49 Ersin and sediment transprt measurement (Prceedings f the Flrence Sympsium, June 1981) Sme bservatins n the mvement f cbbles n a streambed LUNA B. LEOPOLD Department f Gelgy and Gephysics University f Califrnia Berkeley, Califrnia, 94720 USA WILLIAM W. EMMETT U.S. Gelgical Survey Bx 25046, MS 413, DFC Lakewd, Clrad 80225 USA GENERAL STATEMENT Numerus experiments have been undertaken t measure the bed shear stress necessary t mve particles f different sizes. The well knwn Shields curve fr initial mtin is supprted by cmpilatins f ther data, fr example, Lepld, Wlman, and Miller (1964), Fig. 6-11, p. 170. Hwever, flume experiments'have dealt primarily with debris f unifrm size. In natural gravel bed rivers, size distributin makes the applicatin f such curves prblematical fr the effect f hiding small grains being prtected frm stress by larger grains is prly knwn. It has been shwn that the clser ne rck is t its neighbrs, the larger is the shear stress needed t mve either (Langbein and Lepld, 1968). Experiments in an ephemeral stream by Lepld, Emmett, and Myrick (1966) demnstrated that the effect f prximity becmes negligible when adjacent cbbles are separated by 8 diameters r mre.
-. WC>-A-/, *r.- : *.-'. ^<Ci*bw~r:r»t-;: ". '>iu-*6*&l : ; i ~ s If the shear stress is sufficient t mve a rck f a given size, it is nt knwn whether all rcks f that size will mve, whether all rcks f smaller size will mve, r hw far each mved rck will be carried. A preliminary and incmplete experiment t answer thse questins is described here. Because f its simplicity, hwever, the prcedure might be used fr a mre sphisticated experimental design. EXPERIMENT White Clay Creek at the Strud Water Labratry drains 7.25 km 2 in the West Grve Quadrangle, Pennsylvania. The stream at that place has a width f 5.2 m, and a gravel bed the median grain size, D. Q, f which is 58 mm. Its pattern is sinuus r straight with well develped pls and riffles. The drainage area is agricultural, mstly in pasture with mderate amunts f frested wdlt interspersed with sme tilled crpland. Mean annual precipitatin is abut 1200 mm. Three riffles were selected frm which cbbles f varius sizes These 90 the channel were placed flw direct 10 f& rcks f f 10 rcks was a line Tw staf dwnchannel elevatins slpe t be Acrss Frm it, r< n a gage stream is. readings allwed c were cllected, three riff, frm the rcks cllected 90 were selected, representing three size classes. The smallest class was typical f rcks were avail n the riffles 35% finer and is designated D, 5. In this class the stress as dminant size was 47 mm n the B axis (intermediate axis). The middle size rcks represented D 5Q (50% finer) and the dminant B axis dimensin was 58 mm. The largest size represented D g^ (84% finer); the dminant B axis dimensin was 91 mm. T " yds where t O; water, 10'j
51 These 90 rcks were painted yellw and were put in lines acrss the channel bed. On each f the three riffles three lines f rcks were placed, the lines riented acrss the channel rthgnal t the flw directin. On each riffle the upstream line cnsisted f I 0 ff rcks f the D-. size. Dwnstream a distance f 1.5 m was a line f 10 rcks f size D. Further dwnstream a distance f 1.5 m was a line f 10 rcks f size D,. Tw staff gage plates were installed in each riffle, separated by dwnchannel distances f 10 t 17 m. Simultaneus water surface elevatins bserved at a pair f staff gages allwed water surface slpe t be cmputed. Acrss each riffle a representative crss sectin was surveyed. Frm it, relatins f crss sectinal area and mean depth t reading n a' gage plate culd be cnstructed. A few hundred meters dwnstream is a gaging statin with water stage recrder. Simultaneus readings f water surface at the gage and at the riffle staff plates allwed cnstructin f discharge rating curves fr each f the three riffles. Thus fr any discharge, values f mean depth and slpe were available at each riffle allwing an estimate f mean bed shear stress as x " yds where T is shear stress in kg m 2, Y is the specific weight f water, 1000 kg m~ 3, and d is depth in m.
