Hierarchical Bayesian modelling of geotechnical data: application to rock strength

Abstract

With the introduction and revisions of geotechnical limit states design (LSD) standards such as Eurocode 7, rock engineering design is moving towards reliability-based design, a method for which statistical characterisation of design parameters is essential. However, the often limited project-specific data in rock engineering do not allow straightforward application of classical statistical analyses, and thus alternative approaches are required. In this paper, hierarchical Bayesian modelling is first introduced as a means of logically combining data from different sources to augment limited project-specific data. A Bayesian hierarchical non-linear regression model for the analysis of rock strength data is then developed and implemented; it is applied to 40 strength data sets of granite retrieved from the literature. In the context of these data, the advantages of the hierarchical model and the improvements in strength parameter estimations brought about by its application are discussed. Also discussed is the goodness-of-fit of the hierarchical model in comparison with more conventional statistical models. The paper concludes with suggestions for further development of the proposed hierarchical model, and the potential of hierarchical modelling as a general approach to statistical modelling of geotechnical data.