This paper presents a steady-state analytical hillslope stability model to study the role of topography on rain-induced shallow landslides. We combine a bivariate continuous function of the topographic surface, a steady-state hydrological model of hillslope saturated storage, and the infinite slope stability assumption to investigate the interplay between terrain characteristics, saturated storage within hillslopes and soil mechanics. We demonstrate the model by examining the stability of nine characteristic hillslope types (landform elements) with three different profile curvatures (concave, straight and convex) and three different plan shapes (convergent, parallel and divergent). For each hillslope type, the steady-state saturated storage corresponding to given recharge rates is computed for three different average bedrock slope angles. On the basis of the infinite slope stability method, the factor of safety (FS) along the hillslopes is determined. Our results demonstrate that in the steep slopes, the least stable situation occurs in hillslopes with convergent plan shapes and concave length profiles, while the convex ones are more stable. In addition to testing our method for nine characteristic hillslope types, a general relationship between plan shape and profile curvature of landform elements and the factor of safety is derived for a pre-defined hillslope length scale. Our results show that slope stability increases when profile curvature changes from concave to convex. In terms of plan shapes, changing from convergent to divergent, slope stability increases for all length profiles. However, we find that the effect of plan shape is more pronounced for convex length profiles. Overall, we demonstrate that, in addition to bedrock slope, hillslope shape as represented by plan shape and profile curvature is an important control on hillslope stability.

Hillslopes have complex three-dimensional shapes that are characterized by their plan shape, profile curvature of surface and bedrock, and soil depth. To investigate the stability of complex hillslopes (with different slope curvatures and plan shapes), we combine the hillslopestorage Boussinesq (HSB) model with the infinite slope stability method. The HSB model is based on the continuity and Darcy equations expressed in terms of storage along the hillslope. Solutions of the HSB equation account explicitly for plan shape by introducing the hillslope width function and for profile curvature through the bedrock slope angle and the hillslope soil depth function. The presented model is composed of three parts: a topography model conceptualizing three-dimensional soil mantled landscapes, a dynamic hydrology model for shallow subsurface flow and water table depth (HSB model) and an infinite slope stability method based on the Mohr-Coulomb failure law. The resulting hillslope-storage Boussinesq stability model (HSB-SM) is able to simulate rain-induced shallow landsliding on hillslopes with non-constant bedrock slope and non-parallel plan shape. We apply the model to nine characteristic hillslope types with three different profile curvatures (concave, straight, convex) and three different plan shapes (convergent, parallel, divergent). In the presented model, the unsaturated storage has been calculated based on the unit head gradient assumption. To relax this assumption and to investigate the effect of neglecting the variations of unsaturated storage on the assessment of slope stability in the transient case, we also combine a coupled model of saturated and unsaturated storage and the infinite slope stability method. The results show that the variations of the unsaturated zone storage do not play a critical role in hillslope stability. Therefore, it can be concluded that the presented dynamic slope stability model (HSB-SM) can be used safely for slope stability analysis on complex hillslopes. Our results show that after a certain period of rainfall the convergent hillslopes with concave and straight profiles become unstable more quickly than others, whilst divergent convex hillslopes remain stable (even after intense rainfall). In addition, the relation between subsurface flow and hillslope stability has been investigated. Our analyses show that the minimum safety factor (FS) occurs when the rate of subsurface flow is a maximum. In fact, by increasing the subsurface flow, stability decreases for all hillslope shapes.