Roof stability analysis of cylindrical tunnels in hard soil/soft rock with reduced tension strength

Three-dimensional roof stability analyses of cylindrical tunnel segments limited along the tunnel direction were performed based on the modified Mohr–Coulomb failure criterion with reduced tensile strength. A wedge-shaped region of the classical Mohr–Coulomb envelope, where unrealistic tensile and shear strengths are predicted, is truncated by a Mohr circle associated with the true tensile strength. This revised failure criterion with partial nonlinearity allows geomaterials deep into the roof to deform with large velocity gradients under the normality plastic flow rule, observed in field investigations. Using the kinematic approach of limit analysis, rigorous bounds for three quantitative stability measures–stability number, factor of safety, and supporting pressure–were calculated. The roof failure mechanism adopted is relatively elaborate, involving three-dimensional geometry intersecting with a cylindrical tunnel segment; thus, an efficient approach was presented for tunnels with long length constraints. With respect to extremely short tunnel lengths, a modified roof failure mechanism with distinct ridges was proposed. The factor of safety with accommodation of the nonlinear pressure dependency was estimated by a consistent procedure associated with a reduced elliptic failure criterion. The results show that roof stability distinctly depends on the magnitude of the true tensile strength, internal friction angle, and length constraint.