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45 CHAPTER 6 Scour at Piers Skewed to the Flow The local scour data for long piers skewed to the flow is and predicted scour depths are normalized by Schneible's extremely limited. Most of the scour equations use similar measured scour depth for a circular pile whose diameter was methods to predict the effects of skewness on the equilibrium equal to the width of his piers (0.2 ft). The equations used for scour depth. These equations use either the curves proposed the predictions in Figures 48 and 49 are from Sheppard and by Laursen and Toch (1956) to correct for flow skew angle or Renna (2005) and HEC-18. Note that both equations over- equations based on these curves. HEC-18 recommends adjust- predict the effect of skewness and pile shape for all skew angles ing the scour depth computed for zero skew angle by the (including the zero angle). The HEC-18 curves for square and expression in Equation 43. sharp piles are discontinuous because the shape factor applies only for skew angles less than 5. 0.65 L Mostafa (1994) provides another data set for skewed piers. K 2 = cos ( ) + sin ( ) , (43) a In these experiments, measurements were repeated at different water depths. The skewness effect was found to be a function where L is the pier length in the flow direction, is the flow of the relative water depth (y1/a). These measurements are skew angle relative to the axis of the pier, and a is the width of shown in Figure 50 along with the predictions by the HEC-18 the pier. The term in the parentheses is basically the ratio of and the Sheppard and Renna (2005) methods. In the HEC-18 the projected width to the pier width. This term is multiplied method, like other methods based on Laursen and Toch (1956), by the scour depth computed for zero skew angle to obtain the skewness factor is not a function of water depth; therefore, the total scour. Sheppard and Renna (2005) use a different only one HEC-18 prediction is plotted. The Sheppard and approach where the projected width replaces the pier width Renna method takes the effect of depth on the skewness factor in the equations as shown in Equation 44 and Figure 47. into account so two predictions are shown. Note that the Sheppard and Renna method correctly predicts the fact that W cos ( ) + L sin ( ) the skewness effect increases with increasing water depth. Both a* = (44) W methods are conservative for skew angles smaller than 45, but underpredict for angles between 45 and 85. Flow skew Laursen and Toch (1956) do not give the sources for the data angles greater than 45 are, however, rare. that was used to develop the curves in their paper. Schneible's Ettema et al. (1998) showed the effect of pier length on doctoral dissertation (1951) contains the results from labo- scour (Figure 51). Pier length also has a bearing on scour ratory tests performed with piers of various shapes (oblong, depth predictions for skewed piers. The effect of pier length elliptical, and lenticular) and skew angles from 0 to 30. is not taken into account by either of the skew angle methods. Plots of normalized scour depth versus flow skew angle are given Note that for very short (in the flow direction) piers the scour in Figures 48 and 49 for different pier lengths. The measured depth increases.

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46 Figure 47. Diagram showing effective width of a long pier skewed to the flow (Sheppard and Renna 2005). 2 1.8 Oblong ys/ys ( = 0, circular pile) Elliptical 1.6 Lenticular 1.4 Oblong-Schneible 1.2 Elliptical-Schneible Lenticular-Schneible 1 Sheppard Square HEC-18 square 0.8 a = 0.2 ft HEC-18 round L = 0.6 ft HEC-18 sharp 0 5 10 15 20 25 30 Flow Skew Angle (degrees) a = pier width, L = pier length Figure 48. Predicted and measured scour depths as a function of flow skew angle. 1.6 1.5 Oblong ys/ys ( = 0, circular pile) 1.4 Elliptical Lenticular 1.3 1.2 1.1 Oblong-Schneible 1 Elliptical-Schneible Lenticular-Schneible 0.9 a = 0.2 ft Sheppard Square L = 0.4 ft HEC-18 square 0.8 0 5 10 15 20 25 30 Flow Skew Angle (degrees) a = pier width, L = pier length Figure 49. Predicted and measured scour depths as a function of flow skew angle.

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47 3.5 Sheppard y1/a=3 Sheppard y1/a=10 3 HEC-18 Mostafa y1/a=3 ys/ys( =0) 2.5 Mostafa y1/a=10 2 1.5 1 0 10 20 30 40 50 60 70 80 90 Flow Skew Angle (degrees) Figure 50. Normalized scour depth versus flow skew angle for rectangular piers [based on data from Mostafa (1994)]. 2.8 2.7 2.6 2.5 ys/a 2.4 2.3 2.2 2.1 2 -2 -1 0 1 10 10 10 10 L/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)].