Semi-analytical solution for stress and displacement of lined circular tunnel at shallow depths

Abstract

In this study, a new approach is presented to determine the stress and displacement field of a shallow buried circular tunnel subject to gravity and arbitrary lateral stress based on the complex variable method. The soil mass and lining are conformally mapped onto two ring regions. A more effective method than the power series method is used to solve the undetermined coefficients of complex potential functions. The interaction mechanism between the lining and the soil mass is fully considered. The boundary conditions along the inner boundary of the lining and the ground surface and the stress and displacement continuity conditions along the excavation line are used in the analytical derivation. In the verification, the stress and displacement distributions obtained in the semi-analytical solution agree with the numerical results and satisfy the boundary and continuity conditions. Using examples, the stress distributions along the inner boundary of the lining and interface are presented to examine the influence of key parameters including the Young's modulus and buried depth. The effect of the lining in reducing stress concentration and restricting tunnel convergence is quantitatively analyzed.