Seepage and stability analysis of hydraulically anisotropic unsaturated infinite slopes under steady infiltration

An analytical model is derived for predicting the flow field and stability of an unsaturated infinite slope subjected to steady infiltration. The proposed model is novel because it accounts for the hydraulic anisotropy of unsaturated soil. The governing equation for steady-state seepage in an infinite slope is established in terms of matric suction under a constant surface flux boundary condition. On the basis of the available experimental findings on the hydraulic anisotropy behavior of unsaturated soils, the relative hydraulic conductivity for a soil under unsaturated conditions with respect to the soil at saturation is postulated to be a direction-independent scalar. This postulation simplifies the governing equation to a form that is directly solvable via the relative hydraulic conductivity and the saturated hydraulic conductivity tensor. To enable sophisticated applications, an exponential law and a power law that are well established in the unsaturated soil literature are used to relate the relative hydraulic conductivity to the matric suction and the effective degree of saturation, respectively. Closed-form solutions are derived for the matric suction, the flow net (potential function and stream function), and the effective degree of saturation. Analytical solutions are also derived for the soil unit weight and overburden stress. These solutions are incorporated into the unsaturated infinite slope stability formula constructed on a suction stress-based effective stress failure criterion. Hydraulic anisotropy has been shown to directly affect the flow field and the change in matric suction, which, in turn, drastically affects the slope safety factor against shallow landslides. This finding demonstrates that neglecting hydraulic anisotropy can cause a considerable overestimation of the safety factor, resulting in an unsafe slope stability prediction. The proposed model is useful for preliminary evaluation of the long-term stability of unsaturated slopes during wet periods and the antecedent slope conditions for shallow landslide initiation under transient infiltration.