Effect of buried plates on scour profiles downstream of hydraulic jump in open channels with horizontal and reverse bed slopes

Akram Abbaspour*,Sahar Parvini,Ali Hosseinzadeh Dalir

Department of Water Engineering,University of Tabriz,Tabriz 5166616471,Iran

Effect of buried plates on scour profiles downstream of hydraulic jump in open channels with horizontal and reverse bed slopes

Akram Abbaspour*,Sahar Parvini,Ali Hosseinzadeh Dalir

Department of Water Engineering,University of Tabriz,Tabriz 5166616471,Iran

Localscour downstream of sluice gates in erosive beds is one of the main concerns of hydraulic engineers because itcan cause considerable damage to structures.Many researchers have conducted various studies to predictthe maximum depth and length of scour holes and to develop new methods to controlthis phenomenon.In the methods thathave recently been examined,embedded buried plates are used to controlthe scour in the erosive beds.In this study,using a physical model,the effect of buried plates in erosive beds on the depth of scour downstream of a hydraulic jump was studied.Several experiments were performed in which plates were buried at 50°and 90°angles at differentdistances from the apron in open channels with horizontal and reverse bed slopes.The results of experiments in which the scour profiles were drawn in dimensionless forms show thatthe angle and position of the plates are importantto controlling and reducing scour depth.In fact,by reducing the angle of buried plates,the maximum depth of scour is also reduced.Also,comparison of the results of a single buried plate and double buried plates shows that using two buried plates at the distances of 30 and 45 cm from the non-erodible bed is more effective in reducing the scour depth.The best distances of the buried plates with angles of 90°and 50°from the non-erodible bed are 45 cm and 30 cm,respectively,in the condition with a single buried plate.

Local scour;Buried plates;Hydraulic jump;Horizontal and reverse bed slopes

1.Introduction

One of the fl ow types that causes scour in the vicinity of various structures is a hydraulic jump,classified as rapid varied fl ow.A hydraulic jump causes turbulent fl ow and local scour in erosive beds.Turbulent flow due to a hydraulic jump is a random field that can have a signifi cant impact on the movement of sediment particles and formation of scour holes. Several investigations have been conducted in the context of hydraulic jumps to determine the velocity fi eld and the bed shear stress.Some studies on the determination of the local scour depth downstream of hydraulic jumps have been conducted.Hino(1963)has pointed out that turbulence maydecrease in the presence of suspended sediment.Carstens (1966)has used experimental data from Laursen(1952)to determine the depth of scour downstream of the sluice gate. Farhoudi and Smith(1985)studied the scour downstream of hydraulic jumps and the similarity of the scour profi les was tested.Bormann and Julien(1991)conducted a theoretical investigation of local scour downstream of grade-control structures.They concluded that the equilibrium scour depth could be a function of the velocity,flow depth,and particle size.

Local scour downstream of hydraulic structures such as low-head and high-head structures,spillways,and culverts,is an important research fi eld due to its significant practical value.Scour induced by low-head structures such as gates and low dams has been investigated by many researchers(Dargahi, 2003).García(1993)studied the characteristics of a hydraulic jump in the sediment-driven bottom currents.He producedboth sediment-laden and saline fluids,as well as hydraulic jumps,and concluded that the saline and muddy hydraulic jumps have similar characteristics.Omid and Nouzari(2004) investigated the effect of bed load transport on the hydraulic jump characteristics.

Submerged verticalplates installed in the streambed deflect flow and controlsedimentdeposition and erosion.These plates have been successfully used to control erosion in a river,and ameliorate shoaling problems in rivers(Odgaard and Wang, 1987).Previous studies have shown the positive role of the buried plates in controlling and reducing scour downstream of the hydraulic jump(Bateni,2004).In this method,through placements of the buried plates into the bed,with the top of plates at the same level as the surface of the beds,the dimensions of scour holes decrease and the hole is formed away from the apron.Bateni(2004)and Bateniet al.(2007)studied the impact of vertical buried plates on control of the scour in the vicinity of the bridge.Borghei(2006)and Borhani(2012) conducted experiments on buried plates with different angles for low-Froude flow.Up to now,the studies have been performed for the case of hydraulic jumps with a low initial Froude number(Fr＜4.5).The aim of the research presented in this paper was to study the effects of a hydraulic jump on the local scour for Froude numbers ranging from 4 to 9.In this study,laboratory experiments were conducted to investigate the scour phenomenon under the conditions of clear-water scour,uniform sediment,and bed reinforcement,using oblique buried plates which were placed at50°and 90°angles and at different distances from the apron on the horizontal and reverse bed slopes.The effect of buried plates in the erosive bed on the depth and length of scour downstream of the hydraulic jump was also studied.

