build

large alluvial deposits at mountain fronts. The actions of both

nature i n t e rmsofmodi f i ca t ionof thec l ima teandmore recen t lyman in terms of land use can also have a significant impact on the amount of

sediment produced and transported.

Whileacompletediscussionofclimaticchangeonageologictime

scale is beyond the scope of both this book and the expertise of its

author, some discussion of the important subject is required.

The use of the terminology era, period, epoch, and age by the

geologist does not imply an exact number ofyears. Rather, theseare

simplyterms which serve to indicate definite periods of development

in the history of the planet we inhabit. In Table 2 . 4 . 3 , the recent

divisions of geologic time are summarized. Ofthe divisions of time

mentioned in this table, only the Quaternary will be briefly

Quaternary CenozoiclRecent

I [Pleistocene I I I I I I P1 iocene I Miocene I [Oligocene I Eocene I I I I I I

Tertiary 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Age of Man

Glacial Age

Age of Mammals

Great climatic disturbance commonly known as the ice age

Creation of the Grand Canyon of Arizona and the Yosemite Valley of California; final great elevation of the mountain ranges of the western United States

MesozoiclCretaceous lAge of ReptileslFormation of the (Comanchean I (Palisades along

lthe Hudson River, lNew York

I Jurassic I I Triassic I

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 9

discussed. The Pleis tocene Period which is commonly r e fe r r ed t o a s t h e

Quarternary Division o f theCenozo ic Erawas introducedby a c l i m a t i c change which lowered t h e temperature and increasedtheprec ipi tat ion

i n t h e northern hemisphere. This c l ima t i c change continued u n t i l g l a c i e r s covered much of t h e northern hemisphere. Generally, it is believedthatthelastgreatice sheetsdisappeared fromNorthAmerica only 25,000yearsago,butitisnotclearthatthelast1ice a g e ' h a s y e t ended. That is, it is e n t i r e l y possible t h a t w e a r e l i v ing through one of t h e inter-glacial periods t h a t compose t h i s geologic period and t h a t ice may once again accumulate andspread acrossNorth America.

O f more importance t o t h e t o p i c a t hand is t h e e f f e c t of c l ima t i c temperature changes on p rec ip i t a t ion , and hence, on sediment y i e ld . I n the foregoing paragraphs of t h i s s ec t ion , the terminology of average annual e f f e c t i v e p r e c i p i t a t i o n was introduced and sediment y i e l d was r e f e r e n c e d t o e f f e c t i v e annual p r e c i p i t a t i o n normalizedto a reference temperature of 1 0 degrees Centigrade (50 degrees

1600.

1400.

P

e 0 u' d u_

1200.

e 1000. 91 L n

3 800. d

s 2

600.

15.6OC 7

I I I I I I 0. 200. 400. 600. 800.

Mean Annual Runoff, nn. F I G . 2,.4.2* Mean annual runoff a s a function of mean annual p r e c i p i t a t i o n and mean annual temperature.

50

Fahrenheit) , Figs. 2 . 4 . 1 . I n Fig. 2 . 4 . 2 , t h e e f f e c t of average annual temperatureonthe funct ional relationshipbetweenmeanannual p r e c i p i t a t i o n and runoff is shown. I f t h e curves i n t h i s f i g u r e a r e combinedwithasediment y i e l d r e l a t i o n s h i p s u c h a s Equation ( 2 . 4 . 1 ) ,

then Fig. 2 . 4 . 3 canbe constructed, and t h e following conclusions can be reached. F i r s t , a t 1 0 degrees Centigrade (50 degrees Fahrenheit) maximum sediment y i e l d occurs a t approximately a mean annual e f f e c t i v e p r e c i p i t a t i o n of 305 mm ( 1 2 i n ) . A t higher annual average temperatures, the peak 0-f t h e sediment y i e l d curve s h i f t s t o t h e r i g h t i n d i c a t i n g t h a t a t h i g h e r annual average temperatures more p r e c i p i t a t i o n is requiredtoproducethesamesedimentyield. Schumm (1965) argued t h a t the d i r e c t i o n of the s h i f t was co r rec t because a t higher temperaturestherewouldbemore evaporationand t r a n s p i r a t i o n and less water ava i l ab le t o support vegetat ion, but there would a l s o be less runoff. while a f i g u r e

Temperature Increases

F I G . 2,.4. e f f e c t i v e

7

Mean Annual Effective Preclpltatlon

3 Ef fec t of average annual t e m e r a t u r e p r e c i p i t a t i o n and sediment y i e l8 , a f t e r

on mean Schumm (

annual 1 9 6 5 ) .

s imilar t o Fig. 2 .4 .3 could be used t o quant i fy sediment y i e l d a s a function of e f f e c t i v e p r e c i p i t a t i o n and temperature, t h i s is not appropriate; it is t h e d i r e c t i o n of t h e s h i f t of t h e curves with temperature and t h e r e l a t i v e magnitudes of t h e s h i f t s t h a t are important.

Some estimates of the reductions i n temperature and t h e

51

corresponding increases i n p r e c i p i t a t i o n t h a t would have been required t o form t h e l a rge p luv ia l lakes known t o have previously ex i s t ed i n t h e southwestern United S t a t e s have been made. Leopold (1951b) and Antevs (1954) both agree t h a t f o r Lake Estancia t o h a v e ex i s t ed i n north-central New Mexico during t h e Pleis tocene t h a t t h e annual averagetemperaturewouldhavehadtobe 6 .7 degrees Centigrade ( 1 2 degrees Fahrenheit) less and p r e c i p i t a t i o n would have had t o be 2 5 0 mm (10 i n ) g r e a t e r than a t present . Broecker and O r r (1958) estimated t h a t temperatures would have had t o be 3-5 degrees Centigrade (5.4-9 degrees Fahrenheit) less and p r e c i p i t a t i o n 250 mm (10 i n ) g r e a t e r f o r the formation and maintenance of p luv ia l Lake Lahontan i n northern Nevada. Synder and Langbein (1962) calculated t h a t an increase i n p r e c i p i t a t i o n of 200 mm (8 i n ) would have been necessaryfortheexistenceofa lake i n SpringValley i n e a s t - c e n t r a l Nevada during the Pleistocene.

The th reeconc lus ions tha t canbedrawn fromtheabovediscussion with regard t o a l l u v i a l fans are as follows. F i r s t , over t h e l a s t geo log icpe r iod the climate inthenorthernhemispherehaschangedand t hese c l ima t i c changes had a s i g n i f i c a n t impact on temperature, p r e c i p i t a t i o n , runoff , and sediment y i e ld . Second, t h e sediment y i e l d curves i n Fig. 2 . 4 . 3 are co r rec t from t h e viewpoint of t he d i r e c t i o n and magnitude of the curve s h i f t s caused by temperature changes. Third, Schumm (1965) a s se r t ed t h a t i n a r i d regions an increase i n p r e c i p i t a t i o n should increase t h e volume of sed imen t depositedduringaunitoftime while i n semi-aridregions an increase i n p r e c i p i t a t i o n s h o u l d r e s u l t i n a decrease i n thevolume of sed imen t i n a u n i t of t i m e . For f u r t h e r information regarding t h e sub jec t of paleohydrology, t h e reader is re fe r r ed t o Gregory (1983) .

Perhaps of more i n t e r e s t t o t h e reader a r e t h e e f f e c t s of modern and perhaps short-term changes i n t h e amount and seasonal d i s t r i b u t i o n o f p rec ip i t a t ionand l anduse onerosion, fantrenching, and arroyo formation.

I n t h e American Southwest, p r e c i p i t a t i o n records tend t o be r e l a t i v e l y s h o r t , s t a t i o n s a r e poorly d i s t r i b u t e d , and t h e records a v a i l a b l e a r e o f t e n e r r a t i c andunrel iable . I n t h e s e a r e a s , t he re is a l s o evidence t h a t regional weather p a t t e r n s and topography can s i g n i f i c a n t l y a f f e c t both t h e s p a t i a l and temporal d i s t r i b u t i o n of p r e c i p i t a t i o n . For example, t h e Southern Nevada area: i .e . , t he port ion o f t h e s t a t e south of l a t i t u d e 38.5 degree8,divided intotwo p r e c i p i t a t i o n zones separated by an i n d e f i n i t e t r a n s i t i o n zone, a s showninFig. 2.4.4. These zonesof excessand d e f i c i t p r e c i p i t a t i o n

5 2

FIG. 2.4.4 Location of a s t and present r e c i p i t a t i o n gages i n the Southern Nevada a rea , a&er French (19837.

apparently a r e t h e r e s u l t of major topographical f ea tu re s and the paths of storm movement across t h e region, French (1983, 1985). An ana lys i s s i m i l a r t o t h a t of French (1983, 1985) was performed by Osborn (1984) f o r Arizona with s i m i l a r r e s u l t s .

AlsoshowninFig. 2.4.4 a r e t h e p r e c i p i t a t i o n g a g e s forSouthern Nevada, an a rea of approximately 41,200 km2 (15,900 m i 2 ) . Thus, i n t h i s a r ea there is approximately one p r e c i p i t a t i o n gage f o r every

5 3

1 ,300km2 ( 5 0 0 m i ' ) . I n fact, even th i snumber i smis l ead ings ince the d i s t r i b u t i o n is not uniform and while some gages shown i n Fig. 2 . 4 . 4 have been active f o r more than f i f t y years , some of t h e gages have a record t h a t is only four years long.

Compounding t h e problem of p r e c i p i t a t i o n ana lys i s i n t h e southwestern p a r t of t h e United S t a t e s is t h a t many of t he p r e c i p i t a t i o n records a r e not s u i t a b l e f o r intensity-duration- frequency analysis . For example, i n Las Vegas, Nevada the re a r e approximately f i f t y years of record ava i l ab le f o r such analysis: however, t h e r e w a s only one gage located a t t h e a i r p o r t , and one must question how representat ive t h i s record is of t h e whole va l l ey when convective, l oca l i zed storms a r e t h e t y p e t h a t c a u s e t h e most ser ious flooding on a l l u v i a l fans i n t h i s area.

Leopold (1951a) and Bull (1964a) have both presented data which emphasizestheeffectsofchanges i n theamount andseasonal t imingof p r e c i p i t a t i o n on erosion and deposi t ion i n a r i d and semi-arid regions. Leopold (1951a) began h i s discussion by a s se r t ing t h a t although annual values of temperature and p r e c i p i t a t i o n i n the southwesternUnitedStatesdo not exh ib i t s i g n i f i c a n t t r e n d s , t h e u s e of annual values may mask short-term p a t t e r n s which may have g rea t s ignif icance. For example, s h o r t durat ion, low in t ens i ty p r e c i p i t a t i o n events contr ibute very l i t t l e t o erosion and sediment t r anspor t becausetheyproduce l i t t l e o r no runoff. However, i f t h i s type of event occurs during t h e summer months, they may provide the moisturerequired fo r thep rese rva t ionandpropaga t ionof vegetation. Large p r e c i p i t a t i o n events penetrate t o t h e deeper s o i l l aye r s and a l s o con t r ibu te t o vegetat ive growth: but they a l s o produce a large proport ionof t h e runoff. In examining four long-termprecipi ta t ion records i n N e w Mexico, Leopold (1951a) determined t h a t i n t h e period of t i m e following1850SantaFeI NewMexico experienceda r e l a t i v e low frequency of small p r e c i p i t a t i o n events i n both the summer (June- September) and winter (October-May) periods. During t h i s period of t i m e , t h e r e was a l s o a r e l a t i v e l y high frequency of large p r e c i p i t a t i o n events. Beginning i n 1896 and continuing u n t i l 1939,

t hese t r ends i n the frequency of events reversed themselves. I n about1850the southwestern U n i t e d s t a t e s beganto experience ser ious erosion. Although overgrazing of t h e lands i n t h i s area is usually blamed, t h e above discussion suggests t h a t per turbat ions i n the r e l a t i v e frequency of p r e c i p i t a t i o n events may have so weakenedthe vegetat ivecover i n t h i s areathatovergrazingwasonlythetriggering event rather than t h e s ingu la r cause of erosion.

5 4

Bull (1964a) inves t iga t ing t h e causes of channel t renching on a l l u v i a l fans i n c e n t r a l Cal i fornia used t h e same a n a l y t i c methodology as Leopold (1951a) and came t o e s s e n t i a l l y t h e same conclusion. That is, i n c e n t r a l Ca l i fo rn ia , t h e per iods of a c t i v e channel trenching (1875 t o 1895 and 1935 t o 1945) correspond t o periods of above normal d a i l y and annual p r e c i p i t a t i o n . The combination of a high frequency of l a r g e p r e c i p i t a t i o n events a n d a lowfrequencyofsmallprecipitationevents r e s u l t e d i n aboveaverage runoff and hence s u b s t a n t i a l erosion.

I n t h e foregoing paragraphs, t h e e f f e c t of r a t h e r s m a l l changes i n t h e amount of p r e c i p i t a t i o n per event and the seasonal arrangement of t hese events on erosion i n t h e sou thwes te rnun i t eds t a t e s hasbeen discussed. Mancanalsohaveaprofound e f f e c t on e r o s i o n i n a r i d a n d semi-arid climates where there is a very delicate balance between p rec ip i t a t ion , vegetat ive cover, and sediment y i e ld . For example, throughout t h e l a t e r decades of t h e 1800's there w a s a p a t t e r n of s e r ious erosion through the westernuni ted States; see f o r example, Leopold (1951a),Antevs ( 1 9 5 2 ) , andBull (1964a). Thesedecadeswere alsothet imeduringwhichlarge herdsof l ivestockwere in t roduced to t h e area by Anglo-Americans and var ious Indian tribes, p a r t i c u l a r l y theNavajos. Althoughorig inal ly i twasbel ieved t h a t t h e grazingof l a rge herds of cat t le and sheep destroyed t h e vege ta t ive cover and lead d i r e c t l y t o the observed erosion, it now seems t h a t t h i s explanation is much too s impl i s t i c . Rather, it would s e e m t h a t previous t o 1850 thegeomorphologic systemin theWest wasde l i ca t e ly balanced; t h a t is, the gradual change i n p r e c i p i t a t i o n pa t t e rns had weakened t h e vegetat ive cover but not s u f f i c i e n t l y f o r s i g n i f i c a n t erosion t o t ake place. The introduct ion of l i ves tock t o t h e a rea i n l a rge numbers w a s a s u f f i c i e n t per turbat ion of an apparently s t a b l e system t o make t h e system dramatically unstable; and s i g n i f i c a n t and se r ious erosion was t h e r e s u l t .

Therearealsonumerousother examples of s i t u a t i o n s inwhich the a c t i v i t i e s of man have combined with nature t o y i e l d d i sa s t rous r e s u l t s o n a l l u v i a l f a n s . On December31, 1933 and January 1, 1 9 3 4 ,

t h e Los Angeles, Cal i fornia area experienced heavy p rec ip i t a t ion . The r e s u l t was se r ious damage t o t h e communities of Montrose, La Crescenta, andGlendalewhichwerebuilt o n t h e f a n s a n d b a j a d a s o f t h e San Gabriel and Verdugo Mountains. This l oca l i zed d i s a s t e r was caused by heavy p r e c i p i t a t i o n f a l l i n g i n a watershed i n t h e San Gabriel Mountains which had been burned over only a month before and whose drainage led d i r e c t l y through t h e communities. T h e data of

55

Croft ( 1 9 6 2 ) , Table 2 . 4 . 2 , regarding drainage bas ins along t h e Wasatch Mountain Front, Utah a l s o demonstrates t h e e f f e c t s of t h e act ions of man can have on sediment y i e ld . I n t h i s t a b l e , t h e sediment y i e l d s from basins which have been damaged by f i r e and/or overgrazing are s i g n i f i c a n t l y l a r g e r t h a n frombasins withundamaged vegetation.

Athirdexampleoftheeffects of urbanizat ionon a l l u v i a l fans and sediment y i e l d de r ives from t h e experience of the author i n t h e easternpartof theLasVegasV,al ley , Nevada. T h i s v a l l e y l i e s w i t h i n the Basin and Range Province, and t h e topography is character ized by sub-parallel mountain ranges with a c e n t r a l basin modified by encroaching a l l u v i a l fans. L a s VegasWash, wh ich i s aremnant o f t h e Las V e g a s River, d ra ins t h i s v a l l e y and c rosses t h e t o e s of many segmented a l l u v i a l fans on which t h e Las Vegasmetropolitan area is b u i l t , Fig. 2 . 4 . 5 . FromtheLasVegasareatoLakeMead, a d i s t a n c e o f approximately 3 2 km ( 2 0 m i ) , t h e r e is a perennial flow i n L a s Vegas Wash due to the discharge of e f f l u e n t from t h e upstream sewage treatment p l an t s . The r a t e of erosion i n L a s Vegas Wash depends on the s o i l type, t h e v e g e t a t i v e cover, t h e perennial discharge, and the magnitude and frequency of flood events. T h e s o i l t y p e s a r e s i l t a n d f i n e s a n d t y p i c a l o f t h e m a t e r i a l s found a t t h e t o e s o f a l l u v i a l fans, andtheonce lushvegetat ionwhich s t a b i l i z e d t h e banksof thechannel has been destroyed as erosion has lowered t h e bed of t h e channel and t h e l o c a l groundwater t a b l e a l s o dropped i n response to t h e lowering o f t h e channel bed, Figs. 2.4.6aI 2.4.6b, 2 . 4 . 7 and 2 . 4 . 8 . Upstream urbanization has r e su l t ed i n an increase i n both t h e average sewage e f f l u e n t discharge and t h e magnitude of t h e peak flood flows through the channel. French and Woessner (1983) estimated t h a t between August, 1975 and Apri l , 1979 flood events and increased perennial flows r e su l t ed i n t h e erosion of 450 ,000 m 3 (16 mil l ion f t 3 ) of mater ia l . One flood event i n J u l y , 1975, whose ups t r eamef fec t s a r e showninFigs. 1.1.1, aloneeroded anest imated 3 7 , 0 0 0 m 3 (1 .3mi l l i on f t 3 ) o f m a t e r i a l . O the r shavees t ima tea tha t i n L a s v e g a s ~ a s h s t r e a m bed ma te r i a l s have eroded a t t h e r a t e of 0.20-0.76 m/yr (8-30 in/yr) , Anon. (198533). This erosion, which is t h e d i r e c t r e s u l t of t he ac t ions of man, is se r ious and has threatened t h e Las Vegas Valley Lateral which i samajorwatersupplypipel ineconveyingpotablewater

from LakeMeadtothe LasVegasmetropolitanarea. T h i s s i t u a t i o n i s an example of t h e c o n f l i c t i n g and narrowly defined r e s p o n s i b i l i t i e s of governmental agencies t h a t preclude the development of cost- e f f e c t i v e so lu t ions top rob lems ; s e e s e c t i o n 1.1. TheColoradoRiver

5 6

F I G . 2 .4 :5 Las Vegas Wash Nevada in relation to the Las Vegas metropolitan area and Lake head.

Commission of Nevada has the responsibility of preserving the

capability of the Las Vegas Lateral to deliver water to the Las Vegas

metropolitan area. Given this narrowly defined responsibility, the

Commission can only consider measures that will protect the pipeline

while not being allowed to consider measures that will address the

causeoftheproblem- inadequateupstream floodcontrolandarea-wide

erosionprotection. The responsibility for addressingthe causesof

the problem must be addressed by other agencies. Thus, instead of

5 7

FIG. 2.4.6a Modern erosion of Las Vegas Wash, Nevada as a result of

upstream urbanization. Note the remnants of vegetation that was

destroyed as the local groundwater table was lowered in response to

the erosion. Photograph by R. H. French.

5 8

FIG. 2.4.6b Modern erosion of Las Vegas Wash, Nevada as a result of

upstream urbanization. Note the remnants of vegetation that was

destroyed as the local groundwater table was lowered in response to

the erosion. Photograph by R. H. French.

59

FIG. 2 . 4 . 7 Modern erosion i n Las Vegas Wash, Nevada a s a r e s u l t of upstream urbanization. T h i s photograph was taken a f t e r flooding i n thesummerof1984. Thepipesonther ightarewe l l cas ingswhose tops

previous t o t h e floodingwereatthegroundsurface. Photographby D. Z immerman.

6 0

FIG. 2 . 4 . 8 Bridge c r o s s i n g LasVegas Wash, Nevada i n t h e v i c i n i t y o f LakeMead. V a n d a l s p r e v i o u s t o t h e f l o o d i n g d u r i n g t h e summer of1984 s tood on a bank of Las Vegas Wash t o spray t h e g r a f f i t i on t h e br idge p i e r . Subsequent f loods caused t h e e ros ion shown. Photograph by R .

H . French.

6 1

searching for area-wide solutions to problems, the Commission can

only examine local and limited solutions. However, in the near

future it is expected that erosion of channels tributaryto LasVegas

Wash will begin andstructures built on thesurrounding alluvial fans

will be endangered; andthus, involvingother agenciesalso withvery

limited responsibilities.

2.5 FANHEAD ENTRENCHMENT

Acommon andhydraulically important characteristic of alluvial

fans is the temporary or permanent entrenchment of the channel near

theapexofthe fan. By definition, theapex ofthe fan is thehighest

elevation on an alluvial fan and commonly occurs where the stream

responsible for the formation of the fan emerges from the mountains,

Stone (1967). Channel entrenchment occurs when erosion rather than

deposition occurs at the apex, and several explanations of fanhead

channel entrenchment have been offered.

First, Bull (1964a, 1977), Denny (1967), andHooke (1967) have

all hypothesized tectonic effects may be among the reasons that

channels entrenchthemselves. Inexaminingsegmented fans inthe San

Joaquin Valley of California, Bull (1964a) found fans in whicheach

segment had a rather linear profile with the steepest slope being

close to the mountain front and the slightest slope being associated

with the segment furthest from the mountain front. Given these

observations, Bull (1964a) concluded that the fan shape had been

steepened on several occasions as the result of uplift of the

mountains. This scenario is summarized schematically in Figs.

2.5.la- 2.5.ld. InFig. 2.5.laI a streamchannel andan alluvial fan

have formed inresponsetothe initialuplift ofa mountainrange. In

Fig. 2.5.lblthemountainshaveexperiencedasecondepisodeofuplift

which has steepened the slope of the channel and formed a new fan

segment. Fig. 2.5.1~ shows the result after a third episode of

uplift; that is, at this point there is a three segment alluvial fan.

Alluvlal F m

6 2

/- Mounta'ns

Fan

r- Mountains

Upper Fan Segment

Youngest ALluvlal

\ (dl

>v 'i Fan Deposlts

Entrenched Stream Channel

FIGS. 2.5.1 Schematic diagram of alluvial fan development, after Bull (1964~).

6 3

At this point, the stream will cut downward establishing a gentler

slope. The point at which the channel merges with the fan surface is

known as the intersectionpoint, Fig. 2.5.ld. This point is usually

also the locus of deposition, and the material deposited here is

commonly much coarser than the material found in the channel itself.

The observations and hypotheses of Hooke (1967) regarding the

segmentation of fans in the Death Valley, California area generally

support the explanation given by Bull (1964a).

Denny.(1967) describedhow faultingparallel toa mountain front

may loweravalley floorwith respect to amountain rangeand causethe

channel to incise itself on the upper part of the fan surface.

Second, Bull (1964a, 1977) , Denny (1967) , and Hooke (1967) have all noted that rare events such as large-scale flooding may cause

temporary channel entrenchment. In essence, this hypothesis of

fanhead channel entrenchment claims that while the frequent flow

event results inaggradationthat the extreme and rare flow eventwith

much greater sediment transporting competence results in erosion in

the vicinity of the apex and hence channel entrenchment. Note, a

series of moderate flow events with low sediment loadscan alsocause

degradation and channel entrenchment.

Third, as mentioned elsewhere in this chapter, climatic change

is also a possible explanation of fanhead channel entrenchment.

Lustig (1965) noted several featuresassociated withalluvial fansin

Deep Springs Valley, California which are indicative of climatic

change. Among these features were: 1) large shifts in the loci of

deposition; 2) desert varnish on abandoned fan surfaces; 3 )

greater tractive force in entrenched channels than on fan surfaces:

and 4 ) The types of

climatic changewhichwouldshift thebalanceat the apex ofa fan from

deposition to erosion would include increasing storm frequency;

increasing precipitation intensity; declines in annual total

precipitationbutincreasingprecipitationintensity; and increasing

total precipitation.

It is appropriate to note at this point that the visual

examination of a fan surface to determine if there has been recent

flooding can in some cases result in erroneous conclusions. In the

previous paragraph, Lustig (1965) tacitly assumes that the presence

of desert varnish on a fan surface is indicative that it is an

abandoned surface;that is, it isone onwhich flowshave not recently

occurred. However, in their investigation of the flood potential of

Fortymile Wash on the Nevada Test Site, Nevada, Squires and Young

misfit trenches near the apices of the fans.

6 4

(1984) found recent and distinct high water marks above an old fan

surface which showed no evidence of flow. Apparently, in some

situations floodscanpassoverold, f ine-grainedalluvialsurfaces

and leave these surfaces virtually unchanged, Squires and Young

(1984). At this point it should be noted that there is some

controversy regarding the results reported by Squires and Young

(1984). For example, Katzer (1986) disputestheseresults andnotes

that the old fan surface showed no signs of desert varnish.

Fourth, Hooke (1967) in contrast to most investigators who have

tacitly assumed that the material is first deposited at the fan apex

and then subsequently eroded hypothesized that channel entrenchment

could be the natural result of alternating debris and water flows.

That is, in some case fanhead channels are 'born' incised. This

hypothesiswasbasedon laboratoryobservations andthe argument that

debris flows require largegradients for flowto occur relative tothe

gradients required by waterto transport the finermaterials found in

debris flows. As a consequence of this, water flows tend to erode

channels through debris flow deposits, and in fact such erosion of

debris flow deposits has been observed in the field; see forexample,

Pack (1923) and Blackwelder (1928).

Fifth, Hooke (1967) noted on the basis of his laboratory

experiments that channel entrenchment often occurs when the locus of

deposition on the fan shifts to a location that has not received

material foraperiod of time. The justification forthis assertion

is that locations which have not recently received sediment for a

period of time are topographic lows; and hence, the slope to these

locations is greater. Hooke (1967) further noted that channel

entrenchment caused by this mechanism can only last until the

topographic low has been built up to the level of the rest of the fan.

Although erosional processes are dominate at the point of

channel entrenchment, this is balanced by the redeposition of eroded

material further down the fan. That is, fanhead trenches act as

conduits for the material entering the fan from the apex with the

result being that coarse sediment deposition is shifted downslope.

It should also be noted that the fanhead trench is not always a

permanent feature. Bull (1977) attempted to distinguish between

temporarily and permanently entrenched channels. In this

discussion, he noted that channels which appear to be permanently

entrenched, the channel bottom may be as much as 50 m (164 ft) below a

fan surface which has an old soil profile. Other channels which

appeartobetemporari lyentrenchedwerelessthan 15m (50 ft) belowa

6 5

fan surface which appeared t o have no v i s i b l e s o i l p r o f i l e . F ina l ly , s i n c e t o some degree, t h e d i r e c t i o n of an entrenched

fanhead channel may d i c t a t e t h e locus of deposit ion, it is important t o d i scuss t h e deviat ion of present day fanhead channels from the medial r a d i a l l i n e o f t h e fan. Note, b y d e f i n i t i o n , themedial r a d i a l l i n e o n a n a l l u v i a l fan i s t h e s t r a i g h t l i n e f r o m t h e a p e x t o t h e t o e of t h e fan posit ioned so t h a t t h e fan is s p l i t i n t o approximately two equal areas. Bull ( 1 9 6 4 ~ ) determined t h e present-day channel deviat ion faomthemedial r a d i a l l i n e for seventy-five a l l u v i a l fans. These observations are summarized i n terms of a p robab i l i t y of a deviat ion i n degrees fromthe medial r a d i a l l i n e i n Fig. 2.5.2. With regard t o t h i s f i gu re , two-thirds o f t h e channel examined werewithin t h i r t y degreesof themedial r a d i a l l i n e andon ly th reechanne l s hada deviat ion of more than f i f t y degrees. The importance of channel deviat ion with regard t o t h e locus of cu r ren t deposit ion is i l l u s t r a t e d i n Figs. 2.5.3a and 2.5.3b. I n these photographs, two very s m a l l , developing a l l u v i a l deposi ts near Boulder City, Nevada a r e shown. I n F i g . 2.5.3a, thechannel comes almostdirect lydownthe c e n t e r o f t h e f anwhi l e i n F i g . 2.5.3bthechannelfollowsthemountain f r o n t .

0.30

I- 0

1

I I I I I ” I I

0 10 20 30 4 0 5 0 90

Deviation Interval, degrees

F I G . 2 . 5 . 2 P robab i l i t of a, channel deviat ion from the medial Eosi t ion on fanheads o Y aJluvia1 fans found i n p a r t s of Fresno and

ercedCounties, Cal i fornia . AfterFrench andLombard0 (1984) ;da t a from Bull ( 1 9 6 4 ~ ) .

2 . 6 CONDITIONS FAVORABLE TO THE FORMATION O F DEBRIS AND MUD-FLOWS

A s has been d i s c u s s e d i n t h e foregoing s e c t i o n s o f t h i s c h a p t e r , debris and mud-flows a r e believed t o be among the primary hydraulic processes responsible f o r t h e development and modification of

F I G . 2.5.3a Photographofaverysmalldevelopingalluvial f an i n t h e v i c i n i t y of Boulder C i ty , Nevada. Note t h a t t h e c u r r e n t channel on t h i s f an shows very l i t t l e d e v i a t i o n from t h e medial r a d i a l l i n e . Photograph by R. H. French.

6 7

FIG. 2.5.333 Pho tographofave rysma l ldeve lop inga l luv ia l fan inthe vicinity of Boulder City, Nevada. Note that the current channel on

this fan shows a significant deviation from the medial radial line.

Photograph by R. H. French.

6 8

a l l u v i a l fans. Standard geologic d e f i n i t i o n s of t hese phenomena a r e :

Debris Flow: @@Moving rampart o r w a l l of boulders and mud a few f e e t i n height without v i s i b l e water t h a t moves forward i n a series of surges o r waves along an a l l u v i a l fan," Stone (1967,

p. 2 2 0 ) .

Debris Flow: @@A debr i s flow is a form of mass movement of a body of granular s o l i d s , water, and a i r . Debris flows a r e dis t inguished from mudflows on t h e b a s i s of p a r t i c l e s i z e . Debr i s flows have 50 percent of t h e s o l i d s l a r g e r than sand, whereas mudflows a r e a form of earthflow cons i s t ing of mater ia l t h a t is w e t enough t o flow rapidly, and contains mostly sand, s i l t , and c l ay s i zed p a r t i c l e s , @ @ Costa and J a r r e t t (1981) .

Mudflow: @@Debris-laden water o r ig ina t ing on s t e e p s lopes so charged withmud andsand t h a t it formsa f l u i d d e n s e r t h a n w a t e r and iscapableoftransportinghugeblocksandboulderswhichare buoyed up by a viscous mass,@' Stone (1967, p. 2 3 5 ) .

A l t h o u g h t h e s e d e f i n i t i o n s a r e inadequate fromtheviewpoint of f l u i d mechanics; s eechap te r 3 , Sec t ion7 , t h e y a r e comple t e lysa t i s f ac to ry f o r a discussion of these flows and t h e i r o r ig in from a geomorphic viewpoint.

Whilewater flows o n a l l u v i a l fans may l a s t s eve ra lhour s andmay cause damage several kilometers from the apex of t h e fan, debris and mud-flowsareofshortduration-oftenan houro r less, Beaty (1963) - and t h e damage caused by them is usual ly , but not i n a l l cases , confined t o t h e area near t h e apex of t h e fan. The a b i l i t y of deb r i s and mud-flows t o t r anspor t l a rge and very heavy boulders was b r i e f l y described i n C h a p t e r 1 , S e c t i o n l . Figs. 2 .6 . l a , 2 . 6 . l b , and 2 . 6 . 1 ~

summarize, i n a graphical form, t h e s lopes, d i s t ances , and t ransported boulder weights f o r three drainage basins i n Utahwhich have experienced debris o r mud-flows, Croft ( 1 9 6 7 ) .

I n Chapter 3 , Section 5 , t he mechanics of deb r i s and mud-flows w i l l be discussed; but it is a p p r o p r i a t e a t t h i s p o i n t t o d i s c u s s i n a q u a l i t a t i v e fashion t h e hydrometeorologic and geologic conditions t h a t a r e favorable t o t h e formation of deb r i s and mud-flows. Croft ( 1 9 6 7 ) , Price ( 1 9 7 2 ) , and Hooke (1965) have a l l discussed i n some d e t a i l t h e f ac to r swhicha rebe l i eved t o b e conducive t o t h e formation

69

50. UI L

QI E

$ 40

5 30, z 3 20.

p 10,

d -P

FI

d U

L QI

d

0. >

r

End o f Flow

0 100, 200. 300, 400. 500, Horlzontal Dlstance, meters

FIG. 2.6. la Longitudinal rofile ,of one lobe of. the Ka Creek, Utah debris flow of August $950 showing the locat$ons of?some of the largest boulders with their weights noted in metric tons. The lobe is ap roximately 23 m (75 ft) wide, 457 m (1500 ft) long, and 1.2-2.4 rn (4- 8 Bt) thick. Data from Croft (1967).

of these types of flows. Among the factors identified by these

investigators are the following.

2.6.1 Precipitation

Reasonably large volumes of precipitation are required for

debris flow formation. Croft (1967) states that 25-50 mm (1-2 in) o,f

precipitation with intensities in the range of 102-203 mm/hr (4-8

in/hr) and durations of at least 0.08 hours are required for debris

flow formation. Mears (1977) noted that the weather station in

Glenwood Springs, Colorado recorded 21.6 mm (0.85 in) of

precipitation i n a h a l f h o u r p r e c e d i n g t h e d e b r i s flows inthis city on July 24, 1977. Although there are no precipitation data in the

drainage basins where the debris flows originated, Mears (1977)

hypothesized that the precipitation depths in these basins were

similartothoserecorded at the weather station. Campbell (1975) in

discussing the mechanisms of debris flow formation hypothesizedthat

both precipitation intensity and the amount of antecedent

precipitation are important factors. With judgement, the foregoing

comments can be used to assess the potential for debris flows in a

geographic area. For example, precipitation intensity-duration-

frequency data for the southwestern United States is available in

Miller eta1 (1973) andHanseneta1 (1977), andarea reduction factors

70

80.

UI L

01 E

$ 60.

9;

2 .P 2 40. d

d U

L 01

P

’ 20.

0. 0. 200. 400. 600. 800. 1000.

Horfzontal Distance, meters

FIG. 2.6.lb Steed bouldhrs with their weights noted in metric tons. (1967).

for these data can be obtained from Zehr and Myers (1984). If data

appropriate for the Las Vegas, Nevada area are abstracted from these

documents, it can be tentatively concluded that debris flows are a

possibility given the right, but rare, combination of meteorologic

and hydrologic conditions. As isdiscussed inchapter 5, it isquite

possible that data fromdocuments suchas Milleret a1 (1973) for arid

and semi-arid regions may be in error due to among other factors the

poor geographic distribution of precipitation gages and the short

period of record usually available for these gages. For example,

there is evidence that the precipitation data for the Las Vegas,

Nevadaarea inMiller eta1 (1973) underestimates point precipitation

by a significant amount, Anon. (1985a).

The areal extent and frequency of the precipitation are also

important. Hooke (1965) and Price (1972) both noted that if major

precipitation events are too frequent, then sufficient weathered

material for the formation of a debris or mud-flow may not have

accumulated in the drainage basin. Note, such flow conditions will

Longi tud ina lprof i l eo fadebr i s flowat themouth ofthe Utah drainpge basin and the locations of some of the largest

Data from Croft

71

0 0

f

0 0

3

F 1 G . 2 . 6 . 1 ~ LongJtudinal r o f i l e o f a d e b r J s f l o w a t themouth o f t h e Pa r r i sh Utah draAnage pasfn and t h e locatAons of some of t h e l a r g e s t boulder&, w i t h t h e i r weights noted i n metric tons. Data from Croft ( 1 9 6 7 ) .

con t r ibu te t o channel entrenchment. Pr ice (1972) i n developing a numerical model of a l l u v i a l fan deposit ion d i f f e r e n t i a t e d between debris andwater flowson t h e b a s i s o f t h e depthof weatheredmaterial i n t h e drainage basin, see Chapter4, Sect ion2. Mears (1977) s t a t ed t h a t p r e c i p i t a t i o n events t h a t produce l a rge volumes of water r e l a t i v e t o t h e volume of unconsolidated debris i n a drainage basin

72

produce water flooding and the dominant debris transport processes

are bed and suspended load. In examining the drainage basins

upgradient of GlenwoodSprings, Colorado, Mears (1977) concludedthat

thedebris flowsof July, 1977 removedno morethan 5-lo percent ofthe

available debris from thsse basins; and thus 10-20 more events of a

similar magnitude are possible even if no moreunconsolidated debris

accumulates.

In some areas debris and mud-flows are not directly caused by

precipitation but by the rapid melting of snow inthe drainagebasin;

see for example, Sharp and Nobles (1953) and Johnson (1970, pp. 437-

443).

2.6.2 Lithology

Hooke (1965) stated that substantial amounts of clay, silt, and

fine material produced by weathering or derived from alluvial

material is conducive, if not required, for debris flow formation.

For example, the Shadow Rock Fan, California which is underlain with

hard quartzite rock shows little evidence of debris flow deposits.

However, the Trollheim Fan, Californiawhich is inclose proximityto

the Shadow Rock Fan but underlain by easily weathered sandy dolomite

shows significant evidence of debris flow activity. Hampton (1972)

in discussing debris flows in the vicinity of Wrightwood, California

also noted the importance of clay in the formation of debris flows.

Hampton (1972) also mentioned that even small amounts of clay; for

example less than 10 per cent of the total solids, can have a

significant effect. Mears (1977) andcampbell (1975) havealsonoted

the importance of clay in debris flows.

2.6.3 Topography

The slopes of the drainage basin must be sufficiently steep to

support very viscous flows and produce the high flow velocities

necessary to entrain the weathered material into the flow. However,

the slopesmust notbe sosteep that debris cannot accumulate onthem.

Campbell (1975) hasdiscussed drainagebasin slope fromtheviewpoint

of soil slips which is believed to be one of the mechanisms of slope

failure that result in debris flows. Hampton (1972) noted that the

large debris flows at Wrightwood, California that occurred during

February, 1969 apparently were initiated by the remolding of

landslide debris. In some cases, debris flows are the result of the

liquefaction of slope material, Hampton (1972).

7 3

2 . 6 . 4 Land U s e Again, l and use is an important cons ide ra t ion . Cro f t ( 1 9 6 7 )

hypothesized t h a t p r e h i s t o r i c d e b r i s and mud-flows a long thewasa tch Mountain Front i n Utah w e r e t h e r e s u l t of heavy p r e c i p i t a t i o n on unvegetated d e b r i s and d e t r i t u s t h a t w a s exposed whenthe g l a c i e r s i n t h i s a r e a r e t r e a t e d . The a c t i o n s of man and na tu re o f t e n combine t o d e s t r o y t h e v e g e t a t i o n i n a d r a i n a g e b a s i n a n d t h e r e s u l t i n somecases a r e d e b r i s and mud-flows which s k i l l f u l and r a t i o n a l land use management p r a c t i c e s might have prevented, Chawner (1935) and Crof t

Debris and mud-flows a r e o f t e n considered t o be r e l i c s of p a s t geologic ages , b u t t h e formation of t h e s e f lows r e q u i r e s a u n i q u e s e t of hydrometeoro logicandgeologic c i rcumstancewhich f o r a g i v e n a r e a maybe m e t o n l y i n f r e q u e n t l y . However insome a r e a s d e b r i s flowsmay occur much more f r equen t ly than has been p rev ious ly assumed; see f o r example Costa and J a r r e t t (1981) , Mears (1977) , and Campbell (1975) .

(1967) .

2.7 CHARACTERISTICS OF FLOWS I N EPHEMERAL STREAMS Since hydrau l i c processes on a l l u v i a l f a n s t a k e p l ace i n

channels which a r e u s u a l l y d ry , it is both appropr i a t e and u s e f u l t o d i s c u s s , from a r a t h e r q u a l i t a t i v e viewpoint , some of t h e c h a r a c t e r i s t i c s of such flows.

Flows on a l l u v i a l f a n s a r e u s u a l l y produced, a s d i scussed elsewhere, by h igh i n t e n s i t y - s h o r t d u r a t i o n p r e c i p i t a t i o n events w i t h t h e r e s u l t b e i n g t h a t l a r g e q u a n t i t i e s o f w a t e r e n t e r t hechanne l network i n a very s h o r t pe r iod of t i m e . During such flow even t s , t h e peak d i scha rge i n t h e channel is u s u a l l y a t t a i n e d much more quick ly than i n pe renn ia l r i v e r s . For example, Hjalmarson (1984) n o t e d t h a t t h e f lowinTanqueVerdeCreek nearTucson, Arizona increased 1 0 9 m 3 / s

(3,860 f t 3 / s ) i n f i f t e e n minutes du r ing t h e f lood t h a t occurred i n t h i s s t ream on J u l y 25, 1981. During t h e f lood of J u l y 2 6 , 1981, it was r epor t ed t h a t t h e depth of flow i n Tanque Verde Creek increased 0.61m ( 2 f t ) i n f i f t e e n s e c o n d s and 1 . 2 m ( 4 f t ) i n less than aminute , Hjalmarson (1984) . The hydrographs based on s t ream gaging s t a t i o n d a t a f o r t h e f l o o d s t h a t t o o k p l a c e inTanque VerdeCreek d u r i n g J u l y , 1981 a r e p l o t t e d i n F igs . 2 .7 . l a and 2 .7 . lb .

The d u r a t i o n of flow even t s i n ephemeral s t reams i n a r i d and semi-ar id a r e a s a r e s h o r t - t y p i c a l l y minutes o r hours r a t h e r than days; see f o r example, F igs . 2.7.1. Using d a t a from 15 semi-arid watersheds i n Arizona, Murphey e t a 1 (1977) found t h a t t h e mean flow

7 4

Et 0

oooo o600 E!OO ie00 E400 lgoo 1800 e400

July 25, 1981 July 26, 1981

F I G . 2 . 7 . l a e Verde Creek Arizona streamflow gay"% s t a t i o n f o r J u l y 25-26, 19vl. Data from Hlalmarson ( 1 9 8 4 , p . 8 4 ) .

event du ra t ion was reasonably w e l l r epresented by

Discharge *as a func t ion of t i m e a t a Tan

c2 D = C , A ( 2 . 7 . 1 )

whereD=mean f lowdura t ion , A = d r a i n a g e b a s i n a r e a , and C , and C, a r e an empir ica l c o e f f i c i e n t and exponent, r e spec t ive ly . For t h e d r a i n a g e b a s i n s t h e s e i n v e s t i g a t o r s s t u d i e d a n d f o r D i n h o u r s a n d A i n s q u a r e m i l e s , t h e b e s t f i t v a l u e s o f C , a n d C 2 w e r e found t o b e 2.53 and 0 . 2 , r e spec t ive ly . Unlike perennia l r i v e r s whose f lood hydrograph h a s a d e f i n i t e b a s e f l o w recess ioncurve , ephemeral s t reams u s u a l l y d o not have a r eces s ion curve prolonged by groundwater d i scharge . The r eces s ion curve is gene ra l ly t runca ted by i n f i l t r a t i o n through t h e bed of t h e channel , Peebles e t a 1 ( 1 9 8 1 ) .

