The influence of upstream weir slope on live-bed scour at submerged weir

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1 The influene of upstream weir slope on live-be sour at submerge weir L. Wang, B.W. Melville & H. Frierih Department of Civil an Environmental Engineering, University of Auklan, New Zealan ABSTRACT: Shape variation of submerge weirs an hange loal flow patterns an seiment transport. The aim of this stuy is to quantify an ompare the loal sour at weirs with ifferent upstream fae slopes, uner submerge flow an live-be onitions. Experiments were arrie out on 3 mm high weirs in a tilting, seiment reirulating flume with.26 mm uniform seiment. 24 experiments were unertaken involving four ifferent upstream weir fae angles (3, 45, 6 an 9 to the horizontal) an six flow intensities. Two webams were employe to observe upstream aggraation an the loal sour on both sies of the weir. The results iniate that a gentler upstream weir slope reues the upstream sour epth at the submerge weir, for upstream weir fae angle greater than 45. The results also show that the ownstream sour epth is inepenent of the upstream weir slope. 1 INTRODUCTION Weir-like strutures that span the with of the hannel (e.g. be sills, groynes, hek ams, submerge weirs) are frequently installe in rivers to ontrol water level an stabilize the be from exessive egraation (Guan et al., 215). Flow over suh strutures has a potential to ause onsierable sour, possibly leaing to amage or failure. The flow over weirs an be lassifie into free flow an submerge flow. Hager an Shwalt (1994) efine submerge flow as beginning when the upstream water level starts to inrease with inreasing tailwater epth, the flow is efine as submerge flow. Although somewhat arbitrary, this efinition has been foun to be helpful (Hager an Shwalt, 1994, Fritz an Hager, 1998, Shmoker et al., 211). Up to the present, many stuies have investigate souring ownstream of a weir-like struture (Ben Meftah an Mossa, 26, Bormann an Julien, 1991, D'Agostino an Ferro, 24, Gauio et al., 2, Lenzi et al., 22, Lenzi et al., 23a, Lenzi et al., 23b, Lu et al., 212, Marion et al., 26, Marion et al., 24, Pagliara an Kuristani, 213, Surlok et al., 211). However, very few of these stuies inlue the effets of seiment supply or onsiere the situation of submerge flow (Guan, 215). Guan (215) reviewe the existing empirial equations for loal sour at weir-like strutures, an systematially stuie loal sour an its flow pattern at vertial fae submerge weirs in a tilting seiment-reirulating laboratory flume. Base on an analysis of their experimental ata, they propose a series of imensionless equations to preit the upstream sour epth for live-be sour onitions (Eq. 1), an the ownstream sour epth for both live-be sour onitions (Eq. 2) an lear-water sour onitions (Eq.3). All of these equations inlue the effets of seiment size, tailwater epth an weir height us _ a z 5 U U = ht ht ht U U 1 U U 3.65 (1) < s_ a z 5 U.23 = ht ht ht U U.9 U 1 U U 3.65 (2) < s _ a h t z 5 U = ht ht U.4 U U 1 (3) < In these equations, us_a is the average upstream sour epth, s_a is the average ownstream sour epth, h t is the tailwater epth, 5 is the meian iameter of san, z is weir height, where us_a, s_a, h t,

