Viscoelastic analytical solution of deep buried circular tunnel considering support creep in non-hydrostatic stress field

When constructing tunnels in rheological strata, the creep of the surrounding rock increases the load on the supporting structure over time. Additionally, environmental influences may cause creep phenomena in the supporting structure, resulting in a complex interaction mechanism between the tunnel's surrounding rock and support due to the coupling effects of both. This article proposes an analytical method for circular tunnels based on the theory of complex functions and Laplace transform. Unlike previous analytical solutions, the approach presented here incorporates the rheological properties of the surrounding rock, non-hydrostatic stress fields, and the creep characteristics of supporting structures. The Kelvin-Voigt model was employed to simulate the rheological properties of both the surrounding rock and the supporting structures. Displacement and stress solutions were derived from the displacement coordination equation and the stress boundary conditions of the surrounding rock and support structures. The accuracy of the analytical solution was verified through numerical simulations, followed by a parameter analysis. The main conclusions drawn from this study are as follows: (1) For simple mechanical models, the analytical method proposed in this paper is faster, simpler, and retains a degree of accuracy superior to that of numerical simulations; (2) When accounting for the creep characteristics of the supporting structure, the deformation of the surrounding rock is greater compared to existing analytical results, the contact pressure between the surrounding rock and the supporting structure is reduced, and the creep of the supporting structure diminishes its bearing capacity and deformation constraint. A higher creep rate in the supporting structure correlates with a faster rate of deformation in the surrounding rock, a lower creep modulus, and increased deformation of the surrounding rock; (3) In the context of non-hydrostatic stress fields, the coupling effects of creep between the tunnel and the supporting structure can exacerbate tunnel issues such as arch uplift or inward compression of tunnel sidewalls, thereby compromising the safety of the supporting structure. Considering these factors is crucial for the design and construction of tunnels in complex environments; (4) Engineering applications demonstrate that the analytical method proposed in this paper effectively predicts the trends in tunnel surrounding rock deformation and support structure stress, showcasing its potential for practical engineering applications.