An analytical solution to ground stresses induced by tunneling considering ground surface boundary conditions and gravity

Accurately predicting the stress distribution around the tunnel is crucial for designing safe and economical support systems. The stress distribution is closely related to the ground stress release induced by tunneling, as well as the initial gravity stress and boundary conditions. In this study, a two-dimensional analytical model considering the ground surface boundary conditions and gravity is presented to investigate the stress field around the tunnel. Then, a numerical model was developed to validate the proposed analytical model. Finally, parametric analyses were conducted, and the limitations of the load calculation method of the code for design of shield tunnel in China were discussed. The results indicate that: (a) Tunnel excavation induces stress redistribution in the soil, resulting in a soil arching effect around the tunnel. This arching effect causes nonlinear load changes around the tunnel. (b) The soil mass around the tunnel can be divided into undisturbed and disturbed zones. Above the tunnel, the disturbance range is C-2D(C and D represent the burial depth and the tunnel diameter), while below and on both sides of the tunnel, the disturbance ranges are 4D and 1.5D, respectively. (c) Once the stress release rate reaches 0.6, a combined arching effect zone, consisting of both major and minor principal stresses, is formed in the disturbance zone above and below the tunnel. (d) The load distribution pattern calculated by the code for design of shield tunnel in China is gourd-shaped, and this calculation method is insufficient for accurately evaluating the load around the tunnel. The research results can provide a reference for the design of the shield tunnel.