2 h a, h an z are referene to the initial flat be (Fig. 1). U is the average veloity of approah flow, for the ross-setion above the equilibrium be level (i.e. where the flow epth is equal to h ). U is the average ritial approah veloity for initiation of san movement; it is alulate by the logarithmi veloity profile funtion U u* = 5.75log( 5. 53h 5 ). However, the experiments of Guan (215) were limite to retangular weirs with a narrow retangular ross-setion shape. The effets of weir shape oul hange the seiment transport an flow pattern aroun the submerge weir, an these effets shoul be onsiere for esign. In this paper, 24 experiments were onute in a seiment reirulating flume, using weirs with ifferent upstream fae angles to explore the upstream fae angle effets on the loal sour at a submerge weir uner live-be sour onitions. 2 EXPERIMENTS 2.1 Experimental set-up The experiments were onute in a 12 m long,.38 m eep an.44 m wie tilting sanreirulating flume with glass sie-walls, in the Hyraulis Laboratory of The University of Auklan. The reirulating system onsists of a pump an a san pump. The san pump rate was set at a onstant value that is suffiient to reirulate the seiment. The water pump rate is ajuste by an eletroni ontroller. Both water an san are pumpe to a mixing hamber loate at the upstream inlet of the flume, an enter the open hannel via a honey-omb flow straightener. At the flume outlet, be-loa seiment is eposite in a hopper-like sump an reirulate to the inlet through the san pump. The flume slope is ajuste using a jak inorporate in the flume. Four weirs, eah of 3 mm height with ifferent upstream fae angle (3, 45, 6 an 9 to the horizontal) were employe. The submerge weirs eah ha a 1 mm wie rest an were of the same with as the flume. A uniform fine san with 5 =.26 mm was use. The harateristis of the be material are presente in Table 1. The ritial shear veloity, u *, is etermine from the Shiels urve for ifferent grain sizes (Melville, 1997). Table 1. Graing istribution of san use as be material σ g ( ) Δ ( ) u * (m/s) * σ g is the stanar eviation of seiment size; Δ is the relative submerge partile ensity. All the experiments were onute uner livebe sour onitions. The hyrauli onitions an the experimental results are presente in Table Be profile measurements A Logiteh HD webam was plae on eah sie of the flume to reor the souring proess. Both webams were at the same istane along the flume an at the same height. Sour epths were measure with the assistane of transparent gri sheets plae on the glass walls. The loations of the webams an the istane between the webams an the flume glass walls were ajuste to enable the webam s iagonal fiel of view (78 ) to over the sour hole. The sour profiles were obtaine from suessive pitures taken with a onstant frequeny in eah test. The esribe epth measurements tehnique has an auray of ±2 mm. Although the flow an weir were twoimensional, the upstream an ownstream sour holes at the weir were observe to be threeimensional, on aount of the migrating threeimensional ripples an the unsteay seonary flows generate in the sour holes themselves. Thus, the sour epth at any partiular time was not onstant aross a ross setion; sometimes the maximum sour epth was more than two times the minimum. The maximum sour epth was observe to be very near the sie walls of flume most of the time in eah live-be sour test. Aoringly, the maximum sour epths on the sie walls are onsiere to be the sour epths of the sour holes aroun the submerge weir. Sour epths upstream ( us ) an ownstream ( s ) of the weir were extrate at onstant time intervals throughout eah test. The timeaverage value of us an s after reahing the equilibrium onition efine in Guan et al. (214) were onsiere to be the equilibrium average sour epths ( us_a an s_a ). The maximum sour epths uring the test ( us_max an s_max ) an the aggraation height (h a ) were also reore. The efinitions of all measurements above follow Guan et al. (215). For the tests of eah weir type, the be was flattene initially. An experiment uner higher flow-rate (Q) was starte ontinuously after the finish of a lower flow-rate test. The same metho was use by Sheppar an Miller (26). The hannel slope was ajuste to obtain a onstant tailwater epth (h t ) of 15 mm. The water level ifferene between upstream an ownstream of the weir in the equilibrium stage, H was measure with a point gage. The average approah flow epth, h, is alulate as h = h t + H - h a. A sketh of the measurements esribe above is shown in Figure 1. The upstream Froue number, F r, is between.26 an.79.

H Equilibrium be level h a h Suspene loa z h t Initial flat be us s Figure 1. Definition sketh of live-be sour at a submerge weir, after Guan et al. (215) Table 2.

47.27.14.39 85 1 45 73 12.5.395 151 6 5.595.27.2.49 117 128 56 122 6..481 149 9 1.734.27.27.6 126 143 43 116 2.9.532 151 1 9.81.27.33.67 132 147 2.7.615 15 1 1.932.27.33.79 145 152 71.1.218 155 1-4.

943.27.33.76 153 16 52.1.218 157 1-6.316.271.9.26 5 6 17 33 24..38 157 3-4.446.271.14.37 74 88 21 43 12.2.395 155 6 1.579.271.2.48 14 12 24 53 5.6.481 154 9 5.71.271.27.59 115 13 11 26 3.3.532 152 9 7.

