Numerical issues arising in the simulations of transient water flow in layered unsaturated soils

The geotechnical community typically relies on recommendations made from numerical simulations. Commercial software exhibits (local) numerical instabilities in layered soils across soil interfaces. This research work investigates unsaturated moisture flow in layered soils and identifies a possible source of numerical instabilities across soil interfaces and potential improvement in numerical schemes for solving the Richards' equation. The numerical issue at soil interfaces is addressed by a (nonlinear) interface problem. A full analysis of the simplest soil hydraulic model, the Gardner model, identifies the conditions of ill-posedness of the interface problem. Numerical experiments on various (more advanced and practical) soil hydraulic models show that the interface problem can also be ill-posed under certain circumstances. Spurious numerical ponding and/or oscillations around soil interfaces are observed consequently. This work also investigates the impact of different averaging schemes for cell-centered conductivities on the propensity of ill-posedness of the interface problem and concludes that smaller averaging conductivities are more likely to trigger numerical instabilities. In addition, an agent-based stochastic soil model, with hydraulic properties defined at the finite difference cell level, results in a large number of interface problems. This research compares sequences of stochastic realizations in heterogeneous unsaturated soils with the numerical solution using homogenized soil parameters. The mean of stochastic realizations is not identical to the solution obtained from homogenized soil parameters.