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A Procedure for Determining Rock-Type Specific Hoek-Brown Brittle Parameter s

  • F. T. Suorineni
  • D. R. Chinnasane
  • P. K. Kaiser
Original Paper

Abstract

The Hoek-Brown failure criterion constants m and s are equivalent rock friction and cohesion parameters, respectively. On the laboratory scale, m depends on the rock type and texture (grain size), while s = 1 for all rocks. On the field scale, m is a function of rock type, texture, and rock mass quality (geological strength index, GSI), while s is simply a function of rock mass quality. The brittle Hoek-Brown damage initiation criterion (m-zero criterion) is a modification to the conventional Hoek-Brown failure criterion with m = 0 and s = 0.11. The m-zero damage initiation criterion has been shown to better predict depths of failure in excavations in some moderate to massive (GSI ≥ 75) rock masses, but over predicts depths of failure in other rock types. It is now recognized that the Hoek-Brown brittle parameter (s) is not the same for all hard, strong, brittle, moderate to massive rock masses, but depends on the rock type. However, there are no guidelines for its determination for specific rock types. This paper presents a semi-empirical procedure for the determination of rock-type specific brittle Hoek-Brown parameter s from the rock texture, mineralogical composition, and microstructure. The paper also differentiates between brittle and tenuous rocks. It is shown that, while the use of the term ‘brittle’ is appropriate for rock mechanical excavation and mode of failure in weak rocks with limited deformability, it is inappropriate for use in explaining the difference in resistance to stress-induced damage in different rock types, and can cause confusion. The terms ‘tenacity/toughness’ are introduced to describe rock resistance to stress-induced damage in excavation performance assessment, and a rock tenacity/toughness rating system is presented.

Keywords

Hoek-Brown failure criterion Hoek-Brown brittle parameter Excavation stability Damage initiation Tenuous rock Rock tenacity rating index Depth of failure 

List of symbols

a, mb, and s

rock mass constants

σ1

major principle stress (MPa)

σ3

minor principle stress (MPa)

σc

intact rock uniaxial compressive strength (MPa)

σt

intact rock tensile strength (MPa)

ϕ

friction angle (°)

c

cohesive strength (MPa)

GSI

geological strength index

mi

intact rock material constant

D

damage factor

SL

stress level

Df

depth of failure

I

strain-based brittleness index

εp

plastic strain

εfp

accumulated plastic strain at frictional strength mobilization

εcp

accumulated plastic strain at cohesion loss

σn

normal stress

A

constant that depends on the rock mineralogical composition, texture, structure, metal content, etc.

FSR

strength reduction factor

TC

texture coefficient

σ

individual value of the rock property (e.g., strength or modulus)

σ0

mean of the individual rock property (e.g., mean strength or modulus)

υ

Weibull shape parameter (homogeneity index)

φ

dispersion

Q

tunneling quality index

σci

damage initiation stress threshold

σcd

damage coalescence stress threshold

AE

acoustic emission

RTRI

rock tenacity rating index

SHF

stiffness heterogeneity factor

Mi

percentages of the various minerals present

Ki

stiffnesses of the minerals

Kwi

weighted average stiffness

Ktw

weighted total average stiffness

HI

heterogeneity index

HM

harmonic mean

SF

rating of stiffness heterogeneity factor

GF

grain size rating factor

FI

foliation index

FA

foliation strength anisotropic index

FF

foliation rating factor

SR

rock mass strength ratio

Notes

Acknowledgments

This work was funded by the Natural Sciences and Engineering Research Council (NSERC) of Canada and the Canadian Mining Industry Research Organization (CAMIRO). The authors wish to thank Mr. Charles Graham for his support. We also wish to thank the other staff of the Geomechanics Research Centre (GRC) who contributed in various ways during the research. The contribution of previous GRC staff and partners are also acknowledged, in particular, the contributions of Dr. John Henning, Dr. Hajiabdolmajid, and Dr. Mark Diederichs are highly appreciated.

