Analytical solutions to 1-D horizontal and vertical water infiltration in saturated/unsaturated soils considering time-varying rainfall
Analytical solutions to 1-D horizontal and vertical water infiltration in saturated/unsaturated soils are developed that can consider the variation of rainfall with time. In this model, water content and the permeability coefficient are assumed to be exponential functions of the pressure head, and diffusivity is constant. By means of Fourier integral transformation, the analytical solutions are expressed as infinite series. The steady-state solutions for horizontal and vertical infiltration in unsaturated soils are then derived. The solutions can consider both flux and pressure head boundaries. The solutions are easy to implement compared with numerical solutions, although the restricted assumptions may limit their applicability in some ways. The analytical solutions provide a reliable tool for checking the accuracy of various numerical methods under the condition of constant diffusivity. Finally, the analysis carried out in a case study indicates that the pressure head differences caused by the transient infiltration in both the horizontal and vertical directions can be estimated using the steady-state solutions, and the effect of gravity on water infiltration mainly depends on the boundary conditions.
analytical solution unsaturated soil horizontal and vertical infiltration richards equation