System Reliability Assessment for a Rock Tunnel with Multiple Failure Modes

This paper presents a practical procedure for assessing the system reliability of a rock tunnel. Three failure modes, namely, inadequate support capacity, excessive tunnel convergence, and insufficient rockbolt length, are considered and investigated using a deterministic model of ground-support interaction analysis based on the convergence-confinement method (CCM). The failure probability of each failure mode is evaluated from the first-order reliability method (FORM) and the response surface method (RSM) via an iterative procedure. The system failure probability bounds are estimated using the bimodal bounds approach suggested by Ditlevsen (1979), based on the reliability index and design point inferred from the FORM. The proposed approach is illustrated with an example of a circular rock tunnel. The computed system failure probability bounds compare favorably with those generated from Monte Carlo simulations. The results show that the relative importance of different failure modes to the system reliability of the tunnel mainly depends on the timing of support installation relative to the advancing tunnel face. It is also shown that reliability indices based on the second-order reliability method (SORM) can be used to achieve more accurate bounds on the system failure probability for nonlinear limit state surfaces. The system reliability-based design for shotcrete thickness is also demonstrated.