Non conforming finite element model to analyse highly non-linear groundwater problems: the case of Richard's equation

Analytical solutions of the Richards equation for unsaturated flow with varying boundary and initial conditions are difficult to obtain because of nonlinearity in soil hydraulic parameters. This difficulty is exaggerated in the case where soil is heterogeneous. Generally, one has to rely on numerical approaches for predicting moisture movement in unsaturated soils. In this paper the capability of the non-conforming quadrilateral finite element for solving saturated-unsaturated porous media seepage problems is presented. The reliability of the proposed model is checked by comparing the numerical solutions with the analytical solutions available in literature. The accuracy of the numerical solution with increasing element dimensions is examined to find out the proper mesh size compatible with the scale of practical interest in civil engineering problems where unsaturated flow plays an important role.