fttOramcsReseardtWailurgford

EXPERIMENTS ON ALLUVIAL FRICTION OF

SAND-SILT MIXTURES

A Bassi Ingegnere Civ i le

Report No SR 55Septenber 1985

Registered Office: Hydraulics Research Limited,Wallingford, Oxfordshire OXIO 8BA.Telephone: O49l 35381. Telex: 848552

C Crown CopyrLght 1985 pubL ls l :ed by permiss lon o f

Her MaJesty rs S ta tLonery Of f l ce

Th ls repor t descr lbes work par t l y suppor ted under cont rac t

PECD 716/29-204/83 funded by the Departrnent of the Envlronment. The DoE

nominated off lcer was Dr R Thorogood. Dr w R l . lht te was Hydraul lcs

Researchrs nominated o f fLcer . The repor t l s pub l l shed w l th the per rnLss ion

of the Departmenc of the Envlronnent but any oplnlons expressed are not

necessar l l y those o f the fund lng Depar tment .

ABSTRACT

Experinents are descrtbed la whlch the al luvlal f r lct lon was measured forsteady atate flowa over eedlmenta consLetlng of eand and sllt mLxtures vl.thvarylng proPort lone of el l t . The resulta are analysed ln terns of existLngtheorleg for al luvlal f r lct l .on of sand bede to determlne l f these theorLesneed to be adJueted l f gl l t concentratLoos up to 3000ppn are preaent. Thereeulte ehow that the presence of the silt hag oo dl.scernable effect on theal luvlal f r l .ct lon under steady state condlt lone. Co'nneats are made on thepredict lone of the al luvlbl f r lct lon theorl .ee used.

CONTENTS

1I

2

J

4

5

6

7

FIGURES

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

Page

SYMBOLS

INTRODUCTION

EXPERI}MNTAL APPARATUS AND PROCEDURE

DATA SUMMARY

DATA ANALYSIS

4 .1 E ins te in and Ba rba rossa4 .2 Enge lund4 .3 Randk i v i4 . 4 W h i t e e t a l

CONCLUSIONS AND RECOMMENDATIONS

ACKNOI,ITLEDGEMENTS

REFERENCES

TABLES

Table 1 Observed f low dataTable 2 Observed veloc i ty prof i lesTable 3 Observed veloc i ty and concentrat ion prof i les

2

4

5

579

10

T2

13

13

I

2

3

4

5

Grading curve of sand

Grading curve of s i l t

L ist of symbols

Data analysis according

Comparlson with measuredand Barbarossa nethod

Data analysis according

Conparison with measuredmethod

Data analysis according

Comparison with neasurednethod

to Einstein and Barbarossa

f r i c t ion fac to r , E ins te in

to Engelund

f r i c t ion fac to r , Enge lund

to Raudkivi

f r lct ion factor, Raudkivi

6

7

8

9

10

11

Data analysis according to White,

Comparlson with measured fr ict ionPar is and Bet tess method

Grouplng of experiments according

Par is and Bet tess

fac tor , Whl te ,

to the veloci tyFIGURE 12

SYT{BOtS

D (n) Grain diameter for unl form sediments

Dn (n) Grain dianeter for whlch n7" of. the sanple is finer

Dg. Dinensionless sedlment size

d (n) Average deprh of flow

d ' ( n ) b ' / ( p g S )

d ' r ( r n ) . b " l ( p g S )

tg, Dimensionless sedinent nobl l l ty

Ftg Dimensionless sediment mobi1i ty ( f lne gralns)

f Fr i .cr ion facror (V/v*)

t 1ns- 2) Acceleration due to gravlty

k"' (n) Equivalent, sand roughness

S Water surface slope

s Specif lc gravi ty of sediments ( ps/ p)

