A New Version of the Generalized Zhang–Zhu Strength Criterion and a Discussion on Its Smoothness and Convexity

The generalized Zhang–Zhu (GZZ) strength criterion has a high associated fitting accuracy for true triaxial test data. It makes direct use of the parameters of the Hoek–Brown criterion and has become one of the strength criteria recommended by the International Society for Rock Mechanics (ISRM). In this study, a new version of the GZZ criterion is developed by addressing the problems associated with the original version’s non-smoothness and non-convexity on the π plane. (i) The new criterion is smooth and derivable on the π plane with no numerical singularity in the strength calculation. It thus renders the application of complicated Lode dependence functions for modification of the non-smooth GZZ criterion unnecessary. (ii) The new criterion is non-convex only under the triaxial extension stress condition, which is not critical for those criteria developed from the Hoek–Brown strength criterion. The new criterion is transformed from incomplete convexity to full convexity with an increase in hydrostatic pressure I₁. Additionally, there exists a critical transformation radius r₀, which only relates to I₁. The new criterion achieves full convexity when I₁ is high and the quality of the rock mass is poor. (iii) Both the new criterion and the GZZ criterion have high fitting accuracy for rock strength data. Their fitting accuracy is much higher than that of the Pan–Hudson criterion. However, the fitted strength parameter m of the new criterion is closer to Hoek’s recommendation than that of the GZZ criterion, thus proving that the new criterion is applicable and reliable when used for rock strength calculation based on the Hoek–Brown criterion parameter system.