Theoretical Analyses of Surrounding Rock Stress of a Non-Circular Tunnel Considering the Horizontal Inclination of Initial Principal Stress Field

Abstract

It is common for the principal axis of a deep-buried underground tunnel section not to be parallel to the initial principal stress field; however, available analytical theories for evaluating supported tunnels in such cases are still relatively ineffective. This report presents an analytic solution for determining the surrounding rock stress of non-circular supported tunnels considering the horizontal inclination of initial principal stress field based on a power series method. The correctness of the developed approach was verified by comparing the analytical solution with the numerical solution. Additionally, the impacts of the shear stress component and the horizontal inclination of initial principal stress field on the surrounding rock stress distribution were studied by applying the proposed theory. The results show that the shear stress component of principal stress field has a significant effect on the circumferential tensile and compressive stress concentrations in the rock surrounding a horseshoe-shaped tunnel; their maximum values can reach up to five times the shear stress component of initial principal stress field. Moreover, the greater the horizontal inclination of initial principal stress field, the greater the circumferential stress concentration at the right arch shoulder, and the smaller the circumferential stress concentration at the left arch shoulder.

Keywords: Deep-buried underground tunnel, Complex variable function, Non-circular supported tunnel, Horizontal inclination of principal stress field, analytic solution