A New Method for Determining the Safety Distance Between Irregular Karst Cave and Circumferential Shield Tunnel

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.