Analytical solution of stress and displacement of surrounding rock in shallow buried tunnels with different hole-type under surface load

Abstract

Shallow buried tunnels are prone to engineering accidents such as excessive deformation and collapse under surface load, seriously affecting the safe operation of the tunnel. In practical engineering, the complexity of surface load characteristics and tunnel boundary conditions makes it challenging to predict the stress and displacement distribution in the surrounding rock. This unpredictability poses significant challenges to safety control during tunnel construction and support design. Based on the principle of complex function conformal transformation, this paper solves the mapping function of elastic semi-infinite planes with different hole types in combination with the boundary control points. Considering the effect of load on the initial conditions of the surface and the hole boundary, the surface load on the physical plane is transformed into a function with a period of $2\pi$ on the boundary outside the image plane annulus domain, which is expanded into the complex form of Fourier series under the Dirichlet convergence condition. The effect of surface load on the self-weight stress of surrounding rock is analyzed, and the new stress boundary conditions around the tunnel are considered to obtain the analytical solution of stress-displacement applicable to tunnels with different hole-types under the surface load. The results indicate that the position of concentrated loads significantly affects the stress and displacement fields of the tunnel. When the load is positioned directly above the tunnel, the tangential stress at the crown transitions to a different state, increasing the risk of structural failure. Additionally, surface settlement is influenced by both the tunnel excavation and the surface loads. The parameter β effectively reflects the sensitivity of different tunnel shapes to settlement, providing a theoretical basis for selecting tunnel profiles and structural support. Under uniformly distributed loads, the overall deformation is more pronounced, and an increase in lateral pressure coefficients can effectively reduce both surface and crown settlements. The curved-wall arch tunnel is taken as an example to numerically calculate the stress field and displacement field of the tunnel with concentrated load and uniformly distributed load, respectively, under different lateral stress. The results show that the analytical solutions and numerical solutions are in good agreement. This study can provide a theoretical basis for stability evaluation and related design in shallow buried tunnel engineering.