Reliability-based design of tunnelling problems and insights for Eurocode 7

The partial factor design approach has been suggested to replace the factor of safety design in geotechnical practice, such as the Eurocode 7 (EC7) for European countries and the load and resistance factor design (LRFD) for the North America. However, these design codes cover little about rock engineering principles and rock engineers struggle with the application of the partial factor design to rock engineering problems. This paper presents how reliability-based design (RBD) can provide insights to and help the evolution of the partial factor design approach for tunnelling problems. Compared with other reliability methods, the first-order reliability method (FORM) is consistent for different but mathematically equivalent limit state functions. The intuitive expanding ellipsoid perspective and the constrained optimization method for FORM help overcome the conceptual and computational barriers for practitioners. Three case studies are presented to show that RBD via FORM can determine the role (resistance or load factor) of input parameters on a case-by-case basis in ways that prescribed partial factors cannot, including a symmetrical roof wedge above a tunnel, a lined circular tunnel under non-hydrostatic in situ stresses and a circular tunnel reinforced by rockbolts considering multiple failure modes.