Three-dimensional hoek-brown strength criterion for rocks

Lianyang Zhang, Hehua Zhu

Research output: Contribution to journalArticlepeer-review

195 Scopus citations


A great number of rock strength criteria have been proposed over the past decades. Of these different strength criteria, the Hoek-Brown strength criterion has been used most widely, because: (1) it has been developed specifically for rock materials and rock masses; (2) its input parameters can be determined from routine unconfined compression tests, mineralogical examination, and discontinuity characterization; and (3) it has been applied for over 20 years by practitioners in rock engineering, and has been applied successfully to a wide range of intact and fractured rock types. The Hoek-Brown strength criterion, however, does not take account of the influence of the intermediate principal stress, although much evidence has been accumulating to indicate that the intermediate principal stress does influence the rock strength in many instances. In this paper, a three-dimensional (3D) version of the Hoek-Brown strength criterion has been proposed. The original Hoek-Brown strength criterion is just a two-dimensional (2D) version of the proposed 3D strength criterion. The 3D strength criterion not only inherits the advantages of the original Hoek-Brown strength criterion, but can take account of the influence of the intermediate principal stress. Polyaxial or true triaxial compression test data of intact rocks and jointed rock masses has been collected from the published literature and used to validate the proposed 3D Hoek-Brown strength criterion. Predictions of the proposed 3D Hoek-Brown strength criterion are in good agreement with the test data for a range of different rock types. The proposed 3D Hoek-Brown strength criterion is also compared with a simplified 3D Hoek-Brown strength criterion proposed by Pan and Hudson. The Pan-Hudson criterion cannot be considered a true 3D version of the Hoek-Brown criterion, because it does not reduce to the form of the original Hoek-Brown criterion at either triaxial or biaxial state. The Pan-Hudson criterion underpredicts the strength at the triaxial state, but overpredicts the strength at the biaxial state.

Original languageEnglish (US)
Pages (from-to)1128-1135
Number of pages8
JournalJournal of Geotechnical and Geoenvironmental Engineering
Issue number9
StatePublished - Sep 2007


  • Material properties
  • Rock masses
  • Rocks
  • Strength
  • Three-dimensional analysis

ASJC Scopus subject areas

  • Geotechnical Engineering and Engineering Geology
  • General Environmental Science


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