V (ms- ' ) Ve loc i ry o f f low

v. (ms- ' ) Snear ve loc i ty t /gaS)*

v ' ( r n s - ' ) / g d t s*

r o t t ( m s - t ) / g d t t s

Y sediment nobi l i ty

Yr sedinent nobi l l ty based oo v1r

v (n2 s - ' ) k inemat ic v iscos i ty o f wat ,e r

p (kgn n- 3) Density of water

ps (kgn m- 3) Density of sedLment

ro (kg n- z; Bed shear stress

rot (kg n-2) Bed shear stress due to surface roughness

"ott (kg n-21 Bed shear stress due to bed forns

O Funct lon

0 ' L /v '

INTRODUCTIONTo calculate flow or sediment. transport in an alluvialchannel an engineer is faced with the problem ofdeternnining the frictlonal losses on the boundary ofthe channel.

For art i f ic ial , regular channels which are f ixed inshape and carry l i t t le sediment there is data readi lyavailable which can be used as a basis for theest imation of appropriate fr ict ion factors. Whennatural channels are considered the problems ofest imating the fr lct ion losses grow. In this case,not only must. the fr ict ional losses due to thecomposLtion of the banks and bed of the channel beest imated but also due al lowance must be given for theeffects of channel i r regular i t ies and other factors.I f one considers channels with movable beds theproblems are compounded. The fr icEional losses aredependent on the bed features present, but these areinf luenced by the transport of the sedinent. Thesedlment transport . , however, depends on the f lu idmotlon and is hence inseparable fron the determinat ionof the f r i c t lona l losses .

There are a nurnber of t ,heories for predict ing thefr ict ional losses in al luvial channels (Einstein andBarbarossa, L952; Engelund, L966; Raudkivi , L967;t{hi te eE al , 1980). Most of these theories are basedon data, the vast najor i t .y of whieh is from laboratoryexperinents. Laboratory experiment.s are almostinvariably character ised by the use of narrow-graded,clean sand, that. is, sand with a smal l range of s lzesfrom which borh the larger sizes and any smal ler s i l tor c lay mater ial has been renoved. The f iner si l t andclay sizes frequent ly show very di f ferenL propert iesto those of sand since these mater lals demonstratecohesive propert ies whereas sands are non-cohesive.The si l ts and clays are suff ic ient ly snal l that thephysico-chemical propert les associated wirh thesurface of the part ic les become slgnif icant. Inappl icat ions to pract ical problens, however, i t i .srare that the sediments which are encountered aresini lar to the narrowly graded sands used inlaboratory experiments. Much more frequent lysediments are widely graded and contain varyingquant i t ies o f s i l t s and c lays .

Th is f i rs t repor t i s an account o f a s imp le , s teadystate laboratory i -nvest igat ion to discover i f , underthese circumsLances, the presence of s igni f icantproport ions of s i l t n ixed with a sand bed have adiscernible effect on the al luvial roughness i-n terrasof the rnethods used to predict al luvial f r icEion. Theresults were analysed to determine i f the theories forpredict ing al luvia1 fr ict ion based on clean sandneeded nodif lcat ion before they could be appl ied Lo

EXPERIMENTALAPPARATUS A}IDPROCEDURE

channels where a proport ion of s i l t is present. Thework was confined to predomLnantly sand beds, asfrequent ly found in r ivers. I t does not cover thecase, which is more frequent ly found Ln estuaries thanrivers, in whlch the predominant sediment ls cohesivebut contains some non-cohesive sand sizes.

The experiments were performed in a 2.44m wide, 24mlong, reclrculat lng, t i l t ing f lune. The sedlnent bedwas 16m Ln length. At the downstream end of the flumea tai lgate was used to control the depth of f low.

A flat-V Crunp weir located 3n downsrream of thetai lgate was used to measure the discharge. Thetapping point for neasuring the head over the weir was2m upsEream from the weir crest. Durlng some of theexperiments a quant i ty of sediment was depositedirunediately upstream of the weir buE never enough toaffect the stage-dlscharge relat ionship for the weir .The rec i reu la t ing sys tem cons is ted o f two 0 .113rn%- Iand one 0.028n3s-1 pnrp". The entrances where therecirculat ing sysEem returned the f low to t ,he upstreamend of the flune were proporti.oned according to thedownst,ream of where the flow returned Eo the flurne toensure the uniforni ty of the veloci ty distr ibut ionacross t t re f lume.

