The bearing capacity of shallow foundations may decrease when located near slopes, particularly under seismic conditions. However, there is limited work that isolates the destabilising influences of seismicity and finite slope geometry on ultimate bearing capacity in terms of conventional bearing capacity factors. Herein, analytical solutions based on upper-bound kinematic limit analysis are used to isolate both the mechanism of failure and bearing capacity factors (N_c, N_γ and N_q) for shallow foundations near slopes subject to seismic action without using principles of superposition. The analytical solutions of ultimate seismic bearing capacity show good agreement and accuracy compared with numerical results. Seismic bearing capacity factors are assessed considering transitions in failure mechanism, soil properties and finite configurations of slope and footing geometry. The results presented demonstrate significant non-linearity in bearing capacity factors that have not been previously demonstrated, primarily owing to the transition in governing mechanism with geometry, shear strength or seismic loading. This study shows that the isolation of bearing capacity factors without superposition is possible considering slope and footing geometry, and is greatly influenced by the failure mechanism.

Most slope collapses have three-dimensional (3D) characteristics due to the uniform soil. The traditional plane-strain analyses neglect the 3D effects and could yield an overestimation or underestimation of the slope stability. The present study analyzes the stability of 3D slopes characterized by spatially variable undrained shear strength. A 3D slope reliability analysis approach that can fully consider the spatial variability of soil properties is proposed based on the plastic limit analysis upper-bound theorem. Within the framework of Monte Carlo simulation, the effects of strength gradient, the coefficient of variation, and the scale of fluctuation of soil undrained shear strength on the slope reliability index are examined. The length of the 3D failure surface is highlighted as an essential characteristic in 3D slope analysis. The slope failure mechanisms are classified, and the occurrence probability of each type is quantified. The obtained results indicate that the degree of nonstationarity and the coefficient of variation of undrained shear strength have significant impacts on the slope failure width, and the variation of failure mechanism highly depends on the combined effect of slope inclination and soil strength. The findings could guide slope reinforcement and facilitate a more efficient and accurate risk evaluation of slopes.

Slopes forming convex corners are often constructed in practice. Observed failures of such corners possess three-dimensional (3D) characteristics. Hence, assessing corner stability requires 3D analysis. This study used a variationally derived 3D mechanism to analyze the stability of convex turning corners. Results of 3D stability analysis are presented in a convenient form of stability charts considering the effects of pore-water pressure and seismicity. These charts allow for a quick assessment of the 3D factor of safety. Stability of a convex corner increases as its angle decreases. When corners are subjected to localized loading conditions, its stability could be more critical than the straight slopes forming the corner. Comparisons between the current method and results from existing analytical and numerical studies are conducted.