S i g n i f i c a n t t ransmiss ion o r i n f i l t r a t i o n l o s s e s a s t h e f lood wave moves down t h e channel is another c h a r a c t e r i s t i c of f lood flows inephemeralstreamchannels. L a n e e t a l (1985) developedamodel f o r e s t ima t ing t ransmiss ion l o s s e s i n a l l u v i a l channels of t h e form

7 5

1 lab0 2400 0600 12bo

July 31, 1981

FIG. 2.7. l b Arizona streamflow ga i n Hlalmarson (1984, p. 1348.

Discharge as a func t ion of t i m e a t a Tan e Verde Creek, s t a t i o n f o r J u l y 31, 1%1. Data from

where a(x,w) , b(x,w) , and F(x,w) a r e parameters which a r e determined f o r each channel reach, V U p = inf low a t theups t ream endof t h e reach, V, , , = l a t e r a l inf low t o t h e channel wi th in t h e reach, x = reach l eng th , andw=channe lwid th . Lane (1980) us ing da ta from 14 channel reaches i n Arizona, Texas, Kansas, and Nebraska provided t h e fol lowing equat ion f o r e s t i m a t i n g t h e parameters i n Equation (2.7.2)

b(x,w) = exp(-kxw) (2.7.3)

a(x,w) = a[ l . -exp(-kxw)]/( l . -b) = a[ l . -b(x ,w) ]/(l.-b) (2.7.4)

F ( X , W ) = [ 1. -b ( X , W ) ]/kw

where

a = -0.00465 KD

k = -1.09 l n ( 1 . - 0.00545 KD/V)

16

b = exp(-k)

The variables in the above semi-empirical equations and the units in

which they are defined are as follows: a =unit channel intercept of

flow (acre-ft), K = effective hydraulic conductivity (in/hr) with

typical values given in Table 2 . 7 . 1 , D = mean duration of flow (hr)

fromEquation ( 2 . 7 . 1 ) or its equivalent, V=meanvolumeof flow (acre-

ft) , and k = decay factor (miles/ft) . TABLE 2 . 7 . 1 Effective h draulic conductivity for estimating transmission lgsses in alluvia7 channels. These values of h raulic conductivit reflect the sedimentTladen characteristics ogephemeral, streams an8 are not representative of steady-state, clear water infiltration rates, Lane et a1 ( 1 9 8 5 )

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bed Material Group I Bed Material 1 Effective Hydraulic

Characteristics I Conductivity mm/hr (in/hr)

I I I I I

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Very high loss rate

High loss rate

Moderately high loss rate

Moderate loss rate

Very low loss rate

Very clean gravel and large sand dS0> 2mm ( 0 . 0 7 9 in) Clean sand and gravel under field conditions d,,> 2mm ( 0 . 0 7 9 in) Sand and gravel mixture with less than a few per cent silt and clay Sand and gravel mixture with significant amounts of silt and clay Consolidated bed material with high silt-clay content

>127 (> 5 )

( 2 . 0 - 5 . 0 ) 5 0 . 8 - 127

2 5 . 4 - 7 6 . 2 (1.0 - 3 . 0 )

6 . 3 5 - 2 5 . 4 ( 0 . 2 5 - 1.0)

0 . 0 2 5 4 - 2 . 5 4 (0.001 - 0.1)

Although as indicated above, infiltration maybe significant in

manyalluvialchannels, insomealluvialchannelstransmissionlosses

are significantly decreased by the presence of subsurface caliche.

Caliche is a term used to refer to lime-rich deposits in the soils of

a r i d a n d s e m i - a r i d r e g i o n s , Stone ( 1 9 6 7 ) . Some typesof caliche form

almost impermeable barriers to water. Cooley et a1 ( 1 9 7 3 ) examined

the influence of surface and near-surface caliche on infiltration

characteristics of the soils in the Las Vegas area. The field tests

for this study were performed in such a fashion that infiltration

rates through the caliche layer could be compared with infiltration

rates for the material directlybelow this layer. The results with

regard to infiltration rates are summarized in Table 2 . 7 . 2 . These

77

data indicate that the effect of caliche on infiltrationcan bequite

significant. The effects of caliche on channel transmission losses

are a function ofl) theamount ofa l luv ia lmater ia labovetheca l iche layer, 2) thearealextentand distributionof caliche, and 3) whether

Comment I Infiltration rate I Infiltration rate I on caliche surface I below caliche surface I (19 tests performed) I (21 tests performed)

mm/min (in/min)

mm/min I (in/min) I

Average initial in-1 0.0739 I filtration rate I (0.00291) I

I

I I

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.24 (0.167)

I 0.0132 - 23.7 1 Initial infiltra- I 0.000871 - 0.243 tion rate range I (0.0000343-0.00957) I (0.000520-0.933)

I Average final in- I filtration rate 1

0.0181 (0.000713)

2.27 (0.0895)

the caliche layer is fractured or unfractured.

In estimating transmission losses inalluvial channels, extreme

caution, judgement, and familiarity with the local geology is

required. T h e d a t a c u r r e n t l y a v a i l a b l e inmost areas is not adequate to make completely reliable estimates of this factor.

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Beat C.B. , 1968. Sequential stud of desert flooding in the White Moun&ins of California and NevaA. Technical Report 68-31-ES. U.S. Army Earth Science Laboratory, Natick, Massachusetts.

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Blackwelder, E. 1928. Mudflow as a geologic agent in semi-arid mountains. Geoiogical Society of America Bulletin, 39: 465-480.

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Bull, W.B., 1964a. History and causes of channel trenching in wesfern Fresno County, California. American Journal of Science, 262. 249-258.

Bull, W.B., 1964b. Alluvial fans and near-surface subsidence in western Fresno Count California. U.S. Geological Survey Professional Paper 437-%: Washington.

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Bull, W.B., 1968. Alluvialfans. Journalof Geology, 16: 101-106.

Bull W.B., 1977. The alluvial fan environment. Progress in Physical Geography, 1: 222-270.

Campbell, R.H.., 1975. Soil slips, qebris flows, and rainFtorms in the Santa Monica Mountains and vicinity, Southern California. U.S. Geological Survey Professional Paper 851, Washington.

Chawner, W.D., 1935. Alluvial fan flooqing: the Montrose, California, flood of 1934. Geographical Review, 25: 255-263.

Coates, D.R. and Vitek J.D., 1980. Pers ectives on Geomorphic Threshplds. In: Thresholds in Geopor hofo y. D.5. Coates and J.D. Vitek, eds. George Allen and Unwin €&blis%ers, Winchester, Ma.

Cooke, R.U., and. Warren A., 1973. Geomorphology of Deserts. University of California hress, Berkeley.

COOley, R.L., Fiero, G.W., Jr., Lattman L.H., pnd Mjndljng, $.L., $973. Influence of surface and near-suy*ace caliche distribution on inf4ltration characteristics and floodin Las Vegas area Nevada. Prolect Revort No. 21. Center for Water %.sources Research, Desert Research fnstitute, Reno, Nevada.

Costa J.E. and Jarrett R.D. , 1981. Debris flows in spa11 mountain streah channels of Co’lorado and their h drologic im lications. Bulletin of the Association of Engineering dologists, dIII,3: 309- 322.

Croft,,A.R., 1962. Some sedimentation henomena alon the Wasatch Mountain front. Journal of Geophysics? Research, 6? (4) : 1511- 1524.

Croft, A.R., 1967. Rainstorm debris flows: a problem in ublic welfare, Agricultural Experiment Station, College of Agricuyture, University of Arizona, Tucson.

Denn C.S., 1965. Alluvial fans,in the Death Valley re ion Calikniq and Nevada. U. S. Geological Survey Professional gape; 466, Washington.

Denny, C.S 1967. Fans and pediments. American Journal of Science, 265: 81-105.

Flaxman, E.M., 1972. Predicting sediment yield in western United

79

States. ASCE, Journal ofthe Hydraulics Division, 98 (HY12): 2073- 2085.

French R.H., 198.3. Precipitation in Southern Nevada. ASCE, Journai of Hydraulic Engineering, 109 (7) : 1023-1036.

French, R.H., 1985. Daily, seasonal and annual precipitation atthe Nevada Test Site Nevada. Pre ared B Water Resources Center Desert Research Ihstitute Las fe as &. For: U.S. Department of Energy, Las Vegas, Nv. , DbE/NV/1?384-01. French R.H. gndLombardo W.S., 1984. Assessment of flood hazardat the radioactive waste mafiagement site in Area 5 of the Nevada Test Site Prepared By: Water Resoyrces Center, Desert Research Institute, Las Ve as Nevada. For. U.S. Department of Energy, Las Vegas, Nevada, D8E/dv/10162-15.

French R.H.. andwoessner W.W., 1983. ErosionandSa$init Problems in AridRegions. In: V.'D. Adams and V.A., Lamarra (editorsfl, Aquatic Re$ources Mavagement of the Coloracjo River Ecosystem. Ann Arbor Science Publishers, Ann Arbor, Michigan, pp. 425-437.

Gretetner P.E.,, 1967. Si nificance of the rare event in geolo American Association of Pe?roleum Geologists Bulletin, 51: 218YL 2206.

Gregory K.J. (editor), 1983. Background to Paleohydrology: A Perspective. John Wiley and Sons, New York.

Hampton M.A., $972. The role of subaqueous debris flow in Journal of Sedimentary Petrology, 42

Hanqen, E.M., Schwarz F.,K. , and Riedel, J,.T. , 1977. Probable maximum precipitation 'estimates Colorado River and Great Basin drainages. U. S . , Department of Commerce , Nod, National Weather Service , Silver Spring, Maryland. Hjalmarson H.W. 1984. Flash flood in Tpnque, Verde Creek, Tucson, Arizona. ASCE, journal of Hydraulic Engineering, 110 (12) : 1841-

Hooke R. LeB, 1965. Alluvial fans. Ph.p. Thesis, California Institute of Technology, Pasadena, California.

Hooke R. LeB., 1967 Processes on arid-region alluvial fans. Journ61 of Geology, 75': 438-460.

Hooke R. LeB., 1968. Steady-state relationshi s on arid-re ion alluvial fans in closed basins. American Journaf of Science, 166:

Johnson, A.M., 1970. Physical Processes in Geology. Freeman, Cooper and Company, San Francisco.

Katzer, T., 1986. Review of the manuscript entitled Hydraulic Processes on Alluvial Fans, personal communication.

Lane L.J., 1980. Transmission Losses. In: National Engineer4ng Handbook. U. $. Department of Agriculture, Soil Conservation Service, Washington.

Lane, L.J., Purtymum W.D., and Becker, N.M., 1985. Newestimatin {rocedures for surface runoff sediment yield, and contaminan? ransport in Los Alamos Count'y New Mexico. LA-10335-MS. Los

Alamos National Laboratory, Los Alamos , New Mexico. Langbein W.B. 1949 Annual runoff ipthe Unitedstates. Circular No. 52, b.S. deological Survey, Washington.

Langbein, W.B. andLeo old L B 1964 uasi-equilibrium states in channel morphology. %ner)ic& 'dournai 0% Science, 262: 782-794.

Langbein, W.B. andSchumm S.A.,1958. Yielq of sediment inrelation to mean annual preci 'itation. Transactions of the American Geophysical Union, 39 (g) : 1076-1084.

Leogol L.B., 1951a Rainfall fre enc - an pspectpf climatic variatkn. Transactions of the AmerEan &ophysical Union, 32 (3) : 347-357.

Leopold, L.B., 1951b. PleistoceneclimatesinNewMexico. American

enerating turbidity currents. 74) : 775-793.

H drometeorological keport No. 49.

1852.

609-629.

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Journal of Science, 249: 152-168.

Leo old, L.B. and+Langbein, W.B., 1,962. The concept of, entro y in langscape ,evolution. U. S. Geological Survey Professional gaper 500a, Washington.

Leopold L,.B. Wolman M.G. and Miller, J.P. , 1964. Fluvial Process& in deomorphof ogy. h.H. Freeman, San Francisco.

Lustig, I,.K., 1965. Clastjc sedimentation in Deep S rings Vallle California. U. S. Geological Survey Professionaf Paper 352-5: Washington.

Lufti#:Gf.K., 1969. Quantitative analysis-of desert topography. In. McGinn.ies and B.J. Goldman (editors) Arid Lands in Perspective. University of Arizona Press, pp. 4j-58.

Mears A.I., 1977. Debris-fl,owhazard analysis and mitigation: an exampie from Glenwood Springs , Colorado. Colorado Geological Survey, Denver, Colorado.

Melton M.A. 1965. The geomorphic and paleoclimatic significance of alltivial deposits in Southern Arizona. Journal of Geology, 66: 1-38.

Miller J.F., Frederick R.H., and Trace R.J. 1973. Precipitation-frequency atl'as of the Western Unitezktates $01. VII- Nevaaa. U S. De aqtment of Commerce, NOAA, Nationai Weather Service, Silver &ring, Maryland.

Murphe J.B., Wallace, D.E., and Lane, L.,J., 1977. Geomorphic garamekrs predict hydro raRh characteristics in the Southwest.

WRA, Water Resources BulFietin, 13 (1) : 25-38.

Osborn, H.B. 1984. Estimatin precipitation in mountainous re ions. ASCk, Journal of HydrauPic Engineering, 110 (12): 1859- 18?3.

Pack F.J., 1933. Torrential otential of desert waters. Pan American Geologist, 40: 349-358.

Peebles R.W., Smith, R.E., and Yakowitz, S.J., 1981. A leaky reservoir model for ephemeral flow recession. Water Resources Research, 17 (3): 628-636.

Price W.E., Jr., 1972. A random-walk simulationmodel ofalluvial- fan dkposition. Re ort No. 7 Hydrology and Water Resources and Industrial Engineerflng, Univefkity of Arizona, Tucson.

Schumm S.A. 1965. uarterna paleohydrolo Jn: H.E. Wri ht Jr. an4D.G. Prey (edifors) The3uaternary of ty6United States - gart IV, Miscellaneous Studies: Princeton University Press.

Sha? R.P. qnd Nqbles L.H., 1953. Mudflow ,of 194,l at Wri htwgod Sout 6rn California. bulletin of the Geologic Society of %nerica: 64: 547-560.

Squires R R. anq Yo,un 1984. Flood potential of Fortyile Wash an'a its Nevada Test Site, Sou $ern Nevada. Repor! No. 83-4001. U.S. G~ological Survey, Carson City, Nevada.

rinci aq %htaries

Stone R.O., 1967. A desert glossary. Earth Science Reviews, 8: 211-268.

Syn er C.T. and Langbein W.B. 1962. The Pleistocene lake in Sprfng' Valle Nevada and 'its ciimatic implications. Journal of Geophysical &search, 67: 2385-2394.

S idaroyszky F. andyrzysztofowicz R. 1976. Aba es a proachfor sfmulatin se'diment yield. Journal' of the HydrologYcal gciences, 3

Troeh F.R., 1965. L ndform eqyations fitted to contour maps. Amerikan Journal of Scfence, 263.

Viessman W., Knapgj, J.W., Lewis, G.L., and Harbaugh T.E., 1977. Introduction to Hy rology.

Webe J.E., Fogel M.M. a d Duck te n L. 1976. The use of multfble regressioi modefs rn redl)cttn< sediment yield. AWRA, Water Resources Bulletin, 12 (lf:

(1-2) : 39-45.

616-627.

Harper and Row, New York:

1-17.

81

Wolman, Y . G . and Miller J.P., 1960. Magnitude and frequency of geomorphic processes. Journal of Geology, 68: 54-74.

Zehr R.M. andM ers V.A 1984. Deptharea ratiosin thesemi-arid Southwest Unite% St'ates: NWS H drometeorolo ic Repor$ 40. U.S. Department of Commerce, NOAA, )i;ational Weaaer Service, Silver Spl-ing, Maryland.

82

CHAPTER 3

BASIC PRINCIPLES O F OPEN CHANNEL HYDRAULICS

3 . 1 INTRODUCTION I n examining hydrau l i c processes on a l l u v i a l f ans , it is

necessary f o r t h e non-engineer t o become f a m i l i a r wi th some of t h e b a s i c p r i n c i p l e s of open-channel flow: and f o r t h e eng inee r wi th a background i n f lu idmechan ics andhydrau l i ceng inee r ing to re-examine and re -cons ider some o f t h e b a s i c p r i n c i p l e s o f t h e s e t e c h n i c a l a r e a s from t h e viewpoint of a l l u v i a l f ans . I t is t h e purpose of t h i s chaptertoprovideabriefand rudimentarytreatmentofseveral o f t h e b a s i c p r i n c i p l e s of open-channel hydrau l i c s . I n p a r t i c u l a r , t h i s chap te rwi l l cons ide r spec i f i cene rgy :norma lo run i fo rmf lowonmi ld , c r i t i c a l , and s t e e p s l o p e s ; the s t a b i l i t y of a l l u v i a l channels ; and t h e mechanics of debris flows. Although s p e c i f i c r e f e r e n c e s w i l l be

mentioned throughout t h i s chap te r , t h e r e a r e a number of b a s i c r e f e r e n c e s which provide a comprehensive d i s c u s s i o n of these s u b j e c t s ; see f o r example, Chow (1959) , Henderson (1966) , French (1985) , and Graf ( 1 9 7 1 ) .

3 . 2 S P E C I F I C ENERGY By d e f i n i t i o n , t h e s p e c i f i c energy of a one dimensional open-

channel f low r e l a t i v e t o t h e bottom of the channel is

( 3 . 2 . 1 )

w h e r e E = s p e c i f i c e n e r g y ( m ) ; y = d e p t h o f flow ( m ) ; a = k i n e t i c e n e r g y c o r r e c t i o n f a c t o r which c o r r e c t s f o r t h e non-uniformity of t he v e l o c i t y p r o f i l e (dimensionless) ; u = Q/A = average v e l o c i t y of flow (rn/s) ; Q = channel vo lumetr ic flow r a t e ( m 3 / s ) ; A = flow a r e a ( m 2 ) ; and g = a c c e l e r a t i o n of g r a v i t y ( m / s 2 ) . Equation ( 3 . 2 . 1 ) d e r i v e s d i r e c t l y from the Bernou l l i energy equat ion (law of conserva t ion of energy) and is s u b j e c t t o a number of assumptions. Primary among theseassumpt ions i s t h a t c o s 8 I l o r t h a t 8 < 10' where 8 = s l o p e a n g l e of t h e channel . For a more complete d e r i v a t i o n of Equation ( 3 . 2 . 1 ) , t h e r eade r is referred t o French (1985) o r Streeter and Wylie ( 1 9 7 5 ) .

Examination of Equation ( 3 . 2 . 1 ) f o r t h e c a s e t h a t a = 1, Q is known, a n d t h e channe lgeomet ry i s def ineddemonst ra tes t h a t E i s o n l y afunctionofthedepthofflow, y , F igs . 3 . 2 . 1 . For a s p e c i f i e d Qand

-

83

Y

yz

F I G . 3 . 2 . 1 S p e c i f i c energy curve.

a def ined channel geometry, i f y is p l o t t e d a s a func t ion of E, Fig. 3 .2 . lb , t h e r e s u l t i s a hyperbolawi thbranches i n t h e f i r s t a n d t h i r d quadrants . Thebranchof thehyperbo la i n t h e t h i r d quadrant is of no i n t e r e s t s i n c e it rep resen t s nega t ive va lues of both E and y , which have no phys ica l meaning. The branch of t h e hyperbola i n t h e f i r s t quadrant has two limbs. The limb AC of t h i s branch is asymptotic t o t h e E a x i s , and t h e limb AB is asymptot ic t o t h e l i n e y = E. On t h e

curveshown i n F i g . 3 . 2 . l b , t h e po in t l abe led Arepresents theminimum s p e c i f i c energy requi red t o pass t h e flow Q through t h e def ined channel . The co-ord ina tes of t h e p o i n t l abe led A can be found by t ak ing t h e f i r s t d e r i v a t i v e of Equation ( 3 . 2 . 1 ) wi th r e spec t t o t h e depth of flow and s e t t i n g t h e r e s u l t equal t o zero o r

Q 2 E = y + -

2gA2

dE dA - 0 ( 3 . 2 . 2 )

With r e fe rence t o Fig. 3 .2 . la , t h e d i f f e r e n t i a l flow areadA n e a r t h e f r e e s u r f a c e can be approximated by

dA I Tdy

84

o r

dA _ - - = T dY

With t h i s approximation f o r dA/dy Equation (3.2.2) becomes

(3.2.3)

where D = A/T = hydrau l i c depth.

y i e l d s

Rearrangement of Equation (3.2.3)

(3 .2 .4)

o r d e f i n i n g t h e Froude number

(3 .2 .5)

where F = Froude number and Equat ion (3.2.5) d e f i n e s what is termed

c r i t i c a l f l o w ; t h a t i s , t h e m i n i m u m a m o u n t o f s p e c i f i c e n e r g y r e q u i r e d t o pass t h e flow Q through t h e channel geometry s p e c i f i e d . With

regard t o t h e above development and Figs . 3 .2 .1 , t h e fo l lowing should

be noted. F i r s t , i n a channel of l a r g e s lope ang le 6 and a f 1, it can

beeasilydemonstratedthat t h e c r i t e r i o n forminimum s p e c i f i c e n e r g y

o r c r i t i ca l flow is

(3.2.6)

Second, i n Fig. 3 .2 . lb , t h e E-y curves f o r flow rates g r e a t e r t han Q

l i e t o t h e r i g h t of t h e curve BAC; and E-y curves f o r flow r a t e s less than Q l i e t o t h e l e f t of curve BAC. Thi rd , by d e f i n i t i o n , f lows f o r

which F > 1 a r e termed s u p e r c r i t i c a l and l i e on l imb AC of t h e E-y curve ; f lows f o r which F = 1 a r e termed c r i t i c a l and occur a t p o i n t A; and f lows f o r w h i c h F < l a r e t e r m e d s u b c r i t i c a l and l i e onbranch ABof

t h e E-y curve. Fourth, wi th t h e except ion of Po in t A , t h e c r i t i c a l

p o i n t , e v e r y v a l u e o f E s u c h t h a t E > E , ( c r i t i c a l s p e c i f i c energy) has

a s s o c i a t e d w i t h it t w o p o s s i b l e d e p t h s o f flow. Forexample, i n F i g .

3 . 2 . l b , i f t h e s p e c i f i c energy of flow is E l , t hen t h e l i n e D F

85

demonstrates that there are two possible depths of flow; y1 and y2.

FLoodplaln/Ovarbank Floodplaln/Overbank

Sectlon

7 7 Sectlon

Primary "/'\ Channel I,--!!-'

FIG. 3.2.2 Schematic of a channel of compound section.

The depth of flow y1 is associated with a supercritical flow having a

specific energy El; and the depth of flow y, is associated with a

subcritical flow which also has a specific energy E,. The possible

depths of flow y1 and y, are known as the alternate depths of flow.

Fifth, in channels of compound section, Fig. 3.2.2, the problem of

specific energy and the computation of the correct Froude number

becomes complex. Although a discussion of this area of study is

beyond the scope of this treatment , the interested reader may find a summary in French (1985) and specific discussions in Blalock (1980) , Blalock and Sturm (1981) , Petryk and Grant (1975) , and Konemann (1982) .

The comment in the foregoing paragraph regarding alternate

depths of flow leads directly to a consideration of the problem of

accessability and controls. Through the terminology of

accessability, it is meant to indicate that with Q and the chann'el

geometry given a priori a means of deciding which of the alternate

depths on the E-y curve is accessable must be found. The result is the

identificationoftheactual downstreamdepthof flowthat is possible

with the specified upstream conditions.

Accessability arguments appeal to logic rather than

mathematical proof. As an example of such arguments, consider a

rectangular channel of constantwidthb which conveys a steady flowQ.

In the otherwise horizontal bed of the channel, there is a smooth

upward step of height 42, Fig. 3.2.3a. Given this situation, an E-y curve can be constructed, Fig. 3.2.3b. In this figure, assume that

the flowatsection1inFig. 3.2.3ais represented by point Aon theE-

y curve. Note, the point A' has the same specific energy as point A,

and the choice of point A as the starting point derives from prior or

given knowledge of the Froude number at section 1. The choice of

86

point A i nd ica t e s t h a t F < 1; and hence, t h e flow a t s ec t ion 1 is s u b c r i t i c a l . The l oca t ion of the s p e c i f i c energy on t h i s curve representing sec t ion 2 can be determined by t h e app l i ca t ion of t he Bernoulli energy equation between sec t ions 1 and 2 o r

- 2 - 2 u2

= - + y2 + A Z U 1

2g - + y1 2g

E l = E2 + A Z

E 2 = E l - A Z

where i t i s a s s u m e d t h a t t h e ene rgyd i s s ipa t ion betweensections l a n d 2 i s n e g l i g i b l e . Havingmathematically determinedthe va lueof E 2 w e must now determine t h e c o r r e c t depth of flow a t s ec t ion 2 . The w i d t h of t h e channel, by d e f i n i t i o n , does not change: and the re fo re , t h e l l f lowpoint lvcanonlymoveonthecurvedef inedinFig . 3.2.333. I f t h e w i d t h of t h e channel var ied, then flow pe r u n i t w i d t h would vary and t h e flow point could move off t h e curve shown i n Fig. 3.2.3b and onto o the r E-y curves. With regard t o F ig . 3.2.3b, t h e foregoing statement means t h a t the flow point cannot Ivjurnp1* from point B t o B 1 . Thus, i f po in t B' is t o b e a n accessab le so lu t ion o f t h i s problem, t h e flow po in t must pass through point C. Movement of t h e flow po in t t o po in tC i s o n l y p o s s i b l e i f t h e increase i n c h a n n e l b o t t o m e l e v a t i o n i s g r e a t e r than t h a t spec i f i ed . This hypothet ical s i t u a t i o n is represented by a dashed l i n e i n Fig. 3.2.3a. Therefore, t he conclusion is t h a t of t h e poss ib l e depths of flow a t sec t ion 2 , only t h e depth of flow associated with point B is accessable from point A

with t h e upstream flow conditions a s spec i f i ed . The foregoing discussion t a c i t l y assumes t h a t t h e r e is a

so lu t ion t o the problem with t h e upstream condi t ions a s specif ied. I n f a c t , it is q u i t e easy t o specify a s t e p s i z e such t h a t a so lu t ion with t h e given upstream conditions does not e x i s t . For example, i n Fig. 3.2.3a, i f t h e s t e p s i z e e x c e e d s ~ z , , t h e n t h e r e i s n o s o l u t i o n t o t h e problem. This s i t u a t i o n is physical ly explained by not ing t h a t when t h e s t e p s i z e exceeds A Z , t h e channel has been s u f f i c i e n t l y obstructed by t h e s t e p so t h a t t h e upstream s p e c i f i c energy is not adequate t o pass t h e flow. That is, t h e flow has been choked by t h e s t e p , I n s u c h a s i t u a t i o n , t h e f lowups t r eamof thes t epmus t increase indepthunt i l thespec i f i cenergyava i lab leups treamissuf f i c i ent to pass t h e flow over t h e obstruct ion.

87

The following comments regardingspecificenergyshouldbemade.

First , in the vicinity of the critical point , point C in Figs. 3.2.3 , Y

E

(a) (b) FIGS. 3.2.3 Schematic definition of the accessability problem.

small changes in specific energy can result in large changes in the

depth of flow. Second, as noted previously in this section, in

channels of compound section, the problemsof specificenergy andthe

locationofthecrit icalpointorpointscanbecomesignif icantlymore

complex and difficult. Third, the foregoing paragraphs have

provided only a synoptic discussion of specific energy. For a more

detailed discussion of this topic, the reader is referred to either

French (1985) or Henderson (1966).

3.3 UNIFORM/NORMAL FLOW

By definition, uniform flow occurs when

1. The depth, flow area, and velocity at every channel cross

2. the energy grade line, water surface, and channel bottom

section are constant: and

are all parallel.

Although uniform flow is a theoretical ideal which can only occur in

very long, straight channels of a fixed geometry, this theoretical

concept can be used with great effect in the solution of very applied

problems. One of the equations that describes uniform flow is the

Manning equation or

88

(3.3.1)

where Q = flow rate (m3/s) : A = flow area (m2) ; R = A/P = hydraulic

radius (m) : P = wetted perimeter (m) : S = slope of the energy grade

line, water surface, or channel bottom: n = Manning roughness

coefficient; and $ = a coefficient used to account for the system of

units used. Ifthe SI system ofunits specifiedabove isused, then $

= 1; if the English system of units is used, then $ = 1.49. If both

sides of Equation (3.3.1) are divided by the flow area, then a second

form of the Manning equation results or

(3.3.2)

where u = average velocity of flow (m/s if $ = 1.0)

InEquations (3.3.1) and (3.3.2)thecoefficientncharacterizes

the roughness of the channel boundary and is a well established

coefficient for estimating boundary friction effects. There are a

number of methods for estimating values of n in perennial channels:

see for example, Barnes (1967) , Chow (1959) , French (1985) , Henderson (1966) , and Urquhart (1975). Although some of the methods used for

perennial channels are applicable to ephemeral channels on alluvial

fans, it is worth noting several semi-empirical methods which have

beendevelopedtoestimatevaluesof n from amechanical sizeanalysis

of the materials which compose the channel boundary.

Perhaps the best known semi-empirical method of estimating n is thatproposedbyStr ickler in1923; see for exampleSimons andsenturk

(1976), which hypothesized that

n = 0.047d'/6 (3.3.3)

where d = diameter in millimeters of the uniform sand pasted to the

sides and bottom of an experimental flume used by Strickler. While

Equation (3.3.3) has limited validity in natural channels, it

specifies a basic functional relationship between n and d. Among

the results functionally similar to Equation (3.3.3) are:

1/6

n = 0.013d 6 5

(3.3.3a)

where d6 = diameter in millimeters such that 65% of the channel

89

boundary material, by weight, is smaller, Raudkivi (1976).

1 / 6

n = 0.039d 3 0

(3.3.3b)

whered,, =diameter infeetsuchthat50% ofthechannelboundary

material by weight is smaller, Garde and Raju (1978). If the SI

system of units is used, then Equation (3.3.335) becomes

1 / 6

n = 0.047d 50

where d is in meters, Subramanya (1982).

1 / 6

n = 0.038d 9 0

(3.3.3c)

(3.3.3d)

where d,, = diameter in meters such that 90% of the channel

boundary material by weight is smaller, Meyer-Peter and Muller

(1948). Equation (3.3.34) wasdeveloped for channels withbeds

formed of mixed materials with a significant proportion of

coarse grained sizes.

1 / 6

n = 0.026d 75

(3.3.3e)

where d,, = diameter in inches such that 75% of the channel

boundarymaterialbyweight issmaller, Laneand Carlson (1953).

Equation (3.3.3e) was derived from experiments in which the

channels were paved with cobbles.

Of the above equations for estimating a value of Manning's n, in the

case of alluvial fans Equation (3.3.34) is perhaps the most

appropriate.

Jarrett (1984) recognized that the available guidelines for

estimating resistance coefficients for high-gradient; that is,

channelswithslopesgreaterthan0.002, arebased onlimited dataand

are handicapped by a lack of easily applied methods for evaluating

changes of boundary resistance with the depth of flow. Jarrett

(1984) exa.mined 21 high-gradient streams in the Rocky Mountains with

stable beds andminimallyvegetatedbanks and developed an empirical

equation for n or

90

n = 0 . 3 g ~ 0 . 3 8 ~ - 0 * 1 6 ( 3 . 3 . 4 )

whereR=hydrau l i c rad ius i n feet. Whilethe streamsused b y J a r r e t t (1984) t o develop Equation ( 3 . 3 . 4 ) had s lopes s i m i l a r t o those found on a l l u v i a l fans, t h e channel beds were composed of large cobblesand boulders whichmay ormay n o t b e t y p i c a l of channels found o n a l l u v i a l fans. Further, flows i n t h e channels s tudied by t h i s i nves t iga to r were subcritical while flows on a l l u v i a l fans a r e general ly believed t o be cr i t ical o r s u p e r c r i t i c a l .

I n Equation (3.3.1) , t h e parameter AR2 l 3 is known as t h e sec t ion f a c t o r , and f o r a channel of spec i f i ed geometry where A R 2 I 3 always increases with increasing depthsof flow, each f l o w r a t e o rd i scha rge hasacorrespondinguniquedepthof f l o w a t whichuniform flowoccurs.

Examination of Equation (3 .3 .1 ) demonstrates t h a t f o r a uniform flow the flow r a t e i s a function of 1) t h e geometric shape of t h e channel, 2 ) a boundary r e s i s t ance c o e f f i c i e n t such a s Manning's n, 3 ) t h e longi tudinal s lope of t h e channel, and 4 ) t h e depth of flow o r

Q = f ( r , n , s ,y , , ) (3 .3 .5)

where I' = shape f a c t o r and Y,, = normal depth of flow. I f four of t h e f i v e va r i ab le s i n Equation (3.3.5) a r e known, then t h e value of t h e f i f t h va r i ab le can be estimated. Although a d e t a i l e d discussion of t h e computation of uniform flow is beyond t h e scope of t h i s book, t h e i n t e r e s t e d reader is re fe r r ed t o French (1985) f o r a complete discussion of t h i s topic .

I f Q , n, y,, a n d t h e channelgeometry a r e s p e c i f i e d , thenEquation ( 3 . 3 . 1 ) can be solved e x p l i c i t l y f o r t h e s lope of the channel which a l lows the f lowtooccur a t anormal depth. Bydef in i t i on , t h i s slope wouldbethenormal slope. I f t h e s l o p e o f t h e c h a n n e l i s v a r i e d w h i l e Q and n are held constant , then it is possible t o determine a slope value s u c h t h a t normal f l o w w i l l o c c u r w i t h F = l ; t h a t i s , normal depth w i l l a l s o be c r i t i c a l depth. T h i s slopewould betermed t h e l imi t ing c r i t i c a l slope. Slopes g r e a t e r t h a n t h e l i m i t i n g c r i t i c a l slope a r e termed s t e e p s lopes and sus t a in s u p e r c r i t i c a l flow.

3 . 4 ALLUVIAL CHANNEL STABILITY Before considering t h e processes a f f e c t i n g channel s t a b i l i t y

and sediment t r anspor t i n an a l l u v i a l channel e x p l i c i t l y , l e t us consider t h e t r a c t i v e force method of designing unlined channels. Scour o r erosion on t h e perimeter of a channel occurs when the particleswhichcomposethe channel perimeter a r e subjected t o forces

91

which are of s u f f i c i e n t magnitude t o cause movement. The p a r t i c l e s r e s t i n g o n t h e b o t t o m o f t h e channel a r e sub jec t t o o n l y flowgenerated fo rces while t h e material on t h e s loping s i d e s of t h e channel is subjected t o both flow generated forces and a g r a v i t a t i o n a l force which acts t o r o l l t h e p a r t i c l e s down the s loping channel s ide.

I n uniform flow, it can be e a s i l y shown; see f o r example, French (1985), t h a t t h e t r a c t i v e force on p a r t i c l e s due t o flow can be approximated a s

F, = YALS (3.4.1)

where F, = f l o w g e n e r a t e d t r a c t i v e force, Y = f l u i d s p e c i f i c weight, A = flow a rea , L = longi tudinal length considered, andS = long i tud ina l s lope of t h e channel. I f Equation (3.4.1) is accepted, then t h e u n i t t r a c t i v e force is

YALS T o = - - - YRS

PL (3.4.2)

where r 0 = average value of the t r a c t i v e force ( t h i s is ac tua l ly a stress r a t h e r than a force) per u n i t of wetted a rea and P =wet t ed perimeter. I n wide channels, yw I R, and Equation (3.4.2) becomes

T o = vy,s (3.4.3)

A t t h i s po in t , it s h o u l d b e n o t e d t h a t inchannelsoftrapezoidalcross sec t ion t h e maximum t r a c t i v e force on t h e bed has been found t o be approximately yy,S and on t h e sides 0 . 7 6 ~ ~ ~ s .

When p a r t i c l e s on t h e perimeter of t h e channel a r e i n a s t a t e of impending motion, t h e forces ac t ing t o cause t h e motion a r e i n equilibrium with t h e forces opposing motion. In t h e case of p a r t i c l e s on t h e bottom of t h e channel, the force causing motion is AerL where r L = u n i t t r a c t i v e force on a l e v e l surface and A, =

e f f e c t i v e a rea on which r L operates. The force r e s i s t i n g motion is t h e g r a v i t a t i o n a l forceorW,tanawhereW, =submergedparticleweight

and a = t h e angle of repose of t h e p a r t i c l e . Then, when motion is i n c i p i e n t

AerL = W,tana

o r

( 3 . 4 . 4 )

92

ws T~ = - tana

* e

On the sloping sides

both a flow generated

( 3 . 4 . 5 )

of the channel, particles are subject to

tractive force T ~ A , and a downslope

gravitational component W,sinr where 7s = tractive force on side

slopes and r = side slope angle. The resultant forceactingtocause

motion is

(w,tanr)' + ( A , T , ) ' i The force resisting motion is W,cosrtana, and setting these forces

equal for the case of incipient motion

W,(cosr) (tana) = 4 (W,tanr) ' + ( A e 7 , )

or

( 3 . 4 . 6 )

tan2r 1 tan'a z S = - (cosr) (tana) 1 - -

Equations (3.4.5) and ( 3 . 4 . 7 ) are usually combined to form the

( 3 . 4 . 7 ) WE

Ae

tractive force ratio K, or

7 L sin'a

The tractive force

angle and the angle of

( 3 . 4 . 8 )

ratio is a function of both the side slope

repose of the material which composes the

perimeter. Laboratory data are available for bothcohesive andnon-

cohesive materials, Lane (1955) or French (1985).

Fromtheconceptof t rac t ive forcechanneldesign, theconcept of a stable hydraulic section is derived. In the design of a channel

section, usually trapezoidal in shape, the tractive force is equal to

its permissablevalue ononly aportion ofthe perimeter- usuallythe

sides. It seems rational toattempt todefine achannel sectionsuch

that incipient particle motion prevails at all points on the channel

perimeter. Glover and Florey (1951) did this for a channel carrying

clear water through non-cohesive materials. The specific

93

F I G . 3.4.,1 channel i n non-cohesive materials.

Schematic, d e f i n i t i o n of va r i ab le s f o r a s t a b l e h y d r a u l i c

assumptions made by these inves t iga to r s i n t h e i r ana lys i s were:

1.

2 .

3.

4 .

5.

Boundaryparticles a r e h e l d i n p l a c e b y t h e submergedweight component of t h e p a r t i c l e s ac t ing i n a d i r e c t i o n normal t o t h e bed of t h e channel.

A t andabovethewater surface, t h e s i d e s lopeof thechannel is a t the angle of repose of t h e material composing the channel perimeter.

A t t h e c e n t e r l i n e of t h e channel s ec t ion , t h e channel s ide s lope is zero, and t h e t r a c t i v e force generated by t h e flow is alone s u f f i c i e n t t o maintain a s t a t e of i nc ip i en t p a r t i c l e motion.

Atpointsbetweenthecenterlineofthechanneland i t s edge, p a r t i c l e s a r e i n a s t a t e of i n c i p i e n t motion.

The t r a c t i v e force ac t ing on an a rea of t h e channel is equal t o t h e component of t h e weight of the water above t h e area a c t i n g i n t h e d i r e c t i o n o f flow: t h a t is, t h e r e is n o l a t e r a l t r a n s f e r of t r a c t i v e force.

Giventheaboveassumptions a n d t h e schematicdefini t ion o f v a r i a b l e s i n Fig. 3 . 4 . 1 , it can be shownthat thegeometr ic shapeof thechannel of s t a b l e hydraul ic s ec t ion is given by

94

y = yw cos [ '1 the flow area by

2TYN A = -

I(

and the wetted perimeter by

2YN p = - E(sin a )

sin a

(3.4.9)

(3.4.10)

(3.4.11)

where the symbolism E(sin a) designates a complete elliptic integral

of the second kind. The discharge of this stable channel is then

estimated directly from the Manning equation or

8 / 3

2.98 yN (cOS , ) ' I 3 & n(tan a ) [E(sin a ) ] ' 1 3

Q - (3.4.12)

It is worth noting that the tractive force methodology

represents onlyone techniquewhich canbe usedto designor analyzea

channel in non-cohesive alluvial materials. Other methodologies

have equal validity and in some cases have particular advantages.

For example, there isthethresholdofmovementhypothesisof Shields;

see for example, Henderson (1966) or French (1985). This

hypothesis is stated in terms of two dimensionless variables

u*d R, = -

V

and

(3.4.13)

(3.4.14)

where R, = a Reynolds number based on the shear velocity of the flow,

the size of the particles composing the perimeter, and the kinematic

viscosity of the fluid;

95

I- U* I: 4 gRS (3.4.15)

=shearvelocity, v = fluid kinematicviscosity; S, = specificgravity

ofthe soil particles composingthe channel perimeter (S, = 2.65 inthe

general case) ; and d = diameter of the soil particles composing the

channel perimeter. d is usually taken as the diameter such that 25%

of the particles, measured by weight, are larger. Shields' results

are usually summarized in a graphical form, Fig. 3.4.2. In this

figure, the curve denotes and defines the threshold of particle

movement.

SHIELD'S DIAGRAM

Particle Movement -i No Particle Movement

FIG. 3.4.2 number.

Threshold of movement as a function of particle Reynolds

A second alternative to the tractive force methodology is the

regime theory. Although this theory has beenvigorously attackedby

modern engineers because of its lack of a rational and vigorous

derivation, it is essentially the technique recommendedby theU.S.

Federal Emergency Management Agency (FEMA) for identifying flood

hazard zones on alluvial fans; see for example, Anon (1983), Dawdy

(1979) , and Anon (1985). The regime theory has also been termed the

Indian approach because the original field studies performed in

supportofthistheoryweredone inwhat isnow IndiaandPakistan. In

the modern hydrologic and geologic literature, the regime theory is

often termed the theory of hydraulic geometry because it is used to

96

est imate t h e channel widthand depthand t h e v e l o c i t y of flow. Given t h a t FEMA has adapted t h e regime theory ( o r theory of hydraulic geometry) a s its preferred technique of channel ana lys i s f o r f lood flows on a l l u v i a l fans , the apparent ease with which r e s u l t s can be obtained using t h i s theory, and the w i d e d iscussion t h i s theory has received i n t h e hydrologic, geologic, and hydraul ic engineering l i t e r a t u r e , it isworthwhile t o consider t h e o r i g i n , l i m i t a t i o n s , and r e s u l t s avai lable .

