为研究深埋罐式硐室开挖卸荷后的围岩应力分布及潜在破坏区演化规律，提出一种复变函数法与屈服接近度（yield approach index, YAI）相结合的围岩稳定性分析方法。利用高精度保角映射方法将子午面（rz平面）映射至像平面的单位圆外域，通过轴对称积分变换建立平面辅助应力场与轴对称三维应力场的转换关系，将复变函数法从二维平面问题拓展至三维空间轴对称问题。引入双曲代换及边界配点法，根据硐室表面边界条件与远场边界条件，求解得到解析函数系数及围岩任意点应力。在此基础上，根据Mohr-Coulomb 准则计算围岩各点屈服接近度，通过YAI≥0.8区域的范围、分布位置、贯通性及破坏类型，对不同地应力及围岩级别条件下围岩的相对稳定性进行分析，并通过数值模拟验证解析计算的精度。结果表明： 1）硐室开挖卸荷后，围岩应力及YAI的计算结果与数值模拟结果吻合良好，可较准确地反映围岩实际应力及YAI分布规律； 2）参数分析揭示了侧压力系数、埋深、围岩强度对围岩破坏模式的影响规律，即破坏模式由浅层拉剪混合破坏向深部扩展的贯通性剪切破坏转化； 3）将该方法应用于某罐式硐室未支护工况与预应力锚杆支护工况的对比分析，预应力锚杆的等效支护作用可有效减小围岩破损区范围，且监测结果验证了预应力锚杆支护的可靠性。
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.
