Theoretical and numerical study of the failure mechanism and minimum safety thickness of water-resistant rock mass in layered karst tunnels

Abstract

Excavating layered karst tunnels often triggers water and mud inrushes, posing serious risks to life and property. This paper examines the effect of layered rock structures on the failure mechanism and minimum safety thickness of water-resistant rock mass. First, mechanical models for horizontally and vertically layered water-resistant rock mass are established. Utilizing the Mohr-Coulomb criterion and the minimum potential energy principle, analytical solutions for the minimum safety thickness of both models are derived. Next, the discrete element method (DEM) is used to analyze fracture propagation, force chain interactions, and displacement distribution in both horizontally and vertically layered water-resistant rock mass. Finally, based on theoretical and numerical analyses, failure modes of layered water-resistant rock mass with different strata inclinations are proposed: flexural-tensile failure in vertically layered rock, creep-sliding tensile failure in horizontally layered rock, and the combined toppling-bending tensile failure mode in inclined layered rock. The results indicate that (1) the variation curve of crack numbers in a water-resistant rock mass can be categorized into four distinct stages: Stage I, the fracture development and rock mass damage stage; Stage II, the fracture equilibrium and energy absorption stage; Stage III, the large deformation and rapid fracture progression stage; and Stage IV, the complete failure stage. (2) Shear failure occurs along the structural plane within the horizontally layered water-resistant rock mass. Tensile rupture failure occurs in the horizontally layered rock mass when the shear strength of the structural plane exceeds the tensile strength of the rock mass. (3) Bending failure occurs in the vertically layered water-resistant rock mass. The force chain within the rock mass at the tunnel face end undergoes tensile stress, whereas at the cavity end, the force chain is subjected to compressive stress.