A simplified three-dimensional extension of Hoek-Brown strength criterion

The Hoek-Brown (HB) strength criterion has been applied widely in a large number of projects around the world. However, this criterion ignores the intermediate principal stress σ₂. Many evidences have demonstrated that the rock strength is dependent on σ₂. Thus it is necessary to extend the HB criterion into a three-dimensional (3D) form. In this study, the effect of σ₂ on the strength of rocks is identified by reviewing the true triaxial tests of various rock types reported in the literature. A simple 3D strength criterion is developed. The modified criterion is verified by the true triaxial tests of 13 rock types. The results indicate that the modified criterion can achieve a good fit to most of rock types. It can represent a series of criteria as b varies. For comparisons, several existing 3D versions of the HB criterion are selected to predict the strengths of these rock types. It is indicated that the proposed criterion works better than other criteria. A substantial relationship between parameter b and the unconfined compressive strength is established, which guarantees that the proposed criterion can still work well even in the absence of true triaxial test data.