Three-dimensional rock mass collapse mechanism caused by a hidden spherical karst cave above a deep rectangular cavern

When a tunnel or underground cavern is excavated in a karst region, a hidden karst cave may occur close to the planned tunnel or underground cavern, which may potential to cause the collapse damage of the surrounding rock during the excavation. Since many previous studies on this issue are carried out based on a two-dimensional model, the three-dimensional collapse mechanism for the surrounding rock is not well investigated. In this study, a three-dimensional approach to determine the rock mass collapse range caused by a hidden spherical karst cave above a rectangular cavern is developed. Based on the rock mass collapse characteristics caused by a hidden karst cave above the deep cavern roof, a three-dimensional rock mass collapse mechanism is established, and the collapse surface equation is derived from the variational approach in combination with the upper bound theorem. By utilizing the aforementioned collapse surface equation, three-dimensional collapse surfaces influenced with varying parameters are depicted. Moreover, a numerical model that describes a spherical karst cave occurring above a rectangular cavern is established by employing three-dimensional numerical software, and the numerical solution of the collapse surface is obtained, which is represented by contour of maximum shear strain increment. By comparing the collapse surface derived from the latter computation and that attained from numerical simulation, the validity of the proposed approach is demonstrated.