Bayesian inference of rock strength anisotropy: Uncertainty analysis of the Hoek-Brown failure criterion

Strength properties of most sedimentary and metamorphic rocks are known to vary with direction. Knowledge of this so-called rock anisotropy is of utmost importance for reliability analysis and engineering design. The purpose of this paper is twofold. First, we propose a formulation of the Hoek-Brown (HB) failure criterion, which calculates strength anisotropy using a non-uniform scaling of the stress tensor. We use two scaling factors, C-N and C-S, to link the orientation of the anisotropy planes with the loading direction. As we assume isotropic parameters for intact rock, our HB model formulation is relatively easy to use and has the additional advantage that it does not demand any modifications to the HB failure criterion. Second, we embed our HB model formulation in a Bayesian framework and illustrate its power and usefulness using experimental data of anisotropic rock samples published in the literature. Results demonstrate that our HB model formulation predicts accurately measured peak strengths of rocks with different degrees of anisotropy, confining stresses and anisotropy orientations. The uncertainty in peak strength of anisotropic rocks can be quite large, reiterating the need for an explicit treatment of strength anisotropy uncertainty in rock mechanics studies. The Bayesian methodology is general-purpose, and, as such, can help better inform geotechnical engineers, contractors and other professionals about rock conditions and design reliability and assist decision makers in determining the overall risks of engineering structures.

Automated summary

This paper discusses the importance of understanding rock anisotropy for reliability analysis and engineering design, and proposes a formulation for calculating strength anisotropy embedded in a Bayesian framework for practical application. The results demonstrate the accuracy of the proposed model in predicting peak strengths of rocks with varying degrees of anisotropy, confining stresses and anisotropy orientations, emphasizing the need for explicit treatment of strength anisotropy uncertainty in rock mechanics studies. The Bayesian methodology is versatile and can assist in informing geotechnical engineers, contractors, and other professionals about rock conditions, design reliability, and overall risks of engineering structures.