Water surface slope was neasured using f lve tappingpoints located at 2.5m intervals along the f lume. 8mmdiameter plast ic tubing connected the tapping pointsto 60mn diameter st i l l ing pots. The gauged heads inthe st i l l ing pots were measured usl-ng vernier pointgauges reading to 0.02nn. A sirnilar arrangement hrasused to measure the head above the crest of the Crumpwei r .

A 10m sect ion of the f lume had glass wal ls, thlsLransparent sect ion covering the central part of thesedirnent bed. The f low depth was neasured at 6 pointsalong this length on both sides of the flurne. At eachlocation the average bed level and water leve1 weremeasured using a ruler at tached to the wal l .

A total of 29 experinents were performed; the f i rst 6runs, wlth a sand only bed, were used to test theequipment and the range of possible f lows. Runs 7 to14 were also carr ied out with a sand only bed. Thegrading curve of the sand is shown in Figure 1. TheD 5 g s i z e i s 0 . 2 4 m n a n d D 8 5 / D 1 5 = 2 . 3 3 . F o r t h erernaining three ser ies of experiments (Runs 15 to 20,21 to 24 and. 25 to 29) increasing quant i t ies of s i l twere added to the sand bed. The discharges for theexper iments varLed f rom 0 .13 to 0 .21 cumecs.

The sllt was obtained from the River Thames atWal l ingford. I t was f i rst of al l s ieved to removedcobbles, shel ls, leaves and other foreign bodies. Thegrading curve of the resultlng silt ls shown inFigure 2; the speclfic gravlty of the sedinent vras2.65. To add the si l t to the sand bed the water inthe flune was drained down without draining the waterfron the bed and then t,he silt was poured onto thesurface of the bed as a thick slurry.

The bed was sampled periodlcally during theexperinents. The grading curves of the sedimentsehanged very sl ight ly. The D 35 varied fron 0.21nnn to0 '19nm. No sys temat ic change o f D35 w i th the s i l tcontent of uhe flune was observed.

At the end of each sand only experiment t,he pumps werequlckly stopped and the water was allowed to overflowfrom the st i l l lng basin at the downstream end of thef lune. The overf lowing water did not carry anysedlment in suspenslon. The sand bed was neverdrained between the experiments. At the end of eachexperiment with silt the lrater was retalned in theflume to avoid the loss of the flner part of thesuspended sediments.

At least once a day the average sediment concentrat ionIdas measured fron samples taken from the reclrculatingpipes via Pltot tubes. The sampl ing t ime wasapproximateLy 2 minutes and the sample volume wasabout 1 .5 l l t res . The P i to t tubes were s i tua ted invert lcal pipes to ensure that t ,he distr ibut ion ofsediments across the pipe cross-sect i .on was nota f fec ted by grav i ty .

During the experinents involving sl l t some veloci tyand concentrat ion prof i les were measured. A11 themeasurements were taken along the axis of the channeland approximately half way along the sedinent bed.The veloci ty prof i les were determined by placing aminiature current meEer, 10nn in dianeter, at a givendistance from the water surface and recording thepulse rate. The pulse rate was measured by a digi talcounter which averaged the pulses from the meter every10 seconds. For each depth the average number ofreadlngs was 20, corresponding Eo a t ime interval of200 seconds. Each pro f i le cons is ted o f 7 to 10veloci ty measureoents; the local depth of f low wasalso measured by lowering a probe with a f lat baseonto the bed of the channel. Sediment movement insuspension was obtained by taking simultaneousmeasuremenEs of veloci ty and sediment. concentrat ion at6 di f ferent depths. A smal1 plast ic tube of 0.6mndiameter was used to take samples of water andsediment at the sane locat ion as the propel lor meter.

