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Crack is the most prevalent disease of water-rich loess tunnels, which impacts the tunnel safety and reliability. The study aimed to investigate the multi-index of tunnel lining crack based on extension theory and reliability evaluation. A new evaluation model was built, and the matter-element concept was used to describe the reliability of a water-rich loess tunnel with lining crack. Crack width, crack depth, crack length, crack geometry, and water seepage of the Qiaoyuan tunnel were measured by intelligent crack measuring instrument, 10 m tape, laser scanner, and dosing cup. According to the analytic hierarchy process (AHP), the judgment matrix could be used to describe the relative importance of each index. Combining the maximum eigenvalue with checking consistency, the weight coefficients of 5 factors were calculated. A probabilistic statistic method and comparison of specification are performed to confirm the validity of extension theory in reliability evaluation. The results showed that the extension theory provided a reliability evaluation method of a water-rich loess tunnel with lining crack.

Reliability Evaluation of Water-Rich Loess Tunnel with Lining Crack Based on Extension Theory