Design equation for stability of a circular tunnel in anisotropic and heterogeneous clay

Abstract

The safety assessment of tunnel stability is critical to tunnel construction and requires accurate analysis to obtain a reliable prediction. Strength anisotropy is an important aspect of clay behavior, but it is mostly neglected in practical stability analyses. In this study, the effects of undrained strength anisotropy and strength nonhomogeneity on the stability of unlined circular tunnels in clays are investigated. The static approach of lower-bound (LB) analysis using finite-element and second-order cone programming is employed to examine the aforementioned effects. The anisotropic shear strength of clay is modeled by employing an elliptical yield function under plane strain conditions. A complete set of dimensionless parameters covering the cover depth ratios of tunnels, normalized overburden pressure ratios, normalized strength gradient ratios of clays, and anisotropic strength ratios, are systematically investigated. The new LB solutions indicate that the stability load factor of the problem has a nonlinear relationship with the cover depth ratio and the anisotropic strength ratio, and there exists a linear relationship with the normalized overburden pressure and the normalized strength gradient. Their influence on the predicted failure mechanism is parametrically evaluated. A statistically approximate stability equation of unlined circular tunnels in anisotropic and non-homogeneous clay is proposed for the first time, which contains four new stability factors, namely, constant undrained strength, linearly increasing strength gradient, undrained strength anisotropy, and soil unit weight, and it can serve as a fast and accurate tool for predicting the undrained stability of this problem in practice.