Comprehensive statistical analysis of intact rock strength for reliability-based design

Rock engineering design is currently evolving from the traditional use of safety factors and towards the more rational reliability-based design (RBD), as witnessed by the introduction of a number of geotechnical limit states design (LSD) standards worldwide. The probabilistic nature of RBD requires statistical characterization of design parameters, including the strength of intact rock. The triaxial compressive strength of intact rock is commonly characterized as a function of confining pressure, and values of the parameters that define this function are generally obtained by regression analysis of laboratory test data. However, the problem of fitting strength criteria to intact rock strength data has been historically tackled as a problem of obtaining best fit curves only, and has inadvertently omitted characterization of the variability inherent in the strength data. As a result, the uncertainty in parameter estimations resulting from this variability are often not quantified rigorously. Not only does this omission render such regression analyses incomplete, it also limits development of reliability-based design protocols for rock engineering which require statistical characterization of design parameters. To overcome both of these deficiencies, this paper presents frequentist (i.e. classical) and Bayesian regression models that rigorously incorporate variability and uncertainty associated with estimated Hoek-Brown strength parameters. In particular, it discusses the limitations of the frequentist model when dealing with limited data or a combination of tensile and compressive strength data. It discusses the potential of Bayesian data analysis techniques to overcome the issue of limited data in rock engineering design by using informative prior distributions. The paper also demonstrates the main issue in fitting strength criteria to tensile and compressive data simultaneously from a statistical perspective, and presents a Bayesian regression model that rigorously fits the strength criterion to a combination of tensile and compressive data. The paper concludes with suggested statistical approaches - Bayesian or frequentist - for conditions encountered in the analysis of intact rock strength data.