3 H Equilibrium be level h a h Suspene loa z h t Initial flat be us s Figure 1. Definition sketh of live-be sour at a submerge weir, after Guan et al. (215) Table 2. Summary of experimental onitions an results t (h) Q (m 3 /s) h H h a U (m/s) U (m/s) Flume Slope Fr s_a s_max us_a us_max ɑ= 9 ɑ= 6 ɑ= 45 ɑ=

4 Figure 3. Generalize moel of souring at retangular weir (a) an weir with upstream slope (b) 3 RESULT AND DISCUSSION Flow intensities (U o / U ) in the experiments were between 1.2 an 3.5. The imensionless mean upstream an ownstream sour epth ( us_a /h t an s_a /h t ) of eah weir type are plotte in Figure 2 an Figure 4, respetively, for ifferent flow intensities. Figure 2 shows that the average upstream sour epth plotte against the normalize veloity has the same tren for eah weir type. The tren is inreasing when U o / U is between 1.2 an about 2.2, then ereases to zero as U o / U inreases to about 3. For U o / U between 3. to 3.4 (maximum intensity in this stuy), the upstream beform beomes planebe (transition). It an be seen that the upstream sour epth reues as the upstream weir fae angle ereases. For ɑ > 45, the sour epth oes not appear to hange with ɑ. The blak triangular symbol in Figure 2 represents the value ƞ / 2 h a, where ƞ is the estimate beform height using the Van Rijn (1984) preitor. A generalize moel is skethe in Figure 3 to help explain the unerlying mehanism. During the experiments it was observe that a vortex is generate in the trough of the beform. When the be-form trough is approahing the weir, the vortex is squeeze by the weir fae beause of the eformation of the trough shape. As a onsequene, the flow intensity in the vortex is inrease, more seiment is remove from the trough, an the sour hole beomes eeper. The size of upstream sour hole is therefore etermine by the beform height (whih epens on the flow intensity); this is the reason why the normalize upstream sour epth has the same tren for all upstream weir fae angles, an it is also the reason that the upstream sour epth beomes zero when the upstream be form is transition flat. As the upstream weir fae angle ereases, eformation of the vortex reues, an the amount of seiment remove beomes less than that for a retangular weir. When the weir fae angle beomes less than 45, the enhane flow intensity of the squeeze vortex is inaequate to transport more seiment from the trough. In this situation, the upstream sour epth reahes its lower limit, whih is equal to ƞ / 2 h a.

5 4 CONCLUSION Figure 2. Normalize average upstream sour epth vs. flow intensity Figure 4 shows that the average ownstream sour epths of all weir types are approximately the same at eah experimental intensity, whih iniates that the ownstream sour epth is inepenent of upstream fae angle uner live-be sour onitions. The normalize ownstream sour epth inreases as the veloity inreases, but the rate of inrease is less for U o / U between about 2. to 3.. This is reasonable beause, for a partiular flow intensity, the water level ifferene, H (Table 2) is almost onstant for varie weir slope. Beause the ownstream weir shape an the upstream seiment loa are not hange, the flow pattern over the weir is unhange an maintains the ownstream sour hole epth of a retangular weir. Figure 4. Normalize average ownstream sour epth vs. flow intensity The effets of upstream weir fae angle on loal sour at a submerge weir were stuie in a seiment reirulating flume uner live-be sour onitions using four types of weir (upstream weir fae angle 3, 45, 6 an 9 to the horizontal). It is foun that a gentler upstream weir fae angle an reue upstream sour epth. This reution is beause of the unerlying mehanism in the interation between the beform trough vortex an the weir fae; the reution inreases with inreasing weir fae angle for angles up to 45, at whih angle the upstream sour epth reahes its lower limit of alulate half beform height minus upstream aggraation height. The experimental results also show that the ownstream sour epth is inepenent of the upstream slope of weir. ACKNOWLEDGEMENT The authors woul like to aknowlege the valuable suggestions from Dr. Keith Aams. Also, the first author woul like to thank the China Sholarship Counil for the finanial support. NOTATION The following symbols are use in this paper: B = hannel with (m) b = weir with (m) x = seiment size, for whih x% (in weight) of seiment partiles are finer us = sour epth upstream of the weir in eah measurement _ = equilibrium sour epth upstream of the us a weir = maximum sour epth upstream of the weir us _ max s = sour epth ownstream of the weir in eah measurement _ = equilibrium sour epth ownstream of the s a weir = maximum sour epth ownstream of the s _ max weir F r = Froue number upstream of the weir ( ) g = aeleration of gravity (ms -2 ) H = water level ifferene aross the weir h = average approah flow epth h = aggraation height a

