Numerical analysis of flow in partially saturated porous media using the boundary integral element method

The study of flow through heterogeneous unsaturated porous media is of great importance in many applications including the evaluation of groundwater supplies, irrigation, contaminant transport and the siting of waste repositories. Analysis of these flow problems is hindered by the fact that the governing equation, Richard's equation, is highly nonlinear due to the dependence of hydraulic conductivity on soil moisture content. Quasilinearization of the steady-state Richard's equation is considered by using an exponential model of hydraulic conductivity and a Kirchhoff transformation, thus resulting in a steady Fokker-Planck equation. Two and three-dimensional boundary element formulations based upon the Fokker-Planck equation are developed to study unsaturated flow problems. The formulations are implemented as boundary integral element method computer codes which allow for efficient modeling of general curvilinear geometries and different orders of functional approximation. Simple studies of numerical integration are described and methods of improving accuracy in the numerical integration of surface integrals are proposed.;Methodologies for the analysis of steady infiltration and exclusion flows in a homogeneous partially saturated porous medium are described and comparisons with other theoretical studies are performed. Numerical simulations aimed at the development of effective hydraulic conductivity characterization for the unsaturated porous medium are carried out for stony vadose zones and simple two-phase media. These characterizations have possible implications in the design of capillary and permeable barriers. Simplified methods of estimating the effective hydraulic conductivity of periodically fractured porous media are also described.