As notedby Graf (1971) , inanopen-channelwithr igidboundaries and uniform flow, t h e r e is only one degree of freedom - t h e depth of flow which can be estimated fromtheManning equation. Uniform flow i n an open-channel w i t h non-cohesive and moveable boundaries has a minimum of t h r e e degrees of freedom - width, depth, and longi tudinal slope. The t h r e e degrees of freedomderive f romthe h y p o t h e s i s t h a t i n a channel with erodible boundaries a depth of flow w i l l be establ ished which depends on the longi tudinal s lope of t h e channel, t h e width of t h e channel, and t h e discharge. Blench (1961)

introduced a fourth degree of freedomby a s s e r t i n g t h a t a r t i f i c i a l l y s t r a i g h t channel s ec t ions are unstablebecause e ros ionof t h e channel banks w i l l eventually r e s u l t i n channel meanders.

The regime theory w a s apparently f i r s t enunciated by Kennedy i n 1895. Since t h a t t i m e , a rather l a r g e body of da t a and information regarding t h i s theory has and continues t o evolve even i n the face of vigorous a t t a c k s on t h e v a l i d i t y of t h e theory: see f o r example, EinsteinandChien (1956). Theterminologyofhydraulicgeometrywas

apparently f i r s t i n t r o d u c e d b y Leopoldand Maddock (1953) t o d e s c r i b e t h e observed v a r i a t i o n s of width, ve loc i ty , and depth of flow a s a function of flow r a t e , Figs. 3 .4 .3 . Because average da ta w e r e used, Figs. 3 . 4 . 3 is somewhat misleading regarding t h e v a l i d i t y of t h e theory and f o r t h i s reason s i m i l a r d a t a a r e p l o t t e d i n F i g s . 3 . 4 . 3 f o r comparison with t h e data i n Figs. 3 . 4 . 4 , P h i l l i p s and Harl in ( 1 9 8 4 ) .

With reference t o Figs. 3.4.3 and 3 .4 .4 , i n their most general form, t h e regime o r hydraulic geometry equations f o r channel width, depth, and ve loc i ty of flow are

T = C,Qb

Y = C 2 Q f

and

(3 .4 .16)

(3.4.17)

- u = C,Qm ( 3 . 4 . 1 8 )

97

TOP WIDTH, T b t e r s l

10 loo 10 1

non RATE. 0 [cubic metere per second)

98

VELOCITY OF ROn, u haters per eecond) 10 t

H1

ROW UTE. Q (cubic meters per second)

(C) FIGS. 3.4.3 Hydraulic geometry forthe RioPuerco at Rio Puerco, New Mexico, average data from Leopold and Maddock (1953).

whereC1, C,, C,,b, f, andm areundetermined empiricalcoefficients.

It is generally assumed that Equations (3.4.16) - (3.4.18) must

satisfy the continuity equation or if the channel cross section is

appproximately rectangular

~ y i = C,Q~C,Q~C,Q' (3.4.19)

If Equation (3.4.19) is to be satisfied, then the undetermined

exponents must satisfy

b + f + m = l (3.4.20)

and the coefficients

c,c,c, = 1 (3.4.21)

In many cases, Equations (3.4.20) and (3.4.21) are not satisfied.

Among the reasons for this deviation are 1) data error, 2) the method

used to fit the regression line to the data, 3) validity of the power

function relationship, and 4) the absence of physical adjustment of

the channel to some discharges, Rhodes (1977).

In considering the applicability of the regime or hydraulic

geometrytheorytohydraul ic processeson alluvial fans, thecriteria for their use noted by Blench (1957) should be considered. These

criteria are:

99

0

I

0.01 0.1

FLOW RATE. 0 (cubic metere per eecond)

DEPTH OF FLOW, y betere)

0.01 ' 0.01 0.1 1

FLOW R A E , 0 (cubic meters per second)

(b)

100

V M C I l Y OF ROW. u (#tors par recondl

1 ° i

0 O o=

0.1 0.01 0.1

0. 0.01 0.1

ROW RATE. B (cubic w t e r r per rscondl

FIGS. 3 . p . 4 , Hydraulicgeometr OftheHuerfanoRiver, Colorado, data from Phillips and Harlin (198i).

1.

2.

3 .

4 .

5.

6.

The channel is straight.

The channel sides behave as if they were hydraulically

smooth. Note, boundary surfaces are classified as being

either hydraulically smooth or rough by comparing the

laminar sublayer thickness and the roughness height: see

for example, French (1985) or Schlichting (1968). If the

boundary roughness is such that theroughness elements are

covered by the laminar sublayer, then by definition the

boundary is hydraulically smooth.

The bed or bottom width of the channel must be greater than

three times the depth of flow.

The side slopes of the channel must approximate those for

cohesive materials in nature.

The water discharge of the channel is steady.

The sediment discharge of the channel is steady.

101

7.

8 .

9.

10.

Channels that move a non-cohesive load of sediment along

the bed in dune formation.

The Froudenumber ofthe flowmust be less thanone; that is

the flow is subcritical (see for example Section 2 of this

chapter). Note, Chang (1980) mentioned that canal

designers using the regime theory have often used a Froude

number criterion for establishing the range of

applicability of regime theory designs. According to

Chang (1980), the Froude number of the flow should be kept

atavalue of approximately 0.2 and neverallowed toexceed

a value of 0.3.

Thesizeofmaterial composingthe channelboundary mustbe

small relative to the depth of flow.

The channel flow rate and the rate of sediment transport

must be equilibrium; that is, a stable hydraulic section

has been achieved.

Althoughmany investigatorshave assertedthat the coefficients

C,, C,, C, and the exponents b, f, and m are universal constants,

sufficient evidence now existsto demonstrate that this assertion is

without merit. Some ofthe results regardingthese coefficientsand

exponents are summarized in Table 3.4.1. Studies of the regime or

hydraulicgeometryequationshaveprimarilyexaminedthevariationof

the coefficients either at-a-stationwith time or with longitudinal

channel distance. The results in Table 3.4.ldemonstrate that there

is a significant variation in coefficient values with geographical

area, climate, time, and distance along the channel.

At this point, it is appropriate to note that when dealing

empiricalorsemi-empiricalequationsthatthesystemofunitsusedto

derive the exponents and coefficients associated with these are

equations is an important consideration. For example, consider the

situation in which it is asserted that

T = C,Qb (3.4.22)

where the English system of units has been used to estimate values of

C, and b. Further assume that in Equation (3.4.22)

102

TABLE 3.4.1 Summary of regime/hydraulic geometry coefficients and exponents from various literature sources

Leopold 1 I I IData obtained from U.S. Geological and 1 I I lsurvey gaging stations on peren-

Maddock I I I lnial rivers. (1953) I I I I

1 b=0.26 1 f=0.40 I m=0.34 [at-a-station (primarily for arid I I I I and semi/arid regions) I I I I I b=0.50 I f=0.40 1 m=O.10 Idownstream (rivers throughout the I I I IUnited States) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Carlston I I I IData from Leopold and Maddock (1969) I I I

I I I I I I I

I I I I

I I I

I I I I

l(1953). Regression lines fitted Iby principle of least squares.

I b-0.461 I f-0.383 I m=0.155 [downstream (10 U.S. river basins)

I b=0.499 I f=0.320 I m=0.180 [downstream (Yellowstone River I I I IBasin: arid and semi-arid)

I C1=8.36 I C2=0.27 1 C3=0.45 IC values in SI units I C,=4.63 I C2=0.28 1 c3=o.78 IC values in English units ________________________________________-----------------------------------

Dawdy I b=0.40 I fz0.40 I (1979) I I 1

I c1=12. I c2=o.09 I I I I I C,=9.5 I C2=0.07 I

I I Ic values in SI units

IC values in English units

IData from 11 rivers in England land Wales. Equations apply to lrivers with sediment loads so lsmall as to have little effect on lchannel shape. Discharges used

Nixon I I I (1959) I I I

I I I I I I I I I I b=0.500 I f=0.333 I m=0.167 Irepresent bankfull discharges. I I I I I Cl=l.65 I C2=o.5451 c3=1.1121c values in SI units

I I I I Cl=0.9111 C2=0.5461 C3=2.01 IC values in English units ........................................................................... Langbein I I I IRivers construct their own geo- (1964) I I I Imetries. Profiles of rivers in

I I I lhumid climates tend toward equal I I I [power per unit area and per unit I I I [length (minimum work).

I b=0.23 I f=0.42 I m=O.35 lat-a-station

I b-0.53 I f=0.37 I m=0.10 (downstream

I I I I

I I I I ........................................................................... Ee I I I IAt-a-station data from 7 stations (1970) I I I Ion Sungei Kinta, Perak, Western

I I I IMalaysia. Downstream data from 9 I I I [stations. I I I I I b=0.09 I f=0.61 I m=0.31 lat-a-station I I I I I b=0.29 I f=0.44 I m=0.28 Idownstream ...........................................................................

103

Knighton I (1974) I and I

I 10.01<b1 I 0.33 I - I b=0.11

I I h= I

0.61 0.54 0.46

/Data from the Bolin and Dean River /Great Britain. Five reaches of 1500 m were chosen to represent a lwide range of channel sizes and Idischarge conditions. Within each [reach, 3 measurement stations were [chosen. The drainage area was )primarily covered by varied jglacial deposits. Bankfull discharges ranged from 1 m3/s (up- ;stream) to 10 m3/s (downstream)

I I 1.261f~ 10.24~m< lat-a-station 0.63 I 0.71 I

~ I - I f=O.40 I m=O.48 1

I I I I

0.311 0 081 2% Downstream variation at

0 161 0.38150% charge is equaled or f= { 0:23Im= 1 0:23)15% per cent of time dis-

I I exceeded ________________________________________----------------------------------- IAnalysis of at-a-station geometry lof 139 streams and the downstream [geometry of 72 streams represent- ling several different environments I (primarily perrennial streams with [some ephemeral streams)

Park I I I I (1977) I I I I I

I I I I I I I I I I

O<b< 10.06<f< /0.07<m< lat-a-station 0.59 I 0.73 I 0.71 I

1 I I 0.035b~ 10.091fs I-0.51<m< Idownstream 0.89 I 0.70 I 0.75 I ...........................................................................

Phillips 1 I I [Analysis of the Huerfano River Iin a subalpine meadow in southern and l I I

Harlin 1 I I IColorado. 20 at-a-station obser- (1984) I I I /vations under steady flow con-

I I I Iditions. Note, results in the I I I loriginal article are in error

1b=0.289

I C1=4. 5 8 I

I I f=0.0495 lm=0.580 1

I I c2=o.132 1c3=1.37 I c values in SI units

Williams (1978)

I I I I I I I I I I

IChanges in variables are such that lthe total effect of action, work, lor adjustment is a minimum. All lvariables strive to resist any Iimposed change with the net result lbeing that all of them change [equally. In checking this assump- [tion only streams with loose par- lticles on the bed were considered. I

i O<b< io.io<f< io.031ms iat-a-station 1 0 . 8 2 I 0.78 I 0.81 I . ..........................................................................

[Basic principle - minimum rate of lenergy dissipation which states lthat a system is in an equilib- lrium condition when its rate of lenergy dissipation is at its lminimum value.

Y a w , I I I Song, and I I I Woldenbergl I I

I (1981) I I I I I

I I I I I I I lb=0.41 lf=0.41 Im=O.l8 I

104

c, = 1.00

and b has a value of a. I f T has u n i t s of [ f t ] and Q has u n i t s of [f t3/s] , then C , must have t h e following u n i t s t o preserve t h e dimensional homogeneity of t h e equation

T [ f t ] [ft-seca] - c, = - = -

o r

C , = [ f t ' 1-3a)-seca~

The appropriate conversion f o r C , given i n English u n i t s t o C , i n S I

u n i t s would be

Qa [ f t 3 / s ] " ft3U

1 ( 0 . 3 0 4 8 )

1f t1-3a C , [ S I ] = C, [English]

Thus, i n c o n s i d e r i n g c o e f f i c i e n t s involvedin t h e regime o rhydrau l i c geometry t h e o r i e s it is necessary t o transform them from t h e English systen 'of u n i t s t o t h e S I system t h a t t h e value of t h e exponents be known. I n Equation ( 3 . 4 . 2 2 ) , C, and b are usual ly determined from a l e a s t squares regression ana lys i s o f t h e equation obtained by taking thenaturallogarithmsofbothsidesoftheequation, Carlston (1969), o r

log(T) = lOg(C,) + b lOg(Q)

where log(C,) is t h e y a x i s i n t e r c e p t of the l i n e and b is the slope. Therefore, b is independent of the system of u n i t s used and no conversion is required. I n t h e pas t , many inves t iga to r s have been remiss i n specifying t h e u n i t s associated with t h e c o e f f i c i e n t s C , ,

C , , and C, and the reader is cautioned regarding t h i s p o t e n t i a l problem.

Theprimaryadvantageoftheregime orhydrau l i c geometrytheory is t h a t i t p r o v i d e s a v e r y s i m p l e summaryofthecomplicatedandpoorly understood r e l a t ionsh ips t h a t e x i s t among t h e channel and flow c h a r a c t e r i s t i c s i n a l luv ia l channe l s . However, t h i s t h e o r y a l s o h a s a number of inadequacies and disadvantages. F i r s t , as noted previously i n t h i s s ec t ion , t hese t h e o r i e s are empirical and have no t h e o r e t i c a l j u s t i f i c a t i o n .

Second, t h e v a l i d i t y o f simplepower f u n c t i o n s a s d e s c r i p t o r s o f channel c h a r a c t e r i s t i c s during periods of varyingdischarge hasbeen

105

questioned by a number of investigators: for example, Wolman (1955)

and Richards (1973, 1976). Richards (1973) noted among other

objections that there are discontinuities in the depth-discharge

relationship following the transition fromthe lower to upper flow

\ O

0 / 1. b 1, 0,8 0.6 0.4 0.2 0

f O 082 0,4 0,6 0.8 1.0

F I G . 3.4.5 Chan es of at-a-stream hydraulic geometry exponents during a single Flood event, data from Knighton (1975).

regime: see also Dawdy (1961). Richards (1973) hypothesized that

these discontinuities could be the result of non-linear changes in

channelroughnesswiththedepthof f lowandsuggestedthatnon-l inear

power relationships may yield a better description of the system.

Currently, there is not sufficient evidence to substantiate the

suggested modification.

Third, Rhodes (1977) studied 315 sets of hydraulic geometry

equations with the aid of a trilateral diagram: see for example Fig.

3.4.5. Given the scatter of the m, f , and b values in his figure, he concluded that the average values of at-a-station hydraulicgeometry

relationships may have but little meaning and may give erroneous

predictions of actual channel responses to changing discharge.

Fourth, there i sev idencetosuggest thatduringevensmal l flood

events significant changes in channel morphology may occur which

cannot be predicted or explained by these hypotheses. For example,

106

Knighton (1975) mentioned that during one study of at-a-station

hydraulic geometry a flood event with a return period of 2.5 years

significantly modified the hydraulic exponents at one station, Fig.

3.4.5. Knighton (1975) concludedthatat-a-stationrelations canbe

drastically changed by a single flow event if the channel cross

section is in an unstable condition.

Fifth, these theories fail to recognizethe important influence

ofthesediment loadonchannel width, depth, andcapacity, Simonsand

Albertson (1960) . Sixth, regime and hydraulic geometry theory was developed to

describe steady flow, steady sediment transport, and equilibrium

channel conditions. The extension of these theoriesto the analysis

of highly transient condition in an alluvial channel may be both

unrealistic and improper.

3.5 DEBRIS F M W MECHANICS

The terminology debris flow has been imprecisely used to

describe the movement of a wide variety of soil and water mixtures.

For example, there isnot aclear andprecise definitionaldifference

among the movement of soil andwatermixturesvariouslytermeddebris

flows, mud flows, creep, and landslides. For this reason, the

foregoing terms may, and probably do, convey different images to

geologists and geomorphologists than they do to engineers. To some

degree, the lack of precise definitions results from the fact that

mass movements of rock, earth, and water can vary greatly in speed,

water content, characteristicsofthesolidmaterialtransported, and

the distribution of the solid materials within the flow. Some

authors have attempted to differentiate between debris and mud flows

on the basis of the basis of particle size, for example Schuster and

Jkrizek (1978). In contrast to definitions based on the size of

materials transported, the definition of debris flows proposed by

Takahashi (1980) is to be preferred from the viewpoint of fluid

mechanics. This definition states (in paraphrase):

Adebris f l o w i s a m i x t u r e o f a l l s i z e s o f s e d i m e n t . Boulders

accumulate andtumble at the front ofthe debriswave and form

a lobe, behind which follows the finer grained more fluidic

debris, Takahashi (1980, p. 381).

In comparison with this definition, Sharp and Nobles (1953, pp. 551-

552) offeredthe followingdescriptionofa l lmudflowllthatoccurredin

107

1941 at Wrightwood, California:

"A bouldery embankment formed at the front of more viscous

surges, andthebouldersthereinrolled, twisted, andshifted

about but for themost partdid notappear tobe rolledunder.

Instead, theywerepushedalongbythe finermore fluiddebris

impounded behind the bouldery dam and swept along by the mud

leaking through it.

The similarity between the Takahashi definition and the Sharp and

Nobles description is unmistakable. The advantage of the Takahashi

definition is that it focuses on the fluid and flow characteristics

that distinguish debris flows from other fluid flows. The density

andviscosity of debris flows are important fluid characteristics by

whichdebris flowscanbedistinguished fromother typesof flowssuch

asl lpurewaterlgorwatertransportingsediment. Tobeclassifiedasa

debris flow, a flow should have a density approximatelytwice that of

normal water (at 20 degrees Centigrade, the density ofwater is998.2

kg/m3) and a viscosity significantly larger than that of water [at 20

degrees Centigrade, the absolute or dynamic viscosity of water is

1.005 x kg/(m-s)]. Because of their relatively large

viscosities, debris flows are generally assumed to be laminar flows,

and this assumed characteristic accounts for the fact that separate

layers of the flow do not mix except at the leading edge of the flow.

Note, turbulent flow situations are the most common in hydraulic

engineering practice, and in such flows, the flow paths are highly

irregular; that is, there is significant mixing between the layers,

and flow losses vary as the square of the velocity. In laminar flow,

the fluid particles move along smooth flow paths with each layer

gliding smoothly over the adjacent layers, and flow losses vary

directly with the velocity. Laminar and turbulent Newtonian flows

are usually differentiated between on the basis of the ratio of the inertial to the viscous forces in the flow; a ratio commonly known as

the Reynolds number, R, which is by definition

UL p R = -

U (3.5.1)

where u = average velocity of flow, L = a characteristic length which

in open-channel flow is usually taken as the hydraulic radius R, p =

density ofthe fluid flowing, and u =dynamic orabsolute viscosityof

108

I

(1981) I I

Pierson l500-300C

I

(1980) I I I I 1 I

(1923) I I I I I I I I I I

Seger- I ---- stroem I (1950) I

Takahashil----

Pack I - - - -

Black- I ---- welder 1 (1928) I

I I I

Sharp and1 ---- Nobles I (1953) I

I I

0.3

0.01

2.3

_ _ _ _

_ _ _ _

_ _ _ I I 1 I I I I I I 1 I I

_ _ _

---

I I I _ _ _ _ I I I

1.0 (measure

at surface

0.2 (measure

at surface

5 . 0 (measure

at surface

several tens of m/s to several cm/s

:igantic lasses o ietero- leneous iaterial ;hot fro1 barrow :anyons nto ope1 alleys

0.6

0.2

----

1.2-3.0 (average

I I velocity I I I 1

1730 (bulk density)

1740 (bulk density)

:e moto oil

.urry

,arent tonian cosity

- lo5

--

--

_-

I I 2x104 - I 6X1O4

5-7 I 4 0 (bylTurbulent muddy Iweight)lstreamflow be- I [tween surges

5-7 1 4 0 (bylviscous, laminar 1veight)ldebris flow, I I slurry I I I I

I I I

I I I I I I I I

I I I I

5-7 I 2 2 /Higher velocity lviscous debris [flow with re- lnewed turbulence I IFlowage of a [mixture of all (sediment sizes

_ _ _ I ----

I 4-8 I

I I I I I I I I I I

4 1

I ---- JFollowing the \first impulse /were tremendous I quantities of lrock waste rang- ling in size from Jsmall to very (large boulders I I I I ---

I I I I I I

. 8 - 1 --- I

. 5 I I I I I I

I I I I I I boulders I I

-6 I --- JFlood transport- led large quanti- lties of washed lgravel, sand, Iclay, and small

6 I 25-30 /Highly fluidic, 1 (by Islimy, cement- (weight [like mud con-

ltaining abundant I stones

I 1 I I

Reynolds numbers above 12,500 are consideredto beturbulent. Open-

channel flows with Reynoldsnumbers between500 and12,500 aretermed

transitional flows. The critical Reynolds number is by definition

the Reynolds number at which a laminar flow becomes a turbulent flow.

In general, the Ilcritical Reynolds numberww is actually a range of

Reynolds numbers as indicated above. Finally, the assertion that

debris flows are laminar has also been used to account for the

observation that boulders apparently ride on the top of debris flows

109

for long distances.

Rnte o f Angular Deformation

FIG. 3.5.1 Schematic of shear stress as a fupction of the rate of angular deformation for various types of fluids.

Table 3.5.1 summarizes some of the historic field and laboratory

data available regarding debris flows. With regard to these data,

the following observations can be made. First, the Reynoldsnumbers

ofthese flows, Column ( Z ) , arelow, a n d t h i s t e n d s t o s u b s t a n t i a t e t h e

assumption that debris flows are laminar. Second, the velocity of

these flows, Column (4) , are reasonably large. Third, both the

density, Column (5) , and the viscosity, Column (6) , of these flows is large relative to those of pure water. Fourth, the slopes on which

debris flows occur, Column ( 7 ) , are relatively large. Fifth, the

observed water content of these flows is relatively small.

3.5.1 Fluid Types

Of all the fluid properties, from the viewpoint of fluid

mechanics, viscosity is the one which deserves the most serious

consideration. By definition, viscosity is the fluid propertywhich

characterizes the resistance of the fluid to shear: and for this

reason, fluids maybe classifiedbythe functional relationship that

exists between the shear stress applied and the rate of angular

deformation of the fluid. The rate of angular deformation of the

fluid is usually measured by the velocity gradient within the fluid.

110

Four types of f l u i d s a r e and may i n t h e f u t u r e be important t o t h e discussion of debris flow mechanics.

F i r s t , Newtonian f l u i d s , such as water, exhibit a l i n e a r r e l a t ionsh ip between the shear stress applied, T , and the r a t e . o f angulardeformationwhich is measuredby t h e v e l o c i t y gradientdu/dy. In t h i s type of f l u i d ,

T = {z] ( 3 . 5 . 2 )

where u = absolute o r dynamic v i s c o s i t y of t h e f l u i d , Fig. 3.5.1. Second, a Bingham p l a s t i c is a f l u i d i n which t h e shear stress

applied must exceed a y i e l d stress value before a shear r a t e can be defined o r flow occurs.

A f t e r t h e y i e l d stress, rY, is exceeded, t h e r e is a l i n e a r r e l a t ionsh ip between the app l i edshea r s t r e s s a n d t h e r a t e o fangu la r shear. Quan t i t a t ive ly , the r e l a t i o n s h i p between t h e applied shear stress and t h e r a t e of angular deformation f o r a Bingham p l a s t i c is

(3 .5 .3)

where uB = Bingham p l a s t i c v i scos i ty , Fig. 3.5.1. Third, apseudo-plast ic f l u i d h a s n e i t h e r a y i e l d s t r e s s n o r d o e s

it exh ib i t a l i n e a r r e l a t i o n s h i p betweenthe shear stress appl iedand t h e r a t e of angular deformation of t h e f l u i d . Rather, a pseudo- p l a s t i c f l u i d is character ized b y a progressivelydecreasing s lopeof t h e applied shear s t r e s s v e r s u s t h e r a t e of angular deformation, Fig. 3.5.1.

Fourth, a d i l a t a n t f l u i d a l s o h a s n e i t h e r a y i e l d s t r e s s nordoes it exh ib i t a l i n e a r r e l a t i o n s h i p betweenthe app l i edshea r stress and t h e r a t e of angular deformation of t h e f l u i d . I n con t r a s t t o a pseudo-plastic f l u i d , a d i l a t a n t f l u i d is character ized by a

progressively increasing s lope of t h e applied shear stress v e r s u s t h e rate of angular deformation, Fig. 3.5.1.

Mathematical formulations r e l a t i n g t h e shear stress t o the r a t e of angular deformation of t h e f l u i d s imilar t o Equations ( 3 . 5 . 2 ) o r (3 .5 .3) are not ava i l ab le f o r pseudo-plastic and d i l a t a n t f l u i d s due t o t h e f a c t t h a t du/dy is a function of t h e applied shear stress. A

number of empirical r e l a t ionsh ips between T and du/dy have been proposed f o r t hese types of f l u i d s ; and among t h e s implest is t h a t

111

c i t e d by Hughes and Brighton (1967) o r

7 = ( 3 . 5 . 4 )

where k = a constant r e l a t e d t o t h e consistency of t h e f l u i d and n = a constant wh ich i s ameasure ofhow the f l u i d dev ia t e s from aNewtonian f l u i d w i t h n < 1 f o r a pseudo-plastic f l u i d and n > 1 f o r a d i l a t a n t f l u id . Wi th the empirical r e l a t ionsh ip def inedby Equation ( 3 . 5 . 4 ) ,

t heappa ren tv i scos i ty , ua, o f t h e pseudo-plasticand d i l a t a n t f l u i d s is defined by

(3 .5 .5 )

A t t h i s po in t , it is r e l e v a n t t o n o t e t h a t a c h o i c e o f a f l u i d t y p e (o r model) f o r a debris flow is not an i n s i g n i f i c a n t decision. For example, i n t h e foregoing mater ia l laminar and turbulent flows have been d i f f e r e n t i a t e d between on t h e b a s i s of a c r i t i c a l Reynolds number. The concept of a c r i t i c a l Reynolds number der ives from a consideration o f t h e p a r t i a l d i f f e r e n t i a l equationswhich governthe flowof Newtonianfluids. I n t h e c a s e o f Binghamplastic f l u i d s , flow s t a b i l i t y ; and hence t h e c l a s s i f i c a t i o n of a flow as laminar o r turbulent , has been shown t o depend on t h e Binghamnumber r a t h e r t h a n the Reynolds number o r

(3 .5 .6 ) U B U

where u = average ve loc i ty of flow, y = depth of flow, and B = Bingham number; see f o r example, Enos (1977) o r Hampton ( 1 9 7 2 ) . Hedstrom ( 1 9 5 2 ) furtherdemonstratedthatinthecaseof Binghamfluids flowing i n pipes t h a t t h e c r i t i c a l Reynolds number is only a function of t he Bingham number, Fig. 3.5.2. Note, i n pipe flow, t h e c r i t i c a l Reynolds number is usua l ly t aken t o b e approximately2,OOO. Hampton (1972) showedthatthecurvederivedbyHedstromrelatingthecritica1

Reynolds number and t h e Bingham number was i n general agreement with the experimental da t a of Babbitt and C a l d w e l l ( 1 9 4 0 ) and Gregory ( 1 9 2 7 ) regarding t h e flow of c l ay s l u r r i e s i n pipes , Table 3 .5 .2 and Fig. 3 .5 .2 . With r e g a r d t o t h e d a t a inTab le 3 .5 .2 a n d p l o t t e d i n F i g . 3 . 5 . 2 , t h e following observations can made. F i r s t , t h e Babbitt and Caldwell ( 1 9 4 0 ) and Gregory (1927) da t a cons i s t en t ly p l o t above the

112

70.2

73 .5

75 .0

76 .7

79.7

83 .9

- - - - - - - -

42.9 1 I I I

I I I I

21.0 I I I I I

I I I

0 . 9 1 I I I I I

0.39 I I I I

28.6 I

13 .8 1

2.23

2.23

1.63

1 .49

1 .19

0.89

1 ,210 I 0.0254 I 0.0508 1 0.0762

1,200 1 0.0127 I 0.0254 I 0 .0508 I 0.0762

I

I 1 ,180 I 0.0127

I 0.0254 I 0.0508 I 0.0762

1 ,160 I 0 .0254 1 0.0508 I 0.0762

1,150 I 0.0127 1 0 .0254 I 0.0508 1 0.0762

1,120 I 0.0127 I 0.0254 I 0.0508 I 0.0762

I

I

I

5.34 I 4.89 1 4.73 I

I 4 .33 I

4.12 1 4 . 2 1 I

I

3 .94 1

4.48 I

3 .66 I

3.36 I 3 . 5 1 I

7 ,370 I 9 .16 I 13,500 1 20 .0 I 19,600 I 31.0 I

2,960 I 3.76 1 6,140 I 7 .25 I

12,400 1 15.8 I 17 ,300 I 2 3 . 1 1

3,360 I 4 .49 I 7 ,250 I 8 .32 I

12,400 I 1 9 . 5 I 19,400 I 28 .0 I

I I

I I

138,000 248,000 360,000

55,000 114,000 209,000 321,000

46 ,500 100,000 171,000 268,000

I I I 3 .36 1 6,660 I 7 . 0 1 85 ,400 2.75 I 10,900 1 1 7 . 1 I 140,000 2.90 I 17,200 1 24.4 I 221,000

2.35 I 2,880 I 4.14 I 29,800 2 . 4 1 1 5,910 1 8.07 I 61,200 2.32 I 11,400 I 1 6 . 8 1 118,000 2.35 I 17,300 I 24.8 1 17,900

1.65 I 2,640 I 3 .37 1 21,000 1.62 I 5,180 I 6.88 I 41,100 1.55 I 9,920 I 1 4 . 4 I 78,700 1.55 I 14,900 I 21.6 I 118,000

I I I

I I I

____________________----_-___----------- Gregory Data from Hampton (1972)

86.4

81.4

76.7

70.9

0.5271 0.743 I 1 ,170 I 0.0102

0.9581 0.743 I 1,130 I 0 .0102

2.68 I 0.743 I 1 ,175 I 0 .0102

5.60 1 0 .743 I 1,225 I 0.0102

I I I

I I I

I I I

I I I

0.5541 8.910 I 1 3 . 1 I 565,000

0.6711 10,400 I 19.6 1 68,500

1 . 0 9 I 1 7 , 6 0 0 I 33 .8 I 111,000

1.83 1 30,800 I 42 .1 I 187,000

I I I

I I I

I I I

I I I 67.5 1 7 .56 I 0.743 I 1,225 I 0.0102 1 2.14 I 37,100 I 48.6 I 218,000

I I I I I I I I 64.8 I 10.3 I 0.743 I 1,258 1 0.0102 1 2.59 I 44,600 I 54 .6 I 264,000

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ______------------______________________---------------

curve defined by Hedstrom (1952). However, thetwo datasets andthe

curve suggest the same general relationship between the critical

Reynolds number and the Bingham number for clay slurry pipe flow.

Second, although similar data for open-channel Bingham plastic fluid

flows are not available, it can be safely assumed that except for a

scale factor an analogous relationship betweenthe critical Reynolds

number and the Bingham number would exist. In Fig. 3.5.3 critical

Reynolds numbers forNewtonianopen-channel flows andBinghamnumbers

are plotted as a function of the velocity and depth of flow for a

material with a yield stress of r y = 10 N/m2 (0.21 lb/ft2) and a Bingham

fluidviscosityofu, =lkg/m-s (0.02lsl/ft-s). Enos (1977) claimed that these values of r y and u s adequately described the fluid

113

loo. ow

10.000

Turbulent

f ? ! --- BAmm Am

CWwaL DATA

1 10 loo loo0

B I N W MLBER FIG. 3.5.2 Critical Reynolds number as a function of the Bingham number.

VELOCITY OF ROW. ./I

A - wo. - B - 0.001

B - 0.01 - B - 0.10

B - 1.0 ---- B - 10.

B - 100. - - o.ooo1 0.001 0.01 0.1 1 lo

B - 1000. - DEPTH OF R O Y . I

FIG. 3.5.3 Critical Reynolds numbers for Newtonian open-channel flows and Bingham numbers as a function of the velocity and depth of flow for a material with a yield stress of T , = 10 N/m and a Bingham fluid viscosity of uB = 1-kg/m-s.

properties of the material commonly found in debris flows. Third,

Fig. 3.5.2 indicatesthatastheBinghamnumber increasesthecritical

Reynolds number also increases. The implication is that eventhough

a Bingham plastic fluid flow may have a Reynolds number that would

indicate the flow was turbulent, if the fluid was water, Column (9) , Table 3.5.2; the non-Newtonian behavior of the fluid must be

considered. Further, th i sobservat ionsugges t s thatre la t ive lyh igh

energy levels, relative to pure water, are necessary for a Bingham

114

plastic fluid flowtobeturbulent. Fourth, the foregoing discussion

has only considered the question of flow classification from the

viewpoint of clay slurries in pipes and has not considered the effect

of granular materials such as those found in natural debris flows.

However, Bagnold (1956) demonstrated that granularmaterials tendto

make the critical Reynolds number of a flow larger rather than

smaller. Thus, there iscurrentlynoreasontobel ievethattheabove

discusssion is not applicable to fluids which behave as Bingham

plastic fluids even though they contain not only clay but also

granular materials.

Finally, there is the question of how viscosity or apparent

viscosity should be measured i n a debris flow. For example, should

the viscosity ofthe flow as awhole bemeasured oronlytheviscosity

of the dispersion medium, a clay slurry in most debris flows? There

is currently no definitive answer to this question.

3.5.2 Analytic Results for Debris Flows

DeLeonandJeppson (1982) notedthat todate onlytwo closed form

or analytic solutions for the vertical distribution of the

longitudinal velocity in a debris flowhave beendeveloped. Johnson

(1970) assumed that a debris flow behaved as a Bingham plastic fluid

and obtained a form of the Poisson equation; see for example,

Schlichting (1968) , that described the movement of debris flows in a rectangular channel. In contrast, Takahashi (1978 and 1980) assumed

a dilatant fluid model and was ableto defineboth themovement ofthe

fluid-soil mixture, the steady state depth of flow, and a resistance

coefficient which has subsequently shown to be related to the Chezy

resistance coefficient for uniform flow. The original work of

Takahashi was extended by DeLeon and Jeppson (1982) and Jeppson and

Rodriguez (1983) to gradually varied and unsteady debris flows,

respectively. Because of these extensions of the original work by

Takahashi to areas of applied interest, the dilatant fluid model of

debris flows will be considered first and then the Bingham plastic

fluid model second.

Takahashi (1980) in deriving the vertical distribution of

longitudinal velocity in a debris flow occurring in a rectangular

channel began with the equation of volumetric continuity or

aY a (UY)

at ax - + - = 0

and the unsteady equation of conservation of momentum or

(3.5.7)

115

- - au - au

at ax - + + - = g s i n e - g c o s 8 (3.5.8)

where x = longitudinal distance, t = time, u = cross-sectional mean

velocityof flow, y = debris flowdepthof flow, 0 =slope angleofthe

debris channel bed, and k = a resistance or frictional coefficient.

Fromthisstartingpoint, Takahashiproceededtoderive anexpression

for the resistance coefficient k or

(3.5.9)

and an expression for the steady state depth of the debris flow or

k< Y = -

g sine (3.5.10)

wherea=anempirical lyestabl ishedvaluewhichdependsonthe flow, a

= friction angle of the moving grains, cd = grain concentration by

volume of the debris flow, p = density of water, C , = grain

concentration by volume in the stationary bed of the flow, and d =

grain diameter.

Although Equations (3.5.9) and (3.5.10) are analytically and

experimentally useful, from an applied viewpoint these equations are

not useful since they require the quantification of variables not

usually known, a priori, to the investigator. DeLeon and Jeppson

(1982) usedaone-dimensionalhydraulicengineeringapproachandwere

abletoanalytically demonstrate that the resistance coefficient kin

Equations (3.5.9) and (3.5.10) was related to the Chezy C - a standard resistance coefficient for open-channel flow: see for example, French

(1985) , or

(3.5.11)

Substitution of Equation (3.5.11) in Equation (3.5.9) yields

116

(3.5.12)

pm tan 8

(u-pm) (tan a - tan 8 ) cd =

I provided that the value of Cd is less than C,; otherwise,

cd = O.gc*

and pm = density of the debris flow mixture. valueofthechezy C, which is a l s o r e l a t e d t o t h e M a n n i n g n ;

see for example, French (1985), is usually choosen on the basis of

experience and a field inspection of the channel. In the case of

debris flows, standard hydraulic engineering practice may not be

applicable to the selection of an appropriate value of C.

The Chezy coefficient derives from the semi-empirical Chezy

equation for uniform flow in open channels which states

The

(3.5.13)

where R = hydraulic radius and S = in the general case, the friction

slope of the flow. In Equation (3.5.13) , the units associated with the resistance coefficient C are (length) '/*/(time). It can be

easily shown that the Chezy resistance coefficient is equivalent to

Manning n's or

(3.5.14)

In Equation (3.5.14) , $ has a value of 1.49 if English units are used

and a value of 1.00 if SI units are used. The Chezy coefficient is

also related tothe Darcy-Weisbach frictional coefficient f for pipe

flow or

c = J8g/f (3.5.15)

see for example, French (1985). . In the case of laminar flow, the

117

Darcy-Weisbach friction factor f is an inverse function of the

Reynolds number or

64

R f E -

Combining Equations (3.5.15) and (3.5.16) yields

For SI units, Equation (3.5.17) becomes

C = 1 . 1 0 7 6

and in the case of English units

c = 2 . 0 0 6 5

(3.5.16)

(3.5.17)

(3.5.18a)

(3.5.18b)

DeLeon and Jeppson (1982) used the limited field and laboratory

data currently available for debris flows to estimate values of C.

TheresultsofthisanalysisaresummarizedinTable3.5.3. Thereis,

see Columns (8) , (9) , and (10) of Table 3.5.3, reasonably good

agreement among the Chezy coefficients estimated by the three

techniques used by DeLeon and Jeppson.

Given the very limited data available for actual debris flows,

DeLeon and Jeppson (1982) asserted that there were sufficient

similarities between debris flows and sludge flows to allow the data

summarized in Table 3.5.3 to be combined with the sludge flow data of

Babbitt and Caldwell (1939) to yield a data set large enough for

statistical analysis. Fromthis combined data set, a least squares

analysis yielded the following best fit relationship for C and R.

C = 1.02 RoS5'

for SI units and

(3.5.19a)

C = 1.85 R o a S 2 (3.5.19b)

forEnglishunits. Acomparison ofthe coefficientsand exponents in

Equations (3.5.19) and those in Equations (3.5.18) show excellent

agreement.

118

I I I I I I I

Nobles 1 I I I I I I (1953) I I I I I I I

I I I I I I I

(1981) I I I I I I I

Sharp and1 6 1 1.20 1 20,000 1 0.762 1 10.97 1 4.24 I 3.65

Pierson I 5 I 5.00 1 1,000 1 0.4817 I 500 1 24.35 I 24.75

I I I I I I I

I I I I

Takahashil 18 1 1.00 1 1,940 1 0.044 I 8.25 1 8.36 1 3.18 I I to I I to

I 80.9321 I 9.96 (1980) I I I

I I I I I I I

(1980) I I I I I I I I

Takahashil 18 I 1.00 I 1,410 1 0.041 I 10.39 I 9.08 I 3.57 I to I I to 1 1o2.Oe2l I 11.18

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

I Value results from slight modification of the coefficients.

Values assumed by comparison with data given by Babbitt and Caldwell (1939).

At this point, only one problem remains to be solved before

debris flows can be analyzed by the techniques of traditional one-

dimensional open-channel hydraulics. Up to this point methods of

estimating the density and viscosity of a debris flow, a priori, have not been developed; and hence, neither R nor C can be estimated.

DeLeonandJeppson (1982) assertedthatboththedensityandviscosity

of a debris flow vary as a function of the depth and velocity of flow.

These investigators, with some justification, offered the following

approximation forthe ratioofthe densityto thedynamic viscosity in

a debris flow

P k - E -

u R* (3.5.20)

where p = debris flow bulk density, k = an empirical constant, and a =

an empirical exponent whose value is assumed to be one and R =

hydraulic radius. Usingthe dataof Sharpand Nobles (1953), avalue

for k was estimated; and hence,

P 10

u R - I - (3.5.21a)

119

f o r S I u n i t s and

P 3

u R - = - (3 .5 .21b)

f o r English u n i t s . With t h e foregoing hypotheses, t h e Chezy equation f o r uniform

flowinanopenchannelcanbeusedtoestimatedebris flowdepth. For example, b q i n n i n g w i t h Equation (3.5.13)

o r

A 3 S Q 2 = - C 2 ( 3 . 5 . 2 2 )

P

C 2 is estimated by combining Equations (3.5.19a) and (3.5.21a) f o r computations i n t h e S I system of u n i t s

0 . 5 2 2

c2 = [ 1.02 R0.52] * = (,.,, [? '1 ) P u

(3 .5 .23)

Subs t i t u t ing Equation (3 .5 .23) i n Equation ( 3 . 5 . 2 2 ) and rearranging

Q2P - 1 1 . 4 1 A ' ' 9 6 Q1*04S = 0 ( 3 . 5 . 2 4 )

which is an i m p l i c i t equation f o r t h e deb r i s flow depth y. Equation ( 3 . 5 . 2 4 ) can be solved f o r y by t r i a l and e r r o r o r by numerical methods; f o r example, a Newton i t e r a t i v e scheme, Conte (1965) .

DeLeon and Jeppson (1982) and Jeppson and Rodriguez (1983) used t h e r e s u l t s discussed above and t h e techniques of t r a d i t i o n a l o p e n - channel hydraul ics t o develop numerical so lu t ions f o r gradually v a r i e d b u t steady and unsteadydebris flows, respect ively. Ano teo f caution, some ca re should be exercised i n using t h i s approach pr imari ly because t h e lack of da t a t h a t is needed t o v e r i f y the assumptions inherent i n t h i s development. For example, it has not beenproven tha tdebr i s f l owsa re d i l a t a n t f l u i d s nor c a n t h e v a l i d i t y of Equation (3 .5 .21) be b l ind ly accepted. Further, is t h e Reynolds number an appropriate parameter f o r d i f f e r e n t i a t i n g between laminar

120

F I G . 3.5.4 Schematic*defini t ion of va r i ab le s f o r Bingham p l a s t i c f l u i d model of a debris flow.

and tu rbu len t f l u i d s when t h e f l u i d s a r e non-Newtonian?

