Modification of a generalized three-dimensional Hoek-Brown strength criterion

Qi Zhang, Hehua Zhu, Lianyang Zhang

Research output: Contribution to journalArticlepeer-review

49 Scopus citations


To take account of the influence of the intermediate principle stress, Zhang and Zhu [1,2] proposed a three-dimensional (3D) version of the generalized Hoek-Brown strength criterion. The generalized Zhang-Zhu strength criterion is a true 3D version of the Hoek-Brown criterion, not only inheriting the advantages of the Hoek-Brown strength criterion, but predicts the same strength as the two-dimensional (2D) Hoek-Brown strength criterion at both triaxial compression and extension states. However, the failure surface of the generalized 3D Zhang-Zhu strength criterion is not smooth at either the triaxial compression or extension state and concave at the triaxial extension state, which may have problems with some stress paths and cause inconvenience for numerical applications. In this paper, the reason for the non-smoothness and non-convexity of the generalized 3D Zhang-Zhu strength criterion was first discussed by studying its Lode dependence. Then the criterion was modified by utilizing three different Lode dependences with characteristics of both smoothness and convexity to replace its Lode dependence. Finally the smoothness, convexity and prediction accuracy of the modified criteria were evaluated by applying them to analyze both intact rocks and jointed rock masses. The modified criteria not only keep the advantages of the generalized 3D Zhang-Zhu strength criterion, but solve the non-smoothness and non-convexity problem with no loss of accuracy for strength prediction.

Original languageEnglish (US)
Pages (from-to)80-96
Number of pages17
JournalInternational Journal of Rock Mechanics and Mining Sciences
StatePublished - Apr 2013


  • 3D strength criterion
  • Convexity
  • Failure surface
  • Hoek-Brown strength criterion
  • Lode dependence
  • Smoothness

ASJC Scopus subject areas

  • Geotechnical Engineering and Engineering Geology


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