Comprehensive evaluation of three-dimensional Hoek–Brown strength criteria: Properties, applicability, and parameter reliability

Abstract

The Hoek–Brown (HB) criterion has evolved into a mature and widely adopted parameter system in rock mechanics. Although existing three-dimensional HB criteria consider the intermediate principal stress effect, issues concerning the reliability of their parameters and the inheritance of the HB parameter system remain insufficiently addressed. In this study, the failure strength distribution of sandstone on the π-plane is obtained through true triaxial failure test under the given stress conditions. The non-convexity of the rock strength on the π-plane is experimentally demonstrated for the first time, and its dual nonlinear tension-compression transition law on both the π-plane and the meridian plane is revealed. Based on 50 sets of true triaxial test data, a comparative analysis of 12 HB series criteria is conducted. The results indicate that the curvilinear hexagonal strength criterion is more consistent with the failure strength envelope morphology of sandstone and has a better comprehensive strength prediction accuracy of various rock types. Among criteria without introducing additional parameters, the generalized Zhang–Zhu criterion demonstrates the best comprehensive performance, maintaining the inheritance of the accumulated experience of the HB parameter system and facilitating practical engineering applications. While criteria incorporating additional parameters achieve higher prediction accuracy and parameter stability, their practical application is limited by ambiguous physical interpretations, immature parameter determination methods, and potential disruption of the original HB parameters, lacking guiding significance for rock mass engineering.