A new slice-based method for calculating the minimum safe thickness for a filled-type karst cave

A new slice-based method is proposed for calculating the minimum safe thickness for a filled-type karst cave. A computational slice model of the filling medium is put forward with the assumption that the filling medium is in a limit equilibrium state on a straight-line sliding surface. The force expression is calculated, and the most dangerous sliding surface is identified. For intact and fractured resistant bodies, theoretical formulas for the minimum safe thickness are deduced from the tension strength and shear strength criteria of the rocks, respectively. A case study is analyzed, and several influencing factors are discussed. The results show that the cohesion of the filling medium has no effect on the angle of the sliding surface, and the angle of the sliding surface increases by 1.5° if the internal friction angle increases by 3°. The force that filling medium acts on the resistant body decreases nearly linearly with increasing cohesion and decreases nonlinearly as the internal friction angle increases. The minimum safe thickness decreases nearly linearly as the cohesion or internal friction angle of the filling medium increases. As the tensile strength of the resistant body increases, the minimum safe thickness decreases nonlinearly. The minimum safe thickness increases nonlinearly with increasing load. Compared to an intact resistant body, the minimum safe thickness for a fractured resistant body is larger. The method proposed in this paper provides an efficient and reasonable way to explore the mechanism by which filling medium inrush to the tunnel face of a karst tunnel occurs.