Modeling face reliability in tunneling: A copula approach

This research develops a copula-enabled approach for modeling and assessing the reliability of the dependent system with incomplete probability information. A bivariate framework consisting of the supporting pressure and the ground settlement is proposed to estimate the excavation face reliability in tunneling under limited observations. The impacts of the selection of copula functions, the variation of the failure criteria, and the size of the measured data and Monte Carlo simulation sampling on the reliability estimation result are explored. A realistic tunnel case in the Wuhan metro system, China, is used to demonstrate the applicability and effectiveness of the developed approach. Results indicate that: (1) the failure probability will lead to an overestimated result, which is more than twice of the reference value (that is without considering the negative dependence); (2) the commonly used Gaussian copula function is likely to underestimate the failure probability and lead to less conservative designs; (3) a setting size of 10(5) samples is reasonable in the case to achieve the required quality in estimation; and (4) the failure probability gradually rises along with an increase of the limit value of the supporting pressure and decreases along with an increase of the limit value of the ground settlement.