Reliability Prediction of Tunnel Roof with a Nonlinear Failure Criterion

Based on the kinematics-based upper bound theorem and reliability theory, the stability of deep tunnel roofs in nonlinear Hoek-Brown media is investigated. The performance functions of rectangular and circular tunnels are proposed according to the roof collapse mode, respectively, with support pressure and pore water pressure being considered. With the proposed performance function of the rectangular tunnels, the first-order reliability method is utilized to perform reliability analysis. The rock strength parameters are regarded as random variables following the normal or lognormal distribution. To assess the validity of the obtained results, reliability indexes for different support pressure values are calculated and compared with solutions using the response surface method and Monte-Carlo simulation. The agreement shows that the first-order reliability method effectively evaluates the reliability index with the proposed performance function. Sensitivity analysis is performed to throw light on the significance of different random variables, and the impact of the variation coefficient on reliability indexes is discussed. For circular tunnels, MCS is utilized to evaluate the roof stability with the proposed performance function. The influences of the support pressure on the reliability index and the corresponding design points are investigated. The parametric study shows that the normal distribution of random variables has more influence on the failure probability than that of the lognormal distribution. However, the difference between the two distributions is small. sigma(t) is the major factor that influences the reliability index compared to the B and r(u). The supporting pressure for circular tunnels is smaller than that of rectangular tunnels when a target reliability index of 2.5 (failure probability equals 0.62%) is given.