New analytical solutions for stress and displacement in deeply buried noncircular tunnels incorporating the influence of seepage flow

High water pressure is a common condition during the construction and operation of deeply buried tunnels, which is a significant factor in the stability analysis of underground structures. In this study, the complex variable theory is extended to analytically solve the hydro-mechanical coupled problems for tunnelling problems, which is the first time that fully considers the seepage field influence on the mechanical field, any tunnel shape and the actual steady-state pore pressure distribution. The detailed formulations of the extended complex variable theory are provided, by which specific analytical solutions are proposed for stress, displacement and pore pressure around tunnels with arbitrary shapes. The theory extension and solutions are verified by the good agreement between the analytical results and numerical predictions.

Based on an investigation of the mechanical mechanism using analytical solutions, it is found that the influence of the seepage field on the mechanical field can be divided into two parts, including the surface loading effect and the flow effect. The surface loading effect is more significant than the flow effect. We also investigate the influence of key parameters on stress and tunnel convergence, such as Biot coefficient and tunnel shape, providing normalized charts as a reference for engineering applications. The developed hydro-mechanical coupled solutions can be used for both external and internal high-pressure conditions. Furthermore, it is a tool with a high potential for application to several relevant case studies, such as nuclear waste disposals.