Seismic bearing capacity of rectangular foundations near slopes using the upper bound method

When the upper load of a rectangular foundation exceeds its ultimate bearing capacity, its failure mechanism is typically an irregular three-dimensional (3D) geometry. By constructing this 3D failure mechanism, this article introduces a theoretical framework for evaluating the seismic bearing capacity of rectangular foundations adjacent to slopes. This 3D mechanism’s profile is the classical multi-block mechanism, and the construction of the end faces follows strict associated flow rule. Additionally, the pseudo-static method is utilized to calculate the action of seismic loads. Finally, an energy balance equation is constructed, from which the upper bound solution for seismic bearing capacity is derived. To facilitate practical design, a simple superposition method is provided to calculate the seismic bearing capacity. The effects of aspect ratio, slope inclination, and distance to the slope edge on the seismic bearing capacity are extensively explored. A shape factor is introduced to investigate the differences in bearing capacity between rectangular and strip foundations, with results indicating that a smaller aspect ratio yields a larger shape factor. The investigation into critical 3D failure mechanisms indicates that an increase in seismic intensity reduces the overall size of the mechanism, while an increase in internal friction angle enlarges it.