Unsteady Infiltration from Point and Line Sources in Laterally Confined Domains

Abstract

In this study, a linearized form of Richards’ equation is used to derive analytical solutions for the problems of unsteady three-dimensional infiltration from (surface or subsurface) point sources into rectangular, strip-shaped, and cylindrical domains and for two-dimensional infiltration from a line source into a strip. All solutions are given for an inhomogeneous Philip’s soil whose hydraulic conductivity is an exponential function of the pressure head and the depth and for evaporative water loss at the surface. Numerical examples serve to illustrate the effects of lateral confinement, water loss at the soil surface, and change in the hydraulic conductivity with depth on the time-dependent response to constant or cyclic inputs of water from irrigation sources that arise at different depths. Lateral confinement (i) damps the fluctuations in the soil water potential caused by cyclic water inputs, (ii) increases the value of the quasi-steady periodic water potentials, especially at greater soil depths, and (iii) spreads the response to the inputs across longer times. The effect of lateral confinement on the response curves decreases in soils with higher hydraulic conductivity or when the conductivity increases with depth. On the contrary, if the hydraulic conductivity decreases with increasing depth, the effect of lateral confinement increases and the response curves stretch out in time, even for a single, short daily irrigation input. Surface losses reduce the water potential at all depths but do not appreciably affect its temporal evolution. Although the results presented are for surface sources, the analysis may easily be extended to subsurface sources.