SCOUR AROUND PERMEABLE SPURS

Abstract

Permeable spurs of various types have been widely used in river training works the world over for flow guidance, bank protection, land reclamation and as an aid in navigation. Spur failure, often, occurs because of the scouring action at the spur nose. Hence, realistic estimation of the maximum scour depth around spurs is important for their safe and economic design. Most of the effort on scour prediction has centered around solid spurs/abutments and surprisingly very little information is available on scour around permeable spurs. Therefore, the present investigation was taken up to study the influence of permeability of the spur on scour depth and to develop a predictor/mathematical model for scour estimation around spurs considering all important parameters. Most of the experimental data on scour around spurs and abutments are available for the case of solid ones. Scour prediction equations for solid spurs/abutments, mostly empirical, have been given by different workers (2, 28, 33, 69, 79, 101, 126, 133). Kothyari et al. (56) and Sampath Kumar et al. (109) presented mathematical models and computer algorithms for the estimation of scour depth around acylindrical pier, considering the primary vortex in front of the pier to be the prime agent causing scour. However, no mathematical model is available for permeable spurs. An analogy in the mechanism of flow and scouring at bridge piers and abutments has been well recognized (51, 68, 79, 114). Also, from the flow point of view, since the scour at abutments is similar in character to that around spurs, the same analogy exists between bridge piers and spurs. It is recognized that in the case of apier, the vortex system (due to adverse pressure gradient, resulting in a three dimensional boundary layer separation at the bed) results in scouring of bed sediment. For the case of abutment, similar system has been identified as the equivalent flow structure, causing scour (51, 59, 125, 132). In the present study, flow in a mobile bed channel of width B past a spur of length b and permeability P is considered. In such a situation and depending upon the permeability of spur, a part of the flow escapes through the body of the spur and rest through the constricted channel. Accordingly, one should expect the equilibrium scour depth D'sm around the spur to depend on P and blockage ratio b/B. Basically the flow in open channel is governed by gravity and therefore Froude number of flow, Fr (=U/ VgD) is an important parameter. Here Uand Dare the mean velocity and depth of flow respectively. And if the flow occurs in a nonuniform sediment of median size d and gradation og, additional parameters viz. d/D and og also come into picture. Considering the fact that the horseshoe vortex system results from an upstream flow separation, which is a viscous phenomenon, some previous workers like Roper et al.(108), Shen et al.(115), Muzzammil et al.(84) and Ramu (101) included Reynolds number in some form or the other in their analyses of scour around piers/spurs. Accordingly it has been decided herein to include spur (body) Reynolds number in the form Reb (=Ub/v) tentatively. Here v is the kinematic viscosity of the fluid. The justification or otherwise of its inclusion will be ascertained by the analysis of scour data available in literature. Permeable spurs in the field may be of varied composition and width, with openings of different size and distribution. Since all these factors affect the flow through the spur, its permeability may be taken to represent them. For simplicity, the case of perforated plates as spurs, has been considered in the present study. Since the plate thickness is small, the openings are direct from upstream to the downstream side, or the wake side of the spur, offering less resistance to flow through them. It is felt that the ratio of perforated area to the total area of the plate alone will determine the permeability. Hence this ratio is considered to represent permeability. The present study concerns a single permeable spur at 90° angle on a straight reach under unsubmerged conditions. Accordingly, the parameters signifying spacing of spurs L/b, curvature of channel r/B, inclination of spur 0, and its submergence H/D, though important, have not been considered. Thus the various parameters considered to affect the equilibrium scour depth D'sm around such a spur are the permeability (P), blockage ratio (b/B), Froude number of flow (Fr), relative sediment size (d/D), sediment gradation (a.) and spur (body) Reynolds number Reb, i.e. mathematically, D'sm -—=f, (P, b/B, Fr, d/D, ag,Reb) (1) D In fact, since a solid spur is a particular case of a permeable spur when P=0, Eq.