Bearing capacity at tip of rock-socketed pile in karst areas

The approach for calculating the ultimate bearing capacity at the tip of rock-socketed pile in karst areas is proposed considering the coupled bearing effects of rock of socketed part and cavity roof, as well as the influence of the shape of cavity. Firstly, based on the researches on the ultimate failure mechanism at the tip of rock-socketed pile, the critical failure conditions of the cavity are determined in accordance with the position relationship between the cavity and the ultimate failure line of pile tip. Secondly, the failure modes at the tip of rock socketed pile in karst areas are analyzed considering the force-transferring mechanism of the rock at the tip of pile under the critical condition. Then, the punching and collapse failure conditions of the cavity roof are given in the polar coordinate system. Moreover, the formula for the ultimate bearing capacity at the tip of rock-socketed pile in karst areas under different failure modes are deduced. Finally, the results of theoretical calculation agree well with those of tests and engineering examples, which can provide guidance for calculating the ultimate bearing capacity at the tip of rock-socketed pile in karst areas.