Flow Under Weir on Scoured Bed

An approximate analysis for seepage flow under a weir, resting on isotropic porous medium of infinite depth, with a vertical sheet pile at the toe and a segmental circular scour, is obtained using conformal mapping techniques. An exact analysis for semi-circular scour, using conformal mapping, is also given. The results of approximate and exact analysis for semi-circular scour are compared. From the analysis it is shown that the maximum exit gradient is increased by about 75 percent in case of semi-circular scour. For semi-circular scour profile, as s/b increases, where s is the depth of sheet pile and b is width of the floor, the point of maximum exit gradient shifts away from the sheet pile. The exit gradient distribution obtained from approximate analysis is very close to the one given by the exact analysis, but the potentials at salient points under the apron obtained from the two analysis compared closely for values of s/b up to 0.1. The maximum reduction in potential for a semi-circular scour of l/b = 1/8 is about 48 percent, where 2l is the length of scour.