Abstract
The first-order and the second-order reliability method (FORM/SORM) are used to evaluate the failure probability of three performance functions of the ground–support interaction in circular tunnels subjected to hydrostatic stresses. The response surface method (RSM) is used to enable reliability analysis of the implicit convergence-confinement method. The friction angle, cohesion and elastic modulus of the rock mass are considered as basic random variables and are first assumed to obey normal distributions. The quadratic polynomial with cross terms is employed as response surface function to approximate the limit state surface (LSS) at the design point. The strategies for the RSM are presented. The failure probability with respect to different criteria are obtained from FORM/SORM and compared to those generated from Monte Carlo simulations. The results show that the support installation position has great influence on the probability of the three failure modes under consideration. Comparison between analysis using correlated and uncorrelated friction angle and cohesion indicates that the influence of the correlation on the reliability analysis depends on the support installation position and the orientation of the LSS. The reliability analysis involving correlated non-normal distributions and the reliability-based design of the support are also investigated.
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