Advertisement

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

Abstract

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.

Keywords

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

Notes

Acknowledgments

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.

References

  1. Barton N (1976) The shear strength of rock and rock joints. Int J Rock Mech Min Sci Geomech Abstr 13:255–279CrossRefGoogle Scholar
  2. Bésuelle P, Desrues J, Raynaud S (2000) Experimental characterisation of the localisation phenomenon inside a Vosges sandstone in a triaxial cell. Int J Rock Mech Min Sci 37:1223–1237CrossRefGoogle Scholar
  3. Brace WF, Paulding BW, Scholz C (1966) Dilatancy in the fracture of crystalline rocks. J Geophys Res 71(16):3939–3953CrossRefGoogle Scholar
  4. Cai M (2010) Practical estimates of tensile strength and Hoek–Brown strength parameter m i of brittle rocks. Rock Mech Rock Eng 43:167–184CrossRefGoogle Scholar
  5. Cai M, Kaiser PK, Uno H, Tasaka Y, Minami M (2004) Estimation of rock mass strength and deformation modulus of jointed hard rock masses using the GSI system. Int J Rock Mech Min Sci 41(1):3–19CrossRefGoogle Scholar
  6. Cai M, Kaiser PK, Tasaka Y, Minami M (2007) Determination of residual strength parameters of jointed rock masses using the GSI system. Int J Rock Mech Min Sci 44(2):247–265CrossRefGoogle Scholar
  7. Carter BJ, Scott Duncan EJ, Lajtai EZ (1991) Fitting strength criteria to intact rock. Geotech Geol Eng 9:73–81CrossRefGoogle Scholar
  8. Diederichs MS, Kaiser PK, Eberhardt E (2004) Damage initiation and propagation in hard rock tunnelling and the influence of near-face stress rotation. Int J Rock Mech Min Sci 41:785–812CrossRefGoogle Scholar
  9. Eberhardt E (1998) Brittle rock fracture and progressive damage in uniaxial compression. Ph.D thesis, Department of Civil Engineering, University of Saskatchewan, SaskatoonGoogle Scholar
  10. Eberhardt E (2012) ISRM suggested method: the Hoek–Brown failure criterion. Rock Mech Rock Eng 45:981–988CrossRefGoogle Scholar
  11. Eberhardt E, Stead D, Stimpson B (1999) Quantifying progressive pre peak brittle fracture damage in rock during uniaxial compression. Int J Rock Mech Min Sci 36(3):361–380CrossRefGoogle Scholar
  12. Everitt RA, Lajtai EZ (2004) The influence of rock fabric on excavation damage in the Lac du Bonnett granite. Int J Rock Mech Min Sci 41:1277–1303CrossRefGoogle Scholar
  13. Hoek E (1994) Strength of rock and rock masses. ISRM News J 2(2):4–16Google Scholar
  14. Hoek E (2007) Practical rock engineering. http://www.rocscience.com
  15. Hoek E, Brown ET (1980a) Underground excavations in rock. Institution of Mining and Metallurgy, LondonGoogle Scholar
  16. Hoek E, Brown ET (1980b) Empirical strength criterion for rock masses. J Geotech Eng Div ASCE 106(GT9):1013–1035Google Scholar
  17. Hoek E, Brown ET (1997) Practical estimates of rock mass strength. Int J Rock Mech Min Sci 34(8):1165–1186CrossRefGoogle Scholar
  18. Hoek E, Wood D, Shah S (1992) A modified Hoek–Brown criterion for jointed rock masses. In: Hudson J (ed) Proceeding of the rock characterization symposium, International Society for Rock Mechanics, p 209–213Google Scholar
  19. Hoek E, Kaiser PK, Bawden WF (2000) Support of underground excavations in hard rock, Netherlands. AA Balkema, RotterdamGoogle Scholar
  20. Hoek E, Carranza-Torres C, Corkum B (2002) Hoek–Brown criterion. Proceeding of the NARMS-TAC Conference, Toronto, vol 1., p 267–273Google Scholar
  21. Jacobsson L (2006a) Forsmark/Oskarshamn site investigation—borehole KFM01C, KFM01A, KFM03A, KFM04A, KFM05A, KLX03A, KLX04A and KLX12A—triaxial compression test of intact rock. Swedish National Testing and Research Institute. http://www.skb.se. Accessed 15 Nov 2011
  22. Jacobsson L (2006b) Forsmark/Oskarshamn site investigation—borehole KFM01C, KFM01A, KFM03A, KFM04A, KFM05A, KLX03A, KLX04A and KLX12A—uniaxial compression test of intact rock. Swedish National Testing and Research Institute. http://www.skb.se. Accessed 15 Nov 2011
  23. Mahendra S, Anil R, Bhawani S (2011) Modified Mohr–Coulomb criterion for non-linear triaxial and polyaxial strength of intact rocks. Int J Rock Mech Min Sci 48:546–555CrossRefGoogle Scholar
  24. Martin CD (1993) The strength of massive Lac du Bonnet granite around underground opening. Ph.D thesis, Department of Civil and Geological Engineering, University of Manitoba, Winnipeg, ManitobaGoogle Scholar
  25. Martin CD, Chandler NA (1994) The progressive fracture of Lac du Bonnet granite. Int J Rock Mech Min Sci Geomech Abstr 31(6):643–659CrossRefGoogle Scholar
  26. Richards L, Read SAL (2011) A comparison of methods for determining m i, the Hoek–Brown parameter for intact rock material. Proceeding of the 45th US rock mechanics and geomechanics symposium. San Francisco, 26–29 June 2011 (paper ARMA 11-246, Alexandria, ARMA)Google Scholar
  27. Schwartz AE (1964) Failure of rock in the triaxial shear test. In: Proceedings of the 6th US rock mechanics symposium. Rolla, p 109–135Google Scholar
  28. Singh M, Rao KS (2005) Bearing capacity of shallow foundations in anisotropic non Hoek–Brown rock masses. ASCE J Geotech Geoenviron Eng 131(8):1014–1023CrossRefGoogle Scholar
  29. Sonmez H, Ulusay R (1999) Modifications to the geological strength index (GSI) and their applicability to stability of slopes. Int J Rock Mech Min Sci 36(6):743–760CrossRefGoogle Scholar
  30. Wawersik WR, Fairhurst C (1970) A study of brittle rock fracture in laboratory compression experiments. Int J Rock Mech Min Sci Geomech Abstr 7(5):561–575CrossRefGoogle Scholar
  31. Yan P, Lu WB, Chen M, Shan ZG, Chen XR (2011) In-situ test research on influence of excavation method on induced damage zone in deep tunnel. Chin J Rock Mech Eng 30(6):1097–1106Google Scholar
  32. Zhang CS, Chu WJ, Liu N, Zhu YS, Hou J (2011a) Laboratory tests and numerical simulations of brittle marble and squeezing schist at Jinping II hydropower station, China. J Rock Mech Geotech Eng 3(1):30–38CrossRefGoogle Scholar
  33. Zhang XP, Wang SJ, Han GY, Zhang B (2011b) Crack propagation study of rock based on uniaxial compressive test—a case study of schistose rock. Chin J Rock Mech Eng 30(9):1772–1781Google Scholar

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

Personalised recommendations