Upper bound solutions for face stability of circular tunnels in non-homogeneous and anisotropic clays

This paper presents a three-dimensional stability analysis of a circular tunnel face in non-homogeneous and anisotropic undrained clay using the kinematic approach (upper bound) of limit analysis. The proposed failure mechanism consists of a cylindrical rigid block and a toroidal shear zone with variable radius, and the closed-form analytical expressions of velocity field are derived within the framework of an orthogonal curvilinear coordinate system. The critical collapse-supporting pressure and stability ratio are obtained through optimization with respect to the geometrical parameters of the mechanism. Two types of non-homogeneous undrained strength, linearly changing with depth, and two-layer clays with constant undrained strength are investigated. Meanwhile, the 3-D finite element analysis is employed to validate the proposed failure mechanism. The upper bound solutions of the stability ratio of the proposed mechanism compare reasonably well with the upper bound solutions from the finite element analysis and show significant improvements over the existing upper bound solutions in single layer clays with homogeneous and isotropic undrained strength. The results show that the critical collapse pressure decreases with the increase in the non-homogeneous ratio and the anisotropic ratio and increases with the ratio between the undrained strength of the top layer and of the bottom layer.