Asymptotic infiltration into a soil which contains cracks or holes but whose surface is otherwise impermeable

An asymptotic, one-dimensional Green-Ampt model is derived for infiltration into a soil whose surface is impermeable except for regularly spaced vertical cracks, and infiltration into a cylindrical soil column whose top surface is also impermeable except for a central hole. The model is valid at times when the wetting front has become horizontal and corresponds to one-dimensional infiltration initiated from a plane lying above or below the soil surface, depending on the crack spacing/depth ratio (or column radius/hole depth ratio). When applicable, asymptotic Green-Ampt solutions are shown to agree well, in selected cases, with corresponding finite difference solutions of the saturated-unsaturated flow equations.