fttOratlcs ResearcttWalnrgford

EXPERIMENTS ON ALLUVIAL FRICTION

By

l lang Shiqlang[ ' I R Whi te BSc,R B e t t e s s B S c ,

Report No SR 83August 1986

Registered Office: Hydraulics Research Limited,Wallingford, Oxfordshire OXIO 8BA.Telephone: 0491 35381. Telex: 848552

PhDPhD

C Crown Copyright 1986 Publ.ished by peruission of the Controller of

Her Ma jes ty rs S ta t ionery Of f i ce

This repor t descr ibes work par t ly supported under contrac l

PECD 7/6/29-204/83 funded by the Department of the Envi ronaent . The DOE

nominated of f icer was Dr R Thorogood. Dr W R Whi te was Hydraul ics

Research 's nominated of f icer . The repor t is publ ished wi th the perniss ion

of the Departmenr of the Envi ronment . but any opin ions expressed are not '

necessar i ly those of the funding Department . .

ABSTRACT

Durl.ng the deelgn of englneerlng works on rl.vers or canalg lt ls frequentlynecesaary to calculate the flow or sedlnent transport. To calculate thesequantlties the frlctlonal energy-loeses on the boundary of the channel mustbe deternlned. Thls ts partLcularly dtfftcult for alluvlal channels ag thefrlctional losses are related to the size and shape of the bed features guch

ag duaes or rlpples that are developed on the bed of the chaanel aod thesefeatures vary as the flow varles. Frequently the flow and bed features arecategorlsed as belng ln lower or upper regl.me, dependLng upon the nature ofthe bed featureg. Earller sork at ER resulted ln the developuent of amethod for predicting alluvlal frlction. Thls nethod, however, waa notunl.versally applicable to all flows since lt could only be appLied to flowsln lower regime, that ls, wlth plaae bed, r l .pples or dunes.

Laboratory experlmenta are described in thl.s report ln whLch alluvialfrictloa was meaaured for steady-state flows over gaad beds. The observedbed forms are correlated sl.th values of the dlrensionLess unit strean potr€r.It ls shown that the value of the dl.meoslonless unit stream power can beused to determLne the uature of the bed forn and la partlcular whether tbeflow corresponds to upper or lower reglme. The friction ls aaaLysed 1oteras of the I{hlte et al (1980) Eethod for predlctlag alluvial friction aodan exteasion of thls nethod Ls suggested for flows ln upper reglme. Thlsnew method enables predlctlons to be nade of alluvlal frlctlon for a uuchslder range of flose than prevlously. Thls greatly extends the raage ofconditlons for whlch accurate calculatlons can be made of flow and gedl.ment,

transport in alluvial channels.

CONTENTS

Page

SYMBOLS

1 INTRODUCTION 1

2 EXPERIMENTAL APPARATUS AND PROCEDURE 2

3 DATA SIJMMARY 3

4 DISCUSSION OF RESULTS 4

5 CONCLUSIONS 7

6 ACKNOWTEDGEMENTS 8

7 REFERENCES 9

TASLES:

1. Observed f low data

FIGURES:

l . Grading curve of sand

2. F^_ aga ins t F .^ , p resent resu l tsg r - r g -3 . Enge lund f r i c t ion re la t ionsh ip

4 . F a s a i n s t F - . a l l d a t ag r - r g '5 . U- aea ins t DE - g r

SYI.{BOLS

D (n) Graln dlameter for unl forn sedimenrs

Dr, (rn) Grain dianeter for whlch r& of the sanple is finer

Dimensionless graln size

d (n) Average deprh of flow

8r

cgDlmensionless sedinent mobi l i ty (coarse gra ins)

Dimensionless sedinent nobi l l ty

Dimensionless sediment mobl l i ty ( f ine gra ins)

g (rns- 2) AcceleratLon due to gravity

gr

F .rg

s

u,

Irlater surface slope

Speciflc gravl.ry of sedimenrs ( p"/ p)

Dimensionless unit stream porrer

V (rs- r) Veloclry of flow

v* (r"- r) Shear veloclry r'(gds)

v (n2"-I) Klnemat, ic viscosLEy of water

p (kg n- 3) Densiry of water

O" (kS n- 3) Denslty of sedinent

INTRODUCTION

To calculate the f low or sedimenL t ransport in an

al luv ia l channel Ehe f r ic t lonal losses on the

boundary of the channel must be determined. In

response t ,o th is need a number of theor ies for

predict lng the f r icEional losses in aLluv ia l channels

have been developed (Einste in and Barbarossa, L952;

Enge lund , L966 ; Raudk l v i , 1967 and Wh i te eE a l ,

1980). Most of these theor ies are based on

laboratory daca. These laboratory exper iments are

almost invar iably character ised by the use of

narrow-graded c lean sand, tha! is , sand wi th a smal l

range of s izes f rom which boUh the larger s izes and

any snaller silt or clay material has been removed.

