Three-dimensional seismic stability analysis of slopes with linearly increasing undrained shear strength

Undrained stability of slopes has long been of interest to the community of geotechnical engineering due to its practical importance. However, the role of the undrained shear strength cu in the seismic stability and failure geometry of slopes under three-dimensional (3D) condition has not been fully understood. Therefore, this study adopts a modified 3D rotational failure mechanism to develop the upper bound solution to the stability number Ns for slopes with linearly increasing cu with depth based on the kinematic approach of limit analysis. The seismic force is included using the pseudo-static method. Three types of failure mechanisms, i.e., the toe failure, face failure and below-toe failure are considered to capture the critical condition. Stability charts that cover a wide range of parameters and representative failure surfaces are then developed to illustrate the influence of key factors. Results show that the stability and failure geometry of slopes are significantly influenced by the variation ratio of cu with depth. The most significant outcome is that an increase in the horizontal seismic coefficient kh leads to a shallower critical failure surface when the slope with a large variation ratio of cu is constrained within a narrow width.