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Abbreviations

σ 1 :

Major principal stress

σ 3 :

Minor principal stress

C o :

Uniaxial compressive strength

m i :

Hoek–Brown material constant (intact rock)

m b :

Hoek–Brown material constant (rock mass)

s :

Hoek–Brown material constant

a :

Hoek–Brown material constant

GSI:

Geological Strength Index

D :

Disturbance factor

T o :

Uniaxial tensile strength

σ′3max :

Upper limit of confining stress

r 2 :

Coefficient of determination

References

  • Benz T, Schwab R (2008) A quantitative comparison of six rock failure criteria. Int J Rock Mech Min Sci 45(7):1176–1186

    Article  Google Scholar 

  • Benz T, Schwab R, Kauther RA, Vermeer PA (2008) A Hoek–Brown criterion with intrinsic material strength factorization. Int J Rock Mech Min Sci 45(2):210–222

    Article  Google Scholar 

  • Brace WF (1964) Brittle fracture of rocks. In: Judd WR (ed) State of stress in the Earth’s crust: Proceedings of the International Conference. American Elsevier Publishing Co., New York, pp 110–178

    Google Scholar 

  • Brown ET (2008) Estimating the mechanical properties of rock masses. In: Potvin Y, Carter J, Dyskin A, Jeffrey R (eds) Proceedings of the 1st Southern Hemisphere International Rock Mechanics Symposium, Australian Centre for Geomechanics, Perth, pp 3–22

    Google Scholar 

  • Colmenares LB, Zoback MD (2002) A statistical evaluation of intact rock failure criteria constrained by polyaxial test data for five different rocks. Int J Rock Mech Min Sci 39(6):695–729

    Article  Google Scholar 

  • Diederichs MS (2007) Mechanistic interpretation and practical application of damage and spalling prediction criteria for deep tunnelling. Can Geotech J 44(9):1082–1116

    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(5):785–812

    Article  Google Scholar 

  • Ghazvinian AH, Fathi A, Moradian ZA (2008) Failure behavior of marlstone under triaxial compression. Int J Rock Mech Min Sci 45(5):807–814

    Article  Google Scholar 

  • Griffith AA (1920) The phenomena of rupture and flow in solids. Philos Trans R Soc Lond Ser A Math Phys Sci 221(587):163–198

    Google Scholar 

  • Griffith AA (1924) The theory of rupture. In: Biezeno CB, Burgers JM (eds) Proceedings of the First International Congress for Applied Mechanics. Delft. J. Waltman Jr, Delft, pp 55–63

    Google Scholar 

  • Haimson B (2006) True triaxial stresses and the brittle fracture of rock. Pure Appl Geophys 163(5–6):1101–1130

    Article  Google Scholar 

  • Hoek E (1968) Brittle failure of rock. In: Stagg KG, Zienkiewicz OC (eds) Rock mechanics in engineering practice. Wiley, New York, pp 99–124

    Google Scholar 

  • Hoek E (1983) Strength of jointed rock masses, 23rd Rankine Lecture. Géotechnique 33(3):187–223

    Article  Google Scholar 

  • Hoek E (2007) Practical Rock Engineering. e-book

    Google Scholar 

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

    Google Scholar 

  • Hoek E, Brown ET (1988) The Hoek–Brown failure criterion—a 1988 update. In: Curran J (ed) Proceedings of the 15th Canadian Rock Mechanics Symposium. University of Toronto, Toronto, pp 31–38

    Google Scholar 

  • Hoek E, Wood D, Shah S (1992) A modified Hoek–Brown criterion for jointed rock masses. In: Hudson JA (ed) Rock characterization: ISRM Symposium, Eurock ‘92, Chester, UK. Thomas Telford, London, pp 209–213

    Google Scholar 

  • Hoek E, Kaiser PK, Bawden WF (1995) Support of underground excavations in hard rock, A.A. Balkema, Rotterdam

