Approximate Solution to Flow Problem under Dams

A general approximate solution to the flow problem under hydraulic structures resting on a homogeneous and isotropic pervious stratum is obtained. The proposed method is an improvement of Pavlovsky's method of fragments. The flow region is divided into simple fragments by the vertical lines through the ends of cutoffs and it is assumed that the images of these lines onto the plane of complex potential are similar to the images of proper vertical lines through the flow region of the flat bottom dam without cutoffs. On the basis of this assumption, the simple fragments of the flow region are transformed onto a proper auxiliary plane, in simple fragments. Consequently, the Christoffel-Schwarz transformation can be easily applied to give the solution to the problem. The solution gives expressions for discharge, potential distribution, and exit gradient. The results of a numerical verification of the proposed method are given.