The Quasi-Linear Solution of Vertical Infiltration

Abstract

The exact solution of the one-dimensional vertical infiltration equation is deducted, when the hydraulic difusivity is considered constant and the hydraulic conductivity is a combination of both a linear and quadratic functions of the soil water content. This quasi-linear solution includes as particular cases, both the classical solution known as "linear soil" and the Knight solution. The cumulative infiltrated water as a function of time provided by the quasi-linear solution has been compared with the cumulative infiltrated water obtained from the numerical solution of the Richards equation on three different soils of contrasting hydrodynamic properties. The good agreement between the two solutions has shown that the quasi-linear solution can be used on soils where the accepted hypothesis, on hydraulic diffusivity and hydraulic conductivity, for its deduction is not satisfied.