Steady infiltration from line sources into a layered profile

Two-dimensional unsaturated flow emanating from an array of line sources is analyzed for a stratified soil. The present work extends earlier solutions for flow from an array of line sources into a homogeneous soil to the more complex and realistic case of layered conditions. The hydraulic conductivity is of the form K_i exp(αh) where the saturated conductivity K _i is different in each stratum considered, α is a constant in the entire flow domain, and h is the pressure head. An interesting feature of the derived solution is the use of an expression of the gradients of the stream function at the strata interfaces. This is analogous to the change in slope of path lines crossing a region of contrasting conductivities for saturated flow. For a two-layer example, a build-up of pressures is shown within a layer of lower permeability overlying a more conductive soil. The effect of an included finite stratum on spreading (for an inclusion layer of lower permeability) or concentrating flow (for an inclusion layer of higher permeability) is also shown using a three-layered domain.