Procedure to obtain analytical solutions of one-dimensional Richards' equation for infiltration in two-layered soils

Richards' equation (RE) constitutes the most used physically based formula for transient infiltration modeling in unsaturated soils, and it can be solved by using analytical or numerical procedures. Analytical methods require that certain assumptions should be made regarding the closed-form equations that are derived; if the assumptions can be considered reasonable, then the analytical procedures can represent a simple and practical tool (except some cases in which complicated boundary conditions could make the application of the methodology more difficult). Numerical methods do not have the strong limitations of available analytic procedures, and for this reason many numerical schemes are proposed in technical literature to solve RE. Nevertheless, numerical techniques could require high computational costs for application in large areas with respect to analytical procedures. For the frequent case of layered unsaturated soils, analytical solutions were derived by only imposing equal values of capillarity rise for different layers, and this is a clear questionable assumption. A procedure for one dimension is proposed in this work in order to obtain analytical solutions for any soil property: different values of capillarity rise of considered layers, any variation of saturated hydraulic conductivity with depth. The obtained results highlight a good capability of the proposed methodology to reproduce all the considered benchmark cases, constituted by analytical solutions reported in technical literature and application of a software.