Explicit analytical solution to the minimum safety thickness of waterproof-resistant slab in front of karst tunnel face

Abstract

Water and mud inrush disasters are typical disaster for tunnel engineering in karst area, and the rock mass between tunnel face and water-rich karst cave plays a key role in preventing water and mud inrush disasters. In this paper, a modified theoretical model is established and explicit analytical solution to the minimum safety thickness is obtained on the basis of the rigid body limit equilibrium theory and elasticity theory. The theoretical formula is validated through a combination of comparisons with some classical theoretical formulations reported in the literature and numerical simulations. The theoretical formula shows that the minimum safety thickness depends heavily on the hydrostatic pressure in karst cave, the tunnel section size and the rock quality. Parameter sensitivity analysis is conducted and the results illustrate that the minimum safety thickness is positive correlated with karst water pressure and tunnel cross-section size, while negative with the tensile strength of the surrounding rock. In additional, the karst tunnel excavation simulations under four tunnel section shapes are carried out, i.e., actual section, elliptical, circular, and rectangular sections, based on the engineering background of the Pengshui Tunnel in Chongqing Province. Displacement of the monitoring sections and distribution characteristics of the plastic zone are analyzed. The results prove that simplifying the waterproof-resistant slab into an elliptical plate is more accurate than the other models.