An empirical relation for parameter m(i) in the Hoek-Brown criterion of anisotropic intact rocks with consideration of the minor principal stress and stress-to-weak-plane angle

The parameter m(i) accounts for the anisotropy of rock strength, and the accurate determination of m(i) is a primary requirement of the Hoek-Brown (H-B) strength criterion. In this study, a relation for m(i) as a bivariate, second-order, polynomial function of the minor principal stress (sigma (3)) and the angle (beta) between the major principal stress and weak plane is developed. First, the possible contribution of sigma (3) and beta to m(i) is systematically investigated based on substantial uniaxial and triaxial compression test data of various rock types collected from the available literature. This investigation allows m(i) to be described in terms of sigma (3) and beta. A self-defined fitting function is adopted to formulate the functional relationship among these metrics. Using this relation, the H-B strength criterion is modified, and its performance is evaluated in two examples. The examples illustrate the improved ability of the modified criterion to determine the strength of metamorphic and sedimentary rocks. The applicability of this criterion to additional rock types warrants further study.

Automated summary

This study developed a relation for the anisotropy parameter m(i) of rock strength as a bivariate, second-order, polynomial function of the minor principal stress and the angle between the major principal stress and weak plane. The modified Hoek-Brown strength criterion showed improved ability to determine the strength of metamorphic and sedimentary rocks, based on the analysis of extensive uniaxial and triaxial compression test data from various rock types. Further research is needed to explore the applicability of this criterion to additional rock types.