An Anisotropic Strength Equivalent Model of the Step Interlayered Rock Mass in the Muzhailing Tunnel

The Muzhailing Tunnel, Gansu Province, China, runs for most (84.5%) of its length through layered slate. To study the mechanical properties of rock masses containing interbedded soft and hard layers, mechanical tests were conducted in the laboratory on hard limestone and soft carbonaceous slate. To simplify the application of mechanical analysis, an equivalent alternative strength model for soft and hard media was derived based on the strain energy equivalence criterion and the Mohr–Coulomb strength theory, and expressions for calculating the ultimate equilibrium stress point and failure azimuth were obtained. Based on the strength differences between soft- and hard-rock layers, an equivalent substitution calculation model was established for different thickness ratios and stress conditions with a strength ratio of 4:1. The influence of the thickness ratio and stress state on the ultimate stress curve was analyzed.