Validity of Schaffernak and Casagrande Analytical Solutions for Seepage through a Homogeneous Earth Dam and Comparison with Numerical Solutions Based on the Finite Element Method

Abstract

Seepage from earth dams is important to study because of its applications in reservoir management. The loss of water due to seepage is a substantial issue that hydraulic designers consider. Seepage loss depletes fresh water resources while also causing water logging, salinization, groundwater contamination, and health hazards. This research provides both numerical and analytical solutions for seepage from a homogeneous earth dam resting on an impervious base. A steady-state two-dimensional (2D) flow through a homogeneous earth dam is analysed for this purpose. The phreatic line location is computed by the finite element method (FEM). The numerical simulation results are compared to the analytical solutions of Schaffernak and Casagrande. The numerical solution predicts more seepage than the other two solutions, namely Casagrande and Schaffernak methods. In most cases, Schaffernak’s solution has more than 20% error and Casagrande’s solution has more than 30% error. On the other hand, both Schaffernak and Casagrande solutions are for simple cases: (i)- homogeneous embankment (ii)- resting of an embankment dam atop an impervious foundation. None of these assumption or simplification are needed in FEM simulation. This study shows the capability of FEM for modeling water flow in a porous medium comprising complicated conditions including, for instance, non-homogeneous (heterogeneous) embankment dams, non-isotropic soils, pervious foundations and different boundary conditions.