DATA STIM}IARY

The sampling tine was approxinately 1 minute and thesample volume rdas approxinately half a litre.

It was not possible to control the tenperature of thewater which varied fron 14 0C at the beginnlng of anexperlment to 23 k at the end. The tenperature waameasured for every test with a thermoneter reading to0.1k .

The average water surface slope was calculated fromthe measured water levels by using a least-squareslinear regression. Two values of the slope weredetermlned, the f l rst f rom the three central levelsonly, the second using al l 5 points. The f l rst valuewas used for al l calculat ions because i t was lessaffected by end effects. The second value of s lopewas used as a control . .

The average flow depth was calculated by averaging thesix depths measured in the central part of the f lume.The standard deviaEion of Ehe measurements was alwaysless than lcrrr, being greater when Ehe sedinenttransport rate as higher and the bed less regular.

A sumrnary of Lhe measured data for the 146 tests isgiven in Table 1. For each test the fol lowlng data lsprovided:

time from the beginnlng of the experlment, inhours ;nater temperature, in degrees Celsius;average water surface slope, calculated usingthe 3 central rdater levels;average r,rater surface slope, calculated usingal l 5 measured levelsgaverage f low depth, in met,resd ischarge, in l i t res per ,secondaverage f low veloci ty, calculated fron themeasured discharge and mean cross secti.onaverage concentrat ion of sediments, i f measured,in part ,s per mi l l ion by weight, obtained fromsanples taken frorn the water and sedLmentreturn systen. The concentrat ion values refer Eothe mixture of sand and si l t . I t is alsoindicated i f a veloci ty prof i le or a veloci ty andsedlnent, concentrat ion prof i les were recordedduring Ehe test

The observed veloci ty prof i les are given in Table 2.For each water depth (measured in metres from the freesur face) there is :

the average f low veloci ty, ln met,res persecond;

the standard deviation ofin metres per second;the standard deviat ion ofln percentage of the nean

the recorded data,

the recorded data,value

4 DATA ANALYSIS

4 .1 E ins te i . n andBarba rossa (1951 )

The last depth of each prof i le indicat,es the bed1eve l .

The recorded concentrat lon prof i les are glven in Table3. In addition t,o Ehe same values as for t,he velocit,yprof i les, there is also the sediment coneentrat ion, lnparts per ui l l ion by weight.

The experinental data was analysed by using fourdi f ferenc theories on al luvial f r ict , ion: Einsteln andBarbarossa (1951) , Enge lund (L966) , Raudk iv i (1967)and White et al (1980). In the fol lowing secr ions thebaslc theory of these approaches is out l ined togetherwith the data analysis procedures. Figure 3 def inesthe symbols used in Figures 4 to 7 inclusive.

This method was the first working on the principlethat al l f r ictLonal character ist , ics of the f low couldbe related to uhe grain size of the bed mater ial . Theeffect of v iscosity is neglected. The basicassumption ls that part of the tot ,al shear stress bis due to the surface roughness ( rot ) and part is duet,o the bed forms (,rot t ) :

T o = T o * T o t t ( 1 )

The spl i t t ing is attr ibuted to the hydraul ic radiuslfor a two dimensional f low, the depth is usedins tead:

t =

"o

r | =.o

pg s d

p g s d '

( 2 )

(3 )

(4 )r o t t = p g S d t t

and therefore

d = d r + d r l

The ef fect of gra in roughness isone of the fo l lowing formulae:

(s)

considered through

l - = 7 .66v * '

/ d t ' t\kT- J

s

L/o( 6 )

V =V * t

where

y 'B S, dt

The analysis by Einst,einfrorn the l,l issouri Riverrelat ionship between 0'

( 7 )

( B )

and Barbarossa of f ie ld dataBasin suggested a functlonaland V/v*r t where

5;75 1os lo (tz.z f t l

o * t

I, t . I =Y

y l

and

g ( s -1 ) Dgs

(v* ' ) 2(e)

v * t t y'g s dt I ( 10 )

This theory, part lcular ly the proposed relattonshipbetween (rr and V/v*r, has been cr i t lc lsed (Garde andRanga RaJu, L966, and Yal in, L977 ) and in extensivecomparisons wlth both field and laboratory dataWhite et al (1980) found the theory to provide poorpred ic t ions o f f r i c t lon fac to r .

