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

Abstract

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.

Experimental Study on Mechanical Properties of Anisotropic Slate under Different Water Contents

“…Hoek and Brown introduced the Hoek-Brown strength criterion in 1980 [24,25], but this criterion shows limited applicability to anisotropic rock masses. Various scholars have enhanced and refined it by incorporating the anisotropic parameter [26,27], which accounts for the effects of stress and fabric tensors' relative orientations. This enhancement better represents the failure strength of foliated rock masses when combined with the Hoek-Brown criterion.…”

Data-Driven Rock Strength Parameter Identification Using Artificial Bee Colony Algorithm

“…Recently, researchers applied Bayes theory to determine the rock failure criterion [23,24]. Bayesian inference was used to determine the rock strength anisotropy and evaluate the uncertainty of the Hoek-Brown failure criterion [25]. With the development of artificial intelligence, the soft computing method provides an optimal method for determining the parameters of the model [26,27].…”