Modeling strip footings on slopes using the material point method

The footing-on-slope system is very complicated since it is governed, in part, by both the bearing capacity and slope stability. The material point method (MPM), which is specifically suitable for large deformation problems, is utilized to analyze the failure mechanism of the footing-on-slope system. The reliability of the MPM in predicting bearing capacity and identifying failure modes is validated using the published results in the literature. The results show that an increase in the setback distance, cohesion, and friction angle causes a linear increase in bearing capacity, while the bearing capacity decreases with an increasing slope angle. When the footing is sufficiently far from the slope, its response is similar to that of a footing located on horizontal ground. The critical setback distance ratio increases from 3 to 8 as the slope angle varies from 15 degrees to 75 degrees, and it is mainly affected by the friction angle rather than the cohesion. Four distinct failure modes of the footing-on-slope system are identified based on the setback distance and slope angle. A transitional failure mode is identified as a combination of foundation failure and slope instability. Empirical relationships between the setback distance and slope angle are established, enabling the prediction of the reduction factor of the bearing capacity. Finally, a failure mode classification system of strip footings on slopes is proposed, which may provide practitioners with guidelines for designing footing-on-slope systems.