An improved three-dimensional extension of Hoek–Brown criterion for rocks

The Hoek–Brown (H–B) criterion has found widespread application in numerous rock engineering projects. However, its efficacy is compromised by an underestimation of rock strength due to its neglect of the influence of the intermediate principal stress (\(\sigma_{2}\)). Experimental evidence underscores the significant impact of \(\sigma_{2}\). Consequently, there exists an imperative to formulate a three-dimensional (3D) criterion. In this study, a new deviatoric function with two additional parameters (\(k\) and \(A\)) is developed firstly, which ensure compliance with the prerequisites of smoothness and convexity. In addition, the parameters \(k\) and \(A\) are bonded with the weakening effect of the Lode angle (\(\theta_{\sigma }\)) and the strengthening effect of the mean stress (\(\sigma_{m}\)), respectively. Then a new 3D strength criterion for rocks is proposed by combining this new deviatoric function and the triaxial compression meridian function of the original H–B criterion. Four distinct sets of test data encompassing various rock types are employed to validate the proposed criterion. The results demonstrate that the proposed criterion adeptly captures the strength characteristics of the four rock types, providing a good depiction of failure surfaces within the 3D principal stress space. Comparative analyses involve the utilization of several existing 3D H–B criteria for strength predictions. The proposed criterion exhibits superior fitting performance for all the selected rocks.