Closed-form analytical solution for infinite-depth seepage below diversion dams considering the width of cutoff wall

Abstract

ABSTRACT The problem of steady-state seepage flow underneath diversion dams on permeable soil of infinite depth with a cutoff wall at the downstream end with a certain width has not been previously solved. This paper uses conformal mapping and the Darcy equation-based approach to investigate the exact solution. Closed-form analytical equations are given for changes in hydraulic gradient, seepage discharge, and uplift pressure. The results are easily used to create design diagrams. These diagrams show that along the specified length of the structure, with increasing cutoff wall width, hydraulic gradient and seepage discharge decrease, and the pressure difference between the two endpoints of the cutoff wall increases. Also, increasing cutoff wall width has a more negligible effect on reducing hydraulic gradient and seepage discharge at large-length structures. In addition, at greater distances from the downstream end of the structure, the effect of the width on hydraulic gradient reduction and seepage discharge is minimal.