The f lner s i l ts and c lays f requent ly show very

di f ferent propert ies to those of sand s ince these

mater ia ls demonstrate cohesive propert ies whereas

sands are non-cohesive. In pract ica l problems,

however, it is rare that the sedirnent,s which are

encountered are similar to the narrowly graded sands

used in l-aboratory experinent,s. Much more frequently

sediments are widely graded and cont,ain varying

quant i t ies of s i l ts and c1ays.

Recently laboratory experiments rvere carried out at

lIR to investigate the impact of introducing a

proport ion of f ine s l - l t and c lay nater ia l in to a sand

bed (Bass i , 1985 ) . The a l l uv ia l f r i c t l on due to a

sand bed was neasured and then the experiment rras

repeated af ter the in t roduet ion of vary ing quant i t ies

of f ine nater ia l . The resul ts were analysed using an

app roach sugges ted by t he wo rk o f Wh i te e t a l ( 1980 )

for sand beds. No d iscern ib le change was observed in

Ehe a l luv ia l f r ic t ion of the sand bed upon the

inE.roducLion of Ehe f ine mater ia l , buE somewhat more

disturb ingly , there 'sras a d iscrepancy between Ehe

resu l cs f o r j usE Ehe sand bed and the p red i cE ions o f

E .he Wh i te e t a1 theo ry . The i nvesE iga t i on o f

va r i a t i ons i n f r i cE ion caused by t he i nE rodue t i on o f

s i l t and c lay ma te r i a l i s o f doub t fu l va lue i f t he re

EXPERIMENTAI

APPARATUS AND

PROCEDURE

are s t i l l unce r ta in t i es as t o t he f r i c t i on due to a

uni forrn sand bed. I t was Eherefore decided to carry

out exper iuents to lnvest igate fur ther the f r ic t ion

due to a sand bed. The exper iments descr ibed in th is

report were designed to prov ide more in format ion on

the a1luv ia1 f r ic t ion due to sand beds and so act as

a basis for conpar ison wi th exper iments per forned

wi th sediments conta in ing a o ix ture of sand and

s i l t .

The exper inents were per formed in a 2.44n wide, 24m

long, reei . rcu lat ing, t i l t ing f lume. The sediment bed

was 16o in length. At the downstreau end of the

f lune a ta i lgate \ ras used to contro l the depth of

flos.

A flat-V Crump Weir located 3n downstream of the

ta i lgate was used to measure the d ischarge. The

tapping point for measuring the head over the weir

was 0.6m upstreao f rom the weir crest .

The rec i reulat ing system consisted of two 0.113n3s-1

and one 0.028u3s-1 prnps. The entrances where the

reci rculat ing system returned the f low to the

upstreau end of the f lume were proport ioned to ensure

the un i f o r rn i t y o f t he ve loc i t y d i s t r i bu t i on ac ross

the f lune.

Water sur face s lope rdas Beasured using f ive tapping

po io t s l oca ted a t 2 .5n i nEe rva l s a long the f l une .

Smrn d iameter p last ic tubing connected Ehe tapping

po incs t o 60mn d iame te r s t i l l i ng po ts . The gauged

h e a d s i n t h e s E i l l i n g p o t s w e r e m e a s u r e d u s i n g

ve rn i , e r po in t gauges read ing to 0 .O2nm. A s im i l a r

arrangeuent was used to measure the head above the

c res t o f t he C rump we i r .

DATA SI'MMARY

A sect ion of the f lune had g lass wal ls , th is

t ransparent sect ion cover l -ng the centra l par t of the

sediment bed. The flow depth was roeasured at 6

points a long th is length on both s ides of the f lune.

At. each location the average bed level and water

level rdere neasured using a ruler attached Eo the

wa l l .

The bed forms and thei r s ize were observed for each

test . The veloc i tv of the bed forms \ tas ueasured for

s e l e c t e d t e s t s .

The grading curve of the sand used is shown in Fig

The D 35 and D

UO s i zes we re 0 .21nn and O . ! l r nm,

respect ive ly .

A total of 31 tests were performed, the results of

which are summarised in Table l.

The average water surface slope rdas calculated from

the measured wat,er levels by using a least-squares

1laear regression. Two values of the slope were

determined, the f l rst f rom the three cent,ral levels

only, the second using al l 5 points. The second

value was used for al1 calculat ions.

