SCOUR AROUND BRIDGE PIER

Abstract

When an alluvial stream is partially obstructed by a bridge pier, scour takes place in the vicinity of the pier. Estimation of this scour depth is a major concern of bridge engineers. The underestimation of scour depth leads to unsafe design while an overestimation leads to uneconomical design. There fore, estimation of anticipated maximum scour depth lor design discharge is essential. Scour around bridge piers is mainly affected by pier, flow and sediment characteristics. Out of these the effects of pier size and shape and of the approach flow angle on scour depth are fairly well understood. The effects of unsteadiness of flow and sediment nonuniformity and stratification on scour depth have not yet been studied in detail. Scour can be categorised as, (i) Clear-water scour; when the main flow does not carry sediment and (ii) Live-bed scour; when the main flow is sediment-laden. A large number of design relationships given by several inves tigators are in existence for both these types of scour. Out of these the relationships of Lacey, Shen, et al., Laursen and Toch, Jain and Ettema are more often recommended for use. However, the equilibrium scour depth which these relationships are expected to estimate is reached after a long period of scour activity. But the flood discharge which is used for the estimation of scour depth does not last that long. Therefore, the computation of temporal variation of scour depth is important from the practical point of view. It is in this background that the present investigation was taken up. An extensive set of experiments was conducted on uniform, nonuniform and stratified sediments with steady flows and on uniform sediments with unsteady (ill) flows. A fixed bed masonry flume having length 30 m, width 1.0 m and depth. 0.60 m was used. The arithmetic mean size of the uniform sediments used varied from 0.41 mm to 4.0 mm and those of nonuniform sediments were 0.50 mm and 0.71 mm. The geometric standard deviation of nonuniform sediments varied from 1.2 to 7.%. Stratified sediments having two layers with a thin coarser layer at the top were used; a constant thickness of 0.04 m of the top layer was used. Three circular piers having sizes of 0.065 m, 0.115 m and 0.17 m were used. Observations were taken on the variation of scour depth with time and on the equilibrium scour depth. The scour depths were observed using an electronic-bed profile indicator. In addition to these, all the data available in the literature on temporal variation and equilibrium scour depth in clear-water and sediment-transporting flows have been compiled. All the available data have first been used to verify the existing relation ships for the estimation of temporal variation and equilibrium scour depth. Since the existing relationships have not been found to produce satisfactory results, fresh analysis of the data has been carried out. For the purpose of modelling, the horseshoe vortex has been considered as the prime agent causing scour around bridge piers. The following points have been envisaged regarding the horseshoe vortex. i) Before scour begins at the pier horseshoe vortex is having circular shape in cross-section. ii) The shear stress under the horseshoe vortex is about four times the shear stress in the main flow. The following relationship holds good for the diameter of the horseshoe vortex, D : v Dy/D = 0.28 (b/D)0'85 Here D is the flow depth and b is the pier diameter. dv) lii) As the scour hole develops, the horseshoe vortex expands and sinks into it and its cross-sectional area increases to At, Thus A = A + A t OS where A = 0.785 D2 o v and A = Cross-sectional area of scour-hole s = D2 Cot 4>/2 Here <J> is angle of repose of bed material and D is the scour depth. iv) The relation between the shear stress at the pier at time t and that in the approach flow (,T ) can be written as; Cl T + = 4.0 (A /AJ . T p,t o t u Here C, is a constant. CLEAR WATER SCOUR Temporal Variation of Scour Depth in Uniform Sediments Given the shear stress T. that acts on a sediment particle near the pier at any instant, the time required by sediment particle to get scoured . is given by t# =C2d/p0;t uM Here Cy is another constant, d is the sediment size, p is average probability of movement at that instant, u# is the shear velocity at that instant and is equal to/r / p , Paintal gave following relationship for p ; (v) p +, 0.45(T I Ay d) 3A5 for (-T5D^t—) < 0.25 0,t p>l s s Here Ay =y -yf, Y is the specific weight of sediment and Yf is the specific weight of water. The analysis of data indicated that Cj =0.57 and C2 =0.05. Substituting these values in the above equations and rearranging the various terms the following equation is obtained; D2 T 1s3 u^ . t# 0.4^ . 