关键词: 罐式硐室, 复变函数, 围岩应力解析, 屈服接近度, 围岩稳定性分析

Abstract: To investigate stress distribution and evolution of potential failure zones in surrounding rock after excavation unloading of deep-buried tank-type caverns, a surrounding rock stability analysis method integrating the complex variable function method with the yield approach index (YAI) is proposed. Using a high-precision conformal mapping approach, the meridian plane (the rz plane) is mapped onto the exterior of a unit circle in the transformed plane. An axisymmetric integral transform is adopted to establish the transformation between the plane auxiliary stress field and the three-dimensional (3D) axisymmetric stress field, extending the complex variable method from two-dimensional plane problems to 3D spatial axisymmetric problems. Using hyperbolic substitution and the boundary collocation method, the coefficients of analytical functions and the stress at any point in the surrounding rock are solved subject to cavern surface and far-field boundary conditions. The YAI at each point in the surrounding rock is then calculated based on the Mohr-Coulomb criterion. The relative stability of surrounding rock under different insitu stress conditions and rock mass grades is analyzed based on the extent, spatial distribution, connectivity, and failure type of zones with YAI≥0.8, and the analytical solution is validated against numerical simulation results. The results show that after cavern excavation and unloading, the calculated stress and YAI distributions agree well with numerical simulation results and accurately reflect the actual stress and YAI distributions in the surrounding rock. Parametric analysis reveals the influences of lateral pressure coefficient, overburden depth, and rock mass strength on surrounding rock failure modes: the failure mode shifts from shallow mixed tensile-shear failure to deep-seated through-going coalescent shear failure. The proposed method is applied to compare the unsupported and prestressed bolt support conditions in a real tank-type cavern. The results indicate that the equivalent reinforcement effect of prestressed bolts effectively reduces the extent of the damaged zone in surrounding rock, and field monitoring results verify the reliability of prestressed bolt support.

Key words: tank-type caverns, complex variable method, surrounding rock stress analytical solution, yield approach index, surrounding rock stability analysis