Undrained Stability of Unlined Square Tunnels in Clays with Linearly Increasing Anisotropic Shear Strength

In general, the undrained strength anisotropy of clays is found in nature. Its effect on a stability problem during undrained loading should be considered in order to get a more accurate and realistic safety assessment. In this paper, the undrained stability of unlined square tunnels in anisotropic and non-homogeneous clays is investigated by the lower bound finite element limit analysis using second-order cone programming. The anisotropic undrained strength of clays is modelled by using an elliptical strength envelope under plane strain conditions. The stability analyses of the problem are performed by the comprehensive investigations of the effects of the cover-depth ratio, the normalized overburden pressure, the normalized strength gradient, and the anisotropic strength ratio on the stability load factor and associated failure mechanisms. The computed lower bound solutions are validated with the existing results of square tunnels in isotropic clays. The new approximate equations of the stability load factor and factor of safety for square tunnels in anisotropic and non-homogeneous clays are first time presented by using a nonlinear regression, hence providing a reliable, accurate and convenient tool for stability analyses of the problem in practice. The numerical results reveal that the strength anisotropy has a significant impact on the stability load factor, especially when anisotropic clays have much difference in undrained strengths between compression and extension.