Further modification of a generalised 3D Hoek–Brown criterion: the GZZ criterion

This paper presents a further modification of the generalised three-dimensional (3D) Hoek–Brown (HB) criterion – the generalised 3D Zhang-Zhu (GZZ) criterion. Specifically, a modification was made by introducing a 3D version of effective mean stress to replace the original two-dimensional (2D) version of effective mean stress in the GZZ criterion. The modification overcomes the non-smoothness and non-convexity problems of the GZZ criterion and maintains a simple form of the criterion expression. The modified GZZ criterion can also reduce to the 2D HB criterion under both triaxial compression and extension conditions and thus inherits the advantages of and uses the same parameters as the HB criterion. Eleven sets of true triaxial test data were collected from publications to evaluate the newly modified GZZ criterion. The results indicate that the newly modified GZZ criterion has the highest or at least the same accuracy for strength prediction among the various 3D versions of the HB criterion that can reduce to the HB criterion and are smooth and convex. Moreover, of the various 3D versions of the HB criterion that can reduce to the HB criterion and are smooth and convex, only the newly modified GZZ criterion can be expressed explicitly.