(l) is a common relation for both permeable and solid spurs. Here the word "common" is used to include permeable and solid spurs. For a solid spur, Eq.(l) may be written as D sin =f, (b/B, F„ d/D, og, Reb) (la) l2 D Dsm here being the equilibrium scour depth around a solid spur. Under the premise that the effects of b/B, Fr, d/D, og and Rcb are the same on solid and permeable spurs, Eqs. (1) and (la) can be written as : D'sin~=F(P) (2) D,m in The above premise needs to be verified by experimental data of solid and permeable spurs. Also there is a need to develop a common predictor/mathematical model for the estimation of scour depth around a spur in general, considering permeability, and all other important parameters, identified as above. Thus the objectives of the present study are : • to test the available predictors for scour depth around solid spurs with all the data available in literature. • to collect experimental data of equilibrium and temporal scour for different flow conditions and blockage ratios, using a single permeable spur of varying permeabilities. Some runs may also be included on solid spurs to verify the experimental set-up. • to identify the relative importance of permeability on scour depth. • to develop a common predictor, valid for both solid and permeable spurs, considering all other important parameters and using the data of solid spurs available in literature and those of permeable spurs collected in the present study. • to study the flow structure around a spur qualitatively by some visualisation techniques. • to develop a mathematical model for scour depth prediction around a spur, solid as well as permeable, similar to that available in literature for a cylindrical pier. In order to evaluate the performance of some existing predictors for equilibrium scour depth around solid spurs viz. given by Ahmad (2), Ramu (101), Tyagi (126), Zaghloul and McCorquodale (133), Froehlich (28), Lim (69) and Melville (79), the predictors were tested with the data available in English literature. Out of the parameters included in Eq.(la), for solid spurs, different people considered different sets of parameters in their predictors. To mention in particular, Ramu included Reynolds number also in his predictor. IV A regression analysis was carried out between the observed values and those computed by different predictors to determine their relative performance. Based on the statistical parameters viz. R2 , regression coefficient, its standard error, t-value and standard error of estimate, the predictors have been compared and placed in order of their predictive performance as : Melville, Froehlich, Ramu, Zaghloul and McCorquodale, Tyagi, Lim and Ahmad. However, it was noticed that more the influencing parameters considered in the predictor, the better is its performance. It was also noticed from the plots showing comparison of measured and computed scour depths, that the scatter of data in general is high. While the scatter of data is largely on one side of the best fit line in case of predictors due to Melville, Froehlich, Zaghloul and McCorquodale, Lim and Ahmad, thus overpredicting scour depth, it is more even on both sides of the line in the case of predictors due to Ramu and Tyagi. For the development of a common predictor, there is a need of data of solid as well as permeable spurs. While the former is available in literature, it is proposed to make the latter available from out of the present study. Accordingly, experimental studies on permeable spurs were carried out in a tilting bed hydraulic flume 10 m long, 1 m wide and 0.6 m deep installed in the hydraulics laboratory of Central Soil and Water Conservation Research and Training Institute, Dehradun, India. Perforated steel plates were used as the permeable spurs with permeabilities of 0, 19.6, 28.3, 38.5 and 50.2 per cent by drilling holes of 5 to 8 mm diameter at 1 cm centre to centre spacing in rows and columns. The permeability herein is defined as the ratio of the area of the holes to the total area of the plate. Three spur lengths corresponding to blockage ratio of 0.1, 0.2 and 0.3 were used. A nonuniform river- bed material (og=1.35) was used in all the experimental runs. The experiments were conducted under clear- water conditions, for three flow depths corresponding to (tb/tc) = 0.9, 0.75 and 0.6. Here tb is the shear stress on the channel bed and x is the Shields' critical shear stress for the sediment used. A uniform bed slope of 0.083 per cent was used throughout the experimentation. Temporal scour depths were recorded using an electronic bed profile indicator, while the bed levels at equilibrium scour condition were used to obtain the maximum scour depth. In order to verify the premise involved in obtaining Eq.