Rock Mechanics and Rock Engineering

, Volume 47, Issue 2, pp 347–356 | Cite as

An Empirical Failure Criterion for Intact Rocks

  • Jun Peng
  • Guan Rong
  • Ming Cai
  • Xiaojiang Wang
  • Chuangbing Zhou
Original Paper


The parameter m i is an important rock property parameter required for use of the Hoek–Brown failure criterion. The conventional method for determining m i is to fit a series of triaxial compression test data. In the absence of laboratory test data, guideline charts have been provided by Hoek to estimate the m i value. In the conventional Hoek–Brown failure criterion, the m i value is a constant for a given rock. It is observed that using a constant m i may not fit the triaxial compression test data well for some rocks. In this paper, a negative exponent empirical model is proposed to express m i as a function of confinement, and this exercise leads us to a new empirical failure criterion for intact rocks. Triaxial compression test data of various rocks are used to fit parameters of this model. It is seen that the new empirical failure criterion fits the test data better than the conventional Hoek–Brown failure criterion for intact rocks. The conventional Hoek–Brown criterion fits the test data well in the high-confinement region but fails to match data well in the low-confinement and tension regions. In particular, it overestimates the uniaxial compressive strength (UCS) and the uniaxial tensile strength of rocks. On the other hand, curves fitted by the proposed empirical failure criterion match test data very well, and the estimated UCS and tensile strength agree well with test data.


Hoek–Brown failure criterion Triaxial compression test Material parameter mi Confining pressure Rock strength 



The research work presented in this paper is sponsored by the National Basic Research Program of China (“973” Program, grant nos. 2011CB013501 and 2010CB732005), the National Natural Science Foundation of China (grant no. 50979081), the Program for New Century Excellent Talents in University (grant no. NCET-11-0406), and the Fundamental Research Funds for the Central Universities (grant no. 2012206020215). The authors are grateful for this financial support.


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Copyright information

© Springer-Verlag Wien 2013

Authors and Affiliations

  • Jun Peng
    • 1
  • Guan Rong
    • 1
    • 2
  • Ming Cai
    • 3
  • Xiaojiang Wang
    • 1
  • Chuangbing Zhou
    • 1
  1. 1.State Key Laboratory of Water Resources and Hydropower Engineering ScienceWuhan UniversityWuhanChina
  2. 2.Earth Sciences DivisionLawrence Berkeley National LaboratoryBerkeleyUSA
  3. 3.Bharti School of EngineeringLaurentian UniversitySudburyCanada

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