Seismic bearing capacity of rough footings on slopes using limit equilibrium

Abstract

For foundations placed on horizontal ground surfaces, incorporating the effects of earthquake body forces, investigations have been performed by using the method of slices (Sarma & Iossifelis, 1990), limit equilibrium (Budhu & Al-Karni, 1993), the upper bound limit analysis (Richards et al., 1993; Dormieux & Pecker, 1995; Soubra, 1997, 1999) and the method of characteristics (Kumar & Mohan Rao, 2002a). For sloping ground surfaces, on the basis of limit analysis Zhu (2000) has reported an earthquake reduction factor for the bearing capacity factor,$ N_{y}$. By using the method of characteristics, Kumar & Mohan Rao (2002b) have established the variation of the bearing capacity factors with changes in horizontal earthquake acceleration coefficient, h, for different ground inclinations. Two different failure mechanisms (single side and both sides) were used in the analysis. It was indicated that, in the presence of \alpha h, only the single-side failure mechanism remains statically admissible for the computation of Nc and Nq. By contrast, in finding$ N_{y}$, for smaller values of \alpha h and _ both mechanisms were shown to remain statically admissible. As compared with the single-side mechanism, the bearing capacity factor $N_{y}$ was shown to become much smaller on the basis of the both-sides mechanism, especially for very small values of \alpha h and _. It was also indicated that the single-side mechanism remains kinematically admissible in all those cases where no slip has been allowed along the footing–soil interface (rough foundations). Although the approach was quite rigorous, however, it was assumed that the ratio of shear to normal stresses along the foundation–soil interface remains constant. Since the limit equilibrium technique does not require this assumption, it was intended to use this method to determine the seismic bearing capacity of rough foundations on sloping ground. It was simultaneously ensured that the solution remains kinematically admissible in all the cases. The results were thoroughly compared with those reported previously.