Analytical solution of stress and displacement for a circular underwater shallow tunnel based on a unified stress function

Abstract

A unified stress function is represented in a Fourier series to capture the complex stress state of an underwater shallow tunnel perimeter. The first-order unified stress function is employed as stress boundary condition of the tunnel perimeter (SBCTP) to describe the non-symmetrical stress with respect to the horizontal and vertical centerlines of the tunnel. The mechanical analysis model of an underwater shallow tunnel is established. Combining the complex variable theory, the elastic analytical solution of the stress and displacement are obtained. The rationality of the elastic solution is verified by comparing the stress fields between the proposed method and the finite element method (FEM). Based on the obtained elastic solution, the fractional viscoelastic solution is determined by the correspondence principle. The time-dependent ground displacement are investigated considering the effect of stress release. A series of parameter analyses are carried out to discuss the ground vertical and horizontal stress distributions under the influences of SBCTPs.