Comprehensive interpretation of hillslope subsurface flow – An analytical approach to hillslopes with complex geometry

Abstract

Hillslope failure usually occurs as soil resistance diminishes by the saturation of the soil layer during rainstorms. Hence, precise estimation of the subsurface flow movement on hillslopes is crucial for landslide early warning. In this study, the subsurface flow was analyzed using the kinematic form of Darcy’s law and solved by the method of characteristics. Analytical solutions were derived to describe the movement of subsurface flow on hillslopes. A series of tests with comprehensible figures were given to illustrate the time-varying profile of the subsurface flow on hillslopes with different curvatures (concave, straight, convex) and plane lateral shapes (convergent, parallel, divergent) under prolonged rainstorms.We found that the plane curvature was the primary factor in controlling the hillslope subsurface flow. The subsurface-flow discharge on the convex hillslope was larger than that on the concave plane. Nonetheless, rainfall resulted in the fastest saturation on the concave plane; surface runoff occurred shortly after the beginning of the rainstorm. The saturation region on the convex plane contracted quickly after the end of the rainstorm, and the surface runoff vanished simultaneously. Hence, the subsurface flow thoroughly dominated the recession. Moreover, we found that saturation may not always initiate at the hillslope toe. The saturation can start at the upper portion of the concave hillslope to result in Dunne overland flow.