References

  1. AFTES (2003) Guidelines for characterization of rock masses useful for the design of underground structures. In: Proceedings of the ITA World Tunnelling Congress: progress in tunnelling after 2000, Milan, Italy, April 2003Google Scholar
  2. Andreev GE (1995) Brittle failure of rock materials: test results and constitutive models. Taylor & Francis, London, 446 ppGoogle Scholar
  3. Aubertin M, Gill DE, Simon R (1994) On the use of the brittleness index modified (BIM) to estimate the post-peak behavior of rocks. In: Proceedings of the 1st North American rock mechanics symposium (NARMS), Austin, TX, USA, June 1994, pp 945–952Google Scholar
  4. Barla G, Barla M (2000) Continuum and discontinuum modeling in tunnel engineering. Rudarsko-Geološko-Naftni Zbornik 12:45–57Google Scholar
  5. Barton N, Lien R, Lunde J (1974) Engineering classification of rock masses for the design of tunnel support. Rock Mech Rock Eng 6(4):189–236Google Scholar
  6. Bass JD (1995) Elasticity of minerals, glasses and melts. In: Ahrens TJ (ed) Mineral physics and crystallography: a handbook of physical constants. AGU, Washington, DC, pp 45–63Google Scholar
  7. Bell FG (1978) The physical and mechanical properties of Fell Sandstones Northumberland, England. Eng Geol 12:1–29CrossRefGoogle Scholar
  8. Bieniawski ZT (1973) Engineering classification of jointed rock masses. Trans S Afr Inst Civ Eng 15:335–343Google Scholar
  9. Blyth FGH, de Freitas MH (1984) A geology for engineers. Butterworth-Heinermann, London, 336 ppGoogle Scholar
  10. Brace WF (1964) Brittle fracture of rocks. In: Proceedings of the international conference on the state of stress in the earth’s crust, Santa Monica, CA, USA, June 1963, pp 110–178Google Scholar
  11. Brown ET, Trollope DH (1967) The failure of linear brittle materials under effective tensile stress. Rock Mech Eng Geol 5:229–241Google Scholar
  12. Carmichael RS (1988) Practical handbook of physical properties of rocks and minerals. CRC Press, Boca Raton, 744 ppGoogle Scholar
  13. Castro L, McCreath DR, Oliver P (1996) Rockmass damage initiation around the Sudbury Neutrino Observatory Cavern. In: Aubertin M et al. (eds) Proceedings of the 2nd North American rock mechanics symposium (NARMS’96), Montreal, Canada, June 1996. Balkema, Rotterdam, pp 1589–1595Google Scholar
  14. Chinnasane DR (2004) Brittle rock rating for stability assessment of underground excavations. Master’s thesis (in progress), School of Engineering, Laurentian University, Sudbury, ONGoogle Scholar
  15. Cook NGW (1995) Müller lecture: why rock mechanics? In: Proceedings of the 8th ISRM international congress on rock mechanics, Tokyo, Japan, September 1995, pp 975–994Google Scholar
  16. Copur H, Bilgin N, Tuncdemir H, Balci C (2003) A set of indices based on indentation tests for assessment of rock cutting performance and rock properties. J S African Inst Min Metall 103:589–599Google Scholar
  17. Cundall PA, Potyondy DO, Lee CA (1996) Micromechanics-based models for fracture and breakout around the mine-by tunnel. In: Proceedings of the Canadian Nuclear Society International conference on deep geological disposal of radioactive waste, Winnipeg, Canada, September 1996Google Scholar
  18. Diederichs MS (2000) Instability of hard rockmasses: the role of tensile damage and relaxation. Ph.D. thesis, University of Waterloo, 566 ppGoogle Scholar
  19. Diederichs MS (2003) Manuel rocha medal recipient rock fracture and collapse under low confinement conditions. Rock Mech Rock Eng 36(5):339–381CrossRefGoogle Scholar
  20. Diederichs MS, Kaiser PK, Eberhardt E (2004) Damage initiation and propagation in hard rock during tunnelling and the influence of near-face stress rotation. Int J Rock Mech Min Sci 41:785–812CrossRefGoogle Scholar