mi.?* 52 After each significant peak discharge the rck lines were inspected. The distance dwnstream that any rck mved was recrded. After several strms individual rcks were remved frm their dwnstream psitins and replaced n the line where they had been riginally. Only in unusually high discharges were sme rcks mved s far that they culd nt be lcated. ANALYSIS In the winter f 1979-1980, 11 strms ccurred, the discharges frm which were sufficiently high t require measurements f rck mvement. It was assumed that any rck mvement culd be attributed t the dischar : relatic that lc It t : ' mved 1 bservi rcksij i. and sej rcks i largest peak discharge ccurring between dates f rck inspectin. Thus the cmputatin f the shear stress assciated with each rck mvement was based n the highest discharge bserved between inspectins. These discharge values varied frm 0.23 m 3 s 1 t 3.42 m 3 s 1. The crrespnding values f shear stress varied frm 2.15 kg m~ 2 t 14.6 kg ra~ 2. The lcal slpe and depth differed amng the three riffles at the same discharge and therefre any given discharge prduced a different value f bed stress at the crss sectins. The Labratry Riffle N. 1 maintained a cnstant slpe fr different discharges and the value f T thus varied directly as depth. At the White Rck Riffle N. 2, slpe decreased slightly with discharge s the values f shear are smaller than thse at S. 1. At the Willw Riffle N. 3, the cmputed slpe decreased rapidly with f th> mved i bee am' I the fi stresj
S3 discharge but the scatter f data was large and n reliable average relatin f slpe t discharge culd be cnstructed. Therefre, fr that lcatin n values f shear stress are presented. It wuld be expected that the number f rcks f a given size mved by varius flws wuld increase with bed shear stress. The bservatins are presented in Fig. 1 as plts f percentage f rcks mved as a functin f bed shear stress fr each flw event, and separate graphs are shwn fr the small rcks (D,.), medium size rcks (D, ) and large nes (D R /.) On each graph is an arrw indicating the value f shear stress needed t initiate mtin f the rck sizes used; the values f stress were read frm Fig. 6-11, in Lepld, Wlman, and Miller (1964). The figure shws that the shear stress n White Rck Riffle N. 2 exceeded that necessary fr mvement nly n a few ccasins and as a result, the maximum number f rcks mved by any flw was nly 10% f the ttal number, regardless f rck size. On the ther «i?hfi hand, Labratry Riffle N. 1 experienced shear stress abve the minimum necessary in nearly every hydrgraph rise. Cnsequently mvement f all three rck sizes ccurred in abut tw thirds f all flw events. Hwever, the salient fact is that in nly ne instance, did as many as 60% f the rcks mve, and in all ther cases 40% r less f the rcks experienced mtin. This small percentage f rcks mved was characteristic despite the fact that the shear stress became as large as 5 times the value necessary fr mvement. In the flw where 60% f the D,- rcks mved, the experienced shear stress was 2.9 times that needed fr initial mtin. r i**s?\ i'"'! : -^>'v."- Ss'l ^?m- ^Bt%gy#
VCJF ^^.^^4^\^%^^t»^y^^^-:jm^^^^m» *«tiar,t^^^*»j*w.i.* ls5shb*ls«k5 : x r 'i 54 The ttal number f mvements ut f the 90 rcks placed ccurring in the 11 flw events is summarized in Table 1, In each f the riffles the number f rcks mved decreased with increase f rck size as ne might expect because there were fewer flws prviding large values f shear stress than thse prviding small values. Regarding distance that rcks mved, Fig. 2 shws fr each strm at Labratry Riffle N. 1 the ttal distance f all mvements as a functin f shear stress. The ttal distance means the sum f mvement distances f each rck f a given size class that mved. The distance mved increased gemetrically with increase f shear stress. In the single flw event where shear stress exceeded 14 kg m 2, 7 f the 90 rcks were swept' dwnstream s far that they disappeared and distance mved is unknwn. Fig. 2 shws n bvius relatin f distance mved t rck size but when mvement distances are summed fr all 11 flw events, the relatin becmes mre clear as shwn in Table 2. The table shws that the smaller rcks mved a smewhat lnger distance than did the large rcks. Yet except fr the largest flw that mved sme rcks cmpletely ut f the riffle area, the distances mved were small, usually less than 2 m even in flws where the shear stress was several times the value needed fr mtin. t ma ' pe f I**,i\+ #.r &*5i
