SCOUR AROUND CIRCULAR COMPOUND BRIDGE PIERS

Abstract

A main cause of bridge failure is scour by the flow around its piers and abutments. The correct estimation of scour extent and its depth at bridge sites therefore continues to be a major concern for the hydraulic engineers. The circular pier resting on larger diameter circular well or caisson is termed as the circular compound pier. Mostly compound pier foundations are adopted for use in bridges of the Indian sub-continent. In India, presently the design depth of scour for bridge piers is determined as per the procedure explained in IRC: 78, (2000) and IRC: 5, (1998). The procedure explained in these codes is based on Lacey's approach for regime flow depth estimation. However, the Lacey's method gives no cognizance to varying pier geometries such as compound pier, piers on piles and platforms. A large number of investigations have been carried out over past five decades, mostly focused on the development of the relationship for computation of equilibrium scour depth around the circular uniform bridge pier. Only a few investigators (Chabert and Engeldinger, 1956; Tsujimoto et al, 1987; Jones et al, 1992; Fotherby and Jones, 1993; Melville and Raudkivi, 1996; Coleman, 2005) have studied the effect of foundation geometry on scour. The modern trend in scour investigation is to study the temporal variation of scour rather than the equilibrium scour that occurs after very long time period of scour activity. Only little effort has been made so far to study the temporal variation of scour around circular compound bridge piers. Thus there is need for investigation regarding the temporal variation of the scour around circular compound bridge piers. A few studies have been made on study of flow pattern around the circular uniform pier placed in a scour hole (Melville and Raudkivi, 1977; Dey et al, (1995); Ahmed and Rajaratnam, 1998; Graf and Istiarto, 2002; Muzzammil and Gangadhariah, 2003 and Dey and Raikar, 2007). The process of scour and flow structure around circular compound bridge pier is however not studied in detail as yet. The present study was taken up to fulfill these gaps inknowledge. EXPERIMENTAL SET-UP AND PROCEDURE The experiments were conducted in a30mlong, 1mwide rectangular channel.Aworking section was located 12mdownstream ofthe flume entrance, having the dimensions; length - 3m, depth =0.6mand width =1m. Two series ofexperiments were conducted. First series of experiments was conducted to investigate the three-dimensional flow field around the piers.Atotal of6experiment runs were performed for this purpose. Two experimental runs (UPRB and NUPRB) were performed with piers placed on rigid bed. In four experimental runs namely UPSH, NUPSH 1, NUPSH 2, and NUPSH3the scour hole was allowed to develop before taking observations for flow field. The circular uniform pier used had apier diameter of 114 mm while compound pier had pier diameter equal to 114 mm and foundation diameter equal to 210 mm. In the series with circular compound pier, the top of the foundation level was placed at different elevations with respect to original channel bed level i.e. above the bed level (Y=-b. /10) for run NUSPSH2 and NUPRB, at the bed level (Y= 0) for nmNUPSH 1and below the bed level (F - b. /10) forNUPSH3. Here b. is the diameter of the foundation and 7is the difference in elevation of the top of footing and the general bed level of the channel; 7is positive below the channel bed. The experiments were conducted under clear-water scour condition. On the rigid channel bed and also after stabilizing the geometry of scour hole for each experimental run, the instantaneous three-dimensional velocity components were measured with the help of the Acoustic Doppler Velocimeter (ADV) at seven different vertical planes in radial directions at a = 0°, 30°, 60°, 90°, 120°, 150° and 180° from the flow. Here a is the angular direction of the plane with a = 0° corresponding to upstream central line of the flow. Velocity distributions at eight vertical profiles at different radial distances (r) from the centre of pier i.e. r - 100,140, 170, 200,250, 300, 350 and 400 mm, were obtained at each plane. In second series of experiments, the study of the temporal variation of scour depth around circular uniform and compound piers was conducted. Three circular piers of uniform section having diameters of 48 mm, 88 mm and 114 mm and six set of circular compound piers having ratio of foundation diameter to pier diameter as 1.84, 1.89, 2.38, 