  21. Dube AK, Singh B (1972) Effect of humidity on tensile strength of sandstone. J Mines Metals Fuels 20(1):8–10Google Scholar
  22. Eberhardt E (1998) Brittle rock fracture and progressive damage in uniaxial compression. Ph.D. thesis, Department of Geological Sciences, University of Saskatchewan, SaskatoonGoogle Scholar
  23. Eberhardt E, Stimpson B, Stead D (1999) Effects of grain size on the initiation and propagation thresholds of stress-induced brittle fractures. Rock Mech Rock Eng 32:81–99CrossRefGoogle Scholar
  24. Ehrlich R, Weinberg B (1970) An exact method for characterization of grain shape. J Sediment Res 40(1):205–212Google Scholar
  25. Evans I, Pomeroy CD (1966) The strength fracture and workability of coal. Pergamon, New York, 277 ppGoogle Scholar
  26. Falls SD, Young RP (1998) Acoustic emission and ultrasonic-velocity methods used to characterize the excavation disturbance associated with deep tunnels in hard rock. Tectonophysics 289:1–15CrossRefGoogle Scholar
  27. Fang Z, Harrison JP (2002a) Development of a local degradation approach to the modelling of brittle fracture in heterogeneous rocks. Int J Rock Mech Min Sci 39:443–457CrossRefGoogle Scholar
  28. Fang Z, Harrison JP (2002b) Application of a local degradation model to the analysis of brittle fracture of laboratory scale rock specimens under triaxial conditions. Int J Rock Mech Min Sci 39:459–476CrossRefGoogle Scholar
  29. Goktan RM (2008) Discussion on article ‘Influence of rock brittleness on TBM penetration rate in Singapore granite’ by Gong QM, Zhao J [Tunnelling and underground space technology, in press]. Tunn Undergr Space Technol 23:215–216CrossRefGoogle Scholar
  30. Goktan RM, Yilmaz Gunes N (2005) A new methodology for the analysis of the relationship between rock brittleness index and drag pick cutting efficiency. J South African Inst Mining Metall 105(10): 727–734Google Scholar
  31. Gong QM, Zhao J (2007) Influence of rock brittleness on TBM penetration rate in Singapore granite. Tunn Undergr Space Technol 22:317–324CrossRefGoogle Scholar
  32. Griffith AA (1920) The phenomena of rupture and flow in solids. Philos Trans R Soc Lond Ser A 221:163–198CrossRefGoogle Scholar
  33. Grimstad E, Bhasin R (1997) Rock support in hard rock tunnels under high stress. In: Proceedings of the international symposium on rock support—applied solutions for underground structures, Lillehammer, Norway, June 1997, pp 504–513Google Scholar
  34. Gunsallus KL, Kulhawy FH (1984) A comparative evaluation of rock strength measures. Int J Rock Mech Min Sci Geomech Abstr 21(5):233–248CrossRefGoogle Scholar
  35. Hajiabdolmajid V (2001) Mobilization of strength in brittle failure of rock. Ph.D. thesis, Queen’s University, Kingston, CanadaGoogle Scholar
  36. Hecht CA, Bönsch C, Bauch E (2005) Relations of rock structure and composition to petrophysical and geomechanical rock properties: examples from permocarboniferous red-beds. Rock Mech Rock Eng 38(3):197–216CrossRefGoogle Scholar
  37. Hoek E (1968) Brittle failure of rock. In: Stagg KG, Zienkiewicz OC (eds) Rock mechanics in engineering practice. Wiley, London, pp 99–124Google Scholar
  38. Hoek E (1999) Putting numbers to geology—an engineer’s viewpoint. Q J Eng Geol 32(1):1–19CrossRefGoogle Scholar
  39. Hoek E (2001) Rock mass properties for underground mines. In: Hustrulid WA, Bullock RL (eds) Underground mining methods: engineering fundamentals and international case studies. Society for Mining, Metallurgy, and Exploration (SME), Littleton, ColoradoGoogle Scholar
  40. Hoek E, Brown ET (1980) Underground excavations in rock. Institution of Mining and Metallurgy, London, 527 ppGoogle Scholar
