A generalized three-dimensional Hoek–Brown strength criterion
Although the Hoek–Brown strength criterion has been widely used in rock mechanics and rock engineering, it does not take account of the influence of the intermediate principal stress. Much evidence, however, has been accumulating to indicate that the intermediate principal stress does influence the rock strength in many instances. Therefore, researchers have developed three-dimensional (3D) versions of the Hoek–Brown strength criterion. In this paper, three existing 3D versions of the Hoek–Brown strength criterion are reviewed and evaluated. The evaluation shows that all of the three 3D versions of the Hoek–Brown strength criterion have limitations. To address the limitations, a generalized 3D Hoek–Brown criterion is proposed by modifying the generalized Hoek–Brown strength criterion. The proposed 3D criterion not only inherits the advantages of the Hoek–Brown strength criterion but can take account of the influence of the intermediate principal stress. At a 2D stress state (triaxial or biaxial), the proposed 3D criterion will simply reduce to the form of the generalized Hoek–Brown strength criterion. To validate the proposed 3D strength criterion, polyaxial or true triaxial compression test data of intact rocks and jointed rock masses has been collected from the published literature. Predictions of the proposed generalized 3D Hoek–Brown strength criterion are in good agreement with the test data for a range of different rock types. The difference of the proposed generalized 3D Hoek–Brown strength criterion from and its advantages over the existing 3D versions of the Hoek–Brown strength criterion are also discussed. It should be noted that the proposed 3D criterion is empirical in nature because it is an extension of the 2D Hoek–Brown strength criterion, which is empirical. Because of the non-convexity of the yield surface for a biaxial stress state, the proposed 3D criterion may have problems with some stress paths.
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