'» -VV.cfc3l.' i-w-^xaw.,-. i^ *&-»X^'- : *»<*-.^--.'-^la*^ ^,;v~,^.^^4v,.^; ^:5^^ ^f^sla^^#-1..^i^^>" 55 CONCLUDING COMMENT Data n shear stress needed, fr initial mtin f a rck f given size are usually cmpiled either fr an islated rck n a unifrm bed r the first mtin f any rck in a bed cmpsed f rcks f the same size. The interactin f a rck with its neighbrs, the tendency fr a smaller ne t be prtected frm shear stress by larger nes in the vicinity, makes the experimental values f required stress t be minimal. The present mdest experiment suggests that even when shear stress is several fld larger than the minimal value derived frm initial mtin data mentined abve, nly a small prprtin f available rcks will actually be set in mtin. It therefre takes repeated flws f cmpetent shear stress t mve all f the rcks f a given size. If a gravel riffle is an expressin f a kinematic wave as Suggested by Langbein and Lepld (1968), cmplete replacement f rcks in a zne f cncentratin requires nt ne but a series f flw events sufficiently energetic t mve thse rcks. This general cnclusin has been cnfirmed by the authrs in ther marked rck experiments. On the East Frk River, Wyming, marked rcks placed n a gravel bar gradually disappeared ver a perid f 4 t 5 yrs, despite annual flws sufficient t mve rcks f that size. The average distance mved in a flw event f the present experiment was abut 2 m, the rcks being f the rder f size f 0.06 m. This is a mvement f 33 rck diameters, a general cnfirmatin f the estimate f H. Einstein that a single bedlad mvement is usually f the rder f 100 grain diameters. f^h*fe 7*** :.^;^
'" 'JtSteh...' r-. hss****-,/- '.. ^Oimr^iaJ&^Se*. 56 ACKNOWLEDGEMENTS This wrk was carried n thrugh the curtesy f Dr. Ruth Patrick and Dr. Rbin Van Nte. We acknwledge with thanks the assistance f Bernard Andersn in making the bservatins f rck mvement. REFERENCES Table 1. Riffle nam; Labratry White Rck Willw Rif Langbein, W.B., and Lepld, L.B., 1968, River channel bars and dunes thery f kinematic waves: USGS Prf. Pap. 422-L. Lepld, L.B., Emmett, W.W., and Myrick, R.M., 1966, Channel and hillslpe prcesses in a semiarid area, New Mexic: USGS Prf. Pap. 352-G. Lepld, L.B., Wlman, M.G., and Miller, J.P., 1964, Fluvial prcesses in gemrphlgy: ^W.H. Freeman C., San Francisc. Table 2. class in. Riffle na Labratr White Rc Willw Ri
57 Table 1. Ttal number f rck mvements in 11 stra events. -Size class- Riffle name "35 (47 mm) (58 nan) u 84 (91 mm) Labratry Riffle 1 14 15 12 White Rck Riffle 2 3 Willw Riffle 3 19 2 7 1 3 t lift. : s. Table 2. Ttal distance (m) mved by all rcks class in all 11 flw events. Riffle name 35 (47 mm) Labratry Riffle 1 13 White Rck Riffle 2 11 Willw Riffle 3 37 -Size class- D 50 (58 mm) 12 20 "84 (91 mm) 9 6 16 m
J* LB/FT 5 Q Ul > O 2 60.5 1 I r > i ) 1 I D jf4 7MM I i r-i r i I 1 D. 60MM J W.6 1 2 3 -l 1 D 91MM O O cc u. O UJ O < z UJ IT Ul a. 40 20» * y 1 Y 0 t XX if X X * x x n» 7.; tfl 1 IxJ 10 20 jaah-d-julm bull ' lyi, BED SHEAR STRESS, KG/M n r 000*1 xwi i ivi 10 20 * LAB RIFFLE WHITE ROCK RIFFLE { STRESS NEEDED FOR INITIAL MOTION Figure 1. Percentage f rcks mved by flws having different values f bed shear stress. Fr each f three rck sizes a separate diagram is presented. Vertical arrw indicates shear stress value needed fr initial mtin f that rck size. mm^mmmrmmm«k%*iw^aima0,-. *4 15 **s CO A "N>-
r^t^fmf'^ <k T ^St^fc^. JIE-itiwWu. " * * - :. * * < *» 15 CO* CO 111 cr f- c cr < ai x CO a UJ m tf 10 OX -flaaa&i AO LJL J-JUL.1 \ J L ' i i ' I.2.5 1 2 x A X DISTANCE MOVED, METERS J L I I I 10 2 u. «>» m -i W X D 47MM 0^58MM A P, 91 MM #4 Figure 2. Ttal distance mved by all rcks f given size as functin f shear stress, Labratry Riffle N, 1.