Lower bound solutions for undrained face stability of plane strain tunnel headings in anisotropic and non-homogeneous clays

Abstract

In this paper, the face stability of plane strain tunnel heading in anisotropic and non-homogeneous clays is investigated by the lower bound (LB) finite element limit analysis (FELA) with second-order cone programming (SOCP). New LB solutions of the problem are numerically derived and described by the set of the dimensionless parameters consisting of the stability load factor, the cover-depth ratio, the normalized overburden pressure, normalized strength gradient, and anisotropic strength ratio while failure mechanisms associated with these parameters are also discussed and compared. The computed LB solutions are validated with the existing results of isotropic strengths confirming the accuracy and correctness of the solutions. Based on a nonlinear regression, the new design equations for the stability load factor and factor of safety for plane strain headings in anisotropic and non-homogeneous clays are first time proposed for assessing the undrained stability of relatively long-wall tunnels particularly considering the effects of strength anisotropy and non-homogeneity.