Comparative analysis of the nonlinear unified strength criterion for rocks and other three-dimensional Hoek–Brown strength criteria

  • Qun Yang
  • YueWen Zan
  • Li Guang Xie
Original Article


The Hoek–Brown strength criterion, which has been widely used in rock engineering, is one of the most influential rock strength criteria. Because this criterion does not take into account the effect of intermediate principal stress and because there are deficiencies in the theory and its practical application, for nearly 30 years many scholars have carried out research related to this topic. Yu and Zan took the advantages of the unified strength theory and integrated this theory with the Hoek–Brown strength criterion, thereby proposing the nonlinear unified strength criterion for rocks. This criterion takes into account the difference between the tensile strength and the compressive strength of rock, i.e. the intermediate principal stress effect, and the researchers determined that the limit loci in the meridian plane are nonlinear. The parameters of the nonlinear unified strength criterion are the same as those of the Hoek–Brown strength criterion obtained from conventional triaxial tests for rock blocks. The current study compared and analyzed the relationship between the nonlinear unified strength criterion and other three-dimensional Hoek–Brown strength criteria proposed by Pan and Hudson, Zhang and Zhu, and Jiang. Using the comparison of failure limit lines of the various strength criteria in the π-plane, the nonlinear unified strength criterion is superior to other strength criteria. Using the 1stOpt software of the general global optimization algorithm to fit the strength criterion parameters, the comparison of the results of the nonlinear unified strength criterion with the true triaxial test data from six types of rocks shows good agreement, and the true triaxial test of rock strength can be evaluated with high accuracy.


Rock strength criterion Hoek–Brown strength criterion Nonlinear unified strength criterion 



We acknowledge our gratitude toward the sponsors of the work presented in this paper: the MOE’s Program for Changjiang Scholars and the Innovative Research Team (IRT13092).


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.School of Geosciences and Environmental EngineeringSouthwest Jiaotong UniversityChengduChina
  2. 2.College of Physics and Engineering TechnologyChengdu Normal UniversityChengduChina
  3. 3.Sichuan Vocational and Technical College of CommunicationsChengduChina

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