2.81, 3.46 and 4.38 were used as models. The uniform sand having particle size dso-OA mm and 1.8 mm and specific weight 2.65 were used as sediment in this series of runs. The position of top of footing with respect to general bed level is changed as7 = -bt /10, 0 and Y = b, /10 for each set. FLOW FIELD AROUND CIRCULAR PIERS The measured velocity data depict a rotating flow inside the scour hole upstream of the pier and a downward flow in the upstream face close to the pier and near the base of scour hole for all experimental runs involving the scour hole. However size of the principal vortex was noticed to be larger while top surface of the footing is above general bed level of the channel than for circular uniform pier. This is attributed to larger exposure of the footing to the flow. Comparatively smaller size of principal vortex in the scour hole was noticed than that for uniform pier when top surface of the footing was below the general bed level of the channel due to the vortex supporting effect of the footing. This shall cause in asmaller scour depth at the compound pier having top surface of the footing below the general bed level of the channel as compared to that at circular uniform pier for given flow and sediment conditions. The vortex formed at planes with a=30° and 60° was noticed to have aweaker strength than at the plane with a=0° for all experimental runs involving scour hole. The vortex on the plane at a=90° was also noticed to be relatively smaller in size. It is noticed that around the pier and within the scoured region all three components of turbulence intensity and components of Reynolds' stress are higher in magnitude when the top surface ofthe footing is exposed. The observations made in the upstream plane revealed that in the scoured region the bed shear stress is greatly reduced from that in the rigid bed condition. However in case of compound pier runs, over the top of the foundation where scour is not possible, the magnitude ofthe shear stress remains more or less the same as in case ofrigid bed runs. MATHEMATICAL MODELLING FOR TEMPORAL VARIATION OF SCOUR AROUND CIRCULAR UNIFORM PIER The horseshoe vortex has been considered as the basic mechanism for scour around the bridge pier (Kothyari et al., 1992 aand b). The algorithm of Kothyari et al., (1992 a) for computation of temporal variation of scour depth around circular uniform bridge pier is updated with the help ofdata collected in the present study and the similar data collected from the recent literature. The applicability of relation for computation of cross-sectional area of principal vortex of the horseshoe vortex system at any time tduring scour development (Kothyari et al., 1992 a) and relation for computation of shear stress at the pier nose at any time tafter IV start of the scour (Kothyari et al, 1992 a) is validated with the help of experimental data of present study and data of other investigators. Applicability of these equations is also validated for the case of circular compound piers with the help of experimental data of present study. Estimation of Time Required for Removal of a Single Sediment Particle The following relations are proposed for estimation of time required f, for removal of sediment particle following Paintal, (1971) and thus u = c d P0< «., d u.t =1^- \Pf with K =0.8(rJPot =0.181n(r. J+0.17 ; W^o.5 ; W>o.5 Here rtpt is the non dimensional shear stress and is equal to r r ^ pt ys and yf are the specific weight of the sediment and fluid respectively, Pot = average probability of movement of the particle at time t and r is the bed shear stress at the pier nose at time / and d is the size of uniform sediment, c is a parameter, u,t = the shear velocity at time t and pf = density of fluid. On the basis of data analysis, that following relationships are proposed for variation of the parameter c: . Ay, =ys-yf, Vft*x" c = 2.2*10" V v J ; A<25 c=2.5*10-'°(A)3( ru,td^ I-2/.N0.1 V«y 25< A £80 c=9.6*10"I2(A)44 r^0.3 v«y ; A>80 Here bis the diameter of the pier, his the depth of flow, vis the kinematic viscosity of fluid and A is the dimensionless sediment size. The above modifications have been applied in the algorithm of Kothyari et al, (1992 a), which is then used for computation oftemporal variation of scour around circular uniform pier. MATHEMATICAL MODELLING FOR TEMPORAL VARIATION OF SCOUR AROUND CIRCULAR COMPOUND PIER SCOUR The updated algorithm of Kothyari et al, (1992 a) for computation oftemporal variation of scour depth around circular uniform