Analytical stress solution for cold region tunnels with unequal ground stress and support delay under different frost heave conditions of surrounding rock

Abstract

Stress response analysis of tunnels under the frost heave state is a crucial problem in cold region tunnel construction. Hence, in this study, an analytical stress solution for cold region tunnels with unequal ground stress and support delay under different frost heave conditions is presented. The solution simultaneously considers the unequal ground stress along the horizontal and vertical directions, the rock displacement occurring before support installation, and the different frost heave modes of surrounding rock. To resolve the unequal ground stress boundary condition, the complex function method is utilized, and the stress solution is directly acquired by the method under isotropic frost heave (IFH) condition, whereas the solution under transversely isotropic frost heave (TIFH) condition is acquired through combination with the superposition method. In addition, a displacement release coefficient is adopted to depict the support delay. The solution is validated by existing solutions in degenerate cases. Finally, the stress distributions and the influence of key factors for cold region tunnels are discussed with a case study. In the lining, the radial stress increases with the radius and decreases from 0° to 90°, and the maximum of tangential stress occurs at the inner edge. Moreover, the normal contact stress between the lining and surrounding rock is much greater under TIFH condition; however, the tangential contact stress is identical under the two different frost heave modes. The lateral pressure coefficient shows greater impact on the stress in the lining along the vertical direction, whereas the displacement release coefficient exhibits greater effect on the stress along the horizontal direction. The stress in the lining under TIFH condition is much greater than that under IFH condition, and increases significantly as the degree of anisotropy increases, which implies that the TIFH condition is a much severer state.