Reliability-based design in rock engineering: Application of Bayesian regression methods to rock strength data

Abstract Reliability-based design (RBD) is being adopted by geotechnical design codes worldwide, and it is therefore necessary that rock engineering practice evolves to embrace RBD. This paper examines the Hoek-Brown (H B) strength criterion within the RBD framework, and presents three distinct analyses using a Bayesian approach. Firstly, a compilation of intact compressive strength test data for six rock types is used to examine uncertainty and variability in the estimated H B parameters m and σ c , and corresponding predicted axial strength. The results suggest that within- and between-rock type variabilities are so large that these parameters need to be determined from rock testing campaigns, rather than reference values being used. The second analysis uses an extensive set of compressive and tensile (both direct and indirect) strength data for a granodiorite, together with a new Bayesian regression model, to develop joint probability distributions of m and σ c suitable for use in RBD. This analysis also shows how compressive and indirect tensile strength data may be robustly used to fit an H B criterion. The third analysis uses the granodiorite data to investigate the important matter of developing characteristic strength criteria. Using definitions from Eurocode 7, a formal Bayesian interpretation of characteristic strength is proposed and used to analyse strength data to generate a characteristic criterion. These criteria are presented in terms of characteristic parameters m k and σ ck , the values of which are shown to depend on the testing regime used to obtain the strength data. The paper confirms that careful use of appropriate Bayesian statistical analysis allows the H B criterion to be brought within the framework of RBD. It also reveals that testing guidelines such as the International Society for Rock Mechanics and Rock Engineering (ISRM) suggested methods will require modification in order to support RBD. Importantly, the need to fully understand the implications of uncertainty in nonlinear strength criteria is identified.