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.
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