ThedevelopmentofaBinghamplastic fluidmodel o f a debris flow beg inswi tha steady flow forcebalance similartothatusedtodevelop the Chezy uniform flow equation f o r Newtonian f l u i d s . Following Johnson ( 1 9 7 0 ) , steady debris flow i n a semi-circularchannel w i l l b e considered, Fig. 3.5.4. A force balance f o r t h e con t ro l volume defined i n t h i s f i g u r e y i e l d s

(3.5.25)

where F, = g r a v i t a t i o n a l force component causing flow

n r F, = Y - AL sin6

2

F, = viscous f l u i d force r e s i s t i n g motion which is equal t o a shear stress T times t h e area on which t h i s stress acts o r nrAL, and Y =

Binghamplastic f l u i d s p e c i f i c w e i g h t . Fo r sma l lva lueso f 6 , sin6 is approximately equal t o t h e s l o p e o f t h e debris flow s u r f a c e s , . W i t h

t he se d e f i n i t i o n s and assumptions, Equation (3.5.25) becomes

Y n r 2 T i l r A L = - Am,

2

121

and simplifying

Y r T = - SD

2 (3.5.26)

Equation (3.5.26) is v a l i d f o r a l l and a maximum value a t r = R.

and T has value of zero a t r = 0

For a Bingham p l a s t i c f l u i d , T is given by Equation (3.5.3) and s u b s t i t u t i q n of t h i s equation i n Equation (3.5.26) y i e l d s

(3.5.27)

which is o n l y v a l i d f o r T 2 7 , ; when T < throughou out the f l u i d , there is no flow and the above ana lys i s beginning w i t h Equation (3.5.25) is not v a l i d . Rearrangement of Equation (3.5.25) y i e l d s

d r ug

o r

S, - z Y f o r T 2 T~ 1 (3.5.28)

where t h e negative s ign i n Equation (3.5.28) der ives from t h e choice of co-ordinate systems (ve loc i ty decreases w i t h increasing r ) , Johnson (1970). In t eg ra t ion of Equation (3.5.28) and evaluation of t h e c o e f f i c i e n t of i n t eg ra t ion r e s u l t s i n a n e q u a t i o n f o r t h e v e l o c i t y d i s t r i b u t i o n i n a semi-circular channel under steady debr i s flow condi t ions o r

S, - ( R - r ) T y f o r T 2 T~ 1 (3.5.29)

Asnoted intheprecedingparagraphs, t h e shear stress vanishes a t r = 0. Therefore, it is concludedthat theremust be a value of r i n any flow where T = T~ and t h i s a r c separates t h e a rea of t h e channel where t h e v e l o c i t y of f lowvar i e saccord ing toEqua t ion (3.5.29) from t h e area of the channel where t h e f l u i d moves a t a uniform veloci ty ( t h i s is o f t en termed a plug flow) , Fig. 3.5.5. L e t R, be the radius a t which T = T~ and where (du/dr) = 0. R , can then be determined from Equation (3.5.28)

122

7

FIG. 3.5.5 Definition of debris flow plug.

(3 -5.30)

T h e v e l o c i t y a t w h i c h t h e p l u g movescan bedetermined by substituting Equation (3.5.30) in Equation (3.5.29). When R, 2 R, there is no

flow. Johnson (1970) noted that these results are in general

agreement with the limited laboratory results that are available;

that is, debris flows increase their thickness as the flow rate

increases; decrease their thickness as the flow rate decreases: and

reach minimum thickness when flow ceases.

Johnson (1970) also presented results for other channelshapes.

For example, in infinitely wide rectangular channels,

(3.5.31)

123

T Y Yc = -

YSD

(3.5.32)

whereH=totaldepthof flow, y = a C a r t e s i a n c o - o r d i n a t e w i t h t h e zero value being taken at the surface of the debris flow, and yc = the

thickness of the debris plug.

The Bingham plastic fluid model of debris flows proposed by

Johnson (1970) mustbecons ideredav iab lea l t ernat ive to thed i la tant

fluid model discussed previously in this section. However, in

comparison with the dilatant fluidmodel, the Bingham plastic fluid

model is limited f romtheviewpoin tofappl ica t ion . For example, the

Bingham model discussed here

1. requiresthat the yieldstress ofthe Binghamfluid beknown

but provides no method of estimating the value of this

variable from data that would be generally available, and

2. has not been extended to gradually varied or unsteady flows

It must noted that the extensions and hence the usefulness of the

di latantf lu idmodel i sdependentonanumberofempir ica lassumptions

which may or may not be justified; for example, Equation (3.5.20) and

Equations (3.5.21). At the present time, there are not sufficient

field or laboratory dataavailable toeither endorseor reject either

of these models.

3.6 HYDRAULIC/PHYSICAL MODELS

Unlike many other areas of modern engineering and scientific

endeavor, important discoveries, designs, and insights in hydraulic

engineering and geology continue to derive from observations and

theoretical calculations made in conjunctionwith laboratory studies

utilizingphysicalmodels. Theuse ofphysicalmodelsto developnew

knowledge requires a comprehensiveunderstanding ofthe principles of

similitude; see for example, Streeter andwylie (1975). Withregard

to similarity, there are three types of similarity important to

hydraulic/physical model studies:

1. Geometric Similarity: Two objects are only similar if the

ratios of all corresponding dimensions are similar. The

terminology geometric similarity therefore pertains to

similarity in form.

124

2. Kinematic Similarity: Two motions are termed

kinematically similar only when the paths of motion are

geometrically similar and when the ratiosofthevelocities

of the two motions are equal.

3. Dynamic Similarity: Two motions are termed dynamically

similar only if the rasios of the masses involved are equal

and the ratios of the forces involved are equal. l

In most physical model studies, geometric and kinematic similarity

can be rather easily achieved; however, complete dynamic similarity

is often difficult, if not impossible, to achieve. In most complex

modeling situations, themodelingprocessbeginswitha scalingofthe

governing differential equations; see for example, French '(1985).

From the scaling process, a number of dimensionless numbers are

derived such as the Reynolds, Froude, Bingham, and Weber numbers.

In the material which follows, the concepts of

hydraulic/physical models relevant to the study of hydraulic

processes on alluvial fans are summarized. Detailed treatments of

the subject of hydraulic/physical models are available in French

(1985) andsharp (1981). For specificexamples ofthe applicationof

these principles to alluvial fans, the reader is referred to Anon.

(1981) .

3.6.1 Froude Law Models

Froude law models assert that the primary force causing flow is

gravity and that all other forces such as surface tension and fluid

friction are small relative to the gravitational force and can be

neglected. Froude lawmode l scompr i se thep r imary typeof model used to study traditional open-channel flows.

If only Froudenumber similarityis required, then bydefinition

F,, = F, (3.6.1)

where F = Froude number and the subscripts M and P indicate model and

prototype Froude numbers, respectively. Substitution of the

definition of the Froude number, Equation (3.2.5) , in Equation (3.6.1) yields after rearrangement an expression for the velocity

ratio

125

UM UP

1 / 2 ufi g H L N u , = - - - u, - [ g p L p l =

(3.6.2)

where the subscript R indicates the ratio of model to prototype

variables, U, = velocity ratio, L, = length scale ratio, and g, =

gravity ratio. Since the acceleration of gravity cannot, from a

practical viewpoint, be altered between the prototype and model:

i.e., g, = 1, Equation (3.6.2) becomes

(3.6.3)

Hydraulic models must often be distorted: that is, the

longitudinal and vertical scale ratios are not equal. The need for

length scale distortion results from the fact that most channels are

much longer than they are deep and laboratory space for

hydraulic/physicalmodel studies is always limited. For example, in

one physical model study cited by Anon. (1981) the vertical scale

ratio, Y,, wasl/lOwhilethe longitudinal scale ratio, L,, was1/150. If a distorted model is necessary, then Equation (3.6.3) becomes

"R = & and the time scale ratio can be demonstrated

LR T, = -

(3.6.4)

to be

(3.6.5)

Other scaling ratios for a distorted Froude number model are

summarized in Table 3.6.1.

3.6.2 Moveable Bed Models

When the movement of the materials which compose the sides and

b e d o f a c h a n n e l o r t h e m i g r a t i o n o f a c h a n n e l a c r o s s a soil surfaceare primary considerations, as they are in the study of hydraulic

processes on alluvial fans, then the use of a moveable bed hydraulic

modelisnecessary. Theproperdesignand useof amoveable bedmodel

is much more complex and difficult thanthe designand usedof a fixed

126

TABLE 3.6.1 Scaling ratios for a distorted Froude law model

Variable Scaling Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Horizontal Length IJ R

Vertical Length ................................ YR

..............................

Time (hydraulic) ............................... LR/(YR)'/'

Velocity ....................................... (Y,)'/'

Flow Rate ...................................... LR(YR)=/'

Force .......................................... L,(Y,)' _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ~ _ ~ ~ _ _ _ _ _ _ _ _ ~ ~ ~ ~ ~ ~ ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

bed model because

1. The boundary roughness of the moveable bed model is not

determined by design but is controlled by the motion of the

material which comprises the model.

2 . Not only must the moveable bed model correctly simulate the

movement of water but it must also correctly simulate the

movement of sediment.

There are three methods by which moveable bed models can be

designed. Of these, the method commonly referenced as trial and

error;thatis,theadjustmentofmodelvariablesuntilthehistorical

record of prototype performance is reproduced, is not appropriate to

the s tudyofh igh ly t r ans i en tandpoor lydocumen tedephemera l f lowson alluvial fans. For this reason, the trial and error technique of

moveable bed hydraulicmodel designwill not be discussedhere. The

remaining two techniques of design can be classified as theoretical

and semi-empirical.

3.6.3 Theoretical Techniques

Equations (3.4.13) and (3.4.14) , as noted in Section 3.4 , can be used to define the threshold of particle movement. It can therefore

be asserted that if F, and R, are the same in the model and prototype

thatthe stateofthebedofthe channelwill bethe same. Then, using

the hypothesis of Einstein and Barbarossa (1956) regarding the shear

stress on the bottom ofthe channel and a roughness-to-particle size

127

r e l a t ionsh ip such a s Equation (3.3.3) it can be shown: see fa: example, French (1985) , t h a t a moveable bed model can be developed on the bas i s of t h e following equations

(3.6.6)

(3.6.7)

(3.6.8)

where R, = hydraulic radius r a t i o , V , =kinematic v i s c o s i t y r a t i o , a =

S, -.1, S , = sediment s p e c i f i c g rav i ty , and d, = sediment s i z e r a t i o . With regard t o Equations (3.6.6) - (3.6.8) , R, is a function of both Y andL, and v R wouldusual lyhavea va lueof 1. Therefore, i f onemodel r a t i o is selected, then t h e o the r model r a t i o s canbe determined from Equations (3.6.6) - (3.6.8).

comments should be noted and considered: With regard t o Equations (3.6.6) - (3.6.8) , the following

1. I f Y, = L, (an undis tor ted model) , then a s c a l e model cannot be b u i l t ; t h a t is, the model w i l l be t h e same s i z e a s t he prototype.

2 . I f thespec i f icgravi tyrat io , a,, i s s e l e c t e d i n a d v a n c e a n d t h e kinematic v i s c o s i t y r a t i o has a value of un i ty , t h e n

d, = aR-lI3 (3.6.9)

Equation (3.6.9) i nd ica t e s t h a t i f t h e moveable material used i n t h e model has a s p e c i f i c g rav i ty less than the mater ia l in theproto type , thenthes i zeo f themater ia lused

inthemodelmustbelargerthanthat found i n theprototype.

3 . I f R, cannot be assumed t o be equal t o Y,, then t h e sca l e r a t i o s Y, and L, must be found by t r i a l and e r r o r .

4 . The r a t i o of sediment t r anspor t pe r u n i t width t o flow per un i twid thmus tbe l a r g e r i n themodel than i n theprototype.

128

1.0

p 0.10

0.01

1. 10. 100. 1000,

R#I FIG. 3.6.1 R e l a t i o n o f b e d f o r m a t i o n t o p o s i t i o n i n t h e F , - R , p l a n e .

5. The particle size ratio in Equation (3.6.8) characterizes

the roughness of the channel while the same parameter in

Equations (3.6.6) and (3.6.7) characterizes the sediment

transport properties.

6. Inthedesignof traditionalmoveable bedmodels, theFroude

number model law is not considered to be an absolute rule

since if the Froude number is small a slight difference

between F, and F, can be tolerated. However, as will be

subsequentlyshown, it is believedthat theFroude numberof

flows occurring on an alluvial fan may not be small; and

therefore, small difference between F, and F, may be

significant.

Recall that the primary assumption of the foregoing development is

that if F, and R, are the same in the model and the prototype, then an

appropriate physical model will have been developed. A number of

investigators have asserted; see for example, French (1985), that

this requirement can and should berelaxed. Fig. 3.6.ldemonstrates

the relation of bed formation to position in the F, - R, plane. In

viewofthis figure, it is apparentthat toachieve similaritybetween

model and prototype the values of F, and R, do not have to be exactly

129

equal but the points in the F, - R, plane representing the mode

1 and the prototype should be within the same bed form band in Fig.

3.6.1.

Zwamborn (1966, 1967, 1969) has developeda differenttechnique

for designing moveable bed hydraulic models. In summary, this

technique requires that the

following criteria be satisfied.

1. Sioce most water' flows of practical importance are

turbulent , the Reynolds number for the model should exceed 600. This was a tacit assumption in the previous

discussion.

2. Dynamic similarity between the model and the prototype is

achieved when

a. The Froude number for the model and prototype are

equal.

b. The frictional forces acting in themodel andprototype

are scaled correctly.

c. Geometric scale distortion cannot be large: for

example ,

YR - < 1/4 LR

3. Sincesedimentmotion i s c l o s e l y r e l a t e d t o t h e b e d formtype

and bed form types are a function of R*, F,, and u*/Usr the

value of R, for the model should fall within the range

determined by F and u*/U,. French (1985) provided an

appropriate figure for doing this.

4. Given the foregoing criteria, the following scale factors

can be determined

Flow Rate

Q R = LRY,1'5

Hydraulic Time

(3.6.10)

130

LR T, =z - UR

(3.6.11)

Sedimentological Time

(3.6.12)

where T, = sediment time scale, A = relative submerged

sediment density, and qs = sediment bed load per unit

width. If ( q s ) R is not accurately known, T, cannot be

calculated, but Zwamborn (1966, 1967, 1969) suggested

that

(Ts) R I: loT, (3.6.13)

With regard to the discussion above, hydraulic time is a time scale

based on the speed of water wave propagation while sedimentological

time is, at least conceptually, based on the speed of sediment wave

propagation. Finally, themethodologyusedby Anon. (1981) todesign

moveable bed hydraulic models of alluvial fans is similiar to that

discussed above.

3.6.4 Empirical

develop scaling ratios for moveable bed hydraulicmodels.

assumed that

The regime or hydraulic geometry theory can also be used to

If it is

T - h

Y - Q 1 1 3

S .- Q - 1 I s

then it can be shown by induction that

and

Y, = LR213

Q R = L,YR312

(3.6.14)

(3.6.15)

(3.6.16)

(3.6.17)

(3.6.18)

(3.6.19)

(3.6.20)

(3.6.21)

131

With regard to Equations (3.6.14) - (3.6.21), the following

observations can be made. First, the model described by these

equations i sadis tortedscalemode1,Equat ion (3.6.20). Second, the

flow rate scaling, Equation (3.6.21) agrees with the Froude law

scaling, Table 3.6.1. Third, thistechniquetacitlyassumesthatthe

model bed material is the same as that found in the prototype.

3.7 CONCLUSION

The foregoing sections of this chapter have attempted to

introduce the reader to a limited number of the basic and traditional

principles of open-channel hydraulics which the author believes are

important to understanding hydraulic processes on alluvial fans.

The coverage of the various principles discussed in this chapter is,

by intention, not comprehensive. However, there are sufficient

references given forthe interested reader to further investigate at

his leisure all of the topics.

This chapter has also briefly discussed the mechanics of debris

flows which is a rapidly developing area of technology. There is

currently significant interest in the mechanisms which initiate

debris flows, Croft (1967), Campbell (1975), and MacArthur et a1

(1986); the mechanics of debris flows, Chen (1983, 1984, 1985, 1986a,

1986b, 1986~); the identification of areas susceptible to debris

flows, Mears (1977), James et a1 (1986), and Kumar (1986); and the

frequency of debris flows, Campbell (1975) and Mears (1977).

Finally, it should be noted that post-event analysis often mistakes

debris flow floods for fluvial floods, Costa (1983).

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Henderson, F.M., 1966. Openchannel Flow. MacmillanCo., NewYork, 522 pp.

Hughes, W.F. and Brighton, J.A., 1967. Fluid Dynamics, McGraw-Hill Book Company, New York.

James, L.D., Pitcher D.O.,Heefner, S.,Hall, B.R., Paxman, S.W., and Weston, A. , 1986. Flood risk below stee mountain slopes. In: M. Karamouz G.R. Baumli, and W.J. ,Brick ?editors) Water Forum 186: World WAter Issues in Evolution. American kocietv of Civil Engineers, New York: 203-210.

*

Jarrett, R.D. 1984. Hydraulics of hi h- radient streams. ASCE, Journal of Hyhraulic Engineering, 110 7117: 1519-1539.

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134

Compound Open Channel". ASCE, Journal of the Hydraulics Division, 108 (HY3) : 462-464.

Kumar. S.. 1986. Enaineerins methodoloav for delineatins debris flow hazards in Los Afigeles Co'unt In: 7 4 . Karamouz G.R.-Bauml$, and W.J. Brick (vditors) World Waker Issues in Evolution. American Society of Civil Engineers, New York: 19-26.

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301-312.

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136

CHAPTER 4

MODELS OF HYDRAULIC PROCESSES ON ALLUVIAL FANS

4 . 1 INTRODUCTION A s indicated i n Chapter 3, the primary purpose of a model,

physical o r numerical, is t o 'exact ly ' mirror o r dup l i ca t e on compressed spat ia land/or temporal s c a l e s t h e behaviorof aphenomena whichcannotbepracticallyobservedfull-scale. Thepurposeof th i s chapter is t o discuss four modeling e f f o r t s which have examined hydraulic processes on a l l u v i a l fans. Of these , one w a s e n t i r e l y numerical and examined a l l u v i a l fan development on a geologic time scale, Price (1972, 1974); one was e n t i r e l y physical and examined a l l u v i a l fandevelopmentonageologictimescale, Hooke (1965, 1967) ;

one w a s a combinationof numerical and physicalmodeling andexamined flooding on a l l u v i a l f anson aneng inee r ing t imesca le Anon. (1981a); and one w a s e n t i r e l y numerical and examined debris flows confined i n channels, DeLeonandJeppson (1982) and Jeppsonand Rodriguez (1983) .

Although none of themodel ing e f f o r t s c o m p l e t e d t o d a t e hasbeen comprehensive, each study has its own a t t r i b u t e s and is worthy of consideration.

4 . 2 NUMERICAL MODEL, GEOLOGIC TIME SCALE: PRICE (1972, 1974) The primary purpose of t h i s modeling e f f o r t was t o describe

deposi t ion on an a l l u v i a l fan on a g e o l o g i c t i m e s c a l e andby doingso gain a better understanding of t h e permeabili ty and s p a t i a l d i s t r i b u t i o n of water bearing s t r a t a i n an a l l u v i a l fan. Themodel hasasbasisthemathematicalprincipleofMonteCarlosimulation; and the re fo re , themodel is s tochas t i c i n t y p e r a t h e r thandeterminis t ic . Monte Carlo methods can best be described a s t h a t branch of mathematics concerned with experiments with random numbers. I n t h i s methodology, each va r i ab le o r parameter is assigned a probabi l i ty densi ty function tha t describes its s t a t i s t i c a l p rope r t i e s . Values a r e then randomly choosen f o r eachterm; t h e s e v a l u e s a r e i n s e r t e d i n themodel, andapredict ionmade. I f t h i s p r o c e s s is repeated a l a r g e number of t i m e s , a d i s t r i b u t i o n o f p r e d i c t e d v a l u e s is obtainedwhich r e f l e c t s t h e combined unce r t a in t i e s i n a l l t h e va r i ab le s and parameters. The j u s t i f i c a t i o n f o r simulating deposi t ion on an a l l u v i a l fan by a Monte Carlo technique is t h a t while many of the processes involved are de te rmin i s t i c , o the r processes such a s u p l i f t and p r e c i p i t a t i o n are t y p i c a l l y quant i f ied a s s t o c h a s t i c processes.

137

Further, the Monte Carlo approach in which mean values, standard

deviations, and probability distributions are specified tacitly

takes into account our inability to describe some processes with

completeaccuracy; for example debris flow formation. Finally, this

model is continuous in time; that is, event times are drawn from

continuousprobabilitydistributions, but discrete in space; that is,

each event path is a two dimensional, Cartesian random walk between

discrete nodes.

Because this model attempts to describealluvial fandeposition

on a geologic time scale, it has a number of components which are

geologic or geophysical rather than hydraulic in nature. Although

each process simulated by the model will be described, emphasis will

be given to the hydraulic processes rather than the other processes.

The interrelationship of these processes are shown schematically in

Fig. 4.2.1.

4.2.1 Initial and Boundary Conditions

As is the case with all modeling problems, the modeler must

define initial conditions in time and space and spatial boundary

conditions throughout time.

The formation of an alluvial fan requires that there be an

elevational difference between the mountains and valley. From a

geologicor geophysicalviewpoint, this elevation difference results

f romei ther theupl i f t ingof themounta inb lock orthe downfaultingof

the valley block. Therefore, the initial condition for this model

consists of specifying an elevational difference between the

mountains andthevalley; andthe locationofthecanyonmouthwhichis

responsible for transporting sediment from the mountain drainage

basin to the valley. For convenience, the starting time is usually

specified as time zero. The initial conditions are shown

schematically in plan and cross-section in Figs. 4.2.2.

The boundary conditions consist of a specification of the

spatial limits of fan development. Specification ofthe locationof

the fault line or mountain front is one boundary condition. Older

strata or the bedrock on which the alluvial fan will be developed

represents a second boundary condition. The lateral development of

the alluvial fan can either be constrained by other alluvial fans o r can be unbounded. Specification of these boundaries yields two

additional boundary conditions. The downslope boundary condition

couldincludeaplaya, another fan, oranopenboundary. Theboundary

conditions are also shown schematically in Figs. 4.2.2.

138

I 1 Charnel

lYes

FIG. 4.2.1 Schematic showing the interrelation of processes in the Price (1972, 1974) model.

4.2.2 Co-ordinate System

The co-ordinate system for this model is Cartesian and consists

of a system of nodes distributed between the horizontal boundaries,

Figs. 4.2.2.

4.2.3 Input Variables and Parameters

andparameters.

The model requires the specification of values for 23 variables

These inputvariables andparameters are summarized

139

I t

PLAN VIEW

r Canyon Supplying Sedtment

Mountatn Front A ,

0 0 0 0 0

l o o

0 0 0 0 0

Fan or, I 0 0

Boundary Other Y O O

l o o A , \ Fan, Playa, o r

Other Boundary

CROSS SECTION A - A

Mountoh Front

Bedrock o r Other Strata

FIGS. 4.2.2 Schematic definition.of for the Price (1972, 1974) alluvial

in Table 4.2.1.

initial and bpundar conditions fan deposition moJel.

4.2.4 Process: Uplift/Relief Development

As noted in the discussion of initial conditions, relief

development at themountain front can either result fromuplift ofthe

mountain block or downfaulting ofthe valley block. In thismodel,

uplift or downfaulting is correlated with the occurrence of

140

earthquakes. The justification of this assumption is that faulting

has actually been observed to occur with many large earthquakes.

Earthquakes, because of their importance have been extensively

studied, and it hasbeen hypothesizedthattheirdistribution intime

can be adequately described by the Poisson probabi l i tydis tr ibut ion.

Atthispointtwopract ica lproblemsarise . First, areasonable

estimate of the mean uplift rate (Variable 4 in Table 4.2.1) must be

obtained. Price (1972) used earthquake data from a fault area in

Turkey to obtain an estimate of the number of earthquake events per

year. The validity of this estimate and its applicability to other

geographical areas is unknown. Second, an assumption regarding the

stationarity of earthquake occurrences in time must be made.

Although other assumptions arepossible, inthis model the serieswas

assumed to be stationary. Note, the terminology of stationarity

referstothe fact that the probabilitydistributions or at least some

of the moments of the random variables of the processes are

independent of transitions of the initial moment on the time axis.

Given that an earthquake occurs and hence that relief

development also occurs, then the amount of displacement and the

location of this displacement must be .defined. In order to

accomplish this, three assumptions are required.

1.

2.

3 .

Displacements may occur anywhere along the fault line and

theprobabilityofa displacement occurring ata givenpoint

on the fault is equal over the length of the fault, L,.

Agiven faultmovementhasa finite length, L,, and amaximum

displacement, D. The displacement D may have a horizontal

component D,, and a vertical component, D,. Price (1972)

indicatedthat intheBasinandRangeProvinceofthewestern

United States that faults dip an average of 60 degrees and

hence D I 1.1547DV.

The amount of vertical displacement, D,, declines linearly

from the point of maximum displacement at the center of the

fault movement to zero at either side.

The variables defined above are schematically shown in Fig. 4.2.3.

Inthis figure, theamount of verticaldisplacement atthe pointwhere

thechannel crosses the fault is designatedhas H',. Finally, values

of D and L, are estimated from a series of semi-empirical equations

141

1

2

3

4

5

6

7

8

9

10

11

12

Node spacing I I

I I I I raphy.

I 30 m IDistance between nodes. De- Itermines the horizontal re- lsolution in simulated topog-

I lCan be located at any position

(location at the center is Ipreferred.

I Location of mouth I ---- of fan-building I lalong the mountain front but canyon I

I I I

Maximum length of 110,000 yr.IReuresents the maximum possible fan-building I period I

I I I I

Mean uplift rate 10.01 up- I lifts/yr

I I

Length of locus I 1300 m of points of I maximum displace- I ment along the I fault I

Mean peak flow rate

I 28 m’/s

I I

Constant relating I 100 peak flow rate to I number of steps in1 the random walk I

I Mean flow rate I O.Ol/yr occurence I

Immediately ero- I 232m2 dible basin area I

I I

i length of time in years- that the (model will simulate. Tte actual lperiod of simulation might be lless if the limit on flow events lie reached first.

IRefers to the uplift of the lmountain block relative to the Jvalley in terms of the number lof uplifts per year.

I

I lThe locus of points of maximum [displacement of the fault lies Jalong that portion of the fault lcentered at the canyon mouth. IAlthough any length may be Iapecified, the longer the length lthe less the probability that the lmountain block in the vicinity lof the channel will signifi- lcantly be affected by an uplift. I pelf-descriptive but the value of Ithis variable affects the distance lover which erosion may occur. I IRelates the degree of erosion by Iflow events to the mean peak flow 1 rate. I I IFrequency in flows per year of lsignificant flows on the fan. I IPortion of the drainage basin which Isupplies sediment to debris and lwater flows. ltotal basin area.

Upper limit is the

I Average rate of 10.003 m/yrIParameter which characterizes im- development of I lmediate erodibility of rocks in weathered layer 1 lthe basin.

I Critical thickness1 of weathered layerl in basin with re- I gard to debris I flow. I

I I

Critical thickness1 of weathered layerl in basin with re- I gard to water flow1

I I !

I 2 . 7 4 m IIf the thickness of the weathered

(layer is greater than the value of Ithis variable and a flow event ltakes place, then a debris flow lwill occur; otherwise, water flows I occur. I

0.03 m (If the thickness of the weathered llayer is greater than the value of lof this variable and a Zlow event ltakes place, then the water flow (will deposit sediment on the fan; lotherwise, the flow will erode lpreviously deposited material.

142

13

14

15

16

17

18

19

20

21

22

23

Yaximum thickness 3f weathered layer in the basin

Rverage rate of streambed erosion dhere the fault xoesee the main stream channel.

klomentum Eoefficient

Mean thickness of debris flow deposits

Mean thickness of water flow deposit s

Lower limit of initial depositional thickness of debris flow

Lower limit of initial depositional thickness of water flow

Standard deviation of debris flow bed thickness

Standard deviation of water flor bed thickness

Coefficient of fixation

Mean depth of Erosion

3.0 m

0.0003

1.5

0.30 m

0.03 :

0.15

0.015 :

0.15 m

0.15 m

100,000

0.03 m

Greatest thickness of erodible material that can accumulate in the basin.

This parameter becomes particularly important when the rate of downcutting exceeds the rate of uplift. Fanhead channel entrenchment is strongly dependent on this variable.

This coefficient expresses the fact that water flowing in one direction has the tendency to continue flowing in that direction. The value of this coefficient increases with the average stream discharge and decreases with increasing topographic roughness and hetero- geneity of deposits. Values may be 1 or larger.

Most debris flow deposits are 0.30 m or more and decrease in thickness in the downstream direction.

Water flow deposits are usually thinner than debris flow deposits.

Equal to the height of the fault scarp if the scarp is less than the initial depositional thickness and is equal to or greater than some arbitarily set lower limit. If the fault scarp height is less than this lower limit, debris flow will not deposit until random walk has traveled far enough down the fan so that the elevation of the of the top of the debris flow is not greater than the elevation of the top of the scarp where it crosses the channel. If this condition is not met, then no deposition takes place on the fan.

Essentially same as the parameter for debris flow.

Rather arbitrary

Rather arbitrary

Expresses a simple relation between grain size and slope.

Average depth to which eroding water flows will remove material from the upper fan and redeposit material on the lower part of the fan.

143

D - LF . FIG. 4.2.3 Schematic d e f i n i t i o n o f v a r i a b l e s a s s o c i a t e d w i t h u p l i f t events.

abstracted from the study of earthquakes.

4.2.5 Process: Weathering and Accumulation of Material in the

Drainage Basin

From the perspective of simulating deposition on an alluvial

fan, there are two drainage basin processes of interest - the rate of accumulation of weathered material and the rate of erosion.

Weathering rates are a function of the structure of the material

involved, temperature, the amount of water and its rate of movement,

and aridity. Leopold et a1 (1964) suggested that the thickness of a

weathered layer in a drainage basin could be represented as an

exponential function of time. In this model, the thickness of the

weathered layer with time is represented by

Ys = ms[l - exP(-?t) 1 (4.2.1)

where y,=thicknessoftheweathered layer,ms =maximum thicknessof

the weathered layer allowed (Variable 13 in Table 4.2.1),

1000 tC ? = -

mS

c = rate of soil development (Variable 10 in Table 4.2.1) , t =

dimensionless constant equal in numerical value to m,, and t = time

increment in thousands of years. m, andc arevariables whosevalues

mustbeestimated, butthismustbedoneonthebas isofa lmostnodata .

Tables 1.2.1 and 2.4.2 provide some assistance in selecting

144

appropriate orders of magnitude f o r m, and c. A f t e r e a c h u p l i f t e v e n t , e r o s i o n w i l l lowerthe bedof t h e stream

channel i n t h e drainage basin. Of p a r t i c u l a r i n t e r e s t is t h e amount of e r o s i o n t h a t t a k e s p l a c e a t t h e pointwhere thechannel crosses the f a u l t l i n e a t t h e m o u n t a i n f ron t . Erosion is assumed t o lower thebed of t h e channel according t o

h = H, exp( -k t i ) ( 4 . 2 . 2 )

where h = e leva t ion of t h e bed of t h e channel a t t i m e t i , H, elevat ion of t h e bed of t h e channel immediately a f t e r an u p l i f t event which o c c u r r e d a t t i m e t , , andk = a dimensionless parameter quan t i fy ing the average rate of decl ine of t h e rock channel a t t h e f a u l t crossing (Variable 1 4 i n Table 4 . 2 . 1 ) .

4 . 2 . 6 Process: Flow The first t o p i c t h a t must be addressed i n discussing flow

processes - both debris and water - is t h a t of t h e timing of t h e flow events. Although a s noted byWolman andMil ler (1960) the re wereand s t i l l are no models f o r accomplishing t h i s t a s k on a l l u v i a l fans, it seems reasonable t o represent t h e timing of flows as a Poisson process. When t h e Poisson p robab i l i t y d i s t r i b u t i o n is used t o describe a s t o c h a s t i c process it may be wr i t t en as

P[kl = e x p [ - b t ( b t ) ' / k l 1 (4 .2 .3)

where A = mean r a t e of occurrence of flow events (events/year) , t = a period of t i m e ( yea r s ) , k = number of occurrences i n t h e t i m e period t (k = 0 , 1 , 2 , . . . ) , and p[k] = p r o b a b i l i t y t h a t exac t ly k events w i l l occur i n t h e t i m e p e r i o d t . The probabi l i ty thatnof loweventswi l l

occur i n t h e t i m e period t is

PI01 = e x p ( - \ , t ) (4 .2 .4 )

andtherefore , t h e p r o b a b i l i t y t h a t t h e f i r s t flow e v e n t w i l l occur i n t h e t i m e period t is [l -em(-A ft) 1. Let T be t h e random variable represent ing t h e t i m e of t h e f i r s t flow event , then t h e cummulative d i s t r i b u t i o n function of T is

F ( t ) = p[T I t] = 1 - exp(-Aft) f o r t 2 0

The p robab i l i t y dens i ty function of T is

(4.2.5)

145

X,exp (-1,t) for t 2 0 f(t) = - = dF(t)

dt (4.2.6)

For the details of the above derivation, the reader is referred to

Benjamin and Cornell (1970). The equation used in the model to

estimate the period of time between flow events in years is

(4.2.7)

where t, = time in years to the next flow event and Rf = random value

from a uniform distribution over the open interval (0,l). By way of

example of the use of Equation (4.2.7), assume that the rate of

occurrence of flow events is A , = 0.01 per year (Variable 8 in Table

4.2.1) and that R, = 0.5, the

1 0.69 t f = - - ln(1 - 0.5) = - = 69 years

0.01 0.01

which is the time in years to the next flow event.

With the time period between flow events defined, it remains to

estimatethemagnitudeoftheflowevents. Price (1972, 1974) usedan

exponential probability distribution similar to that used by Shane

and Lynn (1964) and Todorovic and Zelenhasic (1970) or

1 f(Qf) = - ex[ - -1

<Qf> <Qf>

(4.2.8)

where Qf = peak flow rate and <Qf> = mean peak flow rate.

(4.2.8) can be represented for use with a digital computer as

Equation

Q f = - <Qf> ln(1 - R,) (4.2.9)

where R, is a random value selected from a uniform distribution over

the open interval (0,l). By way of example of the use of Equation

(4.2.9) assume that <Qf> = 28 m3/s and that R, = 0.6, then

Qf = -(28) ln(1 - 0.6) = 26 m3/s

The frequency of major debris flows appears to depend on 1) the

occurrence of intense precipitation events and 2) the availability

within the drainage basin, particularly in the main channels, of

146

3,

I- t b

1

al

U

A 2, 111 L aJ +, aJ

5 % 1 1 1 " x 2 1,

I

0,

Debrls Flow

d ------

Eroding Water Flow (not to scale)

0, 1, 2, 3, n t

FIG. 4.2.4 as a function of ?t with the oints se arating eroding water flows &om depositing water flows an$ debris Plows indicated.

sufficient weathered material to form a debris flow. The return

periods associated with debris and mudflows can range from at least

yearly, Bull (1964), to 100 years or more. In the present geologic era, itcan alsobe a s s e r t e d t h a t t h e a c t i v i t i e s ofman haveadversely

affected the amount of vegetative cover and infiltration capacity of

many drainage basins and have in this way increased the frequency of

debris and mudflows in some basins, Croft (1967). If sufficient

weathered material for the formation of a debris flow is not

available, then a water flow will occur.

Althoughthe foregoing discussion providesvery littleguidance

for the estimation of the frequency of flows on an alluvial fan

(Variable 8 in Table 4.2.1), it does provide a basis for deciding

whethera f l o w w i l l b e a d e b r i s o r w a t e r flow. InFig. 4.2.4, Equation

(4.2.1) using the values of c (Variable 10) and m, (Variable 13) from

Table 4.2.1 is plotted as a function of qt. In this figure, three

147

depths of weathered material a r e indicated: m, , t h e maximum thickness of weathered mater ia l allowed, y c l and y c . The va r i ab le y c l is t h e d i v i s i o n p o i n t separat ingwater flowswhich erodemater ia l from t h e surface of t h e fan i t s e l f from water flows which deposit material on t h e surface of t h e fan. yc is t h e d iv i s ion point s epa ra t ingdebr i s flows fromwaterflows. That is, whenastormevent occurs, i f y, > y c l , then a debris flow occurs.

S i n c e t h e m o d e l d i f f e r e n t i a t e s betweendebris andwater flowson the b a s i s Of t h e depth of weathered mater ia l i n t h e drainage basin r a the r t h e i n t e n s i t y and amount of p r e c i p i t a t i o n , each flow event simulated must be assumed to be of s u f f i c i e n t magnitude to generate e i t h e r type of flow event. The flow event frequency (Variable 8 i n Table 4 . 2 . 1 ) must be choosen with t h i s l i m i t a t i o n i n mind; t h a t is i n i ts present form only s i g n i f i c a n t flow events can be simulated.

The rout ing of flow events through t h e system of nodes, Fig. 4 . 2 . 2 , represent ing t h e a l l u v i a l fan is accomplished by a physically based p robab i l i t y statement. With reference to Fig. 4 . 2 . 5 , a flow has been routed to node (i , j ) and must now be routed to one of t h e four nodes surrounding (i, j ) . L e t p (i f 1, j f 1) represent t h e probabi l i ty of t h e flow being routed to one of t h e surrounding nodes. Values of p ( i f 1, j f 1) are obtained by f i r s t sub t r ac t ing t h e elevat ion of t he node ( i , j ) , E ( i , j ) , from t h e e l eva t ion of each of t h e surrounding nodes. I f the d i f f e rence i n e l eva t ion between t h e node (i , j ) and one of t h e surrounding nodes is pos i t i ve , then p f o r t h e po ten t i a l movement i n t h i s d i r e c t i o n i s , b y d e f i n i t i o n , zero. I f t h e d i f f e r e n c e i n e l eva t ion between node ( i , j ) and one of t h e surrounding nodes is zero o r negative, then p has a non-zero value i n t h i s po ten t i a l d i r e c t i o n of flow.

The p robab i l i t y p t h a t a flow w i l l move i n a given d i r e c t i o n is assumed to be proportional to t h e s lope i n t h a t d i r e c t i o n o r

p ( i + l , j ) a S ( i + l , j ) ( 4 . 2 . 1 0 )

w h e r e p ( i + l , j ) = p r o b a b i l i t y t h a t t h e flowwillmove fromnode ( i , j ) to node ( i + l , j ) a n d S ( i + l , j ) = s l o p e fromnode ( i + l , j ) to node ( i , j ) . By assumption, i f S = 0 , then p = 0.25; and i f S = 1, then p = 1. Ara the r a r b i t r a r y funct ional r e l a t ionsh ip t h a t s a t i s f i e s both of these assumptions and Equation ( 4 . 2 . 1 0 ) is

p ( i + l , j ) = 0.25 - 0 . 7 5 S ( i + l l j ) ( 4 . 2 . 1 1 )

I t i s a p p r o p r i a t e t o n o t e a t t h i s p o i n t t h a t i n t h e caseo f water flows

148

J Node (I,J+1> 7

a 1 No Flow Boundary

k Node (1,J-l)

F I G . 4 . 2 . 5 Schematic d e f i n i t i o n of flow rout ing va r i ab le s .

S is computedon thebas i so fg roundsur facee leva t ionwhi l e f o r d e b r i s flows S is computed from t h e top of t h e debris flow t o t h e ground surface a t t h e surrounding nodes. Thus, debris flows can move upgradient as long as the elevat ion of t h e t o p of t h e debris flow is g r e a t e r than t h e ground surface elevat ion a t t h e node t o which movement occurs. P r i ce (1972) a s se r t ed t h a t i n computing s lopes i n t h i s fashion tha t t h e e f f e c t s o f t h e d i f f e rences i n viscosi tybetween water and debris flows is taken i n t o account. I n view of t h e discussions presented i n Chapter 3 , t h i s assumption is probably i n e r r o r s i n c e d e b r i s flows requiresteepergradientsthanwaterflowsto maintain motion.

I n e r t i a , t h a t i s t h e t e n d e n c y o f a f l o w t o continue i n a d i r e c t i o n once movement i n t h a t d i r e c t i o n has s t a r t e d , is taken i n t o account with t h e momentum c o e f f i c i e n t , I (Variable 15 i n Table 4 . 2 . 1 ) . I n e r t i a is perhaps an inappropriate term s ince t o some degree t h i s parameter considers not only t h e basic p h y s i c a l p r i n c p l e of i n e r t i a but a l s o t h e unstated boundary conditions; namely t h e flow may be confined t o a channel. The model remembers t h e d i r e c t i o n of flow from t h e previous rout ing s t e p and mul t ip l i e s t h e p robab i l i t y associated with t h i s d i r e c t i o n by I which f o r t h i s d i r e c t i o n is g r e a t e r than one. For example, w i t h reference t o Fig. 4 . 2 . 5 , i f i n t h e previous rout ing s t e p movement was from node ( i - l , j ) t o node ( i , j ) , then t h e ‘p robab i l i t y ’ of movement from node ( i , j ) t o node ( i + l , j ) is

149

F(i+l, j) = Ip(i+l, j) I > 1 (4.2.12)

In other directions of potential flow, the Probabilities p are also

multiplied by I but in these directions I = 1. F is not a true

probability but a weighted flow parameter. True probabilities are

now recalculated from the F values. Let

IF = F(i+l,j) + F(i-1,j) + F(i,j+l) + F(i,j-1) (4.2.13)

The new flow routing probabilities are

F ( i+l , j )

CF pI(i+l,j) = (4.2.14a)

F(i-1, j 1 pI(i-1,j) = (4.2.14b)

CF

F(irj+l) p'(i.,j+l) =

CF

F( i, j-1)

CF ~ ' ( i ~ j - 1 ) =

(4.2.14~)

(4.2.14d)

Equations (4.2.14) hypothesize a uniform probability distribution

andatthispointa randomnumber on the interval (0,l) is selectedand

depending on the value of this random number a routing direction is

selected.

A simple example of the routing procedure discussed above is

defined in Fig. 4.2.6 and solved in Table 4.2.2. In Column 7 of this

table, theroutingprobabilities tothe variousnodes aresummarized.

IftherandomnumberchoosenliesbetweenO and 0.574, the flow willbe

routed to node (11,lO) ; if the random number choosen is greater than

0.574, then flow will be routed to node (10,9). It is somewhat more

probable that the flow will continue in the direction from which it

came; i.e., to node (11,lO).

At this point, the effect of boundary conditions and a number of

other factors such as channel entrenchment must be considered.

Boundary conditions f o r the area in which the alluvial fan will

develop must be specified, Fig. 4.2.2. In general, there are two

types of boundary conditions: no-flow (reflecting) and open. In

the case of no-flow boundaries such as the mountain front or other

fans: the flow is not allowed tomove across the boundary: that is, it

is reflected back into the area of fan development because the

150

;/////////:

9Jlo) = 112.

