A constitutive model based on the modified generalized three-dimensional Hoek–Brown strength criterion

Hehua Zhu, Qi Zhang, Boqi Huang, Lianyang Zhang

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


A new constitutive model is proposed based on the generalized three-dimensional (3D) Hoek-Brown strength criterion which was proposed by the authors in 2007 and 2008 and later modified in 2013. The model involves a 3D continuous multi-segment plastic flow rule that can not only consider the effect of confining stress on the plastic flow and volumetric deformation, but also avoid the use of uncertain parameters such as dilatancy angle. The constant volume and maximum tensile stress flow rules are adopted at the high compressive confining stress condition, and the tensile stress condition, respectively. A new interpolation between the high compressive confining stress condition and the tensile stress condition is proposed to ensure the continuity of the plastic potential function over the entire stress space. The proposed constitutive model is based on the assumption that the rock mass is elastic-perfectly plastic but can be extended to the case when a rock mass shows strain-hardening behavior. The new constitutive model has been successfully implemented in a 3D finite element code, and validated by analyzing a circular ring under plane-strain loading condition and a model test tunnel with detailed instrumentation and measurements and then comparing the numerical results with the corresponding analytical solutions and experimental results. Finally, the new constitutive model is successfully applied to analyze a real highway tunnel excavated in rock mass with detailed instrumentation and measurements. The obtained tunnel roof and horizontal convergence displacements using the new constitutive model based on the modified GZZ criterion are in good agreement with those from the field measurements, further proving the importance in considering the contribution of intermediate principal stress to rock strength.

Original languageEnglish (US)
Pages (from-to)78-87
Number of pages10
JournalInternational Journal of Rock Mechanics and Mining Sciences
StatePublished - Oct 2017


  • Continuous multi-segment plastic flow rule
  • Hoek-Brown strength criterion
  • Modified GZZ strength criterion
  • Rock mass
  • Three-dimensional constitutive model

ASJC Scopus subject areas

  • Geotechnical Engineering and Engineering Geology


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