2.Materials and methods

The experiments were conducted in a metal and glass fl ume with a rectangular cross-section.The fl ume was 0.25 m wide, 0.5 m deep,and 10 m long.The slope of the channel was 0.002.The flume was equipped with a sluice gate at the entrance,and the discharge was measured with a triangular weir placed at the end.The discharge-head relationship(Q-h) for the triangular weir in experiments was Q=0.6918h2.5.In each test the supercritical depth(or the initial depth of the jump)y1and tailwater depth yt,of the jumps were continuously measured using ultrasonic sensors and the data were saved on a computer and processed with VisiDAQ software. Then,the mean water depths of the jump were calculated.In this study the supercritical approach fl ow was produced using a sluice gate.To control the tailwater of the jump and produce a hydraulic jump,a sluice gate was installed atthe outletof the flume.In this study,the gate opening(h0)was 3 cm.

The experiments were conducted in two parts,with and without buried plates.The experiments without buried plates were performed with uniform sedimentwith six differentFroude numbers.A total of six experiments were carried out to determine the equilibriumtime;the scourprofiles were measured over 2,4,6,and 12 h;and 6 h was determined asa reasonable duration to establish equilibrium.The buried plates were made of metal with a thickness of3 mm with two angles,45°and 90°,and were embedded atdifferentintervals in sediment.

Two metalsheets with a width of 0.25 m and lengths of 2.6 and 2 m were used to raise the height of the floor approximately 15 cm upstream and downstream of the fl ume.Two aprons with an interval of nearly 2 m were installed upstream and downstream of the fl ume,and the sediment material was placed between these two aprons.The hydraulic jump was formed at the distance of 0.7 m upstream of the sedimentary bed.The bed was composed of uniform natural sand with a mean diameter of d50=3.3 mm and a geometric standard deviation equal to(d84/d16)1/2=1.24,where d84and d16are the particle diameters equal to or exceeding those of 84%and 16%of the bed particles,respectively.

A horizontalflatbed and a free falltailwater were the initial conditions for the experiments.The sand bed was deformed by the flow,via a process of clear-water scour.Ultimately,the sediment transport vanished throughout and a stable bottom topography was formed.The bed topography was surveyed for an equilibrium time of 6 h.The survey included sediment surface records in selected transversal and longitudinal sections,to determine the geometry of the scour hole.Moreover, water surface measurements were taken without buried plates in the erodible bed in equilibrium conditions.Both the water and scour hole profi les were measured using point gauges of 0.1 mm accuracy.A total of 101 experimental runs were conducted in two parts:withoutburied plates and with a single plate and two buried plates.

The maximum scour depth Dsmaxdownstream of a rigid apron can be expressed as a function of the independent variables of S0，L，u1，y1，yt，ρ，μ，g，ρs，d50，Le，Dsmax，Lp，Ln，θ,and h0,where Leis the maximum length of scour,g is the acceleration due to gravity,ρis the density of water,ρsis the density of movable soil,Lpis the distance of the plate from a non-erodible bed,L isthe distance from the non-erodible bed,Lnis the length ofnon-erodible bed,μisthe viscosity ofwater,u1is the mean velocity underthe gate,S0isthe slope ofthe bed(0.002 and-0.015),andθis the angle of buried plates.Moreover,in this study Lnwas constant for all experiments,so Lnhas a negligible infl uence on scour and can be neglected.

By applying the Buckingham πtheorem,the following equation was obtained:

Becauseρsandρare constants,they can be ignored.The bed slope(S0)and mean particle diameter(d50)are constant. Hence,Eq.(1)is reduced to Eq.(2):

It can be concluded from Eq.(2)that the maximum depth Dsmaxand length of scour Leare dependenton the independent variables Fr1,S0,L,Lp,andθ.

3.Results

3.1.Configuration of hydraulic jump on movable bed

Experimental observations have shown that atequilibrium the bed profile is characterized by a scour hole,usually followed downstream by a ridge caused by the deposition of the eroded material.This shape of the bed profi le has been observed in all the experiments.Equilibrium confi guration of the fl ow fi eld and bed topography is reached after nearly 6 h, during which the system oscillates between two quite different confi gurations.Confi guration type I(Fig.1(a))is characterized by a long form of the scour with a relatively large scour hole in the condition without buried plates.For a hydraulic jump without a buried plate,the scour hole is almost a two-dimensional shape,while the ridge has a large planar curvature.Confi guration type II(Fig.1(b))is characterized by two scour holes in the presence of a buried plate. During the experiments,the sediment moved continuously until,after a time interval of about 6 h,a stable configuration was reached,possibly due to the absence of sediment feeding.

Fig.1.Sketch of flume without buried plate and with a single plate (Bateni,2004)(Huis the water head upstream and y2is the second depth of jump).

