Ultimate bearing capacity of strip footings placed near slopes determined by rigorous slip line field theory

Calculating the ultimate bearing capacity of strip footings placed near slopes has long been a critical component in geotechnical design. In order to obtain the accurate solution of this issue, the statically and kinematically admissible conditions should be satisfied beforehand. Based on the rigorous slip line field theory, the equations for characteristic line and the three kinds of basic boundary value problems are solved together to establish the slip line field of the footing-on-slope system that satisfies the stress and velocity boundaries simultaneously. Then, five types of unilateral failure modes are proposed to determine the corresponding ultimate bearing capacity. The effects of soil shear strength, slope geometry and setback distance from footing edge to slope on the ultimate bearing capacity and the failure mechanism are evaluated in this study. The results indicate that the proposed solutions show good agreement with the experimental results found in the literature. The parametric analysis presents that the ultimate bearing capacity increases with the shear strength, and decreases with an increase in the slope height and the slope angle. When the slope height reaches the critical value, the ultimate bearing capacity is no longer affected by the slope height. Meanwhile, the ultimate bearing capacity increases with the relative distance from footing edge to slope shoulder, and it finally remains unchanged. When the placement position of the footing reaches the critical value, the ultimate bearing capacity is no longer affected by the slope stability. At this point, the failure mechanism obeys the Prandtl’s bearing capacity failure. The failure mechanism gradually transits from the face bearing capacity failure to the face sliding failure or the deep sliding failure and finally follows the Prandtl’s bearing capacity failure with an increase in the relative distance. In this process, the critical sliding range gradually increases until the footing-on-slope system obeys the Prandtl’s failure mode, which results in the corresponding variation in the ultimate bearing capacity.