A solution to transient seepage in unsaturated porous media

This paper presents a solution to seepage problems in porous media considering the complete time-dependent transition from fully saturation to partially unsaturated states and vice-versa; therefore capturing the evolution of the free surface (region with zero liquid pressure). A simple and efficient method to implement the seepage face boundary condition for finite element solutions is proposed. The method is based on an analogy to unilateral constraints in Plasticity and, in essence, adds some extra unknowns to the finite elements with boundaries near the seepage face. The free surface is thus automatically predicted. The resulting enriched elements can also account for ponding or infiltration at the external surface. The solution is accomplished by considering the theory of porous media with slightly compressible liquids. The formulation can easily accommodate liquid retention models with hysteresis. Verification examples are presented in addition to simulations of drainage and infiltration illustrating the capabilities of the proposed solution.