3.2.Scour morphology

Fig.2 shows the non-dimensional longitudinal scour hole profi les for different Froude numbers on horizontaland reverse bed slopes without buried plates.The non-dimensional longitudinal coordinate is x=L/h0.y=D/h0(where D is the depth of scour)is the non-dimensional transverse coordinate. The test data for the longitudinal profi le(Fig.2)show that the dimensions of the scour hole increase with the Froude number.

3.3.Depth and length of scour

The scour hole's evolution and the dune formation deflect the flow(this is recirculating fl ow).For a hydraulic jump,the scour hole is essentially three-dimensional,and it is strongly influenced by three additional parameters:the upstream Froude number,the bed slope S0,and the angle of the buried plateθ.

Fig.3 shows the non-dimensional longitudinal profi les in the horizontal bed with a single buried plate for the Froude numbers of 9,8,and 7.The buried plates were placed at distances of Lp=15 cm,Lp=30 cm,and Lp=45 cm from the apron with two angles,90°and 50°.As shown in Fig.3, the maximum scour hole for a single plate occurred upstream of the buried plate,and the usage of a single plate at the distance Lp=45 cm with an angle of 90°led to good results: the maximum depth and length of scour decreased by 50.0% and 46.3%,respectively,compared to the conditions without the buried plate.The best distance from a non-erodible bed is Lp=30 cm for a single plate with an angle of 50°as the maximum depth and length of scour decreased by 54.7%and50.9%,respectively,compared to the conditions without the buried plate.

Fig.2.Non-dimensionalscour hole profiles on horizontaland reverse bed slopes without buried plates.

Fig.3.Non-dimensional longitudinal profi les of scour holes in horizontal bed without buried plate and with single buried plate with different angles for different Fr1values.

According to the test data,the volume of transported sedimentin the conditionswith the buried plate decreased compared to the conditions without buried plates.The volume of transported sediment with a buried plate that has an angle of 50°is lowerthan thatwith a buried plate thathas an angle of90°.This can be explained by the factthatfl ow wavesgo upward when the buried plate is perpendicular or inclined.As a result,with a decrease of the angle of the buried plate,more turbulence jump waves are deflected upward,the capacity of transported sedimentdecreases,and the scour depth decreases as well.

Fig.4 shows the non-dimensional longitudinal profiles in the horizontal bed with two buried plates,for the Froude numbers of 9,8,and 7.The buried plates were placed at two different distances of Lp1=15 cm and Lp2=30 cm, Lp1=30 cm and Lp2=45 cm,and Lp1=15 cm and Lp2=45 cm from the apron with the two angles of 90°and 50°,where Lp1is the distance of the fi rst plate from the nonerodible bed,and Lp2is the distance of the second plate from the non-erodible bed.As shown in Fig.4,two scour holes were formed upstream of two buried plates but the scour hole dimensions decreased downstream.The usage of two plates at the suitable distances of Lp1=30 cm and Lp2=45 cm with an angle of 90°obtained good results:the maximum depth and length of scour decreased by 40.2%and 28.7%,respectively, compared to the conditions without the buried plate.Also,for two buried plates at Lp1=30 cm and Lp2=45 cm with an angle of 50°,the maximum depth and length of scour decreased by 43.9%and 58.0%compared to the conditions without the buried plate.

Fig.4.Non-dimensional profi les of scour hole in horizontal bed without buried plate and with two buried plates with different angles for different Fr1values.

Fig.5 shows the non-dimensional longitudinal profi les of the scour hole on the reverse bed slope(S0=-0.015)with a single buried plate and with two buried plates with two angles of 90°and 50°,for the Froude numbers of 6,5,and 4.The single buried plate was placed atdifferentdistances of Lp=15 and Lp=30 cm,and the two buried plates were placed at the distances of Lp1=15 cm and Lp2=30 cm,respectively.As shown in Fig.5,with the usage of two plates at the suitable distances of Lp1=15 cm and Lp2=30 cm with an angle of 90°,the maximum depth of scour decreased by 46.0% compared to the conditions without the buried plate.Also, good results were obtained with an angle of 90°for a single buried plate at the distance of Lp=15 cm,where the maximum length of scour decreased by 8.7%compared to the conditions without the buried plate.Good results were obtained with an angle of 50°for a single buried plate at a suitable distance of Lp=30 cm,where the maximum depth of scour decreased by 54.7%compared to the conditions without the buried plate.For two plates at the suitable distances of Lp1=15 cm and Lp2=30 cm the maximum length of scour decreased by 36.1%compared to the conditions without the buried plate.It can be seen from Fig.5 that the impact of two buried plates on reducing scour is better than that of a single plate.

