Determination of the shape of the downstream slope of an earth-fill dam from the seepage strength conditions at the face

Abstract

Inverse boundary-value problems of determining the slope of an earth-fill dam (or its core) for which the local seepage strength conditions are exactly satisfied over the entire face, with no unnecessary margin, are formulated. Variants of these conditions are examined for cases of suffosion (undermining), local slip and contact suffosion. The shape of the boundary of the region in the velocity hodograph plane is established and the possibility of using it to construct a solution is demonstrated. Analytical and numerical methods of solution are proposed and justified. It is shown that problems with a condition similar to that associated with slip can be solved by Polubarinova-Kochina's analytical method [5]. For a number of special cases solutions are obtained in explicit form and the results of numerical calculations are presented.