Reliability analysis of tunnel roof in layered Hoek-Brown rock masses

This paper develops a two-layer model and upper bound solutions for the shape of collapse block in rectangular tunnel subjected to seepage pressure, and then the reliability-based analysis is performed. According to the layered Hoek-Brown rock masses with different characteristics, a continuous failure mechanism of roof collapse in the deep cavities is derived by using upper bound solutions. The performance function of roof stability is proposed and is adopted for reliability analysis and design. Parameters involved in the performance function are random or deterministic variables. For comparison, improved response surface method (RSM) and Monte-Carlo simulation are utilized to calculate the Hasofer-Lind reliability index and the failure probability. It is found that the improved RSM is a reliable method in probabilistic calculation and the supporting pressure has a significant influence on the reliability index. The normal or lognormal distribution of variables has no effect on the failure probability, while the coefficient of variation (COV) of random variables would greatly influence the failure probability. A reliability-based design is performed to determine the probabilistic tunnel pressure for a target reliability index when different COVs of random variables are considered.