Analytical Solutions for Stress and Displacement of a Circular Tunnel Considering Thermal Stress and Lateral Pressure Coefficient Under Unsteady Temperature Field

This paper proposes a new possible workflow to rapidly evaluate the stress and deformation of tunnels in the heated surrounding rock. Thermal expansion in tunnels is understood as a coupled thermo-mechanical process, where the stress and deformation fields are determined by considering both temperature diffusion and stress expansion. A solution to the unsteady temperature field of a circular tunnel was derived using the approach of separation of variables from the one-dimensional unsteady heat conduction equation. Thermal stress is modeled as a body force, using the complex function method and linear superposition principle to calculate stress and displacement in the surrounding rock of a tunnel subjected to non-isobaric pressure. The results indicate that with the increase of lateral pressure coefficient, both the radial and circumferential stresses also increase in all directions. Given its significant impact on stress distribution, the lateral pressure coefficient must be carefully considered. Furthermore, the influence of the thermal expansion coefficient and temperature difference on the stress within the surrounding rock must be addressed. The stress in the surrounding rock increases with the change of temperature difference and the increase of thermal expansion coefficient. Notably, damage is most extensive at the tunnel's inner boundary.