The present experimental data

k " t = D O S = 0 . 2 7 m n

D : S = 0 . 2 l m m

and

s = 2 . 6 5

was analysed assuming

( 13 )

Using the values of V and S, dr was f i rst determinedus ing equaEion (7 ) . Then d I I was ca lcu la ted f romequatlon (5), using the average f low depth d. Thevalues of 0t and V/v*r I were then ealculated and theresult ,s plot ted in Figure 4. The curve represent ingthe relat lonship proposed by Elnstein and Barbarossais also shown in the Figure. I t can readi ly be seenthat the experimental points appear to be unrelated tot ,he Einstein and Barbarossa relat ionship. This issinilar to the behaviour found by Garde and Ranga Raju(1966) for experiments with dune covered beds.Further i t can be seen that there is no discernible

( 1 1 )

(12)

4.2 Engelund

difference between the results with a sand only bedand those with varying si l t concentrat ions.

The fr ict lon factor rdas then calculated uslng theEinstein and Barbarossa nethod using an i terat iveprocedure and the calculated value compared ltith theobserved value. A f l rst value of dl was guessed andYr was calculat,ed. The corresponding value of V/v*I lwas determined fron Flgure 4 and uslng equatlon (7)dtr was determined. The value of dr was adjusted andthe procedure was repeated until equation (5) wassat lsf ied. The comparison of observed and calculatedfr ict ion factors is shown in Figure 5. Less than 2Zof the predictions are within 201l of the observedvalue. Not al l the experinental points are plottedbecause nany of the data yielded values of 0r outsidethe range given by Einstein and Barbarossa. There isno discernable di f ference between the results withsand and silt nixtures and Ehose with sand alone.

The nethod is based on the sirnilarity prlnciple of thehydraul ic nodel theory, and disregards the effect ofviscosity. The energy loss per unlt weight and perunit , length of the uniform f low, S, can be separatedin two terms:

g = S r + S r r ( 1 4 )

Sr account.s for the losses due to skin roughness. S l i

represents the losses due to the drag caused by bedforms, calculat,ed as a sudden expansion of the f low inpassing the forms. I t is then possible to def ine twodif ferent forns of nobi l i ty number (here expressed fora two dinenslonal f low):

u*2= - - -

g ( s -1 ) D

u* ' 2v l = --

c (s - r ) D

D 35 ls an appropriate valueFroude number is the sane,adopted by Engelund ensuresrelat lonship between Y and

(1s)

( 1 6 )

for D. Provided that thethe sini lar i ty pr incipletnat there is a unique

Yr and there fore :

( 1 7 )v*

v * t Y r

Sone flune data ylelded a relationshlp expressed as anexperlmental curve (EngeLund, 1966).

Furthermore, an analyt ical relat ionship for thecalcu1at.lon of the skin roughness frlctlon only wasprovided by:

V

v * t

= 2 .5 t n d + 6 .0k fs

The present experimental data wasthe fol lowing values:

D g s = 0 . 2 1 n n

D e S = 0 . 2 7 m n

s = 2 . 6 5

( 1 8 )

analysed assuming

where k" ' is the skin roughness, for whlch a value of2 D OS ls recommended.