The average flow depth was calculated by averaging

the six depths measured in the central part of the

f luoe.

A summary of the measured data for the 31 Lests is

g iven in Table 1. For each E.est Ehe fo l lowing data

i s p rov ided :

f l ume s lope

ave ra ,ge wa te r su r face s lope , ca l cu la ted us ing

Ehe 3 centra l waLer 1evels

ave rage \ ra t . e r su r face s lope , ca l cu la ted us ing

al l 5 neasured levels

DISCUSSION

RESULTS

OF

average f low depth, in netres

discharge, in l i t res per second

average f low veloc i ty , ca lculated f rorn the

measured discharge and rnean cross sect,ion

bed features

temPerature

Fol lowing the work of Whlre er a l ( f9S0) and Bassi

( f985) the resul ts \ t rere analysed in terms of the

sedinent nobi1 l ty , Fgr , Ehe rat io of the ef fect ive

shear forces to the Lmmersed weight of the par t ic les.

The nobil ity nurnber rdas defined in such a way that

only the re levant shear forces were used, that is ,

to ta l shear for f ine sedlments, gra in shear for

coarse sediments and an int,ermediate value dependLng

upon the dinensionless grain size for the

transltional sedinents.

The dinensionless grain size Do'. was defined by

os, = tsfplr/3 D

where g is accelerat ion due to grav i ty

s is speeific gravity of the sediment

v is k inenat ic v iscoslEy

and D ls sediment diameter

The d imensionless sediuent nobi l i ty was def ined by

] t-"g r

where v* is the shear

V is the average

d i s rhe depEh

and n is an exponent

s e d i r a e n E s ( D ^ _ = 1 . 0 )- g r

/ (32)Log1s(10d/D)

ve loc i t y

f low veloc i ty

wh ich va r i es f r om 1 .0 f o r f i ne

to 0 .0 f o r coa rse sed i -men ts

(ort =

F ' =- f g

60 ). Thus for f ine sediment,s

and for coarse sediments

cs / (eo(s- l ) ) / (32)1og 1s(10d/D)

Values o f F . and F_- a re shown p lo t ted in F igure 2 ,tg grtogether with the equat ion given by l , lh i te eE a1

(f980). I t can be seen that there are two dist inct

relat, ionships, one for a f lat bed, r ipples and

dunes, termed lower regime, and another relationship

for the upper regine of plane bed and anti-dunes wit,h

a transitLon between the two curves. This leads to

the postulation that the -nethod for predictLng

al luvial f r icr ion described by Whire er al ( l9BO)

applies to the Lower regime case and EhaE the nethod

could be extended to predict flows in the upper

regime by the inclusion of a new relationship for the

upper regime case.

The use of two different relationships, one for lower

regime and one for upper regime was first suggested,

by Engelund (1966). Engelund plorted the

dimensionless bed shear due to skin friction against

the tot.al dimensionless bed shear for a sequence of

f lume data, see Figure 3. He postulaLed two

relat ionships, the lower regirne eurve for dunes,

r ipples being excluded from Engelundrs analysis,

whi le the upper regime curve appl ies to f lat beds,

standing waves and anEi-dunes.

The developmenE of equat . ions Eo extend the Whi te et

a l analys ls to the upper regime case is expla ined in

g reaEer de t .a i l i n Wh i te eE a l ( i n p repa ra t i on ) .

A coupa r i son o f t he p resen t resu l t s w lEh those f ron

Bass i ( f 985 ) and Guy e r a I ( L966 ) a re shown i n F igu re

4. I t can be seen that the present resul ts and those

of Bassi (1985) are c lose Eo each oE,her buc that they

are both above rhose of Guy et a1 (f966) and rhe

theoret ica l re lat ionship of Whire er a l ( l9SO). In

the upper regime the present data is also above that

o f Guy e t a l ( 1966 ) .

The postu lat lon of two d i f ferent re lat lonships for

a l luv ia l f r ic t ion leads to the problen of

detern in ing, whlch ls the appropr iate re lat lonship to

use i .n par t ieu lar c i reumstances. I , Ie have so far

dlstinguished the lower and upper flow regimes by

descr ib lng the bed features associated wi th thern.

It, therefore, seems reasonable that the method of

deternining the appropriat,e regime should be related

to a method of determining the dominant bed features.

Following the work of Simons and Richardson (1963) we

were lead to the eonsideratlon of a non-dimensional

unit st,ream porder U., where Uo is def ined by:

r r - V SU i l, , ( gv ; I z r ogr

Figure 5 shows data from the present study and from

Guy e t a l ( 1966 ) .