Inltlal Dlrectlon

o f Flow

/////// /

No Flow Boundary

E<lOJ1O) = 100. ' E(llj10) = 90.

E(10,9) = 85. k F I G . 4.2.6 Defintion of values for example flow routingcalculation in Table 4.2.2.

I (9,lO) I 112

I (10,lO) I 100

I (11,lO) I 90

I (10,9) I 85

I (10,ll)I - - l

I

2

0

-10

-15

----

I 0.02 I 0

I ---- I ---- I

I

I I 0 I

-0.10 I 0.325

-0.15 1 0.362

----

I 0 I 0

I ---- I ---- I

I

I 0 1 0

I

0.488 I 0.574

0.362 I 0.426

b F = 0.850

151

probab i l i t y of movement i n t h i s d i r e c t i o n is zero. I n t h e c a s e of an open boundary, t h e flow and sediment associated with it moves out of t h e s i m u l a t i o n a r e a a n d i s t o a l l i n t e n t s andpurposes ' l o s t ' a s f a r a s t h e simulation of deposi t ion is concerned.

The model assumes t h a t t h e a l l u v i a l fans considered are under s t a t i o n a r y condi t ions and f o r t h i s reason a detailed simulation of permanent fan head trenching is not included. Temporary channel entrenchment takes place i n the model under two conditions. F i r s t , entrenchmentwill occur i f t h e e l e v a t i o n o f t h e fan j u s t downstreamof t h e point where t h e channel providing sediment crosses t h e f a u l t is g r e a t e r than the elevat ion of t h e bed of t h e channel upstream of the f a u l t . Second, i f a flow event occurs when t h e r e is l i t t l e o r no weathered mater ia l i n t h e drainage basin, then an erosive water flow occurs; F i g . 4 . 2 . 4 with ys c y c l . I f e i t h e r of t hese conditions e x i s t , then erosion/channel entrenchment occurs a t t h e head of t he fan. The depth of erosion is governed by t h e spec i f i ca t ion of t he parameter termed t h e mean depth of erosion (Variable 23 i n Table 4 . 2 . 1 ) . The length of t h e temporarily entrenched channel is determined inpartbyaconstantthatrelates thepeak f l o w r a t e t o t h e number of s t e p s i n t h e random walk t h a t routes t h e flow through t h e deposi t ional a r ea (Variable 7 i n Table 4 . 2 . 1 ) .

The model a l s o allows flows t o branch when they become trapped. A flow can be trapped as t h e r e s u l t of one of two c o n s t r a i n t s i n the randomwalk simulation o f t h e f lowrout ing. F i r s t , no flow maycross o r i n t e r s e c t i t s e l f . Second, no flow may be routed i n t h e d i r ec t ion o f a p o s i t i v e g r a d i e n t . I f e i t h e r o f t h e s e c o n s t r a i n t s i s s a t i s f i e d , then t h e model checks back along t h e flow path and searches each node it has passed through f o r a possible flow path. I f another flowpath is found i n t h i s search, it is choosen; otherwise, t h e backchecking process proceeds a l l t h e way back t o t h e o r i g i n of t h e channel a t t he mountain f ron t . When t h e mountain f r o n t is reached, it is assumed t h a t thechannel i sb locked downstreamby a h o l e ordepression, a n d i t isassumedthatthistopographiclowwill f i l l wi thwater andsediment t o t h e l e v e l o f t h e lowest o u t l e t . Whenthelevel o f t h e l o w e s t o u t l e t is reached, t h e remainder of t h e flow w i l l leave t h e hole or depression.

F ina l ly , a t some point every flowmust end; t h a t is, i t m u s t r e a c h an absorbing s t a t e or boundary. I n t h i s model, t h e flow reaches an absorbing s t a t e when a l l t h e sediment being t ransported has been deposited. For water flows, t h e primary causes of sediment deposi t ion are: 1) spreading o f t h e f l o w a t t h e e n d o f t h e channel or

152

2 ) complete inf i l trat ionofthewatertransport ingthesediment . The thickness of t h e deposi t l a id down by a flow event is assumed t o dec l ine fromtwicetheaveragethicknessofthedeposits (Variable17 inTab le 4 . 2 . 1 ) a t t h e p o i n t wheredeposit ion i n i t i a l l y t a k e s place t o zero a t t h e end of t h e flow. T h e t o t a l l eng thof a w a t e r borndeposi t is determined by e s t ima t ing the totalnumber of random s t e p s required t o deposi t t h e t o t a l volume of sediment c a r r i e d by t h e flow. A l l channels i n t h i s model a r e assumed t o be rectangular i n shape and of constant width. Deposition is assumed t o extend ha l f t h e g r i d s p a c i n g o n e i t h e r s i d e o f t h e nodethrough whichthe flowpasses. For thetypicaldatavaluesgiven i nTab le 4 . 2 . 1 , t h e lateral ex ten t o f t h e sediment depos i t s would be 30 m (100 f t ) . Debris flow deposi t ion is handled i n an analogous fashion.

4 . 2 . 7 Calibration/Verification/Validation

The problems associated with properly c a l i b r a t i n g , ve r i fy ing , and hence va l ida t ing any model are d i f f i c u l t . Such problems a r e compounded andmagnifiedwhenthemodeling o r simulation t akes place on a geologic t i m e scale such a s is done i n t h i s model. I n t h i s modeling e f f o r t , t h e r e w a s not a v a l i d attempt t o v e r i f y t h e model. However, i t w a s n o t e d t h a t t h e s i z e o f t h e fanestimatedbythemodelis primari ly a function of

1. t h e s i z e of t h e erodible a rea (Variable 9 i n Table 4 . 2 . 1 ) which is assumed t o be constant over t i m e ;

2 . t h e storm o r flow event frequency (Variable 8 i n Table 4 . 2 . 1 ) ; and

3. t h e r a t e of t h e accumulation of weathered mater ia l i n t h e drainagebasin (Variables10, 11, 1 2 , and13 inTable4.2.1) .

4 . 2 . 8 Summary The s t o c h a s t i c model proposed by Price (1972 ,1974) has many

a t t r a c t i v e f ea tu res and an equal number of disadvantages. Amongthe disadvantages a r e t h e following. F i r s t , s i nce t h e model simulates a l l u v i a l fan deposi t ion on a geologic t i m e scale, it requ i r e s t h e s p e c i f i c a t i o n o f largenumber of va r i ab le s and parameters. Although i n a model as ambitious as t h i s one a large a r r ay of va r i ab le s requir ing d e f i n i t i o n is n e i t h e r uncommon or u n r e a l i s t i c , i n t h i s p a r t i c u l a r c a s e t h e r e a r e a numberofvariableswhich canonly bevery

153

crudely estimated. For example, themeanuplift rate (Variable 4 in

Table 4.2.1). Second,the model, of necessity, assumes the

stationarityofprobabilitydistributions over geologictime. While

such an assumption especially in regardtodepositionalprocesses is

clearly erroneous, it is perhaps no more in error than any other assumption that could be made. Third, only rare or large scale

storm/runoffeventsaresimulated. For example, thetypicalvalueof

Variable 8 in Table 4.2.1 indicates that only flow events with an

average returnperiodof 100 years willbe simulated. Fourth, debris

and water flows are differentiated among on the basisofthequantity

of weathered material available in the drainage basin. Since only

large/rare floweventsare simulatedthis isa reasonable assumption;

however, it would seem desireable that consideration be given to the

other factors involved. Fifth, the hydraulic aspects of the flow

routing scheme are crude. While this scheme is consistent with the

time scale considered, it could be easily improved. Fifth, the

verification of the model is very weak. None of the above

observations are intended to disparage the conceptual progress that

the formulation of this model represents.

Among the positive aspects of this model are the following.

First, because the simulation has a geologic time scale, it tacitly

includes the possibility of large scale catastrophic flow events

taking place. The engineer and planner, given their professional

responsibility of protecting public health and safety must always

take this possibility into consideration. Second, the random walk

formulation of the flow routing is attractive since it tacitly

incorporatesthehypothesisthat flowevents crossing an alluvial fan

may take random paths: see for example Dawdy (1979). Third, and

contradicting one of the objections noted above, the model does not

assume more knowledge regarding hydraulic processes on alluvial fans

than is available. For example, the recommended FEMAmethodology for

evaluating flood hazard on alluvial fans, Anon. (1983), while

incorporatingmanyoftheprinciplesof thismodel alsoassumes 1) the returnperiods of floodsofvarying magnitudeson alluvial fans canbe

accurately predicted and 2) the width and depth of the channels

associated with these events can also be accurately estimated. To

somedegree, aswill subsequentlybe shown, these assumptionsprovide

results whose apparent accuracy is greaterthantheir realaccuracy.

In fact, the magnitude of flow events in arid and semi-arid regions

with specified return periods cannot be accurately estimated using

standard engineering procedures: see for example, Anon. (1981b).

154

The techniques of paleohydraulic reconstruction of flash floodpeaks

may be of use in this area: see for example, Costa (1983). Further,

the validity ofthe regime orhydraulic geometrytheory inpredicting

alluvial channel width and depth in the case of unsteady flow is

questionable. However, the incorporation of these concepts into

this model would be valid given the current state-of-the-art.

Further, the engineers, planners, and managers associated with flood

hazard problems on alluvial fans should divorce themselves fromthe

philosophy that deterministic answers are per semore accurate than

stochastic simulation, especiallywhenthemechanicsoftheprocesses

involved are not well-defined.

While

refinement is needed, the concepts and philosophy on which the model

is based are soundrelative toother methodologiesthatarecurrently available.

In sum, this model has many features that recommend it.

4.3 PHYSICAL MODEL, GEOLOGIC TIME SCALE; HOOKE (1965,1967,1968)

The physical model studies performed by Hooke were based on two

premises. First, the study of limited number of alluvial fans from

widely diverse climatic, lithologic, and tectonic environments

should reveal the influence of these factors on alluvial fan

processes. Second, alluvial fansdeveloped inthe laboratoryshould

betreatedas small fans intheirown right rather thanas scalemodels

of existing fans. This latter premise avoids the scaling problems

inherent in designing and performing physical hydraulic model

studies, Chapter 3, Section8 andchapter 4, Section 4. Thevalidity

of the second premise is questionable and suggests that the results

from this modeling program while they maybe qualitatively correct,

cannot be used to make detailed quantitative predictions or

estimates. In fact, Hooke (1965,1967,1968) has never suggested

otherwise.

4.3.1 Experimental Apparatus

The apparatus used in these experiments consisted of 1) a

constant head tank from which water was conveyed through pipes and a

s e r i e s o f c o n t r o l v a l v e s t o a n inletbox; 2) a sheetmetal channel0.10

m (0.33 ft) wide and 1.27 m (4.2 ft) long with an artificially

roughenedbottomconnectedtothe inletboxwiththeworking area; 3) a

working or model fan development area approximately 1.5 m (5 ft) wide

and 1.5 m (5 ft) long; and 4) an outlet gate with a sediment trap. A

rail mounted point gage was available to measure surface elevation

155

differences relative to a horizontal datum. Flow rates in the

apparatuscouldbevariedbetween5.7x10-5 and5.7 xlO-' m3/s (0.002

ft3/s and 0.02 ft3/s, respectively).

4.3.2 Experimental Procedures

Giventheexperimental apparatus, two series ofexperimentswere

performed. The f irstseriesconsistedofeighttothirteenepisodes.

Eachepisodeconsistedofpackingthe sheetmetal inlet channel wit h a

fixed amount of sediment and then allowing flow out of the constant

head tank for a predetermined period of time. For each experiment,

the amount of time for each episode and the total volume of flow was

constant, but because the inlet channel was packed (blocked) with

sediment, the flow over the fan development area was unsteady and

closely resembled a flood hydrograph. The amount of material that

wasplaced intheinletchannelforeachepisodeweighedapproximately

75.6 N (17 lb,dryweight) and consistedof poorlysorted coarsesand.

The second series of experiments was performed after the

experimental apparatus was modified to eliminate some undesireable

characteristics suchasthe recycling fine sediment through thewater

system. This series consisted of three experiments, and each of

these experiments consisted of 35 or more episodes. Each episode

generally included a debris flow followed by a water flow. The

sediment material used in this series of experiments wasamixtureof

fine sand, pebbles, and a large amount of clay and silt. The debris

flowswerecreatedbymixingaslurryof sediment and water in abucket

and transferring a known quantity of this slurry to the inlet box of

the experimental apparatus. The slurry had fluid properties

characteristic of a Bingham plastic fluid.

4.3.3 Verification

Given the initial premises on which this experimental program

was based, verification emphasized a detailed discussion of the

geometric similarity of the fans developed in the laboratory with

those found in the natural environment. In particular, the

laboratory fans had shapes and slopes similar to those found in the

field. The similarity of water and debris flows simulated in the

laboratory and those that have been observed in the natural

environment was also discussed.

4.3.4 Results

A number of significant conclusions and observations were

156

derived from t h i s experimental program. F i r s t , with regard t o t h e i n t e r s e c t i o n p o i n t , i twasconcludedthatthe locat ionofthis f e a t u r e on an a l l u v i a l fan s i g n i f i c a n t l y a f f e c t s t h e locus of sediment deposit ion. Note, t h e i n t e r s e c t i o n po in t is t h e po in t where t h e channelmergeswiththe f ansu r face , Hooke (1965) . I twou ldappea ron t h e basis of t hese laboratory experiments t h a t t h e loca t ion of t h e i n t e r s e c t i o n po in t on t h e s u r f a c e of an a l l u v i a l fan is related t o t h e r e l a t i v e importance of debris and water flows i n t r anspor t ing sediment on t h e fan system1 when water flows predominate, t h e i n t e r s e c t i o n po in t is found c l o s e r t o t h e apex of t h e fan than when debris flows predominate. Qua l i t a t ive ly , t h i s observation can be j u s t i f i e d by not ing t h a t debris flow deposi t ion usua l ly provides sediment t o t h e a reas of t h e fan above t h e i n t e r s e c t i o n po in t while sediment is provided by water flows t o t h e lower po r t ions of t h e fan with t h e downfan migration of t h e i n t e r s e c t i o n point . I f deposi t ion is t o occur uniformly over a l l p a r t s of t h e fan su r face , then t h e locationoftheintersectionpointmustchangetoreflectthe r e l a t i v e importance and e f f ec t iveness of debris and water flows i n t h e fan bui lding process.

I n the laboratory experiments, t h e up and down fan movement of t h e i n t e r s e c t i o n point w a s general ly t h e r e s u l t of deposi t ion a t t h i s point . T h a t is, a s d e p o s i t i o n a t t h i s p o i n t occurred, thechannelwas backf i l l ed and t h e i n t e r s e c t i o n point moved up t h e fan. This same process has a l s o been observed i n the f i e l d ; see f o r example Eckis (1928).

I n t h e t r ansve r se d i r ec t ion , t h e i n t e r s e c t i o n po in t is commonly located near t h e cen te r of t h e a c t i v e port ion of t h e fan. The loca t ion of t h e i n t e r s e c t i o n point both t r ansve r se ly and longi tudinal ly may dictate t h a t deposi t ion doesno t occuron p a r t s o f a fan surface f o r geological ly long periods of t i m e . Hooke (1965) noted t h a t on fans i n Death Valley, Cal i fornia and Nevada t h e in t e r sec t ion point is found near the t o e s o f t h e fans o n t h e w e s t s ide and n e a r t h e ap iceso f t h e fans loca t edon t h e e a s t side. However, i f only t h e cu r ren t ly a c t i v e segments of t hese f a n s a r e considered, then t h e in t e r sec t ion po in t s a r e reasonably located; t h a t is, near t h e cen te r o f theac t ivesegmen t . Major s h i f t s i n t h e l o c u s o f deposit ion and t h e a s s o c i a t e d renderingof c e r t a i n p a r t s o f a f an inac t ivemaybe the r e s u l t of t e c t o n i c movement, climatic change, o r o the r major environmental changes.

A second important obseryation tha t r e su l t ed from t h i s experimental program regards t h e blockage and divers ion of themain

157

Tread o f Lobe Pebble t o Cobble Sized

Front o f Sieve Lobe Cobble t o Boulder Sized

Horkontal Reference Line

FIG. 4.3.1 (1965).

Cross section of an idealized sieve deposit, after Hooke

channel near the apex ofthe fan. A channel diversion is usuallythe

result of a debris flow stopping and blocking the channel or in

isolated cases a single large boulder blocking the channel, Beaty

(1963) . After the channel is blocked, flows may be diverted to a new

portion of the fan. The channel may also be blocked by what Hooke

(1965,1967) identified as a sieve deposit. Sieve deposits

apparently result when high infiltration rates through the channel

bed rapidly decrease the water available for sediment transport and

cause the deposition of a highly permeable sediment lobe in the

channel, Fig. 4.3.1. Once this lobe is deposited, the channel slope

upstream is reduced by the backfilling of the channel. Sieve

deposits have been observed in the natural environment and sieve

deposition was observed during the course of these experiments.

Hooke (1965) identified two basic requirements forthe formation of

sieve deposits. First, the sediment being transported must have

preponderanceof coarsematerials with insufficient fines to fill the

voids. This condition is necessary because once the sieve lobe is

initially formed, the water must pass through it as well as over it.

Second, there must be a discontinuity in the sediment transport

capacity of the flow; that is, the sediment load must exceed the

sediment capacity of the flow. Although this condition can be

fulfilled by the formation of a sieve deposit, it can also be met by a

discontinuity in the channel slope; specifically from relatively

steep slopes to milder slopes.

One of the possible consequences of sieve deposition is the

migration of the channel. For example, as fine material is

deposited, the infiltration rate of the water at the sieve deposit

decreases and the depth of water upstream increases and eventually

158

causes e i t h e r the erosion of t h e s ieve deposi t of t h e formation of a new channel.

A t h i r d observation is t h a t a t t h e in te rsec t ion point , t h e flow spreads out with t h e coarser mater ia l being deposited and t h e flow becoming concentrated i n several secondary channels. Further down t h e fan a braided o r t r i b u t a r y channel p a t t e r n may be formed, Fig. 1.2.2. Tributarychannelpatternsmaydevelopwhenthewaterbecause

of deposit ion a t o r near t h e in te rsec t ion point has reduced t h e sediment load below t h e l e v e l t h a t t h e flow is capable of t ransport ing. Hooke (1965, p. 137) suggested t h a t on fans with t r i b u t a r y channel pa t te rns t h a t debris flows may be a more important f a c t o r than water flows i n t ransport ing material . I n cont ras t , a downfan braided channel pa t te rn suggests t h a t water flows a r e t h e predominate t ranspor t mechanism below t h e in te rsec t ion point .

Fourth, t h i s experimental program, a s wasmentioned i n c h a p t e r 2, suggests t h a t fanhead channel entrenchment may be t h e na tura l r e s u l t of a l t e r n a t i n g debris and water flows on an a l l u v i a l fan. Debris flows r e q u i r e a f a r s teeper s lope than water flows t o t r a n s p o r t material . Thus, debris flows may deposi t mater ia l both i n the entrenched channel and on t h e fan surface above t h e trench with subsequent water flows eroding and t r a n p o r t i n g t h e smallermater ia l .

Fanhead channel entrenchment may a l s o occur when t h e locus of deposit ion is s h i f t e d t o a locat ion on t h e fan t h a t has not received deposit ion f o r an extendedperiod of t ime. I n suchcases , t h e slopes t o these topographic lows a r e la rge r e l a t i v e t o t h e s lopes t o other locat ions on t h e fan and increase t h e a b i l i t y of t h e flow t o erode a trench. Asnoted i n c h a p t e r a , entrenchment o f t h i s type is temporary andonlylastsuntilthetopographic lowhas aggradedto thee leva t ion of t h e rest of t h e fan.

4.3.5 Summary While t h e model described i n t h i s sect ion has only l i m i t e d

quant i ta t ive u t i l i t y from t h e viewpoint of hydraulic processes on a l l u v i a l fans, it was general ly designed and used t o obtain q u a l i t a t i v e r e s u l t s , and i n doing t h i s it succeeded. Among t h e important r e s u l t s f r o m t h i s programare t h e laboratory discovery and subsequent f i e l d i d e n t i f i c a t i o n of s ieve deposi ts and hypotheses regarding channel entrenchment, t h e movement of t h e loca t ion of t h e in te rsec t ion point with t i m e , and t h e formation of t r i b u t a r y and braided channel p a t t e r n s on t h e fan below t h e in te rsec t ion point.

159

4 . 4 NUMERICAL/PHYSICALMODEL, ENGINEERINGT1MESCALE:ANON. (1981a) The model s t u d i e s described i n t h i s s ec t ion were undertaken t o

g a i n a b e t t e r u n d e r s t a n d i n g o f flood processeson a l l u v i a l fans a n d t o a s ses s t h e r e l a t i v e e f f ec t iveness of var ious flood damagemitigation techniques. The s t a t e d ob jec t ives of t h e study w e r e t o :

1. inves t iga t e t h e bas i c hydraulic and sediment conditions on a l l u v i a l fans:

2 . examine 'whole fan ' f lood damage mit igat ion techniques f o r prototype fans: and

3 . test loca l : t h a t is, less than whole fan, damage mitigation techniques.

O f t h e s tudiesperformedinthismodel ingef fort , onlythoseperformed with an idea l i zed f a n w i l l be discussed s ince t h e s t u d i e s a n d r e s u l t s focused on flood damagemitigation proceduresare beyondthe scopeof t h i s book.

Two idealized a l l u v i a l fans with expansion angles of 90 degrees andwi th2 a n d 5 p e r c e n t s l o p e s weredesigned andcons t ruc t ed tos tudy t h e following

1.

2 .

3 .

4 .

5 .

hydraulicvariablesandchannelgeometryandtheresponseof

t hese va r i ab le s and channel geometry t o a varying supply of sediment ,

flow p a t t e r n s and t h e zones of flooding on an a l l u v i a l fan,

t h e e f f e c t o f t h e s l o p e o f t h e fanontheresultingpatternof channels and t h e hydraul ic c h a r a c t e r i s t i c s of t h e flow,

t h e e f f e c t of t h e channel entrance angle a t t h e apex of t h e fan on both t h e channel p a t t e r n and t h e zones of flooding, and

t h e v a r i a t i o n s i n fanmorphology andhydraul ics inresponse t o mult iple flow events.

Thus, t h e goals , object ives , and t i m e scale used i n t h i s modeling e f f o r t are t o t a l l y d i f f e r e n t than t h e modeling e f f o r t s described i n

160

Sec t ions 4.2 and 4.3 of t h i s chapter . T h i s s tudy was a t r a d i t i o n a l phys ica l hydrau l i c model s tudy which followed t h e p r i n c i p l e s of hydraul ic s i m i l i t u d e described i n Chapter 3, Sec t ion 6.

4.4.1 Experimental Apparatus These s t u d i e s w e r e performed i n t h e r i v e r mechanics flume

loca ted a t Colorado S t a t e Univers i ty , Fo r t C o l l i n s , Colorado. T h i s

flume is 12 m (39 f t ) w i d e , 36.6 m (120 f t ) long, and 1 m (3.3 f t ) deep. A t t h e downstream end, there is a sediment t r a p and a pump/pipe i n s t a l l a t i o n f o r r e c i r c u l a t i n g t h e water-sediment mixture t h a t is recovered a t t h i s po in t .

S ince there a r e no i d e a l i z e d f ans i n ex i s t ence , a number of assumptions w e r e requi red t o e s t ima te t h e appropr i a t e model r a t i o s . For example, t h e fan expansion angle was taken a s 90 degrees ; two uniform s lopes of 2 and 5 pe rcen twereassumed ; t h e m a t e r i a l s i z e w a s a s sumed tobecha rac t e r i zedbyd5 , = 3mm ( 0 . 1 2 i n ) ; a n d t h e w i d t h o f t h e canyon a t t h e apex of t h e f an was taken a s 45.7 m (150 f t ) . These dimensions a r e s i m i l a r t o those of t h e Embudo Fan nea r Albuquerque, N e w Mexico. W i t h these dimensions, the fol lowing model s c a l i n g r a t i o s w e r e determined

L, = 1/150

Y, = 1/10

T, = 1/26

Q R = 1/1.4743

The a c t u a l cons t ruc t ion of t h e model c l o s e l y followed t h e procedures d iscussed i n Sharp (1981) and French (1985).

4.4.2 Theore t i ca l Assumptions and Development These i n v e s t i g a t o r s c o r r e c t l y n o t e d t h a t flow ac ross a n a l l u v i a l

fan is a func t ion of many v a r i a b l e s and t h a t it is d i f f i c u l t t o s epa ra t e t h e independent f r o m t h e dependent v a r i a b l e s . I f on ly t h e fan a r e a f r o m t h e apex t o t h e t o e i s c o n s i d e r e d , t hen it is reasonable t o assume t h a t t h e water d i scharge ; sediment s i z e , g rada t ion , and dens i ty ; and t empera tu rea re t h e independent v a r i a b l e s w h i l e t h e flow width, veloc i tyanddepthandtheenergyandchannelbeds lopes a r e t h e dependen tva r i ab le s . These i n v e s t i g a t o r s f u r t h e r hypo thes i zed tha t sediment d i scharge c l a s s i f i c a t i o n can be made on t h e b a s i s of t h e fol lowing two cases . F i r s t , i f the f an is i n an equi l ibr ium cond i t ion , t h e n t h e v e l o c i t y , depth, and wid tho f flow a r e a d j u s t e d t o

161

a statesuchthattheenergy available is just sufficient totransport

the sediment that is delivered. That is, in the equilibrium

condition, the sediment load which is a function of the flow rate and

the sediment properties determine the otherhydraulic properties and

the channel geometry. Second, if the fan is not in equilibrium, then

the sediment load varies in both time and space and depends on the

hydraulic variables.

If it is assumed that the unknown or dependent variables which

must be determined are the velocity, width, and depth of flow and the

energy and channel bed slopes, then with a number of simplifying

assumptions estimativeequations fortheseunknowns canbedeveloped.

At any cross section, the average velocity of flow, u, can be related to the depth of flow, y, and the sediment size, d,, or

- U Y - a l n - u* ds

where as in Chapter 3 u* = shear velocity or

(4.4.1)

u* = 4%. (4.4.2)

T = bed shear stress, y = depth of flow, and p = fluid density. As

noted in Chapter 3, Shields experimentally determined that the

critical bed shear stress, T , , could be expressed as

T C

Y(S,-l)ds = c (4.4.3)

where Y = specificweight ofthe fluidand S, = specificgravity ofthe

soil particlescomposingthebed ofthe channel. If S, andC areboth

relatively constant and an equilibrium situation is considered, then

Equation (4.4.3) can rearranged to yield

r C a Y d,

and substituting this result in Equation (4.4.2)

u * = a & (4.4.4)

where g = acceleration of gravity and Y = pg. Substitution of

Equation (4.4.4) in Equation (4.4.1) yields

16 2

Y u a - ] l n -

d s ( 4 . 4 . 5 )

It has been observed both i n t h e laboratory and t h e na tu ra l environment t h a t a s t h e flowpasses f rome i the r themountain canyonor an entrenched channel onto t h e surface of t h e fan t h a t it expands l a t e r a l l y and t h e depth and ve loc i ty of flow decrease i n t h e downstreamdirection. From a q u a n t i t a t i v e viewpoint, t h e reason f o r t h i s flow expansion is unclear and t h e l ack of a s a t i s f a c t o r y explanation forthisphenomena con t inues to impedethe development of a r a t i o n a l and j u s t i f i a b l e theory which can be used t o p r e d i c t t h e v a r i a t i o n i n h y d r a u l i c v a r i a b l e s a s a funct ionof downslopedistance. In t h i s study, it w a s a s sumed tha t f lowona fancouldbeapproximated a s s l o t j e t flow. I n t h e c a s e of s l o t j e t flow it can beshown; see f o r example, French ( 1 9 8 5 ) , t h a t - u a x - ' ' ~ ( 4 . 4 . 6 )

where x = longi tudinal d i s t ance from t h e o r i g i n of t h e j e t . One expression tha t s a t i s f i e s t h e p ropor t iona l i t y defined by Equation ( 4 . 4 . 6 ) is

( 4 . 4 . 7 )

where T o = width of the canyon mouth and C and 6 are undetermined coe f f i c i en t s . Application of t h e the boundary condi t ion a t t h e mouth of t h e canyon: t h a t is, a t x = 0 , u = u,, y i e l d s

-

( 4 . 4 . 8 )

whereu, = v e l o c i t y o f f l o w a t t h e canyonmouth a n d t h e a p e x o f t h e fan. Subs t i t u t ion of Equation ( 4 . 4 . 8 ) i n Equation ( 4 . 4 . 5 ) y i e l d s an expression involving a c o e f f i c i e n t of proport ional i tywhich c a n a l s o be evaluated by again invoking t h e boundary condition a t t h e apex of

163

1,o

0,80

0.60

X I S

0,40

0.20

0,

ci = 0,s /-

0. 10. 20, 30, 40, 50. X - To

F I G . 4 . 4 . l a m 3 / s ( 2 , 0 0 0 f t 3 / s ) , B = 60 , and To = 4 6 m (150 f t ) .

y/yo a s a f u n c t i o n o f x / T o f o r d , = l m m (0.039 i n ) , Q o = 5 7

t h e fan: t h a t is, a t x = 0, y = y o . applying t h e equation of cont inui ty; t h a t is,

The r e s u l t a f t e r removing u by

Q u, = -

TOY0

where Q = flow r a t e , yo = depth of flow a t t h e apex of t h e fan and a rectangular channel has been t a c i t l y assumed is

( 4 . 4 . 9 )

wherey=dep thof f l o w a t a n y d i s t a n c e x fromthe apexof the fan. The best f i t v a l u e o f 0 f o r t h e dataobtained i n t h i s experimental program was 60. Fig. 4.4.la i sadimensionlessplotwhichshowsthevariat ion

of y/yo a s a function of x/T, f o r var ious values of u o w i t h d , = 1 mm (0 .039 i n ) . Fig. 4 . 4 . l b is a dimensionless p l o t of y/yo versus x/To

164

1,o

0,80 - \ r u = Oa5 m's

0,60

XIS 0,40

0.20

0,

m / s

0. 10. 20, 30, 40. 50, X

F I G . 4 . 4 . l b m 3 / s ( 2 , 0 0 0 f t 3 / s ) , B = 60, and To = 4 6 m (150 f t ) .

y/yo a s a f u n c t i o n o f x / T o f o r d , - 3 mm(0.12 i n ) , Q o = 5 7

f o r var ious values of u, w i t h d , = 3 mm ( 0 . 1 2 i n ) . I n both of these f igu res Q, = 57 m 3 / s ( 2 , 0 0 0 f t 3 / s ) , B = 60, and T o = 4 6 m (150 f t ) . These f igu res demonstrate t h a t a s u, increases y/y, as a function of x/T, d e c r e a s e s l e s s r a p i d l y . Further, t h e r a t e o f d e c r e a s e o f y / y , a s a funct ionofx/T, decreasesasthesizeofthematerialcomprisingthe fan increases .

A t t h i s po in t , equations f o r the w i d t h and v e l o c i t y of flow and the energy and channel bed s lopes must be developed. These inves t iga to r s chooseto estimatetheManningroughness c o e f f i c i e n t b y assuming t h a t it is composed of two p a r t s o r

n = n1 + nl* ( 4 . 4 . 1 0 )

where nl = r e s i s t ance due t o sk in f r i c t i o n and is given by

( 4 . 4 . 1 1 )

andn"=res is tanceduetoformdrag. InEquation ( 4 . 4 . 1 1 ) , d,, i s t h e s i z e of channel mater ia l such t h a t 65 percent of t h e ma te r i a l , by weight, is smaller. is estimated by

165

FIG. 4.4.2 n8@ as a function of (l/$), Bajorunas (1952).

(4.4.12)

where

4.4.2 and

(l/$) indicates the functional relationship defined in Fig.

166

1 R ' S f - =

(Ss-l)d35

where S f = f r i c t i o n s lope, RI is given by

3 / 2

R l = {<]

( 4 . 4 . 1 3 )

( 4.. 4 . 1 4 )

and d3 = s i z e of material such t h a t 35 percent of t h e mater ia l , by weight, is smaller. The above equations allow a value of n t o be estimatedandtheManning equation, Equation ( 3 . 4 . 1 ) , then providesa funct ional r e l a t ionsh ip among u and n, R , and S , . Note, it is asser ted i n t h i s study t h a t channels which convey flow on a l l u v i a l fans are wide, and the re fo re , t h a t t h e depth of flow, y, can be subs t i t u t ed f o r t h e hydraulic radius i n t h e Manning equation. The r e s u l t i n SI u n i t s is

(4.4.15)

Asecondequat ionis obtainedfromtheprinciple ofconservat ion of momentum f o r steady flow or - u d c dy

g dx dx + - = s 0 - Sf

- - ( 4 . 4 . 1 6 )

whereso = s l o p e o f t h e b e d o f thechannel . I n t h i s s t u d y , a n e x p l i c i t f i n i t e d i f f e rence scheme w a s used t o solve Equation (4.4.16) ; see f o r example, French (1985).

A t h i r d equation i s conse rva t ion ofmass wi thbo th a rec t angu la r channel and m i n i m a l i n f i l t r a t i o n losses assumed o r

Q = u T y ( 4 . 4 . 1 7 )

The fourth equation used by these inves t iga to r s is s i m i l a r t o t h a t developed by Yang (1972, 1973) f o r estimatingthetotalsediment concentration i n a flow or

log(C,) = 5.165 - 0.154 l 0 { 7 ] u d 5 0 - 0.297 lo{'] + (1.78 -

(4.4.18)

167

where = fall velocity of the sediment particle, v = kinematic

viscosity, d,, =median sediment size, andu,' =gyS, = shearvelocity.

4.4.3 Results

Since there is very little, if any, field data available to test

the validity of the analytic equations developed in the previous

section, data obtained from the physical hydraulic models of

idealized alluvial fans was comparedwith the results estimated from

Equations (4.4.9) and (4.4.15) - (4.4.18) . Recall that in these

equations the coefficient 0 was determined from the experimental

data; that is 0 was calibrated but not verified. There was good

agreement between the measured and predicted depths, widths, and

velocities of flow, Figs. 4.4.3a, 4.4.333, and 4.4.3~2, repectively.

There was also reasonable agreement between the measured and

predicted channel slopes, Fig. 4.4.34. In the case of bed slope, it

was suggested that some of the disagreement between measured and

predicted values was due to the experimental procedures and the time

at which the slope measurement was made - after the experiment was completed.

Theotherresult ofthisworkwasthe development of acapability

of intelligently commenting on the effect of the variation of

independent variables on the dependent variables. In particular,

the effects of sediment size and sediment load on the hydraulic

variables were examined in some detail.

For fine sediment material, the rateof increase in flowchannel

width is much larger than for coarse material. As noted in this

investigation, this result is the opposite of the one might be led to

by intuition; that is, in fine materials, the channel should be

rather narrow but deep. This intuitive conclusion is erroneous

because

1.

2 .

In finematerials, the channelbanks arehighly erodibleand

the flowexpandsrapidly asthe banksare cutback. Recall,

fromsection 3.4 thatparticleson thesides ofa channel are

subject to gravitational forces which tend to both roll the

part ic ledownthes ideofthechannelandinthelongi tudinal direction. Particles on the bed of thechannel aresubject

to only the gravitational force in the longitudinal

direction.

Fans comprised of fine materials generally exhibit lower

168

Calculated Depth o f Flow (d

0.038 - 0.03 -

0.025 - 0.02 -

0.015 - 0.01 -

0 0.005 0.01 0.015 0.02 0.025 0.03 0.Om

Measured Depth o f Flow W

F I G . 4 .4 .3aDepthof f l o w e s t i m a t e d b calculationversusthemeasured depth of flow i n t h e h s i c a l hydrau l i c models of i d e a l i z e d a l l u v i a l f ans , a f t e r Anon. ( h f l a ) .

Calculated Channel Hldth (d

Measured Channel Width W

FTG. 4.4.3bWidthof f l o w e s t i m a t e d b calculationversusthemeasured width of flow i n t h e h s i c a l hydrau r i c models of i d e a l i z e d a l l u v i a l f ans , a f t e r Anon. (f9'sB;a).

169

0.04

0.02 0.03

0.01

0

o v ' I 1 I I I I I

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.6 0.9 1

Measured Velocity o f Flow Ws)

r

- - / /---

Ilraaurad O.tr -rk-

calculated Dot8

- .-- /'

--.---- I I I I I I

F I G . 4.4.3~ VeJocit of flow estimated by calculation versus the measured velocity 0% flow in the ph sical hydraulic models of idealized alluvial fans, after Anon. ('198la).

F I G . 4.4.3d Calculated slope of the channel versus the measured slope of the channel in the h sical hydraulic models of idealized alluvial fans, after Anon. PlJ8la).

170

surface s lopes than those composed of coarse mater ia ls . Thee f fec t of s l i g h t s lopes is t o reduce t h e v e l o c i t y of flow and i t se ros ivepower . Note, t h e r e a s o n t h a t f i n e m a t e r i a l s form fans with lowersurface s l o p e s i s t h a t f i n e material is transported much f u r t h e r downslope.

A consequenceoftherapid i n c r e a s e i n widthwith f i n e r m a t e r i a l s i s a corresponding rapid decrease i n t h e depth of flow.

The e f f e c t of t h e sediment load on t h e hydraul ic va r i ab le s and t h e shape of t h e fan surface can a l s o be q u i t e dramatic. When the water-sediment mixture leaves t h e canyon mouth, t h r e e general cases can be recognized. These cases and t h e i r r e s u l t i n g e f f e c t s are:

1.

2 .

3 .

I f t h e sediment load is less than t h e sediment t r anspor t c a p a b i l i t y of t h e flow, the r e s u l t is entrenchment of t he channel a t the apex of t h e fan. The e f f e c t of fanhead channel entrenchment is t o l o c a l l y r educe the channel slope and t o br ing t h e sediment load and flow sediment t r anspor t capacity i n t o equilibrium. The entrenchment process r e s u l t s i n a heavy sediment load which is deposited downstream. T h i s deposit ion reducesthe gradient upstream and c o n t r i b u t e s t o t h e i n i t i a t i o n of a channel backf i l l i ng process. Asthebackf i l l ingprocesscont inues , two r e s u l t s are possible . F i r s t , t h e gradient adjustment process can continue u n t i l an equilibrium condition is a r r ived a t and a s t a b l e channel develops. Second, as t h e deposit ion downstream becomes s i g n i f i c a n t and t h e reduction i n upstreamgradient becomes s i g n i f i c a n t and thedep th of flow upstream increases u n t i l overbank flow occurs. Such a s i tuat ionmayresu l t in thewater leav ingtheo ldchanne land

forming a new channel. These inves t iga to r s termed t h i s phenomena an avulsion.

I f t h e sediment load is equal t o t h e sediment t r anspor t capacity o f t h e flow, and t h e r e i s a n e x i s t i n g channel, then t h e r e s u l t w i l l be a s t a b l e channel. I f there is not a de f inedchanne lon the fan surface, t h e n t h e f lowwi l l spread ou t and deposit ion w i l l occur.

I f t h e sediment load is g r e a t e r than t h e sediment t r anspor t capaci ty of t h e flow, deposi t ion w i l l occur immediately

171

downstream of t h e apex of t h e fan. I f a channel ex i s t s , it w i l l be gradually f i l l e d and e i t h e r a new channel w i l l be formedorthewhole f a n s u r f a c e w i l l f lood. Eventually, t he aggradation process w i l l increase t h e fan slope.

The above t h r e e p o s s i b i l i t i e s a r e obviously idea l i zed cases. Since neitherdischargenorsedimentloadareconstant i n a f l o o d s i t u a t i o n , a l l t h r e e casesmay occur during a s i n g l e flowevent. The problemis f u r t h e r complicated because fan surfaces i n t h e na tu ra l environment do not have uniform slopes a s they d id i n these laboratory experiments.

The e f f e c t of t h e sediment load on t h e width of flow is e s s e n t i a l l y t h e same assediment s i z e ; t h a t i s , w i t h smallersediment loads t h e r a t e of w i d t h increase is more rapid than with l a r g e r sediment loads. The e f f e c t of t h e sediment load on thedep th o f f low cannot be d i r e c t l y evaluated. The sediment load f o r a spec i f i ed discharge v a r i e s inversely with t h e sediment s i z e . Thus, t h e e f f e c t of sediment load on t h e depth of flow is a complex r e l a t i o n between discharge and sediment s i z e .

On fans with s teep s lopes, t h e flow may entrench i t s e l f and reduce the channel gradient w i t h t h e r e s u l t being t h a t t h e width of flow becomes s tab i l ized . As

t h e water moves downslope, i ts t r anspor t capaci ty becomes less and deposi t ion occurs. Thus, on s t eep fans, entrenchment of t h e channel a t t h e apex of t h e fan is expected, and t h e r e w i l l probably be a small increase i n t h e width of channel with longi tudinal dis tance. Downslope, t h e r e w i l l be a braided channel pa t t e rn . On gen t l e s lopes, t h e r e may be a s h o r t entrenched channel or t h e r e may be no channel entrenchment a t a l l .

Theresultsofthiseffortwithregardtotheeffectofthecanyon

entrance angle w e r e not d e f i n i t i v e because the s lope of t h e fan surface inbothcaseswasuniform. S ince the f o r c e o f g r a v i t y o n a f a n a c t s perpendicular t o t h e contours and is proportional t o t h e slope, there was not a preferred d i r e c t i o n of motion on t h e fan i n these experiments.

These inves t iga to r s a l s o s tudied t h e e f f e c t of mult iple flow events on t h e morphology of t h e fan surface and t h e hydraulic va r i ab le s , but t h e r e s u l t s were not conclusive.

Final ly , a l l u v i a l channel p a t t e r n s on a fan are usually c l a s s i f i e d a s being s t r a i g h t , meandering, or braided. On a l l u v i a l fans meandering channels a r e u n l i k e l y tooccurbecausefloweventsdo

The e f f e c t of t h e s lope of is a l s o complex.

112

FIG. 4.4.4 point.

not have durations that are long enough for such channel patterns to

develop. Once the flow passes the intersection point, a braided

channel pattern may develop. In fact, the location of the

intersection point can be estimated from the analytic results

presentedearlier inthis section. Withreference to Fig. 4.4.4, the

curve labeled AD represents the bed of the channel, curve BE

represents the water surface level, and curve CD represents the fan

surface. Point D is the intersection point. The slope of the

channel bed can be represented as

Schematicdefinition forthe locationofthe intersection

s o = - (dz/dx) (4.4.19')

where z is the elevation of the bed of the channel above some datum.

In finite difference form, Equation (4.4.19) becomes

znt1 = zn - Son(Xn+l - Xn) (4.4.20)

where the subscripts indicate computational nodes which have their

origin at the apex of the fan, Point A in Fig. 4.4.4. Since the

material that comprises the bed of the canyon channel is usually

resistant to erosion, the elevation of Point A will remain rather

constant or fixed in time. If this is the case, then Equation

(4.4.20) used in conjunction with Equations (4.4.9) and (4.4.15) - (4.4.18) allowsthe estimationofthechannel bedprofile. Aplotof

the fan surface and channel bed profile together allow Point D, the

intersection point, to be estimated. Note, Equation (4.4.20) isnot

valid downslope of the intersection point.