(1e )

(20)

(2 i )

First of a l l , t ,he value of Vl r was detern ined usingthe relat,ion. Then the values of Y and Yr werecalculated, and the points were p lot ted on a Y - Yld lagram (Fig 5) . On the same dlagram are p lot ted theexperlmental curve suggested by Engelund and there lat ionshlp expressed by the equat ion:

Y ' = 0 .06 + 0 .4 Y2 (22)

The present experiment,al data follows the same trendas the equat ions proposed by Engelund, part lcular lyfor low values of Yr. The bulk of the data, however,plotted below the curve. Again there seemed to be nodiscernible di f ference beEween the experimentalresults wlth sand and si l t mixtures and those for sandalone.

The f r ic t ion factor was Lhen calculated us ing thepresent method using the equat ion:

vq = + (z'so rn d

k rs

+ 6 .0 ) ( 23 )

which is der ived f rom equat ions (17) and ( I8 ) . Thevalue of Yr/Y was deLermined frorn the curve inFtgure 6 using the value of part lc le mobi l i ty Y. ThecalculaLed and observed fr ict ion factors are shown inFigure 7. The predict lons provided by the Engelundmethod were very good; 651l of ttre predictl-ons werewithin 2O% of the observed value and all were wlthin a

factor of 2. Thls is a bett,er performance than thatreported by White et al ( f980). Again there seemed tobe no discernlble difference between the experimental-result,s with sand and silt and those for sand alone.

4.3 Raudklvi (1967)Raudklvi suggested plotting V/ '67- v*cT againstpart ic le nobi l i ty Y, where v is the shear velocl ty

*crat threshold conditions for the movement of thesediments. Plott lng var ious data ln thts form heobtained relat ionshlps for gravels, sands and f inesands.

In the present cal-culations the critical shearveloci ty was determined using the Shieldts curve(Yalln L977). A plot ot Yl fi;T=nxc:/ against Y isshown in Figure 8 together wlth Raudklvirs curve forfine sand. The results follow the same trend asRaudklvirs curve but consistent ly plot above i t .There 1s no discernible difference between the result,sfor sand and si l t and those for sand alone.

To obtain the predicted fr ict ion factor Ehe calculatedaverage veloci ty was direct ly calculaced from thenobllity number Y and the RaudkLvl curve. Flgure 9shows the calculated fr ict ion factor plot ted againstthe observed. Though 5O% of the predict ions l iewithin 2O% of the observed values it can be seen that,the predicted values show a lot less var lat lon thanthe observed values. The agreement between observedand predicted, however, ls better than that reportedby Whlte et a1 (1980). Again, within the resultsthere is no discernible di f ference between Ehe resultsfor sand and silt mixtures and those for sand alone.

4 .4 Whi te , Par is andBeE, tess (1980)

This rnethod concerns two dimensional free surfacef1ow, which is completely determined by the parameters

Pr Ps, v ' 8, V*, s ' D and d. Four non dimenslonalnumbers can be associated with these parameters. ThedLmensionless grain size ls def ined by:

D-- = D le ( : - t )

)L /3gil u2

(24 )

This nethod uses the nobility nunber Fo" introduced byAckers and White in their theory on se8imentt ranspor t . I t s genera l fo rm is :

f--- v-- I l-n'/32 1.s * eEJ.,The exponent n var ies fron 1.0 for f ine sedLments(D, , . = 1 ) to 0 .0 fo r coarse sed iments (Do. = 60) . ThenoBit i ry number for f ine sedinents Ffg iE; therefore,

v*F (2s)gr

/s T'-(s':It

v*t t , =

/s D-fs-D

A select ion of f lunebetween F*, and Ffg

(26)

data suggested a relat lonshtpln the form:

( 27 )F . A

fr== = o lorrl

A ls the value of Fo, at the t,hreshold of movement ofthe sedlments. f t ?s a paraoeter also used byAckers-White theory on sedinent. transport, and ltdepends only on Dgx.

