Richards’ Equation: Transition Between Constitutive Equations and the Mechanics of Water Flow in Unsaturated Soil

Abstract

Water flow in soil is normally governed by Richards’ partial differential equation. Similarly, the equation can be used to investigate water infiltration in the soil. It is well understood that when water hits the surface of the topsoil, it infiltrates into the soil. However, the mechanics behind the infiltration of water is unknown to many researchers. This study aims to reveal the mechanics behind the well-known Richards’ equation that has been used enormously in governing water flow in unsaturated soil since 1931. A classic case study of Haverkamp’s water infiltration into Yolo Light Clay was used in the study. The Richards’ equation has been discretized using finite difference method and the algebraic solution has been coded into Simply Fortran 2008. The partial differential equation of Richards is supported by two constitutive functions. The functions from Haverkamp and van Genuchten were compared. It is often for researcher to change between the hydraulic functions, which have limitation on the simulation outcome. The solution to overcome the limitation by changing the constitutive function variables was provided.