Semianalytical Solution for a Flow over Multilayered Soils

Abstract

In nature, the ground is usually composed of different soils. To simplify the soil structure, we only consider the case of parallel soil layers with a small inclined angle to the horizontal. When a ground surface without vegetative cover is subjected to a rainfall event, overland flow will happen eventually. Therefore, a mathematical model is presented herein to study the integrated surface and subsurface flows over multilayered soils with and without rainfall. The upper layer is a homogeneous water flow over the ground, and the lower layer is a pore-water flow through permeable parallel multilayered soils with infinite thickness. Both water flows are considered as laminar flows. The flow profiles, vertical velocity distribution, and shear-stress distribution are solved analytically by introducing adequate parameters. Furthermore, when a uniform rainfall event is under consideration, the fourth-order Runge–Kutta technique is used to solve the flow profiles. In addition, the phreatic surface is also depicted for the cases of larger slopes; this has never been discussed in the literature.