The forn of the function O was determined by flttl.ng acurve to experiinental points:

ofn I =L g r J

- 0 .76 [ r I <zs)exp [ ( l oe ro Ds r )1 '7 ]

Wlth these re lat ionships, i f pr ps, Vr v : r r D and d aregiven iE is possib le to calculate the average veloc l tyof the f low V and the f r ic t , ion factor f = V/v* .

The application of Ehe theory is l lnited to Froudenunbers less than 0.8; the min inun Dgr is 1.

The experirnental data were analysed using:

D a S = 0 . 2 1 m n

s = 2 . 6 5

The dimensi.onless grain size was f i rst determinedg thevalue of k lnenat, ic v iscosity was calculated on thebasis of water t,euperature. The exponent n was thencalculated according to Ackers and White theory:

n = 1 . 0 - 0 . 5 6 l o g ( D g r )

The values of the parameters Ffg and Ft. were

(2e)

(30 )

10

determined according to equat i .ons (25) and (26) . Theresul ts obta ined f rom the present exper iments areplot ted in F igure 10. ' The theoret ica l re lat tonshtpfro,n the present exper iments are p l -ot ted in F igure l0for va lues of Dgr of 4.7 and 5.2. These are theext.reme values calculaLed with the experlmental daLa:the var iat ion is due to changes in temperature. I tcan be seen that the experimental values follow thesame general trend as that. postulated by the theorybut that they are d isplaced f rom the theoret ica lcurve. This supports the general form of equat . ion(27) but does not agree wi th the value of @ der ivedfron numerous other exper imenta l resul ts . The purposeof carrying ouE the sand only experiments was toprovide a basel ine for judging the sand-s i l t resul t ,sand i t is d isappoint ing EhaE the behaviour of the sandonly resul ts should be at such var iance wi th the t renddisplayed by the largeamount of dat ,a analysed by Whi te eE a l . There is nodiscernib le d i f ference between the resul ts wi th sandand s i l t n ix tures and those wi th sand a lone.

To ca l cu laEe Ehe f r i c t l on f ac to r Ehe va lue o f n and Awere f i rs t deEerrn ined f rom Do. . Then the values of Oand F r r \ ce re ca l cu lac ,ed us in [ -equa t i ons (28 ) and (27 ) ,respeEi ive ly . The average veloc i ty V was deterrn inedf rou Fn . us lng the re la t i onsh ip (25 ) . P red i c ted andobse rvEd f r i cE ion fac to rs a re shown i n F igu re 11 . Thecompar ison is d isappoint ing. The theory consistent lyoverpredicts and none of the predicEions are wi th in2O% of the observat ions. This behaviour isconsiderably worse than that repor ted by Whi te eE a l( f 980 ) . Aga in t he re i s no d i sce rn ib le d i f f e rencebetween the resul ts wi t ,h sand and s i lc mixtures andEhose wi th sand a lone.

The van Ri j r r method for f r ic t ion fact ,or ca lculat ion(van Ri jn , 1984) was br ief ly examined. I t was foundthat t ,he deterrn inat ion of t .he equivalent sk inroughness was based on assuurpt . ions that were notsu i t ab le f o r t he p resen t expe r i nen ts . A f ewca l cu la t i ons w i th t h i s me thod , t haE was o r i g i na l l yconceived for r ivers, y ie lded values of f r ic t ionfactor overest imated by more than B0Z.

To invest igate the scaEter found wi th each rnethod ofanalys is resul ts f rorn just two of the exper iments wereplocted on the appropr iate graphs and are shown inFigure 12. The resul ts were f rom exper inents 12 and20. In the eontext of the avai lable data, exper i rnent12 had a low average veloc i t ,y of 0.25n/s andexper iment 20 had a h igt r average veloc l ty of 0.32a/s.An apparent dependence upon veloc i ty can be observedwhich is conf i rned by Lhe oUher data. This suggeststhaE in each case there is some re levant var iablewir ich is being oni t ted f rom the analys is . There i .s

1 1

CONCLUSIONS AI{DRECOMMENDATIONS

5. I SuggesEions fo rfurther work

theoret leal support for chis in that Yal in (1977)suggest,s that the fr iet lon factor is a funct ion ofthree non-dimefisional variables but none of thetheories considered include this nany degrees offreedom. This suggests that ln the var lous theoriespresented the single curves night possible by morecorrect ly replaced by a fani ly of curves.

