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• An analytical solution for a lined circular tunnel at shallow depths is presented. • The interaction between surrounding rock and lining is considered. • A new approach is proposed based on complex variable method. • The mechanical contribution of lining is analyzed quantitatively. 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. [ABSTRACT FROM AUTHOR]

This paper proposes a method for solving the stress field of a deep circular tunnel affected by an unsteady temperature field. The tunnel is idealized as an infinite domain problem, and the solution of the unsteady temperature field can be regarded as solving the temperature field in the infinite domain under the first type of boundary conditions. The temperature field distribution inside the tunnel surrounding rock is obtained by the Laplace transform method. On this basis, through the stress condition at the boundary of the tunnel and the zero displacement boundary condition at infinity, the solution equations expressed by the analytic functions are listed, and then the power series method of the complex variable function method is used to obtain the desired analytic functions. From this, the temperature stress field caused by the temperature change can be calculated (the displacement field caused by the temperature change is also derived). By superimposing this stress field upon the surrounding rock stress caused by in situ stress, the total stress field inside the surrounding rock can be obtained. The example shows that when the time t is small and the range of the numerical model is suitably large, the results of the analytical method and the numerical method agree well. This paper also discusses two cases in which the tunnel boundary temperature is greater than and less than the initial temperature of the surrounding rock. [ABSTRACT FROM AUTHOR]

An analytical solution is presented for an elastic infinite plate containing an ellipse hole and a circle hole, which undergoes the internal traction along the holes and uniform tensions and shears at infinity. The solution uses the conformal transformation in complex functions, with the multiple connected region mapping onto a circular ring. The stress distribution solved for the infinite plane containing two unequal circle holes in prior literatures is the special case of this article. And contrast between the results of two unequal circle holes obtained by using the present analytical method and the Hoang's results is made in the article. As there is no analytical solution for two non-circular holes, the results obtained using the present analytical method are compared with the numerical results calculated by ANSYS. Computational examples given in this article has been analyzed to study the effect of distance between two holes, the ratio of stress in two directions at infinity, and the ratio of the major and minor axis, on the stress distribution of the hole boundary. [ABSTRACT FROM AUTHOR]

This paper presents a method to solve the stress field of a deep buried circular lining tunnel under the combined action of an unsteady temperature field and in situ stress. The solution of the temperature field can be reduced to a problem of solving the unsteady temperature field in the composite medium under the first type of boundary conditions in the infinite domain, and the distribution of the temperature field in the lining and surrounding rock can be obtained by the Laplace transform method. Through the stress boundary condition of the inner boundary of the lining, the continuous condition of the contact surface and the zero displacement boundary condition at infinity, equations expressed by the boundary values of the analytical functions are established. Then the temperature stresses caused by temperature changes can be obtained. By superimposing these stresses with the stresses caused by in situ stress, the total stresses inside the lining and surrounding rock can be obtained. This article compares the analytical solutions with the numerical solutions obtained by ANSYS. In addition, the influence of temperature field on the stress field of lining and surrounding rock is discussed in the case of temperature decrease and increase through calculation examples. [ABSTRACT FROM AUTHOR]