    Google Scholar 

  • Hoek E, Carranza-Torres CT, Corkum B (2002) Hoek–Brown failure criterion—2002 edition. In: Hammah R, Bawden W, Curran J, Telesnicki M (eds) Proceedings of the Fifth North American Rock Mechanics Symposium (NARMS-TAC), University of Toronto Press, Toronto, pp 267–273

    Google Scholar 

  • Kaiser PK, Diederichs MS, Martin D, Sharpe J, Steiner W (2000) Underground works in hard rock tunnelling and mining. In: GeoEng2000, Proceedings of the International Conference on Geotechnical and Geological Engineering, Melbourne, Technomic Publishing Company, Lancaster, pp 841–926

    Google Scholar 

  • Marinos V, Marinos P, Hoek E (2005) The geological strength index: applications and limitations. Bull Eng Geol Environ 64(1):55–65

    Article  Google Scholar 

  • Martin CD, Kaiser PK, McCreath DR (1999) Hoek–Brown parameters for predicting the depth of brittle failure around tunnels. Can Geotech J 36(1):136–151

    Article  Google Scholar 

  • Melkoumian N, Priest SD, Hunt SP (2009) Further development of the three-dimensional Hoek–Brown yield criterion. Rock Mech Rock Eng 42(6):835–847

    Article  Google Scholar 

  • Mogi K (1971) Fracture and flow of rocks under high triaxial compression. J Geophys Res 76(5):1255–1269

    Article  Google Scholar 

  • Pan XD, Hudson JA (1988) A simplified three-dimensional Hoek–Brown yield criterion. In: Romana M (ed) Rock mechanics and power plants, A.A. Balkema, Rotterdam, pp 95–103

    Google Scholar 

  • Pariseau WG (2007) Fitting failure criteria to laboratory strength tests. Int J Rock Mech Min Sci 44(4):637–646

    Article  Google Scholar 

  • Priest SD (2005) Determination of shear strength and three-dimensional yield strength for the Hoek–Brown criterion. Rock Mech Rock Eng 38(4):299–327

    Article  MathSciNet  Google Scholar 

  • Rocscience (2007) RocLab. 1.031 edn. Rocscience Inc., Toronto

    Google Scholar 

  • Sönmez H, Ulusay R (2002) A discussion on the Hoek–Brown failure criterion and suggested modifications to the criterion verified by slope stability case studies. Yerbilimleri 26:77–99

    Google Scholar 

  • Takahashi M, Koide H (1989) Effect of the intermediate principal stress on strength and deformation behavior of sedimentary rocks at the depth shallower than 2000 m. In: Maury V, Fourmaintraux D (eds) Rock at great depth, A.A. Balkema, Rotterdam, pp 19–26

    Google Scholar 

  • Zhang L (2008) A generalized three-dimensional Hoek–Brown strength criterion. Rock Mech Rock Eng 41(6):893–915

    Article  Google Scholar 

  • Zhang L, Zhu H (2007) Three-dimensional Hoek–Brown strength criterion for rocks. J Geotech Geoenviron Engi ASCE 133(9):1128–1135

    Article  Google Scholar 

  • Zhao J (2000) Applicability of Mohr–Coulomb and Hoek–Brown strength criteria to the dynamic strength of brittle rock. Int J Rock Mech Min Sci 37(7):1115–1121

    Article  Google Scholar 

Download references

Acknowledgments

The author would like to thank Dr. Evert Hoek, Masoud Rahjoo and Prof. Bill Pariseau, together with the reviewers of the Working Group’s report for their constructive review comments and suggestions.

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Correspondence to Erik Eberhardt .

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Eberhardt, E. (2012). The Hoek–Brown Failure Criterion. In: Ulusay, R. (eds) The ISRM Suggested Methods for Rock Characterization, Testing and Monitoring: 2007-2014. Springer, Cham. https://doi.org/10.1007/978-3-319-07713-0_20

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