1.7 5p.0.3 =2.1 5 (VtA-yMd; <^ •"d ) - 0.071 D U S This expression gives the time t# required for the scour depth to increase from D to D + d. This scheme predicted satisfactorily the temporal s s variation of scour depth for all the data. In order to compute the temporal variation of scour depth during unsteady flows, the hydrograph causing unsteadiness has been discretised into steady flow segments. The scheme described above is used separately for each segment. This scheme produced satisfactory results. Temporal Variation of Scour Depth in Nonuniform Sediments The effective size of nonuniform sediments has been defined as that uniform material size which gets scoured at the same rate as the nonuniform material under the given pier and flow condition. The effective size dp y for nonuniform sediments is obtained using the following equation; d /d.n = 0.925 o0-67 for a >1.124 eu 50 g g Here ° is the geometric standard deviation of the nonuniform material g 6 and d5Q is the sediment size such that 50% of the material is finer than this by weight. By using d , in place of d in the scheme for the temporal (vi) variation of scour depth in case of uniform sediments, one can predict the temporal variation of scour depth in nonuniform sediments. This scheme produced results with reasonable accuracy for all the data. Temporal Variation of Scour Depth in Stratified Sediments The scheme for the description of temporal variation of scour depth in uniform sediments gives the variation of scour depth with time in the top layer of the stratified sediment. To obtain the temporal variation of scour depth in the bottom layer of the stratified sediment, the effective size of the bottom layer has been defined as the uniform material size which gets scoured at the same rate as the lower layer of the stratified sediment. The following equation gives effective size d of the lower layer of the stratified sediment; d /d. =0.687 (d./dj0,77 (1 +h/D ,)0'7, for d./d. >1.6 es 1 1 £ sc l i £ Here d, is sediment size of top layer, d? is sediment size of bottom layer, h is thickness of top layer, D . is equilibrium scour depth of top coarse material. Use of d in place of d in the scheme for temporal variation es of scour depth in case of uniform sediments gives the variation of scour depth with time in the lower layer of the stratified sediments. This scheme gave results with reasonable accuracy for all the data. Equilibrium Scour Depth Based on the nondimensional parameters identified through the theoretical analysis the following relationship has been proposed for equilibrium scour depth D , in uniform sediments; U2 - U2 0.4 -0.3 Dsc/d =0.66 (b/d)0'75 (D/d)°-16 (Ay d/ pC ) (Vll) U2 -O.H 0.16 B_b Here £ _ K2 (b/d) (D/d) and a = —— Ic d Here B is the spacing between piers and Uc is the velocity of main flow for which scour depth is zero. Use of deu in place of d in these equations gives the equilibrium scour depth in case of nonuniform sediments. LIVE-BED SCOUR Temporal Variation of Scour Depth The time t^, required for the single sediment particle to get scoured can be computed using the scheme described for the temporal variation of scour depth in nonuniform sediment. During the time t^., the sediment load entering into the scour holes per unit width has been computed using Engelund- Hansen equation. Thus the net scour depth at the end of time t# is known. This scheme has been used for the computation of temporal variation of mean scour depth (i.e., neglecting the fluctuations due to the movement of bed forms). This scheme has also been used for the computation of temporal variation of scour depth in sediment transporting unsteady flows. For this purpose the hydrograph causing unsteadiness has been discretised in steady segments. The temporal variation of scour depth has been computed separately in each segment. Equilibrium Scour Depth The nondimensional parameters affecting the equilibrium scour depth D , in live-bed scour, have been identified through the theoretical analysis. se The following equation has been obtained for the equilibrium scour depth; = 0.88 (b/d) U'D/ (D/d) se „ ™ „ , ,x 0.67 ^iJ% 0.40 ..-0.30 This equation yields satisfactory results for all the data.