173

4.4.4 Summary

While the results of this numerical/physicalmodeling effort are

highly quantitative and may be useful under certain circumstances,

theyaresubjecttoanumberofgeneral l imitat ions. First, whilethe

agreement between measured and calculated variables is good except

for one set of experiments, these results were only compared for

single ratherthanmultiple flowevents. These resultswould bemuch

more satigfying if more experiments consisting of multiple flow

events were available.

Second, in all experiments, the initial sediment concentration

and characteristic sediment sizewerenotvaried. Thus, tacitlyonly

steady flood flows across alluvial fans were studied which is a

contradiction in terms. The extent to which these results can be

extended to very unsteady flows common on alluvial fans is unknown.

Third, debris flows and their effect on the channels and fan

surface were not considered. As has been mentioned previously,

debris f lowscanbeas igni f icanthazardandhavesubstant ia le f fects ,

particularly on the upper portions of the fan. Admittedly, debris

flows are difficult to model.

Fourth, the canyon entrance angle and its effect on hydraulic

processes on alluvial fans was not extensively examined.

Fifth, as admitted bythe investigators, the assumptionof aslot

jet analogy to estimate the depth of flow is questionable. In the

experiments discussed, the results were reasonable, but thevalidity

of this assumption in particular remains somewhat tenuous.

In addition to therather general limitations ofthis model study

noted in the foregoingparagraphs, Anon. (1985) performed a detailed

reviewofthisstudyandidentif iedanumberofspecif icerrors inboth the design of the physical model and the associated theoretical

development. The following paragraphs summarize the discussion

presented by Anon. (1985).

With regard to the design of the physical model, Anon. (1985)

identified numerous scaling problems. For example, in the models

designed by Anon. (1981a) the ratio of model to prototype slopes, S,,

was taken as 1. However, since models were distorted scalemodels;

i.e. L, # Y,, S, is clearly not unity. Anon. (1985) after correcting

other scaling errors found that S, should have had a value of 1.206.

In addition to this primary error, Anon. (1985) noted that

1. the characteristics of incipient sediment motion; see for

174

2.

3 .

4.

example Chapter 3, Section 6, were not properlyconsidered.

the assignment of a friction factor for the model was

arbitrary and did not take into account the model was a

distorted model.

the model distortion; i.e. Y,/L,, is much too large for a

moveable scale model: see for example Anon. (1942).

the use of solid blocks at the toe of the model fan created an

artifical erosion control point which had an unknown effect

on the results.

With respect to the theoretical development presented by Anon.

(1981a) and discussed in this section, there are also a number of

errors and serious problems, Anon. (1985). These errors derive

primarily from the assumption that the bed shear stress is critical,

Equation (4.4.3) and the subsequent use of this assumption in the

theoretical development. As noted by Anon. (1985) if anequilibrium

alluvial channel exists on a fan surface, then the bed shear stress

m u s t b e g r e a t e r t h a n c r i t i c a l s i n c e i f i t i s l e s s d e p o s i t i o n w i l l o c c u r

and the channel will not be in equilibrium. Anon. (1985) also noted

that Anon. (1981a) gave no indication how the system of equations

developed could be solved and discussed the possible

inappropriateness of the slot jet assumption, Equation (4.4.6) . Finally, the development does not include a conservation of mass

equation for the sediment.

Irregardless of the limitations of this study, it does provide a

theoretical, albeit limited, framework for the development of more

complex and comprehensive models. However, the reader is cautioned

to carefully consider the theoretical errors noted above and their

unknown effect on the results.

4.5 NUMERICAL MODELS OF DEBRIS FLOWS IN CHANNELS ; DELEON AND JEPPSON

(1982) AND JEPPSON AND RODRIGUEZ (1983)

As discussed in Chapter 3 Section 5, DeLeon and Jeppson (1982)

developed a functional relationship between the Chezy uniform flow

resistance coefficient and the Reynolds number for laminar debris

flows, Equation (3.5.19). These investigators then hypothesized

anempirical relationshipamong thedebris flowdensity andviscosity

and the hydraulic radius of the flow, Equation (3.5.21). These

results were then used to develop a spatially varied but steady flow

numerical model of debris flows and subsequently to develop an

unsteady numerical model of debris flows, Jeppson and Rodriguez

175

(1983). It is the purpose of this section to discuss these modeling

efforts and the results obtained from them; however, the steady

spatially varied and unsteady flow equations and the numerical

solution of these equations will not be discussed because this is a

traditional area of hydraulic engineering; see for example, French

(1985) or Jeppson (1974).

4.5.1 Debris Flow Relative to Water Flow Depths

Damage resulting from debris flows is among other things

directly related to the depth of the flow, and the depths of flow

associatedwithdebris flows aregreater thanequivalent -volumetric

equivalency - water flows. A comparison of the normal depths of

debris and water flows can be easily obtained if a wide rectangular

channel is assumed. For water flows in such a channel, the Manning

equation in SI units states

Q 1

T n - _ - q = - y 5 J 3 (4.5.1)

or

3 / 5

yw =

where Q = volumetric discharge, q = discharge per unit width, n =

Manning resistance coefficient, S = channel bed slope, T = channel

width, and yw = normal depth of water flow. For a debris flow

occurring at normal depth, Equation (3.5.24) states

Q2P - 11.41A'*96Q''04S = 0

or

Q2T - 11.41(yoT)'*96Q'*04S = 0 (4.5.2)

where P = wetted perimeter of the channel, A = flow area, and yo =

normal depth of debris flow. Rearranging Equation (4.5.2) and

solving for yo yields

(4.5.3)

The ratio of normal debris to normal water depths of flow can be

obtained by dividing Equation (4.5.3) by Equation (4.5.1) or

176

50,

0,00001 0.0001 0,001 0.01 0,1 1. Channel Slope

FIG. 4.5.la yD/yn as a func t ion of S f o r q = 0 . 2 m 3 / s / m ( 2 . 2

f t 3 / s / f t ) .

40,

h3 301

P 20,

\

10.

0. 0.00001 0.0001 0,001 0.01 0.1 1,

Channel Slope

FIG. 4.5.lb yD/yw as a function of S fo r q = 0.5 m 3 / s / m (5.4

f t 3 / s / f t ) .

YO 0.29

Y V q - P

~ 0 . 2 1 ~ 0 . 6 0 . 1 1 0 4 (4.5.4)

177

0. I I I 1 1 1 1 1 I I I I 1 1 1 1 1 I I I 1 1 1 1 I I I I I 1 1 1 I I I I l l l l

0,00001 0.0001 0.001 0,Ol 0s 1,

Channel Slope

FIG. 4.5.1~ y,/y,,asafunctionofsfor q = 1.0m3/s/m (11ft3/s/ft).

In Figs. 4.5.1, yD/yu is plotted as a function of S for q = (0.2 ;

0.5; and 1.0) m3/s/m and for n = 0.035 and 0.017. With regard to the

curves in this figure, the followingcomments canbemade. First, on

mild or slight slopes yo /yU is large indicating that yo is

significantly larger than yw. second, on steep slopes yD/yu is

smaller but yD remains several times larger than y,,, Third, as q

increases, yo/y,, decreases but less rapidly than it does with

increasing slope. Fourth, as n decreases, yo/yu increases.

DeLeonandJeppson (1982) assertedthatthecurves inFigs. 4.5.1

explain, at least in part, why debris flows suddenly stop and leave

wave shaped forms on the landscape. As the bed slope of the channel

decreases, yo increases and to satisfy the continuity equation, the

velocity of flow must decrease; thus, at some point movement must

cease.

4.5.2 Boundary Conditions

As is the case with all models, these models require the

specification of boundary conditions. Typical upstream boundary

conditions for these models would include the specification of the

depth of flow as a function of time or the discharge as a function of

time. In the case of unsteady flow, the specification of an

appropriate downstream boundary condition was difficult. Jeppson

and Rodriguez (1983) discussed a number of possible downstream

178

boundary conditions such as:

1. The use of the continuity and momentum equations at the

leading edge of the debris flow from the viewpoint of a

stationary observer. This proved unsatisfactory because

it resulted in debris wave velocities that were much too

large.

2. T h e u s e o f t h e c o n t i n u i t y , a n d e n e r g y e q u a t i o n s atthe leading edge of the debris flow. This technique was not viewed as

practical because energy dissipation at theleading edgeof

the flow is probably significant but cannot be quantified.

3 . The technique used was the assumptionof aconstant depthof

flow in the vicinity of the leading edge of the flow.

Although this was not felt to be a completely satisfactory

solution of the problem, it yielded the best results of the

techniques considered.

4.5.3 Results

DeLeon and Jeppson (1982) and Jeppson and Rodriguez (1983)

simulated both debris flows for which there are data and a number of

fictitious channel configurations to observe the predicted debris

flow behavior. In the cases where field data was available, these

investigators found good agreementbetween the estimatedandmeasured

results. However, it must be noted that there are an almost

insignificant number of high-quality field measurements of debris

flows, and this hindered both the calibration and verification of

these models.

4.5.4 Discussion

Among the recommendations made by these investigators were the

following. First, sufficient field data are not available for the

validation of these models or any other debris flow models: see for

example, Chen (1984, 1986), that have or may be developed. Second,

additional work is required to develop an accurate and acceptable

downstreamboundarycondi t ion forunsteady debris flows. Particular

attention shouldbegiven to developing analytic or empirical methods

for quantifying energy dissipation at the leading edge of the flow.

In addition, consideration must also be given to developing

quantitative models describing the mechanism(s) which initiate

179

debris flows; see for example, Campbell (1975) and MacArthur et a1

(1986).

Finally, it was observed earlier in this section that the data

presented in Figs. 4.5.lsuggests whydebris flowsmay suddenlystop;

that is, the velocityof flowdecreases tothe pointwhere theviscous

resistance cannot be overcome. DeLeon and Jeppson (1982) notedthat

the steady spatially varied debris flow model does not accommodate

this reasoning. RecallfromChapter 3, Section 5thattheresistance

coefficient in this model is p r o p o r t i o n a l t o t h e v e l o c i t y . Thus, as

the velocity of flow decreases so does the resistance to movement.

This is also a problem which must be addressed in the future.

4.6 CONCLUSION

In this chapter, four alluvial fan modeling efforts have been

presented and discussed. The models and efforts of Price (1972,

1974),Hooke (1965, 1967, 1968), DeLeonandJeppson (1982) andJeppson

and Rodriguez (1983) were undertaken in the academic environment and

perhaps because of this are more comprehensive and complete than the

effort of Anon. (1981a) which was undertaken in the mission oriented

applied research environment. Price (1972, 1974) and Hooke (1965,

1967, 1968) attemptedto completelymodelthe hydraulic processes on

alluvial fans while DeLeon and Jeppson (1982) and Jeppson and

Rodriguez (1983) focused ondebris flowsand Anon. (1981a) focusedon

fluvial processes.

The primary contribution of Hooke (1965, 1967, 1968), which

appears to be the first attempt to model hydraulic processes on an

alluvial fan, was the stimulation of interest in developing a

quantitative understanding ofthe hydraulic processes on analluvial

fan; the identification of various hydraulic processes and their

effects: and the extension of laboratory results to the natural

environment andviceversa. Although f romthev iewpo in to fhydrau l i c engineering, the design of the experiments were weak, compare for

example Sections 4.3 and 3.4: the qualitative results from this work

far overshadow these weaknesses.

The primary contribution of Price (1972, 1974) was the

development of a numerical framework for the study of alluvial fan

processes onageologictimescale. This frameworkallows and in fact

focuses on large scale flow events, both debris and fluvial. Fromthe

viewpoint of a detailed consideration of hydraulic processes on

alluvial fans, this model is very weak. However, this aspect of the

model could be easily improved. The engineer and planner should

180

remember that the relevant time scale for their work is a subscale of

the geologic time scale. Thus, from a conceptual viewpoint, it

should be feasible to refine the temporal resolution of a geologic

time scale model to simulate processes on a shorter time scale.

Theprimarycontributionof Anon. (1981a) was the developmentof

ahypothesis forquantifyingthemechanicsofwaterflowsandsediment

transport on alluvial fans. Althoughthis study was, in the view of

some flawed: see for example Anon. (1985), it does represent an

initial effort at quantifyi g these processes.

Themodelsdevelopedby I: eLeonandJeppson (1982) andJeppsonand Rodriguez (1983) are very promising attempts to model debris flows

withinthe frameworkoftraditionalhydraulicengineering. Thereader

is remindedthatthetheoreticalaspects of thesemodels arepresented

insection 3.5. Theprimarydiff icultywiththeseefforts isthe lack

of reliable data for model validation; a problem which cannot be

easily or inexpensively solved.

At the time of this writing, the most promising avenue for

further work appears to be an attempt to combine the conceptual

framework defined by Price (1972, 1974) with a more detailed

description of the hydraulic processes involved.

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American Society of Civi,l

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Beat C,.B., 1963. Origin of alluvial fans m i t e Mountajns, CaliT6rnia and Nevada Annals of the Association of American Geographers, 53 : 516-935.

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181

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Leopold I,.B. Wolman M.G. and Miller, J.P., 1964. Fluvial Process& in deomorphoiogy . h. H. Freeman , San Francisco. MacArthur, R.C., Schamber, D.R. Hamilton D.L., and West M.H 1986. Generalized methodolog kor. simulqking mudflows. fn: if Karamouz, G.R. Baumli, and W.1. Brick (editors) Water Forum '8 * World Water Issues in Evolution. American kocietv of Civfi Engineers, New York: 227-234.

Price, W.E., Jr., 1972. A random-walk simulationmodel ofalluvial- fan deposition. Re ort N 7 Hydrology and Water Resources and Systems and IndustrPal Eng%ee$ing, University of Arizona, Tucson.

Price, W.E., Jr. 1974. Simulation of alluvial fandeposition bya random walk modei. Water Resources Research, 10 (2) : 263-274.

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Sharp, J.J., 1981. Hydraulic Modelling. Butterworth, London.

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Wolman, M.G. and Miller, J.P., 1960. Magnitude and frequenc of forces in geomorphic processes. Journal of Geology, 68: 54-Y4.

Yanq C . T . 1972. Unit strepnap wer and sediment trans ort. ASCE, Jourhal of the Hydraulics DivisPon, 98 (HY10) :

Yang, C . T . , 1973. Incipient motion and sediment trans ort. ASCE, Journal of the Hydraulics Division, 99 (HY10) :

1805-?826.

1679-P704.

183

CHAPTER 5

METHODS OF FLOOD HAZARD ASSESSMENT ON ALLWIAL FANS

5.1 INTRODUCTION

Many methods have and are being used to assess flood hazard on

alluvial fans, and in this chapter a limited number of these

methodologies are examined and discussed. At the time of writing,

there is nota singlemethodwhich is clearlysuperior forperforming

comprehensive flood hazard assessment on alluvial fans. Each ofthe

methodologiesdiscussedherehas its own strengths and weaknesses and

achoiceamongthemmustbemadeonthebasisoftheanalysisofproject

goals and objectives, regulatory policy, and/or experience and

judgement. Of these, experience and judgement are perhaps the most

important.

5.2 FEMA METHODOLOGY FOR ALLWIAL FAN STUDIES

In recognition of the special problemsassociated with flooding

on alluvial fans, the Federal Emergency Management Agency (FEMA)

developed a special methodology for assessing flood hazard for

insurance purposes on alluvial fans, Anon. (1983) and Dawdy (1979).

In their guidelines for flood insurance studies, FEMA designates

alluvial fans as Zone AF - a special flood hazard zone. Zone AF has

the following definition:

"Alluvial fan high hazard area subject to a one percent or

greaterannualchanceof floodingto'adepth of0.5 ft (0.15 m) or

greater, which is characterizedbyvariable flowpaths, high flow

velocity, erosion, and debris deposition.", Anon. (1983, p A6-

2) *

The development of flood insurance maps defining zone AF requires a

quantitative technique for estimating zone boundaries, and the

development of such a technique requires a number of assumptions.

5.2.1 FEMA Assumptions Explicit and Implicit

explicitly or implicitly incorporates the following assumptions.

The FEMA technique for defining the boundaries of Zone AF

1. Channel Location: During major flood events on active

alluvialfans,theflowdoesnotspreadevenlyoverthetotal

184

s u r f a c e o f t h e fan: r a t h e r , i t i s c o n f i n e d t o a p o r t i o n o f t h e fan surfacewhichconvey s t h e w a t e r f romthe a p e x t o t h e t o e . Below t h e apex of t h e fan o r t h e zone of permanent channel entrenchment, see f o r example Fig. 1 . 2 . 2 , t h e flow channel w i l l occur a t random loca t ions a t any place on the fan surface. That is, t h e flow is no more l i k e l y t o follow an o ld flow path than it is t o follow a new one.

2 . Channel Shape: Thechannel t h a t conveys a flood flow o v e r a fan surface can be approximated as a rectangular channel.

3. S t a t e o f Flow: Flow across a fan su r faceoccur s a t c r i t i c a l depth and veloci ty ,Sect ions 3 . 2 and 3.3. The channel i n which flow occurs is formed by t h e flow itself and a d j u s t s its dimensions t o maintain t h e cr i t ical flow condition.

4 . Probabi l i ty of Point Flooding: The p robab i l i t y of a point on t h e fan being flooded during a p a r t i c u l a r f lood event decreases from t h e apex of t h e fan t o t h e t o e of t h e fan because of t h e widening o r expansion of t h e fan surface i n thedownslopedirection. This expansionprovides a g r e a t e r t ransverse d i s t ance over which a channel of given width can occur.

5 . Avulsions: The terminology of avulsion a s used by FEMA r e f e r s t o t h e p o s s i b i l i t y t h a t du r inga major flow e v e n t t h e flowmaysuddenlyabandononechanneland formanewchannel. This is a p o s s i b i l i t y which must be incorporated i n t h e methodology.

6 . Fan Apex Flood Discharge Frequency Distr ibut ion: A f lood discharge frequency d i s t r i b u t i o n must be ava i l ab le a t t h e apex of t h e fan.

7 . Coalescent Fans: I n the case of coalescent a l l u v i a l fans, t h e p robab i l i t y of a point being flooded is estimated by computingthe p robab i l i t y of flooding fromeach source, and then combining these p r o b a b i l i t i e s f o r t h e po in t under t h e assumption t h a t t h e p r o b a b i l i t i e s are independent.

185

5.2.2 Implementation

The above assumptions provide the framework necessary for the

specification of quantitative methods for defining flood hazard

zones. In the material that follows, the English system of units is

used. The justification for doing this derives from both the

complexity and the semi-empirical nature of many of the equations

involvedandthe fact thatthese equationswere developedand areused

in the English system of units.

The first step is theestimationofthe flooddischarge frequency

distribution at the apex of the fan. This frequency distribution

should be determined in accordance with the log-Pearson Type I11

probability distribution discussed in Anon. (1977, 1981). The

evaluation and use of this distribution requires that a skew

coefficient, G; a standard deviation S; and the mean value of the

logarithms ofthe flood discharges, X, be estimated. Anon. (1977,

1981) describes in detail how these parameters can be estimated when

reasonably long-term and reliable flow records are available.

However, such records are usuallynot available for drainage basins

above the apices of alluvial fans. If such flow records are not

available, they must be synthesized using either the methods of

regional hydrology or watershed modeling. Since a discussion of

drainagebasinorwatershedmodeling is beyondthe scopeof thisbook,

it will be assumed that flood discharges with return periods (or

exceedanceprobabilities) of2 (0.50),10 (0.10), and100 (0.01) years

have been determined by some means. Then, G, S, and 'j? can be estimated

-

(5.2.1)

(5.2.2)

- = log (Q0.50) - K0,50S (5.2.3)

where Q,,,,, Q o , l o , and Qo.ol = flood discharges associated with

exceedance probabilities of 0.50, 0.10, and 0.01, respectively and

KO,,, and KO.,, = log-Pearson Type I11 distribution deviates f o r exceedanceprobabilitiesof 0.Oland 0.50, respectivelyand G = askew

coefficient, see Anon. (1977, 1981). Equation (5.2.1) is an

approximation that is valid when

186

-2.0 5 G 1. 2.5

The FEMAmethodologyrequires at this pointthat the log-Pearson

Type I11 variables be transformed. Define

4

"=z and

2

GS a = - - 0.92

The transformed distribution variables are

For G # 0

A z = m + -

a

-

x s,' = -

a'

- Z = ? + 0.925' s, = s

(5.2.4a)

(5.2.5a)

(5.2.6a)

(5.2.7a)

(5.2.4b)

(5.2.5b)

G , = G = O (5.2.6b)

C = exp (0.92 ? + 0.42 S ' ) (5.2.7b)

In the above equations, the constant 0.92 has no particular physical

meaning but is related to the power law chosen to relate the channel

width to the discharge and the use of the log-Pearson Type I11

probability distribution, Dawdy (1979). In the FEMA methodology,

although it is not clearly stated, it is tacitly assumed that in

187

Engl i sh u n i t s

T = 9.5 Q o e 4 (5 .2 .8)

where T = channel t o p width ( f t ) and Q = d i scha rge ( f t 3 / s ) . system of u n i t s , t h e above equat ion would be

I n t h e S I

T = 1 2 ~ O . ~

Equation (5 .2 .8) is de r ived from t h e assumption t h a t an a l l u v i a l channel s t a b i l i z e s i t s e l f a t t h e p o i n t where a decrease i n depth causes a t w o hundred f o l d i n c r e a s e i n w i d t h , Dawdy (1979) andMagura and Wood ( 1 9 8 0 ) . Note, it is be l i eved t h a t t h e foregoing r e fe rences a r e no t independent a s s e r t i o n s of t h e assumption regard ing channel s t a b i l i t y . W i t h t h i s a s s u m p t i o n a n d T s p e c i f i e d b y E q u a t i o n ( 5 . 2 . 8 ) ,

Dawdy (1979) assertedthatthecorrespondingequationforthedepthof flow i n Engl i sh u n i t s was

y = 0 .07 Q 0 ’ 4 ( 5 . 2 . 9 )

I n t h e S I system of u n i t s , Equation (5.2.9) would be

y = 0.09 Q o k 4

The goa l of t h e FEMA methodology is t o f i r s t d e f i n e t h e boundar i e so f Zone A F , a n d t h e n t o s u b d i v i d e t h i s zone i n t o a r e a s w h e r e t h e depth a n d v e l o c i t y o f f l o w a r e s i m i l a r . Thesubd iv i s ions of Zone AF shouldhave depths and v e l o c i t i e s of f l o w t h a t d i f f e r b y anaverage of 1 . 0 f t ( 0 . 3 0 m ) i n depth o r 1 . 0 f t / s ( 0 . 3 0 m / s ) i n v e l o c i t y . Discharges corresponding t o va r ious zone boundaries a r e es t imated f romanequa t ionde r ived fromtheregimeorhydraulicgeometrytheory, see Chapter 3 , Sec t ion 4 . The equat ion c i ted by FEMA,in English u n i t s , is

Q = 2 8 0 y 2 ” (5.2.10)

where y = depth of f low ( f t ) . would be

I n t h e S I system of u n i t s t h i s equat ion

Q = 155 y 2 “

Equation (5 .2 .10) can be used t o d e f i n e va r ious subd iv i s ions of Zone AF based on t h e depth of flow, Table 5 .2 .1 .

Discharges corresponding t o va r ious v e l o c i t y zone boundaries a r e es t imated from a n e q u a t i o n t h a t is a l s o d e r i v e d f romthe regimeof hydrau l i c geometry theory . The equat ion c i t e d by FEMA i n English

188

1.0 (0.30)

2.0 (0.61)

3.0 (0.91)

(1.2) 4.0

0.50 (0.15)

1.5 (0.46)

2.5 (0.76)

3.5 (1.1)

49.5 (1.40)

172 ,'

(21.9)

2,770 (78.4)

6,420 (182)

I

I

I

(1.1) I (182) I

4.5 I 12,000

1.5 I 772 (0.46) 1 (21.9)

2.5 I 2,770 (0.76) I (78.4)

3.5 1 6,420

(1.4) I (340)

units is

Q = 0.13 (u)5 (5.2.11)

In the SI system of units this equation would be

Q = 1.40 (u)5 Equation (5.2.11) is used to define subdivisions of Zone AF based on

the velocity of flow, Table 5.2.2.

The third step in the implementation of the assumptions is the

computation of the log-Pearson deviates, K, that correspond to the

depth and velocity zone boundaries or

log Q-5 K =

S ,

(5.2.12)

With K and G, known, the probability of dischargesthat correspondto

eachdep thandve loc i tyzoneboundary canbe estimated from thetables in Appendix 3 of Anon. (1977, 1981).

Fourth, alluvial fan widths (that is arc lengthsparallel tothe

alluvial fan contours from one lateral limit of the fan to the other

limit) corresponding to each lower and upper zone boundary can be

estimated. In the English system of units

F = 950 ACP (5.2.13)

where A = avulsion coefficient (usually taken as 1.5 if no other

189

68 (1.93)

240 (6.79)

654 (18.5)

1,510 (42.8)

3 , 080 (87.2)

240 (6.79)

654 (18.5)

1,510 (42.8

3,080 (87.2

5,770 (163) ........................................................... ...........................................................

information is available), C =trans format ioncoe f f i c i entde f inedby

Equation (5.2.7) , and P = probability of the discharge corresponding

to each depth andvelocity of flow zoneboundary. Note, theavulsion

coefficient is intended to take into account the possibility of a

debris flow blocking the flow channel and causing a channel

relocation. With regard to Equation (5.2.13), the following

observations should be considered. First, the fan widths estimated

by this equation are zone boundary widths for the flow event that has

an exceedance probability of 0.01 or a return period of 100 years.

Second, the numerical coefficient in this equation; i.e., 950,

derives from the choice of the coefficient in the power function

relatingchannelwidthto discharge, Equation (5.2.8), and thechoice

of an exceedance probability. For an exceedanceprobability of 0.01

and a coefficient value of 9.5

9.5 - = 950 0.01

If the exceedance probability was taken as 0.50, then the numerical

coefficient in Equation (5.2.13) would be

9.5

0.5

Third, while the avulsion coefficient, A, has a definite physical

- - - 19

190

meaning, there is currently no rational means for determining or

estimating its value. Recall, the avulsion coefficient must be

relatedtothe potential ofthe flowforming, perhapsvery suddenly, a

new channel on the fan surface. Fourth, in addition to the

assumptions on which this methodology is based must be added the

assumption that a log-Pearson Type I11 probability distribution

adequately describes the frequency distribution of flood events at

the apex of an alluvial fan.

As an example of the use of the methodology outlined in the

foregoing paragraphs, consider a case in which the flood discharge

frequency distribution at the apex of the fan has the following log-

Pearson Type I11 parameter values in the English system of units.

Note, this example was first presented by Anon. (1983).

- X = 2.06

S = 0.4965

G = O

Since the skew coefficient , G, has a zero value, Equations (5.2.4b) - (5.2.7b) are usedtoestimatethevalues ofthe transformed frequency

distribution parameters or

- Z = 5 + 0.92 S2 = 2.06 + 0.92(0.4965)2 = 2.29

S, = S = 0.4965

G , = G = O

C = exp (0.92 ii + 0.42 S2)

c = exp [0.92(2.06) + 0.42(0.4965)~] = 7.4

With reference to Table 5.2.1, the log-Pearson deviate forthe 0.5ft

(0.15m) depth boundary can be estimated from Equation (5.2.11) or

- log(Q) - Z log (49.5)-2.29

K = = = - 1.19 s, 0.4965

With K and G, defined, the probability of a discharge greater than or

equal to the discharge that corresponds to the 0.5 ft (0.15 m) depth

canbeestimatedfromthetables inAppendix 3 of Anon. (1977, 1981) or

P = Prob( Z 2 log Q) = Prob( Q 249.5)

P 0.881

191

The fan width that corresponds to this probability is estimated from

Equation (5.2.12) where in this case the value of the avulsion

coefficient is taken as 1.5 or

F = 950 ACP = 950(1.5)(7.4)(0.881) = 9,290 ft (2,830 m)

The distance F is then scaled onto the topographic map of the fan and

the 0.5 ft (0.15m) depthof flowboundary i s locatedwherethewidthof

the fan, parallel to the contours, equals F.

Before this methodology is discussed, it is appropriate to

mention that a computer code existsto implement thismethod: see for

example, Harty (1982).

5.2.3, Discussion

The primary goal of the FEMA methodology is to define flood

hazard areas on alluvial fans for the purpose of setting flood

insurance rates. This goal is accomplished by first adapting a

consistent set of assumptions and then implementing and quantifying

these assumptions with a computational scheme. In discussing this

methodology, onemustdi f ferent iatebetweenexaminingtheval id i tyof the underlying basic assumptions and the implementation and

quantification of these assumptions.

The basic assumptions on which this methodology is based are

generally acceptable and consistent with what is known regarding the

geomorphology of alluvial fans and the behavior of flow events on

these features. However, the following observations should be

considered. First, this methodology assumes that the channel that

conveys flow acrossanalluvial fan hasa randoplocation. It isalso

assumed that the probability of a point being flooded during a flow

event decreases from the apex to the toe of the fan. An idealized

alluvial fan is showninFig. 5.2.1: and inthis figure, 1inesACandAB

are the lateral boundaries: line AD is the medial radial line which

divides the fan into approximately two equal areas: E is the point of

interest onthe fan:and W is the arc lengthofthecontour throughthe

point E. The FEMA methodology asserts that

T P(E1f) = -

W (5.2.14)

where P(E1f) = conditional probability that given the flow event f

occurs that the channel will pass through the point E and T = channel

top width. This approach does not take into account the possibility

192

I* Fan Apex

F I G . 5 . 2 . 1 Schematic de f in t ion of va r i ab le s f o r an ideal ized a l l u v i a l fan.

t h a t an entrenched channel e x i s t s a t t h e apex of t h e fan and t h a t the directionofthisentrenchedchannelmaydeviate f r o m t h e d i r e c t i o n o f t h e medial r a d i a l l i n e . Such a s i t u a t i o n might i nd ica t e t h a t on an engineeringtimescaletheremaybelocationsonthe fanwhicharemore l i k e l y t o be flooded than o the r locat ions. The l imi t ed data presented by Bull ( 1 9 6 4 ) , Fig. 2 . 5 . 2 , i n d i c a t e s t h a t such s i t u a t i o n s do indeed occur. An examination o f t h e data i n Fig. 2 .5 .2 ledFrench and Lombard0 ( 1 9 8 4 ) t o hypothesize

T e

W r P ( E 1 f ) = - (1 - -) (5.2.15)

where e and I' a r e defined i n Fig. 5 . 2 . 1 . Under t h i s assumption, P ( E I f ) has a maximum value equal t o t h a t estimated by Equation ( 5 . 2 . 1 4 ) f o r 0 = 0 and a minimum value of zero when 8 = r . Although ne i the r Equation ( 5 . 2 . 1 4 ) nor Equation ( 5 . 2 . 1 5 ) can be v e r i f i e d a t t h i s t i m e , they both attempt t o quant i fy t h e a s s e r t i o n t h a t channel l oca t ions on a l l u v i a l fans are random.

Second, t h i s methodology does not t ake i n t o account t h e e f f e c t s of development on a l l u v i a l fans. Rather, t h i s methodology assumes a v i r g i n fan surface without improvements such as s t r u c t u r e s and streetswhichmaychannelize a n d d i v e r t flows. S incean a l l u v i a l fan can, a t least i n t h e ideal case, be e a s i l y described by a polar o r c y l i n d r i c a l co-ordinate system, t h e imposition of a rectangular o r Cartesian street pa t t e rn on such a f ea tu re can have a s i g n i f i c a n t

193

impact on flow pa ths . Thus, i n t h e case of p a r t i a l l y o r f u l l y developed a l l u v i a l fans , t h e FEMAmethodology is of l i m i t e d u t i l i t y .

Thi rd , t h i s methodology t a c i t l y assumes i n its implementation t h a t it is p o s s i b l e to accura t e ly e s t ima te t h e f lood d ischarge frequencyrelationshipattheapexofthe fan. A s n o t e d p r e v i o u s l y i n Chapter 2 , Sec t ion 4 , t h e pauc i ty of long-term and r e l i a b l e p r e c i p i t a t i o n and d ischarge d a t a i n a r i d and semi-ar id a r e a s have an adverse impact on t h e v a l i d i t y of t h i s assumption.

Fourth, t h e assumption of c r i t i c a l flow i n t h e channels on an a l l u v i a l f an appears reasonable . O n t h e b a s i s of l i m i t e d f i e l d d a t a from Area 5 of t h e Nevada T e s t S i t e , French and Lombard0 ( 1 9 8 4 ) and French ( 1 9 8 4 , 1986) demonstrated t h a t c r i t i c a l o r s u p e r c r i t i c a l flow was t h e only type of flow c o n s i s t e n t w i t h the s i z e of ma te r i a l s composing t h e f an , the f an s lope , and t h e a n t i c i p a t e d flow r a t e s . Standardhydraulictheoryandpractice i n d i c a t e t h a t w h e n t h e s l o p e o f t h e channel exceeds t h e c r i t i c a l s lope s u p e r c r i t i c a l flow r e s u l t s , Chapter 3 , Sec t ion 3. However, i n h i s s tudy of high-gradient s t reams; t h a t is, s t reams wi th s lopes g r e a t e r t han 0 . 0 0 2 , J a r r e t t ( 1 9 8 4 ) found t h a t n e i t h e r c r i t i c a l nor s u p e r c r i t i c a l flow occurred. The channels examined by J a r r e t t (1984) were cha rac t e r i zed by s t a b l e beds and banks wi th minimal vege ta t ion , and contained cobbles and boulders . This i n v e s t i g a t o r concluded t h a t i n such s t reams the Manning r e s i s t a n c e c o e f f i c i e n t dur ing l a r g e f loods was much h igher t han t h o s e which would be e s t ima tedby s tandardmethods , and t h a t t h e flow approaches b u t does not exceed c r i t i c a l . However, J a r r e t t ( 1 9 8 4 ) n o t e d t h a t c r i t i c a l a n d s u p e r c r i t i c a l f l o w c a n o c c u r l o c a l l y i n f i n e gra ined a l l u v i a l channels . I n c o n t r a s t , Rachocki (1981) found i n h i s f i e l d studiesofman-madealluvial f a n s t h a t t h e f lowwasof t en s u p e r c i t i c a l . Fur ther , Anon. (1980) noted t h a t f i e l d measurements of f lood flows on a l l u v i a l f ans near Cabazon, C a l i f o r n i a ind ica ted v e l o c i t i e s i n t h e range of 4 .6-7 .6 m / s (15-25 f t /s) which sugges ts t h a t f o r reasonable channel w i d t h s and depths of flow c r i t i c a l or s u p e r c i t i c a l flow condi t ions .

F i f t h , t h e u s e o f t h e r e g i m e o r h y d r a u l i c geometrytheory i n t h i s methodology appears to be inappropr ia te . I n Chapter 3 , Sec t ion 4

thesetheorieswerediscussed, a n d i t wasdemonstrated t h a t t h e r e i s a w i d e range of c o e f f i c i e n t and exponentva lues . I n f a c t , t h e r a n g e i s s u c h t h a t w i t h o u t s i t e s p e c i f i c d a t a i t m a y be impossible t o e s t a b l i s h r e a s o n a b l e c o e f f i c i e n t andexponent va lues . Fu r the r , t h e regimeand hydrau l i c geometry t h e o r i e s a r e pred ica ted on quasi-s teady s t a t e or equi l ibr ium sediment t r a n s p o r t condi t ions . During f lood events on

194

alluvial fans, steady state conditions by definition do not exist.

French (1984,1986) againon thebasis of limited fielddata fromArea

5 of the Nevada Test Site demonstrated that the use of these theories

under the flow conditions foundon alluvial fans are inappropriate.

Sixth, the regime or hydraulic geometry theory takes into

account neither the effects of fan slope nor the effect of flow

transmission losses both of which can be significant factors in

channels on alluvial fans. Further, if Equations (5.2.9) and

(5.2.10) are rearranged, the Froude number of the flow can be

estimated, or in English units

Q = 280 y2" ............ y = 0.105 Q o S 4 (5.2.15)

Q = 0.13 us ............ u = 1.50 Qoa2' (5.2.16) -

and - U 1.504' ' "

F = - = [0.105 (32.2) Qo'40]1'2

-1gY Thus, the methodology used by FEMA results for any value of Q in a

constant Froude number flow. If Equations (5.2.8) and (5.2.9) are

used along with the equation of continuity to estimate the Froude

number the result is

F = 0.1

Seventh, althoughthehydraulic exponents in Equations (5.2.8),

(5.2.15) , and (5.2.16) sum to one as they should - see Equation (3.4.20) - the product of the coefficients used in these equations is not one as it should be - see Equation (3.4.21).

Eighth, neither the assumptions on which this methodology is

based nor its implementation takes into account, explicitly, the

possibility of mud and debris flows. The avulsion coefficient in

Equation (5.2.12) couldbeviewedasanattempttotakesuch flows into

account sinceone ofthe primaryreasons anew channel would be formed

ona fan surfacewould bebecause ofthe blockageof the old channelby

a mud or debris flow.

Finally, it should be noted that this methodology is an

innovative approach to a complex problem. Whilemodification ofthe

methodology is needed, it does provide a rational, uniform basis for

identifying potential hazard areas on undeveloped alluvial fans.

195

5.3 ALTERNATIVE METHODOLOGY FOR ALLUVIAL FAN STUDIES

As noted previously inthis chapter, the choiceof amethodology

for analyzing hydraulic processes on an alluvial fan is preferably

made on the basis of a careful consideration of the goals and

objectives of the study. While the FEMA methodology may be

appropriate given its goalsand objectives, it ignoresthe effectsof

urbanization and other important aspects such as channel slope and

roughness. In recognition of this, Anon. (1980) [see also Edwards

and Thielmann (1984)l developed an alternative methodology that is

worth noting.

Based on field observations of historical floods on alluvial

fansbothMaguraandWood (1980,~. 60) andDawdy (1979,pp. 1408-1409)

bothsuggestedthatal luvial fanchannels stabilizeatthepointwhere

a decrease in depth would result in a two hundred-fold increase in

width or

dY - = - 0.005 dT

(5.3.1)

Anon. (1980) used this observation in conjunction with the Manning

equation for a wide rectangular channel to develop equations for the

width, depth, and velocityof flowwhen the flow rate, Mannings n, and

the channel slope are sgesified.. Far a uL& cwS-i~r?rs~L%~ -&%msL

Equation (3.3.1) states

(5.3.2)

where Q = flow rate, T = channel top width, y = depth of flow, 6 =

coefficient used to account for the system of units used, and S =

channel slope. Solving Equation (5.3.2) and taking the first

derivative

dT 5

and setting this result equal to Equation (5.3.1)

(5.3.3)

196

Solving this equation for T yields

19.9 (nQ)3/8 T =

$3/8S3 / 1 6 (5.3.4)

Substitution of this value for the top width in Equation (5.3.3)

yields I

nQ 3 / a

= [120r$i1 (5.3.5)

Using these values of T and y in Equation (5.3.2) yields an equation

for the average velocity of flow or

(5.3.6)

5.3.1 Discussion

This alternative methodology derives directly from the

assumption that an alluvial channel will become stable at the point

where a decrease in depth would cause a two hundred-fold increase in

width. Recall, the FEMA methodology also derives from this same

assumption. Philosophically, these twomethodologies diverge at the

point that this assumptionis imp1emented;that is, Anon. (1980) used

the Manning equation to implement the assumption while FEMA used the

theory of hydraulic geometry. A comparison of the two

implementations of this assumption yields results which should be

noted.

If the theory of hydraulic geometry is represented as it is in

Equations (3.4.16) - (3.4.18), then a comparison of those equations with Equations (5.3.4) - (5.3.6) yieldsthe followingresults forthe exponents and coefficients

f = 3/8 (5.3.7a)

b = 3/8 (5.3.7b)

m = 1/4 (5.3.7c)

197

3 / 8

3 / 8

(5.3.8a)

(5.3.8b)

(5.3.8c)

T h e s a l i e n t p o i n t i s t h a t i f C , , C , , andC, aretohaveconstantvalues, then according t o Equations (5.3.8) t h e parameter n/S'/' o r S ' /2/n must be constant. I n t h e a l l u v i a l fanenvironment, thismay b e t r u e . For example, a s one progresses downslope f romthe apex, t h e f ans lope general ly becomes s m a l l e r w h i l e t h e s i z e o f t h e m a t e r i a l alsobecomes smallerandhencen decreases: see forexample Equation ( 3 . 3 . 4 ) . The foregoing reasoning is v e r y q u a l i t a t i v e a n d t h i s is supported byvery l i t t l e q u a n t i t a t i v e data .

Second, t h e a l t e r n a t i v e methodology is based on t h e assumption of a constant value of t h e r e s i s t ance coe f f i c i en t . Under t h i s assumption, a s t h e s l o p e increases , t h e Froudenumber a l s o increases. I n Fig. 5 . 3 . l a t h e Froude number i s p l o t t e d a s a f u n c t i o n o f t h e s l o p e f o r Q = 28 m 3 / s (1 ,000 f t 3 / s ) and n = 0.015. Recall t h a t J a r r e t t (1984) a s se r t ed t h a t inhigh-gradient channels such a s t h o s e foundon a l l u v i a l fans n is a function of t h e hydraulic r ad ius and t h e slope, Equation ( 3 . 3 . 4 ) . I n t h e case of a wide rectangular channel subject t o t h e boundary condition t h a t dy/dT = - 0.005, it can be e a s i l y shown t h a t i n t h e English system of u n i t s

Q O . 3 6

Y = 8.57550' 0 4

and

12. 9 ~ ' a

so * 0 4 T =

(5.3.9)

(5.3.10)

The r e s u l t s from using t h i s formulation a r e a l s o p l o t t e d i n Fig. 5.3.la. The use of Equation (3.3.4) l i m i t s t h e flow t o t h e subcritical regime while t h e assumption of a constant value of n

198

Qoom a m 0.OlOO OJOOO 1mo

Channel Slope

FIG. 5.3.la Froude number as a function of channel slope for Q = 28

m3/s (1,000 ft3/s) and n = 0.015 and n given by Equation (3.3.4).

c QIO / /"

FIG. 5.3.lb Equation (3.3.4).

n as a function of channel slope with n estimated from

results at some point in a supercritical flow. In Fig. 5.3.lb, the

value ofn estimatedfrom Equation (3.3.4) isplotted asa functionof

S for Q = 28 m3/s and n = 0.015 subject to dy/dT = -0.005. In this

figure, as S increases so does n, and this variation accounts for the

fact that in Fig. 5.3.la when Equation (3.3.4) is used to estimate n the flow remains subcritical.

