Analytical expression of displacement of circular double tunnels in transversely isotropic rock mass in unstable rock zone of southwest mountainous area

Abstract

Due to the instability of the underground rock structure in the southwest mountain area, the influence of different pore shapes on the rock mechanics performance and fracture characteristics under uniaxial compression changes. The analysis and research on the displacement of double circular tunnels in layered rock mass lay an essential foundation for back-analyzing the displacement of anisotropic double caverns. Researchers can derive the displacement analytical solution for two circular tunnels in a transverse isotropy rock mass using the complex function and Schwarz alternating methods. This analytic solution can simplify the analytical solution of displacement within an isotropic rock mass and the displacement analytical solution for a single circular tunnel in a transversely isotropy rock mass. The solution demonstrates that even when the tunnel cross-section is presumed to be parallel to the isotropic plane during derivation, the displacement of the surrounding rock is influenced by the elastic modulus and the Poisson ratio in both the isotropic plane and the plane perpendicular to it. Hence, in the displacement back-analysis of two tunnels in transversely isotropic rock mass viewed in cross-section, it is necessary to determine six parameters that meet discernible conditions and use the corresponding sensitivity coefficients to invert the uniqueness of the parameters. By comparing the analytic solution with the numerical solution, it was found that the trends of both solutions were mainly consistent. Moreover, the error between the analytic and numerical solutions was relatively small within the 90 to 105 degrees data, which indicates that the analytical solution can effectively reflect the actual deformation pattern of circular tunnels. This finding is pivotal for back analysis of tunnel excavation displacement in layered rock masses.