The results from Figs.3-5 show that in a horizontal bed the usage of buried plates with an angle of 50°leads to a better performance in comparison with buried plates with an angle of 90°,so thatthe maximum depth and length of scour decreased by 60.4%and 20.0%,respectively,compared to the conditions with the plates with an angle of 90°.Also,for reverse bed slopes using buried plates with an angle of 50°,the maximum depth and length of scour decreased by 51.3%and 43.0%, respectively,compared to the conditions with plates with an angle of 90°.In other words,the direction of the buried plate can directly affect the depth and length of scour.With reduction of the angle of the buried plate,the depth and length of scour decrease.Itcan be seen from Figs.3-5 thatthe effect of the Froude number is also prominent.As the Froude number increases,the dimensions of the scour hole increase with other constant variables.

These testdata in the experiments withoutburied plates and those of Sarkar and Dey(2005)were compared(Table 1).The maximum depth and length of scour in the experiments of Sarkar and Dey(2005)were determined by Eqs.(3)and(4), respectively:

Fig.5.Longitudinal profiles of scour hole on reverse bed slope without buried plate and with single buried plate and with two plates with different angles for different Fr1values.

where Gs=ρs/ρ.

Acomparison between Eqs.(3)and(4)and the experimental data indicates the agreement between the values from the equations and the experimental data.It can be seen that the valuesofmaximumdepth ofscourusing Eq.(3)have differences of19.58%and 19.13%from the experimentaldata on horizontal and reverse bed slopes for Fr1=6,respectively.Also,the value of the maximum scour length using Eq.(4)has a difference of 7.74%from the experimentalresulton the reverse bed slope for Fr1=6.This is because the experiments of Sarkar and Dey(2005)were conducted for the Froude numbers of up to 5 and Eqs.(3)and(4)were established for Fr1＜5.

Table 1 Comparison of maximum depth and length of scour of present data and those from Sarkar and Dey(2005).

3.4.Multiple linear regressions

In order to develop a general equation for the profi le of scour,multiple linear regression(MLR)analysis for all experimental data was performed.The statistical models for Dsmax/h0and Le/h0were determined as follows:

Eq.(5)has a coeffi cient of determination R2of 0.95 and a standard error of the estimate(SEE)of 0.23 while Eq.(6)has an R2of 0.91 and a SEE of 3.4.Also,the values of statistical coeffi cients show that the initial Froude number Fr1of the fl ow has the greatest impact on geometrical features of bed profiles.

4.Conclusions

One of the main problems in the design of structure was represented as a scour hole located downstream of the structure toe.The erosive action of water causes local scour,which can undermine the work.It is evident that such structures can be designed only if the scour mechanism and geometrical parameters are well known.This paper gives valuable suggestions for quantifying and minimizing these problems.An experimentalanalysis of a hydraulic jump on a movable bed in a flume with differentdischarge levels has been presented.The main conclusions are as follows:

(1)The experiments have shown thatan equilibrium configuration isattained aftera transitory period with two quite different scour profi les.Configuration type Iis formed for the conditions without buried plates and type II is formed by the presence of buried plates.For a hydraulic jump without a buried plate the scourhole is almosta two-dimensionalshape,while the ridge has a large planar curvature.

(2)The maximum scour hole for the single plate occurs upstreamofthe buried plate.Fortwo buried plates,two scourholes are formed upstream of the buried plates butthe scour hole dimensions decreased downstream.

(3)Both the reverse bed slope and Froude number affectthe scour hole geometry in the stilling basin.The scour hole geometry is essentially three-dimensional.For identical hydraulic and geometric conditions,the reverse slope causes a decrease of the scour hole dimensions.The effect of the Froude number is also prominent.As the Froude number increases,the dimensions of scour hole increase under other constant variables.

(4)Measurements of the equilibrium free surface and bed profile have been theoretically interpreted in order to obtain predictive relationships for the amplitude of maximum scour at equilibrium.It is shown that geometrical features of the bed profile can be expressed as a function of the upstream initial Froude number,the bed slope,and the buried plate angle.

(5)In experiments without the buried plate and with an increasing initial Froude number,the maximum depth and length of scour downstream of the hydraulic jump is increased. In general,the impactof two buried plates on reducing scour is better than that of a single plate.

(6)In the horizontal bed slopes,the best distances of two buried plates are Lp1=30 cm and Lp2=45 cm with an angle of 50°.In this case the maximum depth and length of the scour have been reduced by 43.9%and 58.0%,respectively.Finally, with reduction of the angle of the buried plates the depth of scour is decreased.

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Received 7 November 2015;accepted 15 September 2016

Available online 6 January 2017

*Corresponding author.

E-mail address:akabbaspour@yahoo.com(Akram Abbaspour).

Peer review under responsibility of Hohai University.

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