In this paper

we propose a simplified analytical method for computing the minimum safety thickness of water and mud inrush induced by filled-type karst water bearing structures. The theory of slice method widely used to analyze the slope stability is applied to investigate the stability of the karst filling material. A simplified computational model is established for the complex system which consists of tunnel

karst filling material and karst conduit. In this model

it assumes that the stress of filling material along the surface to reach the state of limit equilibrium and the failure of filling material along the sliding surface to obey Mohr-Coulomb failure criterion. An equation is derived by using the equilibrium of forces to calculate the minimum safety thickness of water and mud inrush induced by filled-type karst water bearing structures

in which it is used for the application of the practical engineering problems. The results calculated by the proposed method are in good agreement with numerical simulations. It indicates that this method is applicable for the determination of the minimum safe thickness of water and mud inrush

which also provides an efficient way to explore the mechanism of water and mud inrush in karst tunnels.