An Improved 3D Hoek-Brown Model Based on Pan-Hudson and GZZ Criterion

The Hoek-Brown strength criterion has been widely used in the study of rock and rock mechanics, particularly in the analysis of rock slope stability, rock tunnel design, and other related fields. Nevertheless, the traditional Hoek-Brown strength criterion fails to account for the influence of intermediate principal stress. The generalized Zhang-Zhu strength criterion (GZZ criterion) incorporates the benefits of the Hoek-Brown strength criterion and considers the impact of intermediate principal stress on rock. However, the yield surface of this criterion displays a distinct convex point, which does not completely satisfy the requirements for the outer convexity of the yield surface. This study proposes an enhanced GZZ criterion to tackle the issues of non-smoothness and non-convexity on the deviatoric plane observed in the original version. The enhancement involves substituting the sigma m,2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sigma }_{m,2}$$\end{document} term of the original GZZ criterion with a new sigma m,2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sigma }_{m,2}$$\end{document} term, drawing upon the commonalities between the Pan-Hudson and GZZ criteria. An analysis of true triaxial experimental data from eight different types of intact rock examines the suitability of the proposed criterion against four existing failure criteria. Both the new criterion and the GZZ criterion demonstrate high precision in fitting rock strength data, beating the Pan-Hudson criterion and the original Hoek-Brown criterion by a substantial margin. The multi-axial strength data exhibits a satisfactory average fitting performance, indicating that the criterion accurately predicts rock strength. The proposed criterion establishes the foundation for the future development of in-situ rock mass strength theory.Kindly check and confirm the edit made in the title.I have confirmed the title is correct.