pier has been further developed herein for modelling of temporal variation of scour around the circular compound bridge piers. The mathematical model for computation of scour depth has been developed taking into account the concept of effective pier diameter. The "effective diameter" of the circular compound pier is defined herein for scour computations as that diameter of the uniform circular pier which shall produce same temporal variation of scour depth as the circular compound pier. The effective diameter of a circular compound pier is computed as: (Melville andRaudkivi, 1996): VI 'h + Y^ b=b + b. fdsl-Y^ \ds,+h Here be is the effective diameter of the circular compound pier, b, is the diameter of the foundation, dst is the depth of scour below the initial bed level at time t. When top of bridge foundation is above generalbed level (negative Yvalues), the uniformpier diameter is replaced by the effective diameter of a circular compound pier and the temporal variation of the scour depth around circular compound piers can be computed by using the proposed algorithm for computation of temporal variation of scour depth around circular uniform piers by using be instead of b in the computations. When the 7 values were positive, i.e. the top of the footing was placed below the channel bed, the circular compound pier acts as a simple circular pier having diameter b and temporal variation of the scour depth can be computed by the method for computation of temporal variation of scour depth around circular uniform pier, as long as the scour depth dst < 7. In case when depth of scour at time t becomes equal to the difference between the initial bed level and top level of foundation i.e. dst ~ 7 (the case 7 = zero is also covered under this scenario), the principal vortex rests on the top of foundation upstream to nose of the pier. However, the principal vortex continues to expand due to scouring activity on the sides and downstream of the foundation. This expansion of principal vortex during this scenario is considered in the present study to occur in the same manner as it would have occurred in case of a uniform circular pier. Vll The lateral extent of scour hole We, (while the principal vortex of horseshoe vortex reaches at the outer edge of the foundation) under such condition is computed by the following equation W = K-b + • Tan<f> Here $is the angle of repose of sediment. The rate Pat which principal vortex expands over the top ofthe foundation and reaches to the value of We is given by p_(Y+ClJ.d\ K Tan<f> J Here Jis an integer counter, the value of which is unity while the expansion of principal vortex initiates on the top surface of the foundation and c, is acoefficient depending on the hydraulic characteristics of the stream bed. Analysis of data indicated Cj = 0.8 for hydraulically smooth boundaries i.e. whileA<25, whereas c, =1 for the rough surfaces and the surfaces in transition i.e. while A > 25. When the principal vortex has reached the outer edge of the foundation on upstream ofthe pier nose; the scour depth begins to increase beyond the value of7and for this scenario dst >Y. The foundation is exposed in that case and the methodology for computation oftemporal variation ofscour depth proposed for such case is similar to the case while 7 is negative. RESULTS AND DISCUSSIONS The mathematical model proposed for temporal variation of scour around uniform and compound circular piers was applied to large data set from present study and the literature. Vlll The updated model of Kothyari et al, (1992 a) for temporal variation of scour depth around circular uniform piers has produced satisfactory results for the data ofpresent study and those of most of the previous investigators. The mathematical model developed for computation of temporal variation of scour depth around the circular compound bridge pier by using the concept of effective diameter is used in computation of temporal variation of scour depth. Reasonably good agreement between the corresponding observed and computed values of scour depth was noticed for almost all the data of present study and those of Melville andRaudkivi, (1996). It may be mentioned that no other investigation is reported as yet on the topic of temporal variation of scour depth around the circular compound piers. The mathematical model developed herein has potential of application for computation of temporal variation scourdepth around prototype circular compound bridge piers duringthe passage of the flood hydrograph. IX