Exact and Approximate Solutions for Seepage through Semipermeable Cutoff Walls

Abstract

An explicit analytical solution is developed for the problem of steady, two-dimensional seepage in the vertical plane through a fully penetrating, semipermeable cutoff wall. The flow is driven by a head drop across an overlying dam, whose width is equal to the width of the wall. Results including the discharge beneath the dam, the differential head across the wall, the hydraulic efficiency of the wall, and the exit gradient along the bed of the downstream reservoir are presented as dimensionless charts. Rigorous comparisons are made with solutions obtained by approximate methods, which are applicable to more-general problems. The analytical solutions and approximate methods are used to estimate the discharge and the differential head at the Shikwamkwa Dam in Ontario, Canada, and to assess the need for more-detailed seepage modeling.