Finite element modeling of variably saturated flows in hillslopes with shallow water table

Abstract

During heavy rainfall episodes, subsurface flow can saturate the soil in various regions near the surface and, therefore, contribute to the production of overland flow. This paper investigates numerically the dynamics of water tables in partially saturated porous media and their role in the genesis of surface runoff. The water movement in variably saturated soils is modeled with Richards' equation. The water table position being an unknown of the problem, its intersection with the ground surface yields an unsteady obstacle-type problem. The governing equations are discretized by finite elements in space and an implicit Euler scheme in time. At each time step, the approximate solution is obtained using Newton's method embedded into a fixed-point iteration to determine those points lying on the soil surface where artesian conditions are met. Numerical results are presented for a simple hillslope test case. Particular attention is given to the impact of both the soil water retention curve and the unsaturated hydraulic conductivity function on model results, especially near saturation.