6 h t = tailwater epth Q = flowrate (m 3 s -1 ) t = sour time (h) U = average approah flow veloity (ms -1 ) U =ritial average approah flow veloity (ms -1 ) u * = ritial shear veloity (ms -1 ) z = weir height ɑ = upstream weir fae angle = relative submerge partile ensity ( ) η = alulate beform heights ν = kinemati visosity of flui (m 2 s -1 ) σ = stanar eviation of seiment size ( ) g REFERENCES MELVILLE, B. W. (1997) Pier an Abutment Sour: Integrate Approah. Journal of Hyrauli Engineering, 123, PAGLIARA, S. & KURDISTANI, S. M. (213) Sour ownstream of ross-vane strutures. Journal of Hyroenvironment Researh, 7, SCHMOCKER, L., HALLDÓRSDÓTTIR, B. & HAGER, W. (211) Effet of Weir Fae Angles on Cirular-Creste Weir Flow. Journal of Hyrauli Engineering, 137, SCURLOCK, S. M., THORNTON, C. I. & ABT, S. R. (211) Equilibrium Sour Downstream of Three-Dimensional Grae-Control Strutures. Journal of Hyrauli Engineering, 1, 289. SHEPPARD, D. M. & MILLER, W. (26) Live-Be Loal Pier Sour Experiments. Journal of Hyrauli Engineering, 132, VAN RIJN, L. C. (1984) Seiment transport, part III: be forms an alluvial roughness. Journal of hyrauli engineering, 11, BEN MEFTAH, M. & MOSSA, M. (26) Sour holes ownstream of be sills in low-graient hannels. Journal of Hyrauli Researh, 44, BORMANN, N. E. & JULIEN, P. Y. (1991) Sour Downstream of Grae-Control Strutures. Journal of Hyrauli Engineering, 117, D'AGOSTINO, V. & FERRO, V. (24) Sour on Alluvial Be Downstream of Grae-Control Strutures. Journal of Hyrauli Engineering, 13, FRITZ, H. & HAGER, W. (1998) Hyraulis of Embankment Weirs. Journal of Hyrauli Engineering, 124, GAUDIO, R., MARION, A. & BOVOLIN, V. (2) Morphologial effets of be sills in egraing rivers. Journal of Hyrauli Researh, 38, GUAN, D. (215) Sour at Submerge Weirs. New Zealn, University of Auklan. GUAN, D., MELVILLE, B. & FRIEDRICH, H. (214) Flow Patterns an Turbulene Strutures in a Sour Hole Downstream of a Submerge Weir. Journal of Hyrauli Engineering, 14, GUAN, D., MELVILLE, B. W. & FRIEDRICH, H. (215) Live-Be Sour at Submerge Weirs. Journal of Hyrauli Engineering, 141, HAGER, W. & SCHWALT, M. (1994) Broa Creste Weir. Journal of Irrigation an Drainage Engineering, 12, LENZI, M. A., MARION, A. & COMITI, F. (23a) Interferene proesses on souring at be sills. Earth Surfae Proesses & Lanforms, 28, LENZI, M. A., MARION, A. & COMITI, F. (23b) Loal souring at grae-ontrol strutures in alluvial mountain rivers. Water Resoures Researh, 39, LENZI, M. A., MARION, A., COMITI, F. & GAUDIO, R. (22) Loal souring in low an high graient streams at be sills. Journal of Hyrauli Researh, 4, LU, J.-Y., HONG, J.-H., CHANG, K.-P. & LU, T.-F. (212) Evolution of souring proess ownstream of grae-ontrol strutures uner steay an unsteay flows. Hyrologial Proesses, 27, MARION, A., LENZI, M. A. & COMITI, F. (24) Effet of sill spaing an seiment size graing on souring at graeontrol strutures. Earth Surfae Proesses an Lanforms, 29, MARION, A., TREGNAGHI, M. & TAIT, S. (26) Seiment supply an loal souring at be sills in high-graient streams. Water Resoures Researh, 42, W6416.

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