Closed-Form Theoretical Solution for Finite-Depth Seepage below Flat Apron with Equal End Cutoffs and a Downstream Step

Abstract

The paper gives a closed-form theoretical solution for the steady seepage below the flat horizontal impervious apron of a hydraulic structure with equal end cutoffs, with a step at the downstream end, founded on a pervious medium of finite depth. This is obtained by using Schwarz-Christoffel transformation in two stages. The numerical solution of the resulting implicit equations involving elliptic integrals gives the uplift pressures at key points, seepage discharge factor, and exit gradient factor in terms of nondimensional floor profile ratios. Design charts have been given for these seepage characteristics.