Analytical-Numerical Computation of Infiltration

An approximate, analytical-numerical solution has been developed for one-dimensional, vertical infiltration of water into soil. The soil diffusivity is assumed to vary either exponentially or as a power law; however, other analytical formulations can also be accommodated. The solution is physically based, involving parameters related to the soil properties, and is valid for short times of infiltration. Its center piece is a simple, rapid, and sufficiently accurate solution for the sorption process. This solution is of the similarity type and the moisture gradient is given in analytical form. The remaining integration of the initial value problem is performed numerically to obtain the moisture distribution. Comparisons with exact numerical solutions are used to test the accuracy of the solution. The influence of gravity is accounted for approximately, following Philip's theory, by an additive series term, that is determined numerically from the integration of a linear ordinary differential equation. Sorptivity is expressed completely analytically, thus providing a simple, and physically rational, algebraic relationship for the cumulative infiltrated volume and the infiltration rate.