Reliability analysis of roof wedges and rockbolt forces in tunnels

• The ambiguities in factors of safety resolved in reliability analysis.
• A transparent computational approach for the first-order reliability method.
• Probabilistic analysis of tunnels reinforced with rockbolts.
• Reliability-based design of rockbolts for a target reliability index.
• Design-point of reliability analysis compared with partial factors of Eurocode.

The ambiguous nature of the factor of safety is first discussed in the context of a symmetric roof wedge of a circular tunnel, where two different definitions of the factor of safety are shown to be reconcilable when using the reliability index computed with the first-order reliability method (FORM). The probabilities of failure based on the second-order reliability method (SORM) are also obtained for comparison with those of FORM and Monte Carlo simulations. The FORM and SORM analyses are then applied to a circular tunnel supported with elastic rockbolts in a homogeneous and isotropic elasto-plastic ground with the Coulomb failure criterion. The similarities and differences between the ratios of mean values to design-point values, on the one hand, and the partial factors of limit state design, on the other hand, are discussed. Finally, all this is used to show how a reliability-based design can be performed to obtain the length and spacing of rockbolts for a target reliability index.