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An Empirical Failure Criterion for Intact Rocks

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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.

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References

  • Barton N (1976) The shear strength of rock and rock joints. Int J Rock Mech Min Sci Geomech Abstr 13:255–279

    Article  Google Scholar 

  • 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 37:1223–1237

    Article  Google Scholar 

  • Brace WF, Paulding BW, Scholz C (1966) Dilatancy in the fracture of crystalline rocks. J Geophys Res 71(16):3939–3953

    Article  Google Scholar 

  • Cai M (2010) Practical estimates of tensile strength and Hoek–Brown strength parameter m i of brittle rocks. Rock Mech Rock Eng 43:167–184

    Article  Google Scholar 

  • 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):3–19

    Article  Google Scholar 

  • 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):247–265

    Article  Google Scholar 

  • Carter BJ, Scott Duncan EJ, Lajtai EZ (1991) Fitting strength criteria to intact rock. Geotech Geol Eng 9:73–81

    Article  Google Scholar 

  • 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 41:785–812

    Article  Google Scholar 

  • Eberhardt E (1998) Brittle rock fracture and progressive damage in uniaxial compression. Ph.D thesis, Department of Civil Engineering, University of Saskatchewan, Saskatoon

  • Eberhardt E (2012) ISRM suggested method: the Hoek–Brown failure criterion. Rock Mech Rock Eng 45:981–988

    Article  Google Scholar 

  • 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):361–380

    Article  Google Scholar 

  • 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 41:1277–1303

    Article  Google Scholar 

  • Hoek E (1994) Strength of rock and rock masses. ISRM News J 2(2):4–16

    Google Scholar 

  • Hoek E (2007) Practical rock engineering. http://www.rocscience.com

  • Hoek E, Brown ET (1980a) Underground excavations in rock. Institution of Mining and Metallurgy, London

    Google Scholar 

  • Hoek E, Brown ET (1980b) Empirical strength criterion for rock masses. J Geotech Eng Div ASCE 106(GT9):1013–1035

    Google Scholar 

  • Hoek E, Brown ET (1997) Practical estimates of rock mass strength. Int J Rock Mech Min Sci 34(8):1165–1186

    Article  Google Scholar 

  • 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 209–213

  • Hoek E, Kaiser PK, Bawden WF (2000) Support of underground excavations in hard rock, Netherlands. AA Balkema, Rotterdam

  • Hoek E, Carranza-Torres C, Corkum B (2002) Hoek–Brown criterion. Proceeding of the NARMS-TAC Conference, Toronto, vol 1., p 267–273

  • 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

  • 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

  • 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 48:546–555

    Article  Google Scholar 

  • 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, Manitoba

  • Martin CD, Chandler NA (1994) The progressive fracture of Lac du Bonnet granite. Int J Rock Mech Min Sci Geomech Abstr 31(6):643–659

    Article  Google Scholar 

  • 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)

  • Schwartz AE (1964) Failure of rock in the triaxial shear test. In: Proceedings of the 6th US rock mechanics symposium. Rolla, p 109–135

  • Singh M, Rao KS (2005) Bearing capacity of shallow foundations in anisotropic non Hoek–Brown rock masses. ASCE J Geotech Geoenviron Eng 131(8):1014–1023

    Article  Google Scholar 

  • 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):743–760

    Article  Google Scholar 

  • 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):561–575

    Article  Google Scholar 

  • 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):1097–1106

    Google Scholar 

  • 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):30–38

    Article  Google Scholar 

  • 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):1772–1781

    Google Scholar 

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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.

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Correspondence to Jun Peng.

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Peng, J., Rong, G., Cai, M. et al. An Empirical Failure Criterion for Intact Rocks. Rock Mech Rock Eng 47, 347–356 (2014). https://doi.org/10.1007/s00603-012-0355-6

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  • DOI: https://doi.org/10.1007/s00603-012-0355-6

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