The above discussion is not intended to be an endorsement of the

hypothesis of Jarrett (1984) ; rather, it indicates the importance of

having a valid functional relationship for n in channels of large slope.

Third, this alternative methodology also does not consider mud

199

or debris flows.

5.4 PROPOSED MODIFICATION OF THE FEMA METHODOLOGY

The limitation softhemethodologies for floodhazardassessment

on alluvial fans discussed in the foregoing sections of this chapter

have long been recognized. Anon. (1985a) under the sponsorship of

FEMAstudiedeighteen fans inNevadaandCalifornia fromtheviewpoint

of developing modifications to the current FEMA flood hazard

assessment methodology. The selection criteria for the fans

examined adapted by Anon. (1985a) were:

1. The fan must be well-defined so that both physical

characteristics of the fan (slope, expansion angle,

upstream watershed arealand upstream canyon slope) and the

channel patternsonthe fansurfacecouldbe determined from

available topographic maps and aerial photographs.

2. A U.S. Geological Survey gaging station with data regarding

major flood discharges across the fan must be available.

3. Aerial photographs of the alluvial fan before and after a

measured major flood event must be available.

The eighteen alluvial fans selected for this study included both

undeveloped fans, primarily in Nevada, and highly developed fans,

primarilyin California. Thus, this study enabled the investigators

to examine on the undeveloped alluvial fans the geomorphological

processes which build and form natural fans and the effects of man-

made structures on alluvial fan flooding. The physical data

regarding the fans examined in this study.are summarized in Table

5.4.1.

1. Flood channels on alluvial fans can be divided into three

distinct patterns. Generally, near the apex of the fan

there is a single channel: as this channel progresses down

the fan a split channel pattern develops: and in the

vicinity of the toeof the fan abraided channel patternis

generally found. Note, this conclusion closely matches

the channel zones described in Fig. 1.2.2. 2. The length of the single channel region down the €an from the

canyon mouth appears to be related to the ratio of the canyon

slope to the fan slope by the curve shown in Fig. 5.4.1. In

thesinglechannel region, thechannel widthcan beestimated

by the present FEMA methodology, Section 5.2.

3. In the split channel region of the fan the total width of all

200

1 INorthumber- Jland Canyon Inear Austin, I NV. I

2 Inason Valley ltributary Inear Mason,N I

[River tribu- ltary near Ry IPatch, NV. I

4 IRocky Canyon Inear Oreana, INV. I

I River tribu- ltary near Ioreana, NV. I

6 ILas Vegas /Wash near 1Henderson.W I

7 /Las Vegas [Wash near I Henderson, NV I

ltributary at ISearchlight, I NV. I

JWash near

I

IValley near Ilelson, NV.

11 ILytle Creek

3 lHumboldt

5 IHumboldt

8 IPiute Wash

9 lSan Antonio

ITonopah, NV.

10 IEldorado

I

Inear Fontana, 1 CA. I

12 ]Day Creek I near IEtiwanda, CA. I

13 IDeer Creek I near IGuasti, CA. I

ICreek near IUpland, CA. I

lCreek near I Clarernont, CA I

ICreek near IPalm Springs,

I

14 lmcamonga

15 lsan Antonio

16 ITahquitz

I CA.

17 (Palm Canyon I near Palm Isprings, CA. I

18 loevil Canyon I near San

0.03:

0.05E

0.llC

0.108

0.124

0.058

0.061

0.016

0.070

0.036'

0.031

0.149

0.168

0.075

0.055

0.111

I. O5Ec

1.085

0.03:

0.03!

0.07:

0.05L

0.07(

0.05C

0.056

0.016

1.053

1.036

1.026

0.103

0.109

0.048

0.046

0.046

0.055

0.062

60

75

90

110

90

50

40

e -

60

30

95

80

90

55

90

90

25

33

6096 (20000)

1067 (3500)

2225 (7300)

3810 (12500)

3962 (13000)

975 (3200)

1981 (6500)

e -

5395 17700)

1768 (5800)

14935 49000)

12558 41200)

11430 37500)

12863 42200)

17617 57800)

2195 (7200)

4877 16000)

1951 :6400)

4420 (14500

4 -

323 (1060

f -

f -

937 (3075

991 (3250

3200 10500:

f -

610 (2000)

1341 (4400)

732 (2400)

183 (600)

2408' (7900)

2484' (8150)

f -

1166 (3825)

457d (1500)

4 0

9 -

45

90

38

30

20

e -

10

h -

20

65

30

45

65

60

20

30

39.1 (15.1)

6.7 (2.6)

2.2 (0.85)

10.5 (4.05)

2.0 (0.76)

0.16 (0.06)

8.80 (3.40)

3.63 (1.40)

120 (46.3)

30.8 (11.9)

8.81 (3.4)

26.1 (10.1)

67.8 (26.2)

113 (43.5)

242 (93.3)

14.5 (5.61)

201

I I I I I I

I (8980) I ( 8 8 0 ) I (640) I I (57.40) I I I I

IBernardin0,CAl I I I I I I I I

I River, White- 1 I I Iwater, CA. I I I I I I

19 IWhitewater I 0.034cI 0.030 70 I 2737 I 26Sd I 195d 15 I 148.7 I

-===-=======.===-=== _=3=I_=_=--*_L--__p_s=-====--~--~-=

aChannel width measured within a well-defined reach.

bThe direction of a single channel was taken as the angle between the single fan boundary - looking downstream. angle was approximated with the

'The fan slope extends into the canyon upstream of the mountain front.

dThe alluvial fan channels are affected by manmade structures - levees, dikes, eNot a well defified alluvial fan. According to Anon. (1985a) a well defined alluvial fan would be characterized by a rather uniform radial slope from the apex.

fThere is not a single channel region on the fan.

gNo flood channels were identified.

hsingle channel width is not well defined.

channel and the left In the case of alluvial fans without a single channel, this

direction of the major channel.

etC.

channels across the fan at a specified radial distance from

the apex of the fan is approximately 3.8 times the channel

width in the single channel region.

4 . Flood channels on developed alluvial fans and on fans below

well-vegetatedwatersheds appeartobemore stablethanthose

found on undeveloped alluvial fans or on fans below sparsely

vegetated watersheds. However, Anon. (1985a) cautioned

that there is not yet sufficient data to unequivocally

conclude that apparently stable channels will not relocate.

5. At present, there are not sufficient data to accurately

estimate the value of the avulsion coefficient in the FEMA

methodology.

5.4.1 Proposed Modifications to the FEMA Methodology

Giventheaboveconclusions, Anon. (1985a) hasproposedthatthe current FEMA methodology; see Anon. (1983) in the following ways.

A given alluvial fan is divided into two areas; that is, an area

in the vicinity of the apex of the fan where there is a single channel

and a second area further down the fan where there is a split channel

pattern.

The length of the single channel area is estimated from Fig.

5.4.1andwithinthisareathe methodologydiscussed insection 5.2 is

used. In this region Equation (5.2.13) is used to estimate the fan

widths; that is, the arc lengths taken parallel to the fan contours

from one lateral limit of the fan to the other.

In the multiple channel region of the fan, the discharges Q

(ft3/s) correspondingtothe variousdepth zoneboundaries inColumns

(1) , (2) and (3) of Table 5.2.1 are calculated by solving

202

whereS=fansu r faces lope , n=Manningresistancecoefficient, D = y + u2/2g = t o t a l energy head, y = depth of flow, and u = average ve loc i ty of flow. For example, i f n = 0.02, S = 0.03 and D = 0.5, then from Equation (5.4.1) Q = 310 f t 3 / s ( 8 . 8 m 3 / s ) .

I n t h e mult iple channel region, t hed i scha rges correspondingto t h e ve loc i ty zone boundaries, Columns (1) , ( 2 ) and ( 4 ) i n Table 5.2.2 , are calculated from

-

5000,

E 2 4000, 2 !i I u b d

3000. G d

cc 0

I

c b -J

3 b > L

Q 0

2000.

t 1000,

0. 1.0 1.2 1.4 1.6 1.8 2.0

Canyon Slope/Fan Slope

F I G 5.4.1 r a t i o of canyon slope t o fan slope, a f t e r Anon. (1985a).

Observed length of a s i n g l e channel as a function of t he

Q = gg314n4"7 s-'.25 u 4 . 1 7 (5.4.2)

F o r t h e m u l t i p l e channel r eg ion the fanwidths a rees t ima ted from

F = 3610 ACP (5.4.3)

203

1 INorthumber-1 39.1 [land Canyonl(15.1) I near I IAustin,NV. I I I

IRiver tri- I (0.85) lbutary near1 lRye Patch, I I w . I I I

2 IHumboldt I 2.2

3 lLas Veqas I 0.16 ]Wash near I (0.06) [Henderson, 1 IW. I I I

[tributary I (3.40) lat Search- I Ilight, NV. I I I

5 JLytle Creek1 120 I near I(46.3) IFontana,CA. I I I

I near I(11.9) IEtiwanda,CAl I I

I near I(11.9)

I I

4 [Piute Wash I 8.81

6 lDay Creek 1 30.8

7 lDay Creek I 30.8

IEtiwanda,CAl

8 [Cucamonqa I 26.1 [Creek near l(lO.1) IUpland, CA. I

1 near Clare- I (26.2) Imont, CA. I

I I 9 lSan Antonio1 67.8

I I 10 IPalm Canyon1 239

Inear Palm l(92.3) 1Springs.CA.I I I

11 IDevil Can- I 14.5 lyon near 1 (5.61) lSan Berna- 1 Idino, CA. I 1 I

. . . . . . . . . . . . . . . . . . . . . . . .

0 . 0 3 3

0.110

0.058

0.016

0.031

0.149

0.149

0.075

0.055

0.058

0.085

_ _ _ _ _ _ _ _ _ _ _ _

0.03318/7/79 I 217 I I(7-580) I I I I I I

I I (8940) I I I I I I I I

I I (655) I I I I I I

I I (370) I I I I I I

I I I I

I l(9500) I

0.07115/31/731 253

0.050/7/30/681 18.5

0.0161 9/11/76! 10.5

0.026 I 1/25/69 I 1017 I I(35900)

0.10311/25/691 269

I I 0.10313/2/38 I 119

I I (4200) I I I I

I I

3.04813/2/38 I 292 I I(10300)

I I 1.04613/2/38 I 606

I I I I

I I(3850) I I I I

I I(21400)

).05512/6/37 I 109

71.0 ( 2 3 3 )

65.2 (214)

26 (85)

26 ( 8 6 )

133 466)

6 2 204)

45.7 150)

74.1 243)

98.1 322)

50.0 164)

46.0 151)

I I I I

28 I 30 I 21 (92) I (97) I (68)

I I I I I I

28 I 30 I 27

I I I I

(92) I (97) I (90)

I I 142 I 151 I 232 435) I(494) I(761)

I I I I

68 I 71 I 80 219) l ( 2 3 2 ) I(263)

I I I I

49.1 I 52.1 I 81.7 161) I(171) I ( 2 6 8 )

I I I I

79.2 I 84.1 I 109 260) l(276) ( ( 3 5 8 )

I I I I

105 I 112 I 113 345) I ( 3 6 6 ) I(370)

I I I I

I I I I

19.4 I 52.4 I 65.8 (162) l(172) I(216)

I I I I

53.3 I 56.7 I 168 175) l(186) I(550)

5 . 4 . 2 Discussion Thede ta i l eds tudybyAnon . (1985a) of e i g h t e e n a l l u v i a l f ans f o r

which r e c e n t f lood d a t a are a v a i l a b l e provides a number of i n s i g h t s regardinghydraulicprocesseson a l l u v i a l f ans whichare wor thnot ing and d i scuss ing .

F i r s t , a s noted both i n t h i s s e c t i o n and i n Sec t ion 5.2, t h e avu l s ion c o e f f i c i e n t used i n Equations ( 5 . 2 . 1 3 ) and ( 5 . 4 . 3 ) is intended t o t a k e i n t o account t h e p o s s i b i l i t y t h a t a channel on an a l l u v i a l f an may suddenly r e l o c a t e t o a new p o r t i o n of t h e fan. To d a t e , thereare v e r y l i t t l e r e l i a b l e d a t a onwhich t o b a s e anabso lu te va lue of t h i s c o e f f i c i e n t . Themost probablecause of an a v u l s i o n i s

204

the rapid deposit of debris or mudflow material in the channel. The

causes and factors affecting mud and debris flows were discussed in

Sections 2.6 and 4.2. Anon. (1985a) concurs that a primary

consideration inevaluat ingthepotent ia l foramudordebris flowata specific site is the amount and condition of the vegetative cover in

the upstream watershed. In a relative sense, the avulsion

coefficientshouldhaveasmallervaluewhentheupstreamwatershedis

well-vegetated and a larger value in the case of a barely vegetated

watershed. However, recall from Sections 2.6 and 4.2 that the

formation of a mud or debris flbw usually requires a very unique set of

circumstances. Anon. (1985a) further notes thata value of 1.5 for

the avulsion coefficient, the value currently recommended by FEMA,

Anon. (1983).

Second, small flood flows on alluvial fans develop thalwegs in

existing channels while larger floods tend to widen and deepen the

existing channels or develop additional channels.

Third, flood flow son urbanizedalluvial fansare oftenmodified

by structures such as levees, dikes, lined channels, and debris and

detention basins. Where such structures exist and when they have

beenproperlydesigned, they determinethe boundariesof alluvial fan

flooding. This observation by Anon. (1985a) tacitly assumes that a

comprehensive coordinated drainage plan for the fan has been

developed - an assumption that is often not valid in rapidly

urbanizing areas with no one agency responsible for planning and the

implementation of plans.

Fourth, for the single channel region of the fan, Anon. (1985a)

compared the channel widths estimated by Equation (5.2.8) and

Equation (5.3.4) with those actually observed. The results ofthis

comparison are summarized in tabular form in Table 5.4.2 and in

graphicalforminFig. 5.4.2. Anexamination ofthese data indicates

that Equation (5.3.4) for constant values of n generally results in

channel widths that are smaller than both those observed and those

predictedbyEquation (5.2.8). Further, inthis figurenote thatthe

predicted widths for the fans near Rye Patch Reservoir and Las Vegas

Wash are a considerable distance from the line of perfect agreement.

Anon. (1985a) attributed this discrepancy to possible errors in flow

estimation for these fans.

Fifth, as mentioned previously in this section, in the split or

multiple channel region of the fan the data indicates that an

equivalent single channel with a width 3.8 times the width in the

single channel region, Equation C5.2.8) may be substituted. Anon.

205

Calculated Channel Width. a. lo00 1

lo0

Obrrrved Channel Width. a.

1000

(1985a) statedthat this observation indicates that the flowmigrates

from one sub-channel to another sub-channel. These investigators

further asserted that if normal flow is assumed and the Manning

equation is assumed to hold, then the following equations can be

developed (in English units)

(5.4.4)

(5.4.5)

(5.4.6)

A cornparsion of Equations (5.4.1) and (5.4.6) indicates an apparent

discrepancy; however, recall that D in Equation (5.4.1) is the total

energy head or

D = Y + 1x1 (5.4.7)

Sixth, the technique proposedby Anon. (1985a) for estimating

the lengthofthesingle channel region onan alluvial fan, Fig. 5.4.1

can best be described as empirical. The similarity between this

206

approach and those presented in Section 2.3 should be noted.

The observations and proposedmodification ofthe present FEMA

methodology by Anon. (1985a) are a significant addition to the

literature regarding hydraulic processes on alluvial fans. The

primary objections to these methods remains the use of the regime

method for estimating channel widthand the empirical approachused

throughout. Even with these results, our qualitative knowledge of

alluvial fans remains much more advanced than our quantitative

knowledge.

5.5 CONCLUSION

At the time of this writing, there is not a commonly accepted

methodology for quantitatively analyzing flood flow events on

alluvial fans. Each of the methods discussed in the foregoing

sections of this chapter was developed in response toa problemwhich

could not be solved by traditional or conventional hydraulic

engineering principles. None of the methods discussed have been

adequately validated with field or laboratory data; and therefore,

both of them should be used with caution. Common to both of the

methods discussed are a number of general problems which should be

mentioned.

First, both of the methodologies discussed in this chapter have

assumedthatthe flowrate at theapexofthe fan is eitherknown or can

be accurately estimated. In areas where adequate stream gaging

records exist, the traditional methods of hydrology can be used to

estimatepeakfloodflows; see forexample, Anon. (1981). Inaridand

semi-arid areas adequate stream gaging records are usually not

available andsuch recordsmay not even exist in thearea of interest.

In such cases, alternativemeans of estimating dischargesat theapex

of the fan must be sought. Among the techniques available for

accomplishing this are watershed models. Such models attempt to

numerically simulate the response of a watershed to a precipitation

event of a knownduration, arealextent, and average intensity. The

assumption inherent in sucha model is that either ona regionalbasis oronas i t e - spec i f i cbas i sprec ip i ta t iondata i sava i lab le tosupport

suchamodelingeffort. In fact, thismaybeanerroneousassumption.

For example, in the Las Vegas, Nevada area peak flood flow

estimates have often been baaed on the point rainfall distributions

given in Miller et a1 (1973). These point precipitation values are

thenmodifiedtoarealvaluesbyusingthedepth-arearatiospublished

by the National Weather Service; see for example, Zehr and Myers

207

(1984). Anon. (198513) choose to analyze the actual precipitation

data available for the first order National Weather Service station

located in Las Vegas rather than blindly use the data presented in

Miller et a1 (1973). After analyzing the actual data, Anon. (198533)

estimated that the three hour design storm for the Las Vegas area

should be 66 mm (2.48 in) ; that is, the precipitation event with a 100

year return period and a three hour duration will deposit 66 mm (2.48

in) of water on the ground. In comparison, Miller & a (1973) estimated the three hour design storm for this area to be 44 mm (1.13

in). Thus, the use of site specific data results in a prediction of

approximately 50 percent more precipitation than the standard

recommended regional method. Anon. (1985b) also presented a

comparison of the results obtainedusing the TR-20 watershedmodel;

Anon. (1965) using both the three hour design storm developed from

site specific data and the three hour design storm derived from

regional methods and compared the results with measured peak flood

flow data, Table 5.5.1. These results indicate that the TR-20

watershedmodelusingthe site specific precipitationdata provides a

s igni f icant lybet terest imateofthemeasuredpeakf loodf low. Thus,

while regional estimates of precipitation may provide adequate

approximations in areas where no data are available, care and

judgement must be exercised in interpreting the results when these

estimates are then used to predict peak flood flows.

A second observation by Anon. (1985b) was that while a number of

storms have caused precipitation over the total drainage basin

studied, others have been concentrated, in small areas. The

implication of this observation is that the depth-area ratios

available forthe SouthernNevada area may also besomewhat inerror.

The salient point of the above discussion is that at specific

locations in arid and semi-arid areas there may be sufficient data

available to adjust precipitation estimates derived from regional

hydrometeorological data; however, thereareusuallynotsuff ic ient data to comprehensively revise the regional estimates.

Asecondmethodofest imatingpeakflood flowdischarges inareas

where there are not adequate stream gaging records for site specific

analyses is the method of regional streamflow analysis; see for

example, Riggs (1968). This type of regional analysis attempts to

develop multi-variate regression equations that relate peak flood

discharges of a specified return period to drainage basin

characteristics such as area, mean elevation, mean slope, and

location. In arid and semi-arid regions, the lack of long-termand

208

reliablestreamgagingrecords f o r v a s t areasmake i t d i f f i c u l t i f n o t impossible to deve lopre l i ab le regional regression equations. A s an example, consider again t h e Southern Nevada area. I n t h i s area several sets of regional regression equations f o r es t imat ing peak flood flow discharge a r e avai lable . Christensen and Spahr (1980) analyzed data from 7 1 streamgaging s t a t ions th roughou t Nevada with only 19 of these s t a t i o n s being i n Southern Wevadaand concludedthat

Q l o o E 11900 A0*55E-'*28L-1*16 (5.5.1)

where Q l o o = peak flood discharge with a 100 year r e t u r n period ( f t 3 / s ) , A = drainage basin a rea ( m i 2 with 0 .2 < A < 1000) , E = mean basinelevationin1000'sof f e e t w i t h 2 < E < 1 0 , a n d L i l a t i t u d e m i n u s 35' ( 1 < L < 7 ) . SquiresandYoung (1983) analyzed da ta from 1 2 stream gag ings t a t ion inSouthernNevadawithperiodsofrecordupto20years and concluded

Q l o o = 482 A 0 * 5 6 5 (5.5.2)

Regionalstreamflowanalyseshave alsobeenperformed f o r t h e s t a t e o f Arizona, Roeske (1978). I n t h i s study, t h e s ta te of Arizona was divided i n t o f i v e hydrologic regions, Fig. 5.5.1. Arizona Regionl, which is conterminous with Nevada, contained 17 stream gaging s t a t i o n s and t h e r e s u l t of analyzing these w a s

Q l o o = 584 (5.5.3)

FrenchandLombardo (1984) n o t e d t h a t geology, topography, andannual average p r e c i p i t a t i o n of Arizona Region 2 w a s more s i m i l a r t o t h a t found i n Southern Nevada t h a t t h a t of Arizona Region 1. For the 26

209

4

5 HE

M L 2 s 80 7Sm11..

*Lo ?,5hllomt.r.

-. --. '--

'.. ' -. '-.

Numbered flood-region boundary

Approxlmate a r e a o f f lood-frequency reglon HE

F I G . 5.5.1 Arizona hydrolo ic regions f o r regional streamflow analyses, a f t e r Roeske (19787.

stream gaging s t a t i o n s i n Region 2 t h e r e s u l t w a s

Q l o o = 1100 ( 5 . 5 . 4 )

I n Table 5.5.2 t h e r e s u l t s obtained from Equations (5.5.1) - (5 .5 .4)

a r e compared f o r two drainage a r e a s t r i b u t a r y t o Flamingowash inLas Vegas, Nevadawiththeresultsobtained byAnon. (1985b) usingtheTR- 2 0 watershed model with t h e revised p r e c i p i t a t i o n estimates previously discussed i n t h i s sect ion. It canbe s e e n f r o m t h i s t a b l e t h a t t h e r e is a s i g n i f i c a n t difference between these peak flood flow estimates. Although it would be na tu ra l t o assume t h a t t h e r e s u l t s

210

TABLE 5.5.2 Comparison of Q l p o estimates obtained by various methods for two drainage basins near Las Vegas, Nevada.

Drainage1 Area I Q j o o Basin I km2 I m /s

-------------------------------------------==================

I (mi2) I (ft3/s) I I TR-20 I Eq. I Eq. I Eq. I Eq.

I I I I

I (53) I (9,070) I(llr400) I (4,540) I (4,090) I (7,980)

I(5.4.1) I(5.4.2) I(5.4-3) I(5.4.4) -------------------------------------=I========

1 I 137 I 257 I 323 I 129 I 116 I 226

I I I I I I 2 I 259 I 303 I 603 I 184 I 158 I 309

I (100) 1 (10,700) I(21,300) I (6,500) I (5,580) I (10,900) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

obtained from detailed watershed modeling are more accurate, the

problems assoc ia t edwi th th i sapproach , someofwhicharenot obvious, must also be taken into account.

Athird method lofestimating peak flood flowdischarges isthat

ofpaleohydraulic reconstruction. This type ofmethodology has been

of interest to geologists and hydrologists for a number of years and

hasbeenusedforpost-event estimation ofvelocity anddepth of flow,

peak discharge, and channel morphology: see for example, Jopling

(1966) , Harms (1969) , Ethridge and Schumm (1978) , Koster (1978) , and Schumm (1972). As noted by Maizels (1983) and Costa (1983) , the paleohydraulic reconstruction of flow events must always rest on one

ormore assumptions. Assumptionsused have included steady, uniform

flow: logarithmic velocity profiles: small relative bed roughness:

uniform distribution of representative boundary roughness elements:

the absence of bed forms; low suspended sedimentconcentrations; anda

wide range of particles available to be eroded and transported. ‘“he

use of these assumptions have resulted in skeptics asserting that

paleohydraulic reconstructions are not valid: see for example,

Nummedal (1973) and Shaw and Kellerhals (1977). However, commonly

accepted engineering methods for post-event estimation of flood

discharge such as the slope-area method are also subject to

assumptions which are limiting. For example, the slope-area

technique requires an estimate ofthe resistance coefficient and the

assumption that there wasminimal scouror depositionduringthe flow

event in the channel reach considered: Dalrymple andBenson (1976) or

French (1985). Thus, all methods of post-event peak flood flow

estimation rely on assumptions and may produce results of

questionable validity.

Costa (1983) compared peak flow rates estimated by a variety of

211

Spring Creek trib. to Dry Creek

Love 1 and Heights trib.

to Big Thompson River

Dark Gulch at Glen Comfort

Big Thompson River at the canyon mouth

Tucker Gulch

Indian Gulch

Cold Spring Gulch

Cold Spring Gulch trib.

Sawmill Gulch

-------_-_--- ------__-----

3.8

3.5

2.6

790

29

3.9

11.6

1.6

5.8

325

100

14 1

1552

281

71

188

29

46

329

246

2 04

329

54

255

58

181

paleohydraulic techniques with those estimated by the slope-area

technique for a number of events that occurred in the Colorado Front

Range, Table 5.5.3. Where possible and appropriate, Costa also

estimated the peak flow rate by assuming critical flow conditions

(Chapter 3) and with rainfall-runoff models. With two exceptions,

the paleohydraulic reconstruction always produced estimates of peak

flow that were less than those obtained by the slope-area technique.

Peak flow estimates derived from the assumption of critical flow

conditions and rainfall-runoff modeling were similar to those

obtained by paleohydraulic reconstruction, Table 5.5.3.

Theconclusion i s t h a t t h e t a c i t a s s u m p t i o n t h a t f l o w r a t e s w h i c h

212

are the basis of the computations discussed in this section are

accurately known at the apex of the fan is probably erroneous.

REFERENCES

Anon 1965. Computer forogram for project formulati,on hydrology. TechAical Release No. U. S. Department of Agricuiture, S o i l Conservation Service, Washington.

Anon. 1977. Guidelines for determining flood flow frequency. Bulletin 17A. U. S. Water Resources Council , Washington. Anon., 1980. Cabaqon flood qtudy. Prepared by: PRC Toups Riverside Caligornia. For: Riverside County Flood Control an6 Water Con&ervation District, California.

Anon. 1981. Guidelines for determining, flood ,flow frequency. Bulletin 17b. U.S. Water Resources Council, Washington.

Anon., 1983. Appendix G: Alluvial fan studies. In: Flood Insurance Stud Guidelines and Specifications for Study Contractors. F&-37. Federal Emergency Management Agency, Washington.

Anon., 1985a. Alluvial fan flooding metQodolo y: an analysis. Prepared By: DMA Consulting Engineers, Marina de,? Rey, California. For: Federal Emergency Management Agency, Washington.

Anon., 198511. Study of flood controJ facilitiea on Flamingo Wash. Prepared By: Black and Veatch/Engineers-Architects, Las Vegas, Nevada. For: Clark County Department of Public Works, Las Vegas, Nevada.

Bull, W.B., 1964. Geomorpholo ented alluvial fans in western Fresno Count Cal,i%rRlfa .se?? S . Geological Si-!rvey Professional Paper 352-%; Washington.

Christensen R.C. and Spahr N.E., 1980. Flood otential ofTo o ah Wash and triLutaries, easterh part of Jacka$s Flp&, Nevada Test gite Southern Nevada. Wafer Resources Investigations Open File Report 80-963. U.S. Geological Survey, Lakewood, Colorado.

Costa, J.E. , 1983. Paleohydraulic reconstruction of flash-f$ood’ geaks from boulder deposits in the Colorado Front Range. Geological

Dawdy D.R., 1979. Flood frequency estimates on alluvial fans. ASCE,’Journal of the Hydraulics Division, 105 (HY11): 1407-1412.

ociety of America Bulletin, 94: 986-1004.

Dalr ple T. and Benson M.A. 1976 Measurement of eakdischarge by i??e s3ope-area methog. h: T’echniyes of WaFer Resources Investigations of the United States Geo.ogica1 Survey, Book 3, Chapter A2. U.S. Geological Survey, Washington.

Edwards K.L. and Thie$mann J. , 1,984. Alluvial fans: novel flood challenbe. ASCE, Civil Enbineering, 54 (11) : 66-68.

Ethrid e, F.G. and Schumm, S.A., 1978. Reconstructing aleochannel morpho?ogic and flow characteristics: methodolo y !?imitations, and assessment. In: A. D. Miall editor) FLyviaq hedimentology. Canadian Society of Petroleum Geologists kemoir 5: 703-721.

French. R.H.. 1984. Flood hazard assessment on alluvial fans: an examination ‘of the methodolog Prepared b Water Resources Center Desert Research Instituk Las Ve as Sevada For: U.S. Departhent of Energy, Las Vegas, kevada, 8OE;/NV/1016i-19.

French, R.H., 1985. Open-Channel Hydraulics. McGraw-Hill Book Company, New York.

FrenGh, R.H., 1986. Flood Hazard Assessment on Allqvial Fans: An Examination of the Methodology. In: Proceedings of the International Symposium on Flood Frequency and Risk Analysis, Baton

213

Rouge, Louisiana, (in press).

French R.H. andLombardo, W.S.,1984. Assessment of flood hazardat the radioactive waste management site in Area 5 of the Nevada Test Site. Prepared by: Water Resoyrces Center Desert Research Institute, Las Ve as Nevada. For. U.S. Department of Energy, Las Vegas, Nevada, D&/dV/l0162-15.

Harms J.C. 1969. Hydraulic si nif,icance. of some sand ripples. Geolobical Society of America Bulyetin, 81. 363-396.

Harty, D,.S., 1982. Copputerprogram fordetermining flooddepths and velocities on alluvial fans. Pre ared by. Dames and Moore, Bethesda Maryland. For: Fedqral Emergency Management Agency , Off ice of- Natural and Technological Hazards, Washington.

Jarrett, R.D.: 1984. Hydraulics of hi h- radient streams. ASCE, Journal of Hy6raulic Engineering, 110 7117: 1519-1539.

Joplin A.,V., 1966. Some principles and techniques used. in recons%uct in the hydraulic parameters of a paleo-f low regime. Journal of Se%imentary Petrology, 36:

Kogter, E.H. 1978. TranFveyse ribs: their characterigtics, orig+n and paleoh draulic si nificance. In: A.D. Miall (editor) , Fluv ai Sedimento!ogy, Canac?ian Society of Petroleum Geologists, Memoir 5. 161-186.

5-49.

Magura, L.M. and Wood, D.E., 1980. Flood hazard identification and flood plain manqgement on alluvial fans. AWRA, Water Resources Bulletin, 16 (1). 56-62.

Maizels , J . K. 1983. Palaeovelocity and palaeodischarge determination for coarse qnravel deposits. In: K.J. Gre ory

John Wiley and Sons, Lzd. , Jew Yori! 101-139. editor Background to Palaeo ydrology.

Miller J.F., Frederick R.H., and Tracey, R.J., 1973. Preci itation-frequency atfas of the Western United States , Volume VII Revadq U.S. fepartment of Commerce, NOAA, National Weather SeAice, Sliver Spr ng, Maryland.

Nummedal, D. 1973. Paleo-flow characteristics ofa latecretaceous river in ytah from anaJysis of sedimentary tructures in the Ferron sandstone. a discussion. Journal of Sedfmentary Petrology, 43 : 1176-1180.

Rachocki, A.H., 1981. Alluvial Fans. John Wileyand Sons, Limited, New York. Rigcfi H.C., 1968. Some Statistical Tools in Hydrolo In: Tec n ques of Water-Resources Investigations of the Uniterktates Geological Survey. U.S. Geological Survey, Washington.

Roeske, R.H., 1978. Methods for estimating the magnitude and frequenc of floods in Arizona. ADOT-RS-15(121). Pre ared By: U . S . Geoyooaical Survev. Tucson, Arizona. For: Arizona ADartrnent of-Transpo?tation,- Ph’den-ix, Arizona.

Schumm S.A,, 1972 Fluvial palegchannels. In: J.K. Rigby and W.K. kamblin (editors) , Reco nition of Ancient Sedimenta Environments. societ of Zconomic Paleontologists a 3 Mineralogists , Special Publication 16: Shaw J. andKellerhals, R. 1977. Paleohydraulic interpretationof antidune bedforms with appficFtion to antidunes in gravel. Journal of Sedimentary Petrology, 47. 257-266.

98-107.

Squires Wash and f<s prynci a1 southwestern tr butaries Nevada Test Rite Southern Nevada. 8ater Resources Investiaatiolis ODen File ReDOrf

R. a d young, R.L. , 1983. flood gotential of Fort

- - - -_. - - . . - - - - - . 83-4001. U.S. Geological-Su?%ey, Carson City, Nev’ada.

Zehr R.M. and Myers V.A., 1984. Deptharea ratios in thesemi-arid Southwest United ‘States. NWS Hyd 0-40 . U.S. Department of Commerce, NOAA, National Weather Servfcce, Silver Spring, Maryland.

214

CHAPTER 6

CONCLUSION

6.1 INTRODUCTION

The foregoing chapters have discussed hydraulic processes on

alluvial fans from several diverse viewpoints; an engineer's

interpretation of geomorpho1ogy;theoretical hydraulic engineering;

andappliedhydraulicengineering. Thereaderwhoexpected th isbook to provide solutions to specific problems must at this point be

somewhat disappointed since there are no well-defined, commonly

accep tedorva l ida t ed techn iques f o r a n a l y z i n g h y d r a u l i c p r o c e s s e s on alluvial fans have been presented. In fact, the engineer or

geologist attempting to analyze hydraulic processes on alluvial fans

can only rely on his or her own experience, judgment, and

understandingofgeomorphology, hydrology, andhydraulics of arid and

semi-arid areas. For many the lack of accepted techniques and

guidelines for analysis will make the experience traumatic; however,

for others it will be the beginning of an exciting adventure.

Given that the state-of-the-art in analyzing hydraulic

processes onalluvial fans is atbestprimative, there is a clear need

for multi-disciplinary research, coordinated, regional data

collection efforts, and aboveall, thecoordination of all effort son

a regional basis.

6.2 SOCIO-ECONOMIC AND INSTITUTIONAL PROBLEMS

As indicatedinSection1.1,thereareanumberofsocio-economic

and institutional problems that hinder the development of rational

and cost-effective flood control in the American political

environment. Primaryamongthese problems is the lackof central or

regional authorities in many arid and semi-arid areas for the co-

ordinationand implementationof floodcontrolplanning. The lackof

co-ordinated planning on a regional basis often results in one

governmental unit solving a problem by creating a bigger and more

difficult problem for a neighboring governmental unit. While the

lawyerspracticinginlitigation look forward to such situations, the

technical community is embarrassed, or should be, by such 'solutions'

to problems. Not only must rational and effective flood control

plans be co-ordinated on a regional basis, but there must also be

incentives and dis-incentives for the private and public sectorsto

215

adopt these plans.

need for public involvement in the development

of flood control plans for arid and semi-arid regions. From the

perspectiveof financing, it is the publicwho willultimately pay for

the level of protection they desire. This is true whether the plans

developed are purely structural solutions, involve land use planning

and zoning, or a combination of structural and zoning measures.

Further, in sparsely populated areas, long-time residents may have

more knowledge regarding channel locations and flow rates than the

technical professional can estimate fromthe best models, given the

very limited data available.

, The lack of regional co-ordination a l s o affects the funding of critically needed basic and applied research and data collection

efforts. Forexample, i f t w o c i t i e s o r s t a t e s h a v e a s i m i l a r p r o b l e m , a jointly funded, co-operative investigation may be cost-effective.

However, the American sys t emofgovernmen t t ends tobo thencourageand reward political parochialism and chauvinism; and as a result, there

is only a very limited framework for developing and funding joint

efforts. Inpractice, eachpoliticalentity solves its own immediate

problem and allows its neighbors to also solve the problem. At the

Federal level, the framework for developing regional investigations

exists, but one cannot be optimistic that the Federal Government is

either ableorwillingtoundertake sucheffortsat thispoint intime.

Further, with exceptions, the Federal Government is a very

inefficient administrator of research, particularly when its own

agencies have a vested interest in the results or in performing the

research.

The engineers and planners responsible for flood and drainage

control on alluvial fans tend to approach the problem from a

structuralviewpoint; that is, des ign ingandbu i ld ing l inedchanne l s , detention and retention basins, and installing storm sewers. While

in some instances structures are cost-effective, solutions to

flooding and drainage on alluvial fans, other than building

monuments, should be considered. For example, in developing areas

with 'stable' natural channels, consideration should be given to

maintaining and preserving these channels. In suburban areas,

individual cisterns to both control and capture runoff from

impervious areas suchas roofsand deckswiththecaptured waterbeing

usedforon-site irrigation couldbe considered. Thereal problemis

the lackof imaginationandthe f a c t t h a t e n g i n e e r s h a v e b e e n t a u g h t t o design structures and that contractors earn money by building

There is also a

216

s t r u c t u r e s . A s t r u c t u r e a l s o provides t a n g i b l e proof t h a t something is being accomplished. Fu r the r , s t r u c t u r e s a r e o f t e n attractivetodevelopersbecausetheyreducetheamountoflandneeded

f o r f lood c o n t r o l purposes and maximize t h e amount of l and a v a i l a b l e f o r development. However, s t r u c t u r a l f l ood c o n t r o l o f t e n irreparablydamagestheaestheticappealof a n a r e a , and i n manycases no long-range maintenance program is provided r e s u l t i n g i n delayed and o f t e n dangerous s i t u a t i o n s i n t h e f u t u r e .

F i n a l l y , t h e people l i v i n g on a l l u v i a l f a n s i n a r i d and s e m i - a r i d r eg ions p r e s e n t a problem i n t h a t most of t h e s e people have migrated t o t h e d e s e r t from humid a r e a s wi th pe renn ia l r i v e r s conta ined inreasonablystablechannels. Thus, when look inga thomes i n t h e d e s e r t , t hey have no b a s i s f o r judging t h e p o t e n t i a l f o r f lood and dra inage problems, much less t h e p o t e n t i a l f o r d e b r i s o r mud flows. It is a l sohumanna tu re t o f o r g e t howbadthe f l o o d i n g w a s t w o o r t h r e e yea r s ago and t o convince yourse l f it w i l l never happen aga in . Thus, whenthe v o t e r s a r e a s k e d t o fund f lood c o n t r o l o r r i go rous land use planning, t hey o f t e n r e f u s e .

6.3 RESEARCH NEEDS

The need f o r b a s i c and app l i ed r e sea rch i n t o h y d r a u l i c processes o n a l l u v i a l f a n s is c l e a r . On ly recen t ly have i n v e s t i g a t o r s begun to combine q u a n t i t a t i v e modeling wi th q u a l i t a t i v e observa t ion . I n gene ra l , t h e g e o l o g i s t and geomorphologist has focused onassembling q u a l i t a t i v e observa t ions and examining of t h e geomorphology of a l l u v i a l f a n s on geologic r a t h e r t han engineer ing t i m e s c a l e s . I n c o n t r a s t , engineers have concent ra ted on e x t r a p o l a t i n g t h e i r knowledge of t h e hydrology and hydrau l i c s of humid a r e a s t o a r i d and semi -a r id reg ions . Theeffortsoftheengineeringcommunityhavetoo

o f t e n focused on very narrow t o p i c s seeking immediate s o l u t i o n s t o fundamental problems. The b a s i c need is f o r i n t e r - d i s c i p l i n a r y th ink ing t h a t combines t h e e x c e l l e n t q u a l i t a t i v e d a t a and obse rva t ions of t h e geosc iences community wi th t h e q u a n t i t a t i v e s k i l l s a v a i l a b l e i n t h e engineer ing community.

Among t h e r e sea rch t o p i c s t h a t r e q u i r e a t t e n t i o n a re : 1. Although t h i s book has focused on hydrau l i c p rocesses on

a l l u v i a l f ans , t h e r e is a c r i t i ca l need t o understand t h e h y d r o l o g y o f t h e d r a i n a g e b a s i n s t h a t a r e l o c a t e d above the a l l u v i a l fan . The models of a l l u v i a l f a n s d i scussed i n Chapters 4 and 5 a l l assumed t h a t bo th t h e q u a n t i t y of flow and t h e shape o f t h e hydrographare knownat t h e a p e x o f t h e

217

2.

3.

4.

5.

fan. These variables and parameters are functions of

drainage basin hydrology.

Althoughthe techniques for predicting when fluvial flows

occur onalluvial fans andtheir subsequentbehavior onthe

fan is primitive, the analogous techniques and

methodologies available for debris flow are even more

primative and unproven. Although debris flows may be

infrequent events, their impact on a developed area can be

catastrophic.

From the viewpoint of the behavior of alluvial channels

located on fans, much of the material presented in Section

3.4 is not valid. An understanding of the behavior of

alluvial channels in response to high velocity, unsteady

and infrequent flows is essential.

Relatedtothequestion of alluvial channel geometry is the

questionofthetypeof flowthat occurs innatural channels

located on alluvial fans: that is, is the flow critical,

subcritical, or supercritical? Further, is the

resistance coefficient in such channels appropriately

represented as a constant which is a function of the

material size or is it a variable? The assumptions

regarding channel shape presented in Chapter 5 is semi-

empirical and has not been validated.

There is a need to incorporate the concepts of

paleohydrology: see for example Costa (1983), into the

analysis of flood frequency andmagnitude in thewatersheds

above alluvial fans and on the fans themselves. Given the

paucity of precipitation and stream gagesand theshortness

of the record when there are such gaging stations, other

means of performing the traditional analyses of estimating

peak flood flows and frequencymustbe sought. However, in

developing such techniques, care must be used to

differentiate between water and debris flows which is not

always an easy task; see for example, Costa and Jarrett

(1981) and Costa (1984).

The above is buta limitedattempt to identify a few crucial technical

areas in which basic research is needed. The issues raised are so

fundamental that it must be concluded that our understanding of

hydraulic processes on alluvial fans and our understanding of arid

basin hydrology is, at the very best, primitive.

Related to the research issues is the need for additional data

218

regarding hydrometeorology, hydrology and hydraulics inthe aridand

semi-arid environment. For example, as indicated in Section 5.5,

there are not sufficient data to accurately estimate the frequency,

duration, and depth ofprecipitation inthe LasVegas Valley, Nevada.

The situation in the Las Vegas Valley is unfortunately not unique.

The paucity of precipitation and flow records in arid and semi-arid

areas puts the engineer, geologist and planner in the position of

making crucial and expensive decisions on the basis of inadequate

knowledge. The collection and analysis of hydrologic data is

unglamorous and expensive anddoes not produce noticeable or salable

results in the near term. Rather the collection of essential and

meaningful hydrologic data requires a long term philosophical and

financial commitment whose benefits may not be realized for many

years.