The analysis of the experimental data lndicates thatthe presence of s i l t f ract ions in concentrat ions. of upto 3000ppm has no effect on the determinat,ion ofal luvial f r iet ion using accepted theories forpredict ing al luvial f r ict ion of sand beds for steadys taLe, we l l n ixed s t ruc tu res . I t i s , there fore ,recomnended that in sl tuat ions where si l t is presentln a sand bed but the sediment concentration in thef low does not exceed 3000ppn theories for predict ingal luvial f r lct lon of sand beds are used wit .houtnodif icat lon. The results further show that thetheory of Einstein and Barbarossa provides poorpredict ions of al luvial roughness as has been reportedelsewhere and thaE of the theories tested that byEngelund provided the best prediet ions.

1. Per form exper iments to determine ef fect of f inerc lay mater ia l on a l luv ia l f r ic t ion developed bysand beds formed of sand of th is s ize range.

2. Per form s imi lar exper iments wi th sand beds composedof sand of d i f ferent s izes. The s ize and form ofbed features that develop depend upon the s ize ofthe sedinent present and so exper iments wi thd i f f e ren t s i zes may l ead to d i f f e ren t resu l t s .

3. Consider var l -at ions in f low. In the presentrestr ic ted range of exper iments l t was not possib leto look at ef feets generaE.ed by var iat ions in thef low. In a natura l r iver the f low var iess igni f icant ly and t .h is resul ts in var iat ions in theshear s t ress appl ied to the bed. This ean producea cyc le of eros ion and deposi t ion whlch mayinf luence the in teract lon of the sands and s i l ts .In extreme cases, parts of the bed rnay dry outleading to changes in the propert ies of the s i l t .

4 . Sediment t ransport of sand and s i l t mlxtures. Thiswork has not, considered the related problem of thesedLment t ransport of sand and s i l t mixtures andwhether the presence of boEh sands and s i l tsin f luences the indiv ldual behaviour of each.

The work was perforned whlle the author was visit ingi lydraul lcs Research, Wal I ingford. Dur ing the per iod

6 ACKNOWLEDGEMENTS

L2

he was supported by a scholarship fron the ItalianDepartnent of Education.

The cost of the use of the facillties and ofsupervlsion and advice at Hydraulics Research wascovered by contract PECD 7/6/29-204/83 funded by theDepartnent, of the Envlronment.

7 REFERENCES1. Ackers P and White W R, 1973. Sedlnent

transport : new approach and analysls. ASCE JHD99, HY 11, pp 2O4L-2O60.

2. Einstein H A and Barbarossa N C, 1952. Rlverchannel roughness. Trans ASCE, IL7,p p 1 1 2 1 - 1 1 3 2 .

3. Engelund F, L966. Hydraul lc resl .stance ofal luvial streams. ASCE, JHD, 92, l tY 2, pp 315-326and closure 93, HY 4, pp 287-296.

4. Garde R J and Ranga-Raju K C, L966. Resistancerelat ionships for al luvial channel f low. ASCE,Jt lD, 92, t tY 4, pp 77-100.

5. Raudkivi A J, L967. Analysls of reslstance inf luvial channels. ASCE, JHD, 93, I IY 5, pp 73-84.

6. van Ri jn LC, 1984. Sedirnent transport , part I I I :Bed forms and al luvial roughnesses. ASCE, JI ID,I10 , No 12 , pp L733-L754.

7. Yal in ) ,1 S, L977. Mechanics of sedinent transport , ,Pergamon Press, Second Edit ion.

13

DDB Dd 650449 11,/85

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