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45 The local scour data for long piers skewed to the flow is extremely limited. Most of the scour equations use similar methods to predict the effects of skewness on the equilibrium scour depth. These equations use either the curves proposed by Laursen and Toch (1956) to correct for flow skew angle or equations based on these curves. HEC-18 recommends adjust- ing the scour depth computed for zero skew angle by the expression in Equation 43. where L is the pier length in the flow direction, α is the flow skew angle relative to the axis of the pier, and a is the width of the pier. The term in the parentheses is basically the ratio of the projected width to the pier width. This term is multiplied by the scour depth computed for zero skew angle to obtain the total scour. Sheppard and Renna (2005) use a different approach where the projected width replaces the pier width in the equations as shown in Equation 44 and Figure 47. Laursen and Toch (1956) do not give the sources for the data that was used to develop the curves in their paper. Schneibleâs doctoral dissertation (1951) contains the results from labo- ratory tests performed with piers of various shapes (oblong, elliptical, and lenticular) and skew angles from 0° to 30°. Plots of normalized scour depth versus flow skew angle are given in Figures 48 and 49 for different pier lengths. The measured a W L W * ( )= ( ) + ( )cos sinα α 44 K L a 2 0 65 43= ( ) + ( )âââ ââ âcos sinα α . , ( ) and predicted scour depths are normalized by Schneibleâs measured scour depth for a circular pile whose diameter was equal to the width of his piers (0.2 ft). The equations used for the predictions in Figures 48 and 49 are from Sheppard and Renna (2005) and HEC-18. Note that both equations over- predict the effect of skewness and pile shape for all skew angles (including the zero angle). The HEC-18 curves for square and sharp piles are discontinuous because the shape factor applies only for skew angles less than 5°. Mostafa (1994) provides another data set for skewed piers. In these experiments, measurements were repeated at different water depths. The skewness effect was found to be a function of the relative water depth (y1/a). These measurements are shown in Figure 50 along with the predictions by the HEC-18 and the Sheppard and Renna (2005) methods. In the HEC-18 method, like other methods based on Laursen and Toch (1956), the skewness factor is not a function of water depth; therefore, only one HEC-18 prediction is plotted. The Sheppard and Renna method takes the effect of depth on the skewness factor into account so two predictions are shown. Note that the Sheppard and Renna method correctly predicts the fact that the skewness effect increases with increasing water depth. Both methods are conservative for skew angles smaller than 45°, but underpredict for angles between 45° and 85°. Flow skew angles greater than 45° are, however, rare. Ettema et al. (1998) showed the effect of pier length on scour (Figure 51). Pier length also has a bearing on scour depth predictions for skewed piers. The effect of pier length is not taken into account by either of the skew angle methods. Note that for very short (in the flow direction) piers the scour depth increases. C H A P T E R 6 Scour at Piers Skewed to the Flow
46 0 5 10 15 20 25 30 0.8 1 1.2 1.4 1.6 1.8 2 Flow Skew Angle (degrees) y s /y s (α = 0, c irc u la r pi le ) Oblong-Schneible Elliptical-Schneible Lenticular-Schneible Sheppard Square HEC-18 square HEC-18 round Lenticular Elliptical Oblong HEC-18 sharp a = 0.2 ft L = 0.6 ft a = pier width, L = pier length Figure 48. Predicted and measured scour depths as a function of flow skew angle. 0 5 10 15 20 25 30 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 Flow Skew Angle (degrees) y s /y s (α = 0, c irc u la r pi le ) Oblong-Schneible Elliptical-Schneible Lenticular-Schneible Sheppard Square HEC-18 square a = 0.2 ft L = 0.4 ft Lenticular Elliptical Oblong a = pier width, L = pier length Figure 49. Predicted and measured scour depths as a function of flow skew angle. Figure 47. Diagram showing effective width of a long pier skewed to the flow (Sheppard and Renna 2005).
47 0 10 20 30 40 50 60 70 80 90 1 1.5 2 2.5 3 3.5 Flow Skew Angle (degrees) y s /y s (α = 0) Sheppard y1/a=3 Sheppard y1/a=10 HEC-18 Mostafa y1/a=3 Mostafa y1/a=10 Figure 50. Normalized scour depth versus flow skew angle for rectangular piers [based on data from Mostafa (1994)]. 10 -2 10 -1 10 0 10 1 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 L/a y s /a a = pier width, L = pier length Figure 51. Effect of pier length on scour for flows with zero skew angle [reproduced from Ettema et al. (1998)].
