A Spatiotemporal Coupling Method for Reliability Analysis of Tunnel Linings in Cold Karst Regions

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Abstract
This study proposes a spatiotemporal reliability analysis framework for tunnel linings to evaluate their long-term safety in cold karst environments, where structures are subjected to coupled geological and freeze-thaw actions. The methodology systematically integrates the spatial randomness of geology with the temporal degradation of materials. It introduces a total probability analysis to encompass the complete influence chain: from geological uncertainty to induced mechanical response, to subsequent stress-accelerated material degradation, and ultimately to the time-dependent evolution of failure probability. The proposed approach comprises three main components. First, a probabilistic model of the karst cave radius is established on the basis of field borehole data via a negative exponential distribution. The geological uncertainty is then propagated to the probability distribution of the lining stress ratio η via a random variable transformation method. Second, a stress ratio‐regulated Gamma process model for concrete strength degradation under freeze‐thaw cycles is constructed, revealing the nonlinear regulatory effect of the stress state on the material degradation rate. Accordingly, a three-dimensional response surface relating time, stress ratio, and strength degradation is developed. Finally, the stress ratio distribution and conditional failure probability are coupled via the total probability formula to derive the time-varying marginal failure probability curve of the lining, which explicitly accounts for geological randomness. A case study of a karst tunnel along the Benxi–Huanren Expressway in Liaoning Province, China, is conducted to validate the framework. The results demonstrate that neglecting the spatial randomness of karst caves may lead to overestimation or underestimation of the lining service life. The proposed method provides a theoretical foundation for the durability design and operation‐maintenance decision‐making of karst tunnels in cold regions. This study offers a systematic and quantifiable analytical tool for the reliability assessment of tunnel linings under the coupling effect of multiple factors.

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