  41. Hoek E, Carranza-Torres C, Corkum B (2002) Hoek-Brown criterion—2002 edition. In: Proceedings of the NARMS-TAC conference, Toronto, Canada, July 2002, vol 1. Balkema, Rotterdam, pp 267–273Google Scholar
  42. Hoek E, Kaiser PK, Bawden WF (1995) Support of underground excavations in hard rock. Balkema, Rotterdam, 215 ppGoogle Scholar
  43. Howarth DF, Rowlands JC (1987) Quantitative assessment of rock texture and correlation with drillability and strength properties. Rock Mech Rock Eng 20:57–85CrossRefGoogle Scholar
  44. Howarth DF, Adamson WR, Berndt JR (1986) Correlation of model tunnel boring and drilling machine performances with rock properties. Int J Rock Mech Min Sci 23(2):171–175CrossRefGoogle Scholar
  45. Kaiser J (1950) Untersuchung über das Auftreten von Geräuschen beim Zugversuch. Dr.-Ing. Dissertation, Fakultät für Maschinenwesen und Elektrotechnik der Technischen Universität München (TUM)Google Scholar
  46. Kent FL, Bigby D, Coggan JS, Chilton JL (2002) Comparison of acoustic emission and stress measurement results to evaluate the application of the Kaiser effect for stress determination in underground mines. In: Proceedings of the 21st International Conference on ground control in mining, Morgantown, West Virgina, USA, pp 270–277, ISBN 0-939084-56-9 Google Scholar
  47. Lavrov A (2003) The Kaiser effect in rocks: principles and stress estimation techniques. Int J Rock Mech Min Sci 40:151–171CrossRefGoogle Scholar
  48. Manutchehr-Danai M (2005) Dictionary of gems and gemology, 2nd edn. Springer, Heidelberg, 565 ppGoogle Scholar
  49. Martin CD (1989) Characterizing in situ stress domains at the AECL Underground Research Laboratory. In: Proceedings of the 42nd Canadian geotechnical conference. Winnipeg, Canada, pp 61–74Google Scholar
  50. Martin CD (1993) The strength of massive Lac du Bonnet granite around underground openings. Ph.D. thesis, University of Manitoba, 278 ppGoogle Scholar
  51. Martin CD, Read RS, Martino JB (1997) Observations of brittle failure around a circular test tunnel. Int J Rock Mech Mining Sci Geomech Abstr, 34 Google Scholar
  52. Martin CD, Kaiser PK, McCreath DR (1999) Hoek-Brown parameters for predicting the depth of brittle failure around tunnels. Can Geotech J 36:136–151CrossRefGoogle Scholar
  53. McDonough WF (2004) Lecture notes. Department of Geology, University of Maryland, MarylandGoogle Scholar
  54. Merriam-Webster Inc. (2003) (Gove PB, ed) Webster’s new international dictionary. Merriam-WebsterGoogle Scholar
  55. Obert L, Duvall WI (1967) Rock mechanics and the design of structures in rock. Wiley, New York, p 278Google Scholar
  56. Olsson WA (1974) Grain size dependence of yield stress in marble. J Geophys Res 79:4859–4862CrossRefGoogle Scholar
  57. Onodera TF, Asoka Kumara HM (1980) Relation between texture and mechanical properties of crystalline rocks. Bull Int Assoc Eng Geol 22:173–177Google Scholar
  58. Pelli F, Kaiser PK, Morgenstern NR (1991) An interpretation of ground movements recorded during construction of the Donkin-Morien tunnel. Can Geotech J 28(2):239–254CrossRefGoogle Scholar
  59. Ramsay JG (1967) Folding and fracturing of rocks. McGraw Hill, LondonGoogle Scholar
  60. Read RS (1994) Interpreting excavation-induced displacements around a tunnel in highly stressed granite. Ph.D. thesis, Department of Civil and Geological Engineering, University of Manitoba, Winnipeg, 324 ppGoogle Scholar
  61. Read RS (2004) 20 years of excavation response studies at AECL’s Underground Research Laboratory. Int J Rock Mech Mining Sci 41:1251–1275 CrossRefGoogle Scholar
  62. RocScience (2005) Phase2 software: 2D finite element analysis of excavationsGoogle Scholar
