Undrained stability of plane strain active trapdoors in anisotropic and non-homogeneous clays

Abstract

Despite a large number of studies on the active failure of trapdoors conducted in the literature, there are very limited studies examining the combined influences of undrained strength anisotropy and non-homogeneity of clays on the problem. This paper presents the new lower bound solutions of the active failure of plane strain trapdoors in clays with linearly increasing anisotropic strengths. To achieve this purpose, the lower bound (LB) finite element limit analysis (FELA) of an anisotropic undrained strength criterion using second-order cone programming (SOCP) is developed to investigate the undrained stability of the problem under plane strain conditions. The anisotropic strengths of clays are modelled by employing an elliptical strength envelope requiring strengths in plane strain compression, extension and direct simple shear. The LB FELA is formulated by using a discrete form of the LB theorem of classical plasticity and a resulting optimization problem of anisotropic clay is cast and solved using the framework of conic quadratic optimization. A dimensionless technique is adopted to express the undrained stability of the problem in terms of adhesion factors of trapdoor roughness, cover-depth ratios, strength gradient ratios, and anisotropic strength ratios. The effects of these parameters on the trapdoor stability factor and associated failure mechanisms of trapdoors are also examined and discussed. Employing a nonlinear regression analysis to the computed LB solutions, the new design equations for the estimation of the undrained stability of trapdoors are proposed, where the effects of strength anisotropy and non-homogeneity as well as width and depth of trapdoor and its roughness can be considered for practical stability applications.