The foregoing comments have primarily addressed the need for

research in geomorphology, hydraulic engineering, and engineering

hydrology. There are also research needs in other areas such as

atmospheric science which are closely related to the study of hydraulic processes onalluvial fans. For exampleas notedelsewhere

in this book and by Randerson (1986) there is a crucial need to

understand mesoscale convective complexes (MCCs). MCC is a

technical terminology used to refer to large and long-lived

convective storm systems, Maddox (1983). AlthoughMCCs arebelieved

to account for a significant portion of the growing season

precipitation in the corn and wheat belts of the United States, MCCs

are also known to produce intense precipitation which may result in

flash flooding, Bosart and Sanders (1981) , and one out of four MCCs produce death or injury, Maddox (1983). The size and ferocity of

these complexes is such that it is critical that we have more

information regarding the circumstances under whichthey form; their

subsequentmovement; andtheir frequency. Todate, such information

and analysis is not available for the Southwest, and this lack of

knowledge impairsour ability to protect the public fromcatastrophic

flow events on alluvial fans.

Although the above comments indicate some of the critical

researchanddataneeds requiredto understandhydraulic processes on

alluvial fans, one cannot be optimistic regarding the willingness or

ability of governmental units (Federal, state, county or municipal)

to sponsor this work. One reason is that the research required is

neither high-tech nor glamorous; rather it is in traditional

disciplines. Secondly, one never realizes the need f o r data

219

c o l l e c t i o n u n t i l t h e r e is an u rgen t problem which r e q u i r e s t h e da t a . A l l t o o o f t e n agenc ie sdo no t r e a l i z e t h a t t h e r e i s n o s u b s i t i t u t e f o r long, r e l i a b l e d a t a records : r a t h e r , d a t a c o l l e c t i o n e f f o r t s a l l t o o oftenareeithernotfunded, underfunded, o r c u t b a c k f i r s t whenthere is a sho r t age of funding.

I n c o n t r a s t t o t h e above, it must be noted t h a t l o c a l and n a t i o n a l needshave andcontinuetoresultinacontinuously improving understanding of hydrau l i cp rocesses o n a l l u v i a l f ans . For example, d e b r i s and mud flows i n Utah l e d t o t h e s t u d i e s of DeLeon and Jeppson ( 1 9 8 2 ) , Jeppson and Rodriquez ( 1 9 8 3 ) , Chen ( 1 9 8 4 ) , James e t a 1 (1986)

and Wieczorek ( 1 9 8 6 ) . S imi l a r concerns i n Los Angeles County have a l s o r e s u l t e d i n progress : see f o r example, Kumar (1986) , and on a n a t i o n a l l e v e l t h e r e a r e t h e s t u d i e s of Chen (1983, 1985, 1986a, 1986b, 1986c) and MacArthur e t a 1 ( 1 9 8 6 ) . The concern of t h e U . S .

Department of Energy regard ing t h e p o t e n t i a l f o r rad ionucl ide migra t ion a t t h e Nevada T e s t S i t e has r e s u l t e d i n b a s i c and appl ied s t u d i e s desc r ibed by French (1983 , 1 9 8 4 , 1985) among o t h e r s .

Among t h e o t h e r developments which should be noted is t h e t h e o r e t i c a l and app l i ed p rogres s being made i n understanding t h e behavior of a l l u v i a l channels . A s noted elsewhere i n t h i s book, t h e primary problem of f l u v i a l h y d r a u l i c s i s t h a t t h e r e a r e moreunknowns than t h e r e a r e equat ions . The concepts of minimumunit s t ream power andminimum stream powerare p r o m i s i n g a t t e m p t s t o so lve t h i s c l o s u r e problem. The minimum stream power hypothes is a s s e r t s t h a t an a l l u v i a l s t ream a d j u s t s i t s e l f i n response t o changes i n t h e environment so t h a t t h e t o t a l s t ream power of t h e channel reach is minimized; see f o r example, Chang and H i l l ( 1977) and Chang (1982a, 1 9 8 2 b ) . Chang (1982b) has a s s e r t e d t h a t h i s model is a p p l i c a b l e t o channels on a l l u v i a l fans : however, f i e l d v e r i f i c a t i o n of t h i s a s s e r t i o n is no t y e t a v a i l a b l e .

6 . 3 . 1 Prognosis The o v e r a l l p rognos is f o r r e sea rch and development i n

understanding hydrau l i c processes on a l l u v i a l f ans is p o s i t i v e i f on ly because t h e r ap id u rban iza t ion i n a r i d and semi-ar id a r e a s w i l l cont inue a n d t h e commitments o f b o t h t h e p u b l i c a n d p r i v a t e s e c t o r s t o t h e taxpayers and owners of bu i ld ings i n t h e s e areasdemands a b e t t e r q u a n t i t a t i v e understanding of t h i s t o p i c . However, p rogress may be s lowbecause t h e taxpayers a n d t h e i r elected r e p r e s e n t a t i v e s o f t e n d o not recognize t h a t is is much more c o s t - e f f e c t i v e t o sponsor focused app l i ed r e sea rch t o develop both an understanding of t h e problem and

220

solutions than it isto simplydesign andbuild a system that everyone

hopes or assumes works. Hopefully, as the political systems in

developing arid and semi-arid regions mature their attitudes toward

growthwill also change sothat rational, well-designed floodcontrol

systems will be developed and built. In one sense, litigation over

flood damage is positivebecause it forces the representatives ofthe

taxpayers to find methods of repaying those who have been damaged by

the shortsightedness of past representatives and hopefully suggests

that there must be planning and ioning on a regional basis.

It is hoped that this book will aid the engineer,

geomorphologist, and planner in understanding hydraulic processes on

alluvial fans and planningfor safedevelopment inarid andsemi-arid

regions.

REFERENCES

Bosart L.R. andSande,rs, F:, 1981. TheJohnstown floodofJuly1977. Journai of Atmospheric Science, 77: 260-271.

Chan H.H., 1982a. Stable alluvial channel design. ASCE, Journal of t% Hydraulics Division, 106 (HY5) : 873-891.

Chang, H.H., 1982b. Fluvial hydraulics of deltasand alluvial fans. ASCE, Journal of the Hydraulics Division, 108 (HY11): 1282-1295.

Chang, H.H. andHill J.C., 1977. Minimumstreampower forriversand deltas. ASCE, Jourfial of the Hydraulics Division, 102 (HY12) : 1375- 1389.

Chen, C., 1983. On frontier between rheolocpand,mudflowmechanics. In: Proceedin s of the Conference on rontiers in H draulic En ineering. zmerican Society of Civil Engineers, New Yorx: 1137

Chen, C. 1984. Hydraulic concepts in debris flow simulation. In: D.S. Bodles (editor) , Delineation of Landslide Flash Flood and Debris Flow Hazards in Utah. Utah WaterResearch’Laboratory, LAgan, Utah: 236-259.

Chen, C., 1985. Present status of research in debris flowmodeling. In: Proceedin s of the Speciality Conference Hydraulics and Hydrology in t%e Small Com uter Age. American Society of Civil Engineers, New York: 733-781.

Chen C., 1986a. Bingham plastic or Bagnold’s dilatant fluid as a rheoiogiGa1 model of a debris flow? Proceedings of the Third International S m osium on River Sedimentation. Jackson, Mississippi: 162i-P635.

Chen C., 198633. Chinese concepts of modeling hyperconcentrated streAmflow and debris flow. In.: Proceedjngs of the Third International S m osium on River Sedimentation. Jackson, Mississippi: 164Y-P657.

Chen, C., 1986c. Viscoplastic fluid model for debris flow routing. In: .M. Karamouz, G.R. BaumJi, and W:J. Brick (editors) Water FQrUm ‘86. World Water Issues in Evolution. American SociIety of Civil Engineers, New York: 10-18.

Costa J.E., 1983. Paleohydraolic reconstruction of flash flood eaks’from boulder depositg in the Colorado Front Range, Geological gociety of America Bulletin, 17:

11%.

In:

986- 1004.

221

Costa. J.E., 1984. Physical geomorpholo of debris flows. In: J.E. Costa and P.J. Fleisher (editors) , Deveyo ments and Applications of Geomorphology. Springer-Verlag, New Yorf : 268-317.

Costa J.E. and Jarrett R.D. , 1981. Debris flows in small.mountain streaA channels of Colorado and their hydrologic implications. Bulletin of the Association of Engineering Geologists, XVIII (3): 309-322.

DeLeon, A.A. and Jeppson, R.,W., 1982. Hydraulics and numerical solutions of steady-state but spatially varied debris flows. UWRL/H:82/03. Utah Water Research Laboratory, Utah State Univeristy, Logan, Utah.

French, R.H.., 1983. Precipitation in SouthernNevada, ASCE, Journal of Hydraulic Engineering, 109 (7): 1023-1036.

French, R.H., 1984. Flood hazard assessment on alluvial fans: an examination of the methodolog Pre ared by: Water Resources Center, Desert Research Instixite Eas Vegas NV. For: U.S. Department of Energy, Las Vegas, NV: DOE/NV/10162-19.

French R.H. 1985. Daily, seasonal and annual precipitation atthe Nevada Test 'Site , N,evada. Prepared by: Water Resources Center Desert Research Institute, Las Ve as Nevada. For: U. S . Department of Energy, Las Vegas, NV, DOE/N?10184-01.

James, L.D., Pitcher D.O., Heefner, S.,Hall, B.R., Paxman, S.W. and Weston, A. 1986. Flood risk beJow steep mountain slopes. In: M. Karamouz, 6.R: Baumli a,nd W.J. Brick (editors), Water Forum, '86: World Water Issues in Evolution. American Society of Civil Engineers, New York: 203-210.

Jep son R.W. and Rodriguez S.A. 1983. H draulics of solvin unsfeadjr debris flow. UhR$/H-d3/03. Uta% Water Researcz Laboratory, Utah State University, Logan, Utah.

Kumar S., 1986. Engineering methodolog for delineating debris flow liazards in Los Anaeles Countv. In: %. Karamouz. G.R. Baumli. and W.J. Brick (editoPs) Water F,or.um '86: World Water Issues in Evolution. American Society of Civil Engineers, New York: 19-26.

MacArthur R.C. Schamber D.R., Hamilton D.L. and West, M.H., GeneralizAd metdodolo y,fok simulatinRmudflows. In: G.R. Baumli, andoW.J. jrick, (editors) ater Forum '86: World Watef- Issues in Evolution. American Sociedy of Civil Engineers, New York:

M. Karamouz

227-234.

Maddox, R.A. 19.83. Lar e-scale meteorological conditions associated with m;dlatitu$e, mesoscale convective complexes. Monthly Weather Review, 111: 1475-1493.

Randerson D., 1986. Amesoscale convective complexty e stormover the desert southwest. U. S . De artment of Commerce, NOAA, National Weather Service, Salt Lake CiFy, Utah.

NOAA Technical Memorandum NWS 6R-196

Wieczorek, G.F., 1986. Debris flow and hy qrconcentrated streamflows. Water Forum '86: World Water 'rssues in Evdlution. American Socie&$ of Civil Engineers, New York: 219-226.

In: M. Karamouz G.R. BFumli andW.J. Xrick (editoys

222

GLOSSARY

Active channel: Channel on an alluvial fan through which runoff

occurs.

Alluvial fan: Triangular or fan-shaped deposit of boulders, gravel,

sand, and finer sediment at the base of desert mountain slopes

deposited by intermittent streams as they debouch onto the valley

floor.

Alluvial plain: A plain formed by the deposition of water

transported sediment.

Alluvium:

is in transit, and consisting of gravel, sand, silt, and clay.

Material that haseither beendeposited by streams orthat

Alternate depths: For every value of specific energy except one,

there aretwo depths of flowwhich will produce thisvalue of specific

energy, the alternate depths.

Apex: The point of highest elevation on an alluvial fan. Most

commonly the apex is at the point where the major stream that formed

the fan emerges from the mountain front.

Arid region: An area of scant rainfall, commonly 152 mm (6 in.) or

less. Precipitation is seasonal and there are wide variations from

the average.

Arroyo: Spanish term used in the southwestern United States to

designate thechannel of atemporary stream. Thechannel usuallyhas

vertical walls of unconsolidated material 0.61 m ( 2 . ft) or more in

height. A dry wash.

Avulsion:

channel and the formation of a new channel.

Atermusedto indicate the sudden abandonmentof one flow

Bajada: Ablanketdepos i to fa l luv ium atthe baseof desertmountain

slopes formed by the coalescing of alluvial fans. A bajada can also

be termed an alluvial apron or a piedmont plain.

223

BasinandRangeProvince: Amajorgeomorphic provinceof thewestern United S t a t e s . T h i s area is t y p i f i e d by longi tudinal f a u l t block mountains separated by va l l eys f i l l e d w i t h alluvium.

Bingham number: A dimensionless number whose magnitude ind ica t e s whether t h e flow of Bingham p l a s t i c f l u i d is laminar o r turbulent .

Braided channel: An i n t r i c a t e network of r e l a t i v e l y shallow, i n t e r l a c i n g channels.

Caliche: L i m e - r i c h deposi t i n s o i l s of a r i d and semi-arid regions formed by c a p i l l a r y rise of lime-bearing water toward t h e surface where by evaporation lime-rich ca l i che is deposited. Also, gravel , sand, o r d e s e r t deb r i s cemented by calcium carbonate o r t h e calcium carbonate i t se l f .

Canyon: Steep-walled va l l ey o r gorge i n a mountainous area. A

canyon has s t eep and preciptous s lopes which d i s t ingu i shes it from va l l eys .

Coalescing a l l u v i a l fans: The surface produced when individual a l l u v i a l fans grow and jo in .

Colluvium: s t eep s lope t h a t has been t ransported by gravi ty .

Loose deposi t of rock mater ia l a t t h e foo t of a c l i f f o r

Conjugate depth: I n a hydraulic jump, t h e depth of flow changes rapidly. Takenasapa ir , thedepthups treamof the jumpandthedepth

downstream of t h e jump a r e t h e conjugate depths.

C r i t i c a l flow: A flow i n which t h e Froude number, F, has a value of one.

Debris flow: Moving rampart o r w a l l of boulders and muda fewmeters i n height without v i s i b l e water t h a t moves forward i n a s e r i e s of surges orwaves alongan a l l u v i a l fan. Also, a d e b r i s i s a flowageof a mixture of a l l s i z e s of sediment. Boulders accumulateat the f ron t of t h e deb r i s wave and form a lobe behind which follows t h e f ine r - grainedmore f l u i d i c d e b r i s . S e e a l s o t h e d e f i n i t i o n s o n p a g e s 68and

224

106.

Desert: Abar renandun inhab i t ed reg ion ; aregionoflowrainfalland high evaporation as the result of which plant growth is scanty and

specialized. Insuch area, erosion carves a distinctivetopography.

Desert lacquer:

gravel rock surfaces in desert regions.

desert patina.

Surface stain orcrust ofmanganese or iron oxideon

See also desert varnish and

Desert patina: Darkbrown and black surface coating of manganese or

iron oxide on rock surfaces in desert regions. See also desert

lacquer and desert varnish.

Desert pavement: Coarse, angular to subround rock fragments on

undissected portions of alluvial fans, terraces, and valley flats

arranged in such a way as to make a smooth and interlocking surface.

Formed by the continual removal of fine material by wind and by rain

splash and sheetwash which leaves behind a mosaic of fragments.

Desert polish:

action of wind blown sand and dust.

Smooth and polished surfaces on rocks formed by the

Desert varnish: Surface stain or crust of manganese or iron oxide

which characterizes many exposed rock surfaces in deserts. It coats

ledges or rocks as well as boulders and pebbles, imparting a black or

brown color and a shiney luster to these surfaces. See also desert

patina and desert lacquer.

Effective precipitation: The amount of precipitation required to

produce a specified amount of runoff.

Ephemeral: Existing or continuing for a short time: transitory or

temporary, as an ephemeral stream or lake.

Fanhead trench: Linear depression formed by dry washes and other

drainage lines which are incised considerablybelowthesurface of an

alluvial fan.

225

Flash flood: convect ive p r e c i p i t a t i o n event : fol lowing a heavy r a i n .

Sudden d e s e r t f lood u s u a l l y r e s u l t i n g from an in t ense extreme runoff event i n a dry wash

Froude number: The r a t i o of dynamic o r i n e r t i a l f o r c e s t o g r a v i t a t i o n a l fo rces . When t h e Froudenumber, F, is one, t h e flow is t e r m e d c r i t i c a l ; w h e n F > l , t h e f lowistermedsupercrit ical; andwhen F < 1, t h e flow is termed s u b c r i t i c a l .

Great Basin: Region i n t h e SouthwesternUnited S t a t e s cha rac t e r i zed by f a u l t block mountains and in t e rven ing depressed blocks forming bas ins . The reg ionof theBas inandRange topography inUtah , Nevada, sou theas t e rn C a l i f o r n i a , and p o r t i o n s of N e w Mexico, Arizona, southern Oregon, and w e s t Texas.

Hydraul ic depth: a r ea t o t h e w i d t h of t h e flow channel a t t h e depth of flow.

A d e f i n i t i o n of convenience: t h e r a t i o o f t h e flow

Hydraul ic jump: Inagivenreachofchannelwhereanupstreamcontrol

d i c t a t e s s u p e r c r i t i c a l flow w h i l e a downstream c o n t r o l d i c t a t e s s u b c r i t i c a l flow, t h i s con t r ad ic t ion may be reso lved by a hydraul ic jump. I n e s s e n c e , t h e h y d r a u l i c jump i s a r a p i d c h a n g e i n t h e d e p t h o f flow wi th h igh energy l o s s e s .

Hydrau l i c rad ius : a r e a t o t h e wet ted per imeter .

A d e f i n i t i o n o f convenience: t h e r a t i o o f t h e flow

I n t e r s e c t i o n po in t : The po in t on an a l l u v i a l fanwhere t h e channel merges wi th t h e s u r f a c e of t h e fan . T h i s p o i n t is o f t e n t h e locus of sediment depos i t ion .

Laminar flow: A flow i n which t h e f l u i d p a r t i c l e s move along smooth pa ths i n l a y e r s wi th one l a y e r g l i d i n g smoothly over an ad jacent l a y e r . Losses i n laminar flowsareproportionaltothe first powerof t h e v e l o c i t y .

226

Mud flow: Debris ladenwater originating on steep slopes so charged

with mud and sand that it forms a fluid far denser than water and is

capable of transporting huge blocks and boulders which are buoyed up

by the viscous mass.

Pediment: Slightly inclined rockplain thinlyveneered with fluvial

gravels; arock-carvedplain formedas desertmountains retreat under

the influence of planatation by streams, sheetwash, rillwash, and

backweathering.

Piedmont plain: An extensive and continuous plain developed along

the base of desert mountain slopes. A piedmont plain can also be

termed an alluvial apron or a bajada.

Playa: A very flat, vegetation-free area of clay and silt in the

lower portion of hydrologically closed drainage basins in arid and

semi-arid regions. Playas are formed by temporary lakes which

rapidly evaporate leaving behind fine sediment.

Rain shadow:

mountain or mountain range.

on the windward side of the range.

Region of diminishedprecipitation onthe leeside ofa

Precipitation is appreciably less than

Reynolds number:

whether the flow of a Newtonian fluid is laminar or turbulent.

A dimensionless number whose magnitude indicates

Segmentedalluvial fan: An alluvial fan composedof several segments

that are the result of erosional and depositional changes over a

period of time.

Semiarid (semi-arid): Partially arid; on thebasis of precipitation

a region in which the average annual precipitation is 305-406 mm (12-

16 in) , and by some observers between 254 and 508 mm (10 and 20 in).

Specificenergy: Theenergyperuni twe ighto f the fluid flowingwith

the elevation of the datum taken as the bottom of the channel.

Subcritical flow: Aflowinwhich theFroudenumber , F, hasavalueof

227

less than one.

S u p e r c r i t i c a l flow: g r e a t e r t han one.

A f l o w i n w h i c h t h e Froudenumber, F, has a v a l u e

Turbulent flow: A flow i n which t h e f l u i d p a r t i c l e s move i n very i r r e g u l a r pa ths caus ing an exchange of momentum from one p o r t i o n of t h e f l u i d t o another . Losses i n t u r b u l e n t flows a r e p ropor t iona l t o t h e second power of t h e v e l o c i t y .

Uniform f l o w : A s t a t e of flow i n which t h e channelbot tom s lope , t h e channel cross-section, the dep thof flow, and t h e a v e r a g e v e l o c i t y o f flow remain cons t an t wi th long i tud ina l d i s t ance .

Wettedperimeter : Thelengthof thecurverepresent ingthe i n t e r f a c e between t h e l i q u i d and s o l i d boundary which conf ines t h e f l u i d .

228

AUTHOR INDEX

Albertson, M.L. 106

Anstey, R.L. 1,15,30,36,40,

41

Bosart, L.R. 218

Bradley, W.C. 24

Bretz, J.H. 2 4

Antevs, E. 46,51,54

Brighton, J.A. 111

Babbitt, H.E. 111,117,118

Babcock, H.M. 16

Bagnold, R.A. 114

Bajorunas, L. 165

Baker, V.R. 24

Barbarossa, N.L. 126

Broecker, W.S. 51

Bue, C.D. 2 4

Bull, W.B. 1,16,17,33,35,36,

48,53,54,61-65,146,192

Caldwell, D.H. 111,117,118

Campbell, R.H. 69,72,73,131,

179 Barnes, H.H.Jr. 8 8

Carlson, C.W. 89,102,104

Beaty, C.B. 15,17,18,29,30,

68 , 157

Bell, J.W. 18

Benjamin, J.R. 145

Benson, M.A. 24,40,210

Birkeland, P.W. 24

Blackwelder, E. 64,108

Blalock, M.E.111 85

Blench, T. 96,98

Chang, H.H. 101,219

Chawner, W.D. 13,14,73

Chen, C. 131,178,219

Chien, N. 96

Chow, V.T. 82,88

Christensen, R.C. 208

Coates, D.R. 30

Conte, S . D . 119

229

Flaxman, E.M. 48 Cooke, R.U. 32,36

Cooley, R.L. 76,77 Florey, Q.L. 9 2

Cornell, C.A. 1 4 5 Franzini, J.B. 1 8

Costa, J. E. 24 , 68 , 73 , 1 3 1 , 1 5 4 , French, R.H. l7 I 24,521551 6 5 t

210,211,217 82,85,87,88,90-92,94,100,

115,116,124,127,128,129,160,

Crippen, J.R. 24 162,166,175,192-194,208,210,

219

Croft, A.R. 46,47,55,68-71, Garde, R.J. 89 73,131,146

Cushing, E.M. 1 6 Glancy, P.A. 12,24

Glover, R.E. 92

Dalrymple, T. 24,210 Graft, W.H. 82,96

Dawdy, D.R. 95,102,105,153, Grant, E.U. 8 5 183,186,187

DeLeon, A.A. 114,115,117-119, Gretetner, P-E. 29,30

136,174,177-180,219 Gregory, G. 111

Gregory, K.J. 5 1 Denny, C.S. 34,35,61,63

Eckis, R. 1 5 6 Gupta, A. 24

Edwards, K.L. 14,195 Hampton, M.A. 72,111,112

Eel C.S. 1 0 2

Einstein, H.A. 96, 1 2 6

Enos, P. 111,112

Ethridge, F.G. 2 1 0

Hansen, E.M. 69

Harlin, J.M. 96,100,103

Harms, J.C. 2 1 0

Harmsen, L. 12,24

230

Harty, D.S. 191 Knighton, A.D. 103,105,106

Hedstrom, B.O.A. 111,112

Henderson, F.M. 82,87,88,94

Hetzel, D.R. 55

Konemann, N. 85

Krzysztofowicz, R. 48

Kumar, s. 131,219

Hill, J.C. 219 Lane, E.W. 89,92

Hjalmarson, H.W. 12,73-76 Lane, L.V. 74,75

Hooke, R. LeB. 35,36,61,63,

64,68,70,72,136,154,156-

158 , 179

Hughes, W.F. 111

Imhoff, J.C. 12

James, L.D. 131,219

Jarrett, R. D. 68173 , 89 , 90, 193,197,198,217

Jeppson, R.W. 114,115,117-

119,136,174,175,177-180,

219

Jkrizek, R. 106

Johnson, A.M. 72,114,120-123

Jopling, A.V. 210

Katzer, T. 18,64

Kellerhals, R. 210

Langbein, W.B. 29,43-47,51,

102 , 103

Leopold, L.B. 29,51,53,54,

96,98,102,103,108,143

Linsley, R.K. 18

Lombardo, W.S. 17,65,192,

193 , 208

LUStig, L.K. 35,63

Lynn, W.R. 145

MacArthur, R.C. 131,179,219

Maddock, T. Jr. 96,98,102

Maddox, R.A. 218

Magura, L.M. 187,195

Maizels, J.K. 210

Malde, H.E. 24

231

Mears, A.I. 24,69,71-73,131

Melton, M.A. 36,37,40

Meyer-Peter, E. 89

Miller, J.F. 69,70,206,207

Miller, J.P.' 24, 144

Murphey, J.B. 73

Muller, R. 89

Myers, V.A. 70, 206

Nixon, M. 102

Nobles, L.H. 72, 106-108,

118

Pierson, T.C. 108,118

Price, W.E. Jr. 47,48,68,70,

71,136,138-141,145,148,

152,179,180

Rachocki, A. 1, 193

Randerson, D. 6, 218

Ranga Raju, K.G. 89

Rantz, S.E. 14,15

Raudkivi, A.J. 89

Rhodes, D.D. 98,105

Richards, K.S. 105

Riggs, H.C. 23, 207

Nummedal, D. 210

Rodriguez, S.A. 114,119,136,

174,177-180,219

Orr, P.C. 51

Osborn, H.B. 52

Pack, F.J. 30,64,108

Pardee, J.T. 24

Park, C.C. 103

Peebles, R.W. 74

Petryk, S . 85

Phillips, P.J. 96,100,103

Roeske, R.H. 23, 208,209

Sakamoto, C.M. 22

Sanders, F. 218

Santarcangelo, S.A. 14

Schlichting, H. 100,114

Schumm, S.A. 43-47,50,51,

210

Schuster, R . L . 106

232

Scott, K.M. 12.14

Segerstroem, K. 108

Senturk, F. 88

Shanahan, E.W. 12

Shane, R.M. 145

Sharp, R . P . 72,106-108,118

Sharp, V.J. 124,160

Shaw, J. 210

Simons, D.B. 88,106

Song, C.C.S. 103

Spahr, N.E. 208

Squires, R.R. 63,64,208

Stone, R.O. 1,32,33,45,61,

68,76

Streeter, V.L. 82,123

Sturn, T.W. 85

Synder, C.T. 51

Subramanya, K. 89

Szidarovszby, F. 48

Takahashi, T. 106-108,114,

115,118

Thielmann, J. 14,195

Todorovic, P. 145

Troeh, F . R . 33

Urquhart, W.J. 88

Viessman, W. 24,31

Vitek, J.D. 30

Warren, A. 32,36

Weber, J.E. 48

Williams, G.E. 24

Williams, G . P . 103

Wieczorek, G . F . 219

Winograd, I. 15

Woessner, W.W. 55

Wolman, M.G. 29,105,144

Wood, D.E. 187,195

Wylie, E.B. 82,123

Yang, C.T. 103,166

Young, R.L. 63,64,208

233

Zehr, R.M. 70,206

Zelenhasic, E. 145

Zwamborn, J.A. 129,130

234

INDEX

Albuquerque (see New Mexico,

Albuquerque)

Alluvial fan:

age 16,17

apex 12,14,19,20,33,37,41,

63-65,68,157,159,160,162,

163,170-172,184,185,190-

193,197,199,201,206,212

area 35,36,40

definition 1,32

rate of growth 17,18

segmented 33,40,61

shape 33,40,61

slope i9,36-42,61,158,159,

171,193,194,197,199,200,

202 , 203 trenching 51,54,151,158

unsegmented 33,35,36,40

zones of flow 21

Arid region, definition 45

Arizona 15,37,48,73,208,209

Bullhead City 2

Phoenix 1

Tanque Verde Creek 12,73-

75

Tucson 1,12,16

Arroyo, definition

Arroyo Ciervo Fan

California, Arroyo

Fan)

Austin (see Nevada

33

see

Ciervo

Austin)

Avulsion 170,184,188,189,

194,201,203,204

Bajada 1,54

definition 33

Beatty (see Nevada, Beatty)

Bingham number (see Number,

Bingham)

Bingham plastic fluid (see

Fluid, Bingham plastic)

Black Mountains (see Cali-

fornia, Black Mountains)

Blythe (see California,

Blythe)

Boise (see Idaho, Boise)

Boulder City (see Nevada,

Boulder City)

Boundary Conditions 137-139,

149 , 177 , 178

Bullhead City (see Arizona,

Bullhead City)

Cactus Flats (see California,

Cactus Flats)

Calibration 37,152,178

235

Caliche 76,77

California 14-16,48,199

Arroyo Ciervo Fan 17, 47

Black Mountains 39

Blythe 40

Cactus Flats 35

Central Valley 36

Claremont 200

Cucamonga Creek 200

Day Creek 200

Death Valley 35,36,39,63,

Deep Springs Valley 35

Deer Creek 200

Devil Canyon 200

Etiwanda 200

Fontana 200

Glendale 54

Guasti 200

La Crescenta 54

Los Angeles 1,13,15,54

Milner Creek Fan 17

Montrose 13,54

Owens Valley 35,36

Palm Canyon 200

Palm Desert 2

Palm Springs 39,200

Panamint Mountains 39

Pyramid Peak 39

Rancho Mirage 2

San Antonio Creek 200

San Bernardino 200

San Diego 1

San Gabriel Mountains 54

San Jacinto Mountains 39

San Joaquin valley 15-17,

Shadow Rock Fan 72

Tahquita Creek 200

156

47,61

Trollheim Fan 72

Upland 200

Verdugo Mountains 54

White Mountains 17,18

Wrightwood 72,107

Catastrophism 29,30

Central Valley (see California,

Central Valley)

Channel :

braided 20-22,158,171,

compound 85,87

entrenchment 22,61-65,149,

151,158,162,170,171,184,192

slope 61-84,89,90-92,96,

109,115,118,157,158,160,

166,~67,169,170,172,175,

177,193,195,197,198

stability 12,18,19,64,65,

82,90-106,170,187,190,201,

215

172 , 199

Chezy Equation (see Equation,

Chezy)

Chezy resistance coef-

ficient 114-117

Cisterns 215

Claremont (see California,

Claremont)

Clark County (see Nevada,

Clark County)

Clay 16,68,72,76,111,114,

155

236

Climate and climatic change

36,40,43,48,49,53,54,63,101,

154,156,157

Cohesive materials 92

Colorado:

Big Thompson River 211

Cold Spring Gulch 211

Colorado Front Range 211

Dark Gulch 211

Dry Creek 211

Glenwood springs 2,69,72

Huerfano River 99,100

Indian Gulch 211

Sawmill Gulch 211

Spring Creek 211

Tucker Gulch 211

Convective storm 53,218

(see also Thunderstorm)

Cost 2-6,14 (see also Cost-

effective)

Cost-effective 14,15,28,55,

214,215

Critical flow (see Flow,

critical)

Cucamonga Creek (see Cali-

fornia, Cucamonga Creek)

Damage, economic 1,2,6,14,

68,159,175 (see also Cost)

Darcy-Weisbach friction

coefficient, 116,117

Day Creek (see California,

Day Creek)

Death Valley (see California,

Death Valley)

Debris Flow 1,2,6,8,9,14,

~~18,64,65,68-73,106-123,144-

1 4 8 , 1 5 2 , 1 5 3 , 1 5 6 - 1 5 8 , 1 7 3 1 1 7 4 -

179,194,204,216,217 (see also

Flow)

depth 115,119,175

frequency 72,146

return period (see

Frequency)

Deep Springs Valley (see Cali

fornia, Deep Springs Valley)

Deer Creek (see California,

Deer Creek)

Density (see Fluid, density

Deposition 2,14,15,18,19,28

29,33 , 51,53,64,65,71,136,137, 139,146,147,151-153,156,158,

170,183,210

Depth :

critical 211

hydraulic 84

normal 90,175

of flow 12,13,19,82-84,96,

100,105,111,112,119,123,

160,162,163,166-168,170,

175,178,187,188,189,193,

195,202

Devil Canyon (see Cali-

237

f ornia , Devil Canyon)

Dilatant fluid (see Fluid,

dilatant)

Dixie Valley (see Nevada,

Dixie Valley)

Drainage basin 12,30,36,37,

44,47,48,55,69-73,137,143-

145,147,151,152,185,207

area 12,35,36,74,200,203,

208,211

Dynamic similarity (see

Similitude, dynamic)

Earthquake (see Tectonic)

Eldorado Canyon (see Nevada,

Eldorado Canyon)

Eldorado Valley (see Nevada,

Eldorado Valley)

Embudo Fan (see New Mexico,

Embudo Fan)

Engineering time scale (see

Time, engineering)

Entrenchment (see Channel,

entrenchment)

Equation

Bernoulli 82,86

Chezy 116,119,120

continuity 114,166,177,

178 , 194 energy 82,178

Manning 87,94,96,166,175,

195,196,205

momentum 114,166,178

Erosion 12,15,28,29,33,36,

46,51,53-61,64,96,143,144,

147,151,158,172,183,210 (see

also Scour)

Etiwanda (see California,

Etiwanda)

Experimental apparatus 154,

160

Experimental procedure 155

Fanhead entrenchment 61-65

Flamingo Wash

Flamingo Wash

Flood:

control 1,2

216

(see Nevada,

14,15,56,214,

damage 1,2,6,15,18,

159 (see also Cost)

duration 68,73,74,76

envelope curve 24

frequency 21-23,30,55,144-

147,152,207,217

peak flow 12,20-24,55,145,

203,206,209,211

plain 14

Floodplain (see Flood, plain)

Flow: (see also Debris Flow)

critical 84,184,193,211,

217

238

laminar 30,107-109,111,

paths (see Channels)

steady 100,119,121,166,

173 , 174 subcritical 30,84,90,217

supercritical 30,84,90,

turbulent 30,107,108,111,

uniform 87-90,96,116,119,

120

unsteady 114,119,155,173-

113,116,119,174

193,197,198,217

113,114,120,129

175,177,217

Fluid:

Bingham plastic 111,112,

114,120,121,123,155

density 197,115,118,161,

dilatant 110,111,119,123

Newtonian 108-111,113

pseudo-plastic 110,111

174

Fontana (see California,

Fontana)

Frenchman Flat (see Nevada,

Frenchman Flat)

Froude Number (see Number,

Froude)

Geologic time scale (see

Time, geologic)

Geometric similarity (see

Similitude, geometric)

Glendale (see California,

Glendale)

Glenwood Springs (see

Colorado, Glenwood Springs)

Guasti (see California,

Guasti)

Henderson (see Nevada,

Henderson)

Huerfano River (see Colorado,

Huerfano River)

Humboldt River (see Nevada,

Humboldt)

Hydraulic depth (see Depth,

hydraulic)

Hydraulic geometry 96-106,

130,154,187,193,194,196

(see also regime theory)

Hydraulic radius 88,90,107,

116,118,174,197

Idaho:

Boise 2

Incipient motion 91-93 (see

also threshold of movement)

Infiltration 16,75,77,146,

152,157,166

Initial conditions 137-139

Intersection point 63,156,

2 39

158,172 Manning n 88-90,116,164,175,

193,195,197,198,202

Kinematic similarity (see Mason Valley (see Nevada,

Similitude, kinematic) Mason Valley)

La Crescenta (see California,

La Crescenti)

Lake Estancia (see New Mexico,

Lake, Estancia)

Lake Lahontan (see Nevada,

Lake Lahontan)

Lake Mead (see Nevada,

Lake Mead)

Laminar flow (see Flow,

laminar)

Land use 15,43,73

Mesoscale convective

complex 218

Milner Creek Fan (see

California, Milner Creek Fan)

Models:

distorted 125,160,173 , 174 Froude Law 124-131

moveable bed 125-131,154-

174

numerical 71,136-154,174-

179

physical 123-131,154-174

Monte Carlo simulation 136,

137

Las Vegas (see Nevada, Las Montrose (see California,

Vegas) Montrose)

Las Vegas Wash (see Nevada, Mudflow 46,65-73,106,146,

Las Vegas) 194,204,216

Locus of deposition 158

Log-Pearson (see Probability distribution, log-Pearson) Nevada 199,208

Los Angeles (see California, Beatty 15

Los Angeles) Boulder City 11,65-67

Nelson (see Nevada, Nelson)

Austin 200

Clark County 22,23

Dixie Valley 18 Manning equation (see Eldorado Canyon 6

Equation, Manning)

240

Eldorado Valley 200

Flamingo Wash 208,209,213

Frenchman Flat 17

Henderson 6,7,200

Humboldt River 200

Lake Lahontan 51

Lake Mead 55,56

Las Vegas 1-6,10,15,16,

5 3 , 5 5 - 6 0 , 7 0 , 7 6 , 7 7 , 2 0 0 ~ 2 0 4 1

206,207,209,210,218

Mason Valley 200

Nelson 200

Nevada Test Site 15,17,

63,193,194,219

North Las Vegas 12

Northumberland Canyon 200

Ophir Creek 6,8,9

Oreana 200

Piute Wash 200

Rye Patch Reservoir 200,

204

Searchlight 200

Spring Valley 51

Tonopah 200

White Mountains 17,18

Nevada Test Site (see Nevada,

Nevada Test Site)

New Mexico:

Albuquerque 2,160

Embudo Fan 160

Lake Estancia 51

Rio Puerco 97,98

Santa Fe 53

Newtonian Fluid (see Fluid,

Newtonian)

Normal depth (see Depth,

normal)

North Las Vegas (see Nevada,

North Las Vegas)

Northumberland Canyon (see

Nevada, Northumberland

Canyon)

Number:

Bingham 111-113,124

Froude 30,84,85,101,124,

129,194,197,198

Reynolds 30,94,95,107,111,

112,113,114,117-119,124,

129,174

Weber 124

Ophir Creek (see Nevada,

Ophir Creek)

Oreana (see Nevada, Oreana)

Overgrazing 53-55

Owens Valley (see California,

Owens Valley)

Pakistan 40-42,95

Paleohydraulic 154,210,211

Paleohydrology 24,51

Palm Canyon (see California,

Palm Canyon) Non-cohesive materials 92,

94,96,101

241

Palm Desert (see California, Pseudo-plastic fluid (see

Palm Desert) Fluid, pseudo-plastic)

Palm Springs (see California, Pyramid Peak (see California,

Palm Springs) Pyramid Peak)

Panamint Mountains (see

California, Panamint Quaternary 16,48,49

Mountains)

Pediment 32,33 Radioactive waste 15

Phoenix (see Arizona, Rancho Mirage (see California,

Phoenix) Rancho Mirage)

Piedmont plain, Random number 136-145,149

definition 33

Regime theory 130,54,187,

Piute Wash (see Nevada, 193,194 (see also Hydraulic

Piute Wash) geometry)

Pleistocene 48,49,51 Return period 31,153,185,207

Precipitation 6,20,22,24, Reynolds number (see Number,

30,36,43-46,49-54,63,69-72, Reynolds)

145,193,208,209,217

duration 21,22,53,63,73, Rio Puerco (see New Mexico,

206,207,218 Rio Puerco)

effective 43-48

frequency 22,53,54,63,70, Rye Patch Reservoir (see

218 Nevada, Rye Patch

intensity 53,63,69,73,147, Reservoir)

206,207

Probability 22,31 Salt Lake City (see Utah,

Probability distribution:

Salt Lake City)

exponential 145 San Antonio Creek (see

log Pearson 185,186,190 California, San Antonio

Poisson 140,144 Creek)

uniform 145,149

242

San Bernardino (see California, Scour)

San Bernardino)

San Diego (see California,

San Diego)

San Gabriel Mountains (see

California, San Gabriel

Mountains)

San Jacinto Mountains (see

California, San Jacinto

Mountains)

San Joaquin Valley (see

California, San Joaquin

Valley)

Santa Fe (see New Mexico,

Santa Fe)

Scour 2,15,19,210 (see also

Erosion)

Searchlight (see Nevada,

Search1 ight)

yield 43-46,49,50,51,54,

55

Semi-arid region,

definition 45

Shadow Rock Fan (see

California, Shadow Rock

Fan)

Shear velocity (see Velocity,

shear)

Shield's diagram 30,95

Sieve deposit 157

Simil itude :

dynamic 124,129

geometric 123

kinematic 124

Slope-area method 24,210,

211

Socio-economic 14

Section factor 90 Specific energy 82-87

Sediment :

incipient motion 91-95,

173

load 167,170,171

production 36,43-48,50,71

source area 37

transport 13,14,18,19,32,

33,36,48,63,90,100,101,127,

128,137,151,152,157,161,

170,180,193,210 (see also

Deposition and Erosion and

Specific gravity 95

Spring Valley (see Nevada,

spring Valley)

Stochastic process 136,144

Subcritical flow (see Flow,

subcritical)

Subsidence 16

243

Supercritical flow (see Flow, Trollheim Fan (see California,

supercritical) Trollheim Fan)

Tucson (see Arizona, Tucson)

Tahquita Creek (see California Tahquita Creek) Turbulent flow (see Flow,

turbulent)

Tanque Verde Creek (see

Arizona, Tanque Verde

Creek)

Tectonic 29,36,43,61,139-

143,154,156

Temperature 43,49-51,143

Threshold of movement 95

(see also Incipient motion)

Uniform flow (see Flow,

uniform)

Uniformitarianism 29,30

Upland (see California,

Up1 and )

Uplift 61,136,137,140,143,

144,153 (see also Tectonic)

Thresholds 30

Urban area 6,14,15,25

Thunderstorm 12,21,22,218

(see also Convective storm

and Mesoscale convective

complex )

Time :

engineering 18,24,31,192

geologic 17-19,24,28,48,

scale 17,48,159

136,137,152,153,180

Tonopah (see Nevada,

Tonopah)

Tractive force 91-95

Transmisssion loss 74-76,

194 (see also infiltration)

Urbanization 14,55,57-60,

195,204

Utah 68,219

Salt Lake City 1

Wasatch Mountain Front 47,

55,73

Vegetative cover 43,46,47,

50,54,146,201,204

Velocity :

average 12,13,19,72,82,

88,96,107,109,111,118,161,

162,196,202

of flow 13,19,112,121,122,

160,164,167,169-179,187,

189,193,195

244

profile 82,110,111,114,210

shear 94,95,161

Verdugo Mountains (see

California, Verdugo

Mountains )

Verification 152,153,178

Viscosity (see Fluid,

viscosity)

Weathered material 70-72,143,

144,146,147,151-153

Wetted perimeter 94,175

White Mountains (see

California and Nevada,

White Mountains)

Wrightwood (see California,

Wrightwood)

Wasatch Mountain Front (see Yield stress 110-113,121-

Utah, Wasatch Mountain Front) 123

Watershed 14,16,20,22,24,

43,54,185,199,201,204,206- Zoning 2,15,215,220

208 (see also Drainage

area)

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