(2) plots of D'sm/Dsm versus P were made, using the data collected in the present study. They all revealed that the premise is not well founded, i.e. D'sm/Dsm ratio is also affected by parameters other than permeability viz. b/B, Frand d/D, inspite of the fact that permeability is the most significant of all the parameters. Accordingly, the scope of dependence of D'sm/Dsm may be enlarged and Eq.(2) may be written as D'sm ---= f (P, b/B, Fr, d/D, og,Reb) (3) D.„, Using the past clear-water data of solid spurs along with the present data of permeable spurs (in all 205 data points), regression analysis of the relation (3) resulted as D'sm ----- = 1.1 (1-P)0782 (b/B)0'027 (Fr)0'017 (d/D)"0013 (ag)-0018 (Reb)-0006 ...(4) D,m Further, the following non-linear equation was found suitable for D'sm/Dsm in terms of significant parameters D'sm ----- = 1.0 (1-P)0776 (b/B)0020 (Fr)0009 (d/D)"0011 ...(5) D.„ VI Using the above mentioned data points, the regression analysis for the relationship given by Eq.(l) resulted as D'sm =117.0 (1-P)092 (b/B)066 (Fr)102 (d/D)"025 (og)"2-58 (Reb)"0-25 ...(6) D The most significant parameters affecting the equilibrium scour depth in Eq.(6) in the order are, og , Fr and P. Next is b/B followed by d/D and Reb The higher correlation with og is understandable in that the armoured layer formed in nonuniform material helps to limit the erosion from the scour hole and to attain the equilibrium scour depth early. A close look at Eqs.(5) and (6) shows that the permeability P is more or less equally significant for D'sm/Dsm and D'sm/D, whereas the other parameters are more significant for D'sm/D than for D'sm/Dsm. To study the flow structure around a spur qualitatively, flow visualisation techniques using wet paint, thread and aluminium powder were attempted. In view of the anaolgy of flow structure and mechanism of scouring at bridge piers and abutments/spurs, it has been decided to take a cue from Kothyari et al.'s (56) mathematical model for bridge piers towards developing one for the spurs. They presented an algorithm for computation of temporal and finally the equilibrium scour depth around bridge piers. The following relation was used by them for the computation of vortex, diameter, Dv Dv/D=0.28(b, /D)0-85 (7) where b; = pier diameter ; and D = flow depth Vll In the above model, the ratio of nose shear at the pier to approach bed shear, Xpo/Tb , at the begining of scour i.e. time t =0, is assumed to be constant at 4.0. However, for spurs this ratio may be expected to be afunction of b/B and P, i.e. Tp,0/rb = f(b/B,P) Rajaratnam and Nwachukwu (98) reported the ratios tp,o/tb=3.0 and 5.0 for b/B=0.083 and 0.167 respectively for solid spurs at time t=0. Using these limited data and the condition of tp,A=1.0 for b/B=0.0 and P=0.0, the following equation was obtained for Eq.(8) v/Tb=[l+12.87(b/B)a70(l-P)] Eq. (9) implies linear variation of tp>0/tb with P. .(8) .(9) Introducing other terms as for bridge pier, as the scour progresses, the corresponding temporal variation of nose shear stress for spur, tp,t may be given by Tpt =[1 +12.87(b/B)a70 (1-P)] tb (A0/At)c, (10) where A0 =cross sectional area of the primary vortex at time t=0 ; A=cross sectional area of the primary vortex at any time t; and Q=a coefficient adopted the same as that in the bridge pier model i.e. 0.57, assuming that the progressive development of the scour hole is similar in case of spur also. As A, » A0 , tp,t becomes small. Obviously, the scour would cease when value of tp,t tends to approach tc , the critical shear stress of the bed material. Regarding the development of arelationship for vortex diameter, Dv , Kothyari et al. (56) related it with pier diameter whereas it was closely related with Reynolds number (Reb) by Roper et al. (108), Shen et al. (115) and Muzzammil et al. (84). Therefore, in the case of spurs Dv can be expected to be a function of b/B, P and Reb. In order to develop a relationship for Dv, the equilibrium scour depth data of solid spurs available in literature and of permeable spurs obtained in the present study, is used. The value of Dv was obtained by trial, such that the computed equilibrium scour depth equalled the measured one. Using these data of Dv, the following predictor, in line with the above discussion, was developed for the case of solid and permeable spurs Dv ----- = 10.32 (b/B)a58 (1-P)081 Reb"0-18 (ID D Evidently, the dependence of Dv/D on Reb in Eq.(ll) is small but not insignificant. Eq.(7) is now replaced by Eq.(ll) in the spur model. Temporal scour depths were computed for the present data using the model so developed for spurs and compared with the experimental data of present study. The agreement was found good. The model was also tested using the available clear-water solid spur data of other workers and was found to predict the equilibrium scour depth satisfactorily within 40 per cent confidence limits.