Rock mass collapse mechanism of concealed karst cave beneath deep tunnel

Local collapse of the surrounding rock often occurs during tunnel construction in a karst area, partidularly when the rock pillar between the tunnel and the karst cave is very thin. The collapse of the surrounding rack in tunnel construction is sudden and may lead to great economic loss or even loss of life. To predict the collapse of rock mass where a tunnel is excavated above a karst cave, an analytical expression of the collapse surface is derived from variational calculation in the framework of the upper bound theorem. Based on the analytical solution, the shape of the collapse surface is plotted to investigate the effects of rock parameters on the collapse surface of the rock mass where a karst cave exists beneath a tunnel. According to the changing law of the collapse surface varying with the distance between tunnel and cave, the computational formula of the minimum safety thickness for preventing the collapse of rock pillar is derived. To evaluate the validity of the proposed method in this paper, we compared the analytical solution with numerical solution. The comparison result indicates the analytical solution matches up with the numerical solution very well, which suggests that the analytical approach proposed in this paper is valid.