When a shield tunnel passes through a karst area, the water‐filled cave can easily make the surrounding rock metamorphic, resulting in water inrush, ground collapse, and shield machine failure and other engineering hazards. Natural cavities have a significant degree of geometric irregularity due to groundwater alteration and soluble rock erosion. Considering the difficulties in describing the shape of a natural irregular cavity, circular, rectangular, and elliptical geometries have been simplified in most related studies. Based on the upper bound theorem of limit analysis, we established a three‐dimensional failure model including the karst caves located directly above and below the circumferential side of the tunnel. Then, we deduced the corresponding analytical solution of the critical safety distance (CSD). Furthermore, the effects of rock mass parameters, cave parameters, and geometric parameters on the CSD were analyzed. Then we designed the numerical simulation considering the irregular geometry shape at the circumferential side of tunnel using the Fourier descriptors. In addition, we estimated the CSDs for two failure models using the revised dichotomy and failure criterion. The findings demonstrated a quantifiable association between CSD and Fourier descriptors of irregular cave shape, resulting in the development of a CSD prediction model. These test results can provide a theoretical foundation and direction for predicting water inrush caused by the constrained irregular cave.

中文翻译：

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不规则岩溶洞与环向盾构隧道安全距离的确定新方法


当盾构隧道穿过岩溶区域时，充满水的洞穴很容易使周围的岩石变质，导致突水、地表塌陷和盾构机故障等工程危害。由于地下水蚀变和可溶性岩石侵蚀，天然空洞具有很大程度的几何不规则性。考虑到描述自然不规则腔形状的困难，在大多数相关研究中都简化了圆形、矩形和椭圆形的几何形状。基于极限分析的上界定理，我们建立了一个三维破坏模型，包括位于隧道圆周侧正上方和下方的岩溶洞穴。然后，我们推导出了临界安全距离 （CSD） 的相应解析解。此外，分析了岩体参数、洞穴参数和几何参数对 CSD 的影响。然后，我们使用傅里叶描述符设计了考虑隧道圆周侧不规则几何形状的数值模拟。此外，我们使用修订后的二分法和失效准则估计了两个失效模型的 CSD。研究结果表明，CSD 与不规则洞穴形状的傅里叶描述符之间存在可量化的关联，从而开发了 CSD 预测模型。这些试验结果可为预测约束性不规则洞穴引起的突水事件提供理论依据和方向。