Estimation of deformation modulus of rock masses based on Bayesian model selection and Bayesian updating approach

• Model selection is conducted based on information criteria.
• A Bayesian framework is employed to develop predictive distributions.
• The predictive distribution can be updated using new project-specific data.
• Influence of Bayesian updating on the estimates of probability of failure is illustrated.

The deformation modulus is one of the most important parameters to model the behavior of rock masses, but its direct measurement by in situ tests is costly, time-consuming and sometimes infeasible. For that reason, many models have been proposed to estimate the deformation moduli of rock masses based on geotechnical classification indices, such as the Rock Mass Rating (RMR), the Geological Strength Index (GSI), the Tunneling Quality Index (Q), or the Rock Quality Designation (RQD). We present an approach, based on model selection criteria —such as Akaike information criterion (AIC), Bayesian information criterion (BIC) and deviance information criterion (DIC)— to select the most appropriate model, among a set of four candidate models —linear, power, exponential and logistic—, to estimate the deformation modulus of a rock mass, given a set of observed data. Once the most appropriate model is selected, a Bayesian framework is employed to develop predictive distributions of the deformation moduli of rock masses, and to update them with new project-specific data that significantly reduce the associated predictive uncertainty. Such Bayesian updating approach can, therefore, affect our computed estimates of probability of failure, which is of significant interest to reliability-based rock engineering design.