Analytical Stress Solutions for a Deep Buried Circular Tunnel Under an Unsteady Temperature Field

Abstract

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.