Bayesian inference of rock strength anisotropy : uncertainty analysis of the Hoek–Brown failure criterion.
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Date
2021
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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, CN and CS
, 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.
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Keywords
Anisotropic rocks, Hoek–Brown strength criterion, Bayesian inference, Model calibration
Citation
GOMES, G. J. C. et al. Bayesian inference of rock strength anisotropy: uncertainty analysis of the Hoek–Brown failure criterion. International Journal of Rock Mechanics & Mining Sciences, v. 148, 2021. Disponível em: <https://www.sciencedirect.com/science/article/pii/S136516092100335X>. Acesso em: 29 abr. 2022.