Reliability Analysis of Lined Circular Tunnels in Hoek-Brown Media with Isotropic In Situ Stresses

This paper has illustrated the application of reliability analysis to the problem of a lined circular tunnel excavated in a Hoek-Brown medium with isotropic in situ stress filed. The uncertainties in the values of in situ stress and mechanical properties of the rock mass and lining are considered in the analysis. Tunnel convergence and lining load are regarded as critical factors which indicate the acceptable or unacceptable performance of the system. It is shown that deterministic methods can lead to overestimation of safety level while reliability analysis can evaluate the system more realistically. The higher values of probability of failure using convergence criterion relative to those of lining load criterion indicated that the former criterion is more vulnerable to uncertainties. Changing the coefficient of variation of the parameters revealed that geological strength index and lining uniaxial compressive strength have the most significant effects on the convergence and lining load criteria, respectively. Increase of 0.2 in the coefficients of variation of geological strength index and lining uniaxial compressive strength can result in about 30 and 8% increase in the probability of failure, respectively. In addition, the observed relationship between the coefficient of variation of effective parameters and probability of failure was nonlinear in most cases.