For the lowest values of U, the bed was plane. As U,

increased the bed forn changed fron plane to ripples,

this ls for values of U, larger rhan 0.00035.

Ini t ia l ly, the r lpples were sual l and regular, for

example, the ripples formed in Run 17 were

approxirnately lOcrns long wlth a height of 1.2ems.

The value of U, was 0.00f5. As che value of U,

lnc reased the r lpp les inc reased in s ize . In run 16 ,

wi- th a UU value of 0.0028, rhe r ipple lengrh was

l9cns and the height was beEween 2 and 4.5crns. For

larger values of U, dunes were formed, the lengt,h of

the dunes being bet,ween 80 and 100cns for a value ofU, o f 0 .0067. The dunes d isappear fo r U, va lues

CONCLUSIONS

larger than 0.011. There is then a transi t ion Eo a

f lat bed reglme. For larger values of U, ant i -dunes

are formed, then chute and pools.

Using a criterLon based on the value of U, Whice et

a l ( to appear) developed an a lgor l thn for the

calculaEion of a l luv ia l f r ic t ion. There are sEi1 l '

however, unresolved problens in connection wlth the

transi t ion f rom one regime to the other . I t ls

unclear whether there are stable states ly ing between

the two regimes and whether the transiEion displays

hysteresis. These problerns can only be resolved by

fur ther carefu l exper iments.

The development of a meLhod of deternining the

dominant bed features together with the recognltion

that the White et al (f98O) analysis can be extended

to upper regime flows has enabled the development of

a comprehensive theory to predict al1uvial frietion.

It is hoped that the theory that has been developed

will act as a basis for future work to elucidate

further problems of a11uvial frlction such as the

effect of the int,roduction of cohesive material,

alluded Eo ln the introduction, and the inpact of

unsteady f lows.

A set of experiments carefully measuring the alluvial

f r ic t ion due to a sand bed have been per formed.

The type of bed features developed has been relat,ed

to the d imensionless uni t s t ream power Ur.

Two dis t incE re lat ionships have been observed

descr ib ing the a l luv ia l f r icEion, one for lower

regime and one for upper regime. This is Ehe basis

fo r an ex tens ion , p roposed by Wh i re e t a l ( t o

appea r ) , t o Ehe neEhod o f p red i c t i ng a l l uv ia l

f r i c t , i on desc r i bed by Wh i te eE a1 ( f 980 ) .

The observations in the lower regime are sinilar t,othose o f Bass i (1985) bu t bo th se ts o f resur rs d i f fe rfrom those of Guy eE al (L966) and the theoret ical

re la r ionsh ip o f i lh i re e r a1 ( I9g0) .

The detai ls of the transi tr .on from one regime to theother are unknown and further experlments are

requlred to elucidate Ehem.

6 ACKNOWLEDCEMENTS

The work descr ibed in this paper was carr ied outwhi le !{ang shlqiang was visiLing Hydraurics Research,UK, funded by the Chinese government. The IIRinvolvement in the work was funded by the Departx'ent

of the Environment und,er Contract IECD 7/6/29 -

204/83 and rhis report is publ ished wirh theagreemenL of the Department of Ehe Environmenc.

7 RBFERENCES

Bass i , A , 1985, Exper iments on a l luv ia l f r l c t lon o f

sand-si l t mixtures. Report SR 55, Hydraul ics

Research, I ' Ia l l ingford, UK.

E ins te in , I l A and Barbarossa, N C, L952, R iver

channel roughness. Trans ASCE, 117, pp LLZL-LL3?.

Enge lund, F , !966, Hydrau l i c res is tance o f a l luv ia l

st ,reams. ASCE, JHD 92, HYz, pp 315-326 and closure

9 3 , H Y 4 , p p 2 8 7 - 2 9 6 .

Guy, H P, SLmons, D B and R ichardson, E V, 1966,

Summary of alluvial channel data from flune

experinents 1956-1961, US Geol. Survey Professional

Paper 462-I .

Raudklvi , A J, L967, Analysis of resistance in

f luvial channels, ASCE, JD 93, [ IY5, pp 73-84.

Whi te , W R, Par is , E and Bet tess , R, 1980, The

fr ict ional character ist ics of al luvial streams: a

new approach, Proc Ins t , C iv , Engrs , Par t 2 , 69 ,

pp 737-750.

White, W R, Bettess, R and l{ang Shiqiang, The

fr ict ional character lst ics of al luvial streans in the

loser and upper f low regimes, in preparat ion

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Fig 3 Frict ional relat ionship by Engetund

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