Calculation Method for the Critical Thickness of a Karst Cave Roof at the Bottom of a Socketed Pile

The thickness of a karst cave roof at the bottom of a socketed pile plays an important role in the vertical bearing capacity of the socketed pile in the karst region. In practice, its thickness is simply recommended to be not less than 3 times the diameter of the socketed pile, regardless of the geological conditions and the size of the cave itself. In this study, we present an approach for calculating the critical thickness-to-diameter ratio of a karst cave roof η (η = h/d, the ratio of karst cave roof thickness to pile diameter) based on the generalized Hoek–Brown criterion by virtue of the limit analysis method, which considers the pile tip load, hardness degree of the intact rock, and rock mass quality. The analysis results show that less load at the bottom of the pile, higher quality of rock mass, and more hard rock all lead to a smaller critical thickness-diameter ratio, whereas the critical thickness-to-diameter ratio is greater. The validity of the proposed method is verified through a physical model test.