Stability of 3D slope under steady unsaturated flow condition

Slope stability has commonly been analyzed by considering dry or saturated soils under two-dimensional (2D) plane-strain conditions. However, in practice, soils are often unsaturated, and many slope failures exhibit a three-dimensional (3D) feature. In this study, the kinematic limit analysis method is adopted to estimate the stability of slopes subjected to vertical unsaturated steady flow in the context of a 3D rotational failure mechanism. A closed-form representation is employed to express the shear strength behavior of unsaturated soils. According to the work-energy balance equation, the critical cohesion for a slope in the limit state is calculated and listed in the form of a stability number. An optimization scheme is used to search for the maximum stability number. By comparing with the previously published 2D and 3D solutions, the proposed method is validated. Charts of different parameters are plotted for parametric analysis and practical use in the design of slopes. It is shown that accounting for the 3D effect and the soil suction can lead to a less conservative result. This paper provides a useful method for assessing the combined effect of 3D boundary conditions and unsaturated flow conditions on the stability of slope and gives some useful suggestions for engineering application.