Stability Analysis of Shield Tunnels Considering Spatial Nonhomogeneity and Anisotropy of Soils with Tensile Strength Cut-Off

The issue of working face stability in shield tunnels crossing inclined layered soil is addressed by a modified version of the Mohr–Coulomb strength criterion. This model considers spatial nonhomogeneity and anisotropy of the soil layer, and enables a 3D tunnel stability analysis. It derives the energy equation using virtual work, finds the ultimate support stress at the working face, and solves for its optimal upper bound using an algorithm. This research examined the impact of soil nonhomogeneity, anisotropy, and reduced tensile strength parameters on the stability of tunnel working faces. The results demonstrate the validity of the model, as the findings are consistent with existing research when only tensile strength is considered. The ultimate support force decreases with the nonhomogeneous coefficient and increases with the nonhomogeneously directional angle. The ultimate support force decreases first, and then increases with the soil layer’s inclined angle. Soil layers between 10° and 30° have the lowest ultimate support force. This ultimate support force gets stronger with an increasing anisotropic coefficient. Case studies show that using a method that accounts for soil tensile strength to calculate tunnel working face support force results in a relative error of only 1.92%, improving tunnel stability assessment accuracy.