  63. Seto M, Utagawa M, Katsuyama K, Nag GK, Vutukuri VS (1997) In situ stress determination by acoustic emission technique. Int J Rock Mech Min Sci 34(3/4):638 (paper 238)Google Scholar
  64. Singh SP (1986) Brittleness and the mechanical winning of coal. Min Sci Technol 3:173–180CrossRefGoogle Scholar
  65. Singh SP (1987) Criterion for the cutability of coal. In: Szwilski AB, Richards MJ (eds) Underground mining methods and technology. Elsevier, Amsterdam, pp 225–239Google Scholar
  66. Skinner WJ (1959) Experiments on the compressive strength of anhydrite. Engineer 255–259:288–292Google Scholar
  67. Stacey TR (1981) A simple extension strain criterion for fracture of brittle rock. Int J Rock Mech Min Sci 18:469–474CrossRefGoogle Scholar
  68. Stacey TR, Page CH (1986) Practical handbook for underground rock mechanics. Trans Tech Publications, Germany, 145 ppGoogle Scholar
  69. Suorineni FT, Kaiser PK (2002) Characteristic acoustic properties of sulphide ores and host rocks. In: Hammah R, Bawden WF, Curran J, Telsnicki M (eds) Proceedings of the 5th North American rock mechanics symposium (NARMS), Toronto, Canada, July 2002. University of Toronto Press, pp 403–410Google Scholar
  70. Suorineni FT, Chinnasane DR, Kaiser PK (2004) Safe rapid drifting—drift stability. In: Proceedings of the CIM annual meeting, Edmonton, Alberta, CD-ROM, 8 ppGoogle Scholar
  71. Tanaka JS (1987) “How big is big enough?” Sample size and goodness of fit in structural equation models with latent variables. Child Dev 58(1):134–146CrossRefGoogle Scholar
  72. Tang CA (1995) Numerical simulation of rock failure process. In: Proceedings of the 2nd youth symposium on rock mechanics and rock engineering in China, ChengduGoogle Scholar
  73. Tang CA (1997) Numerical simulation of progressive rock failure and associated seismicity. Int J Rock Mech Min Sci 34:249–262CrossRefGoogle Scholar
  74. Tang CA, Kaiser PK (1998) Numerical simulation of cumulative damage and seismic energy release during brittle rock failure—part 1: fundamentals. Int J Rock Mech Min Sci 35(2):113–121CrossRefGoogle Scholar
  75. Tang C, Liang Z, Zhang Y, Tao X (2005) Three-dimensional material failure process analysis. Key Eng Mater 297–300:1196–1201CrossRefGoogle Scholar
  76. Tapponnier P, Brace WF (1976) Development of stress-induced microcracks in Westerly granite. Int J Rock Mech Min Sci Geomech Abstr 13:103–112CrossRefGoogle Scholar
  77. Thierry F (2007) XLSTAT softwareGoogle Scholar
  78. Tsidzi KEN (1990) The influence of foliation on point load strength anisotropy of foliated rocks. Eng Geol 29:49–58CrossRefGoogle Scholar
  79. Tullis J, Yund RA (1977) Experimental deformation of dry Westerly granite. J Geophys Res 82:5705–5718CrossRefGoogle Scholar
  80. Villaescusa E, Seto M, Baird GR (2002) Stress measurements from oriented core. Int J Rock Mech Min Sci 39(5):603–615CrossRefGoogle Scholar
  81. Wagner H (1987) Design, support of underground excavations in highly stressed rock. In: Proceedings of the 6th ISRM Congress, Montreal, Canada, September 1987, pp 1443–1457Google Scholar
  82. Weibull W (1951) A statistical distribution function of wide applicability. J Appl Mech 18:293–297Google Scholar
  83. Yuan SC, Harrison JP (2006) A review of the state of the art in modelling progressive mechanical breakdown and associated fluid flow in intact heterogeneous rocks. Int J Rock Mech Min Sci 43:1001–1022CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • F. T. Suorineni
    • 1
  • D. R. Chinnasane
    • 2
  • P. K. Kaiser
    • 1
  1. 1.MIRARCO Mining Innovation/Geomechanics Research CentreLaurentian UniversitySudburyCanada
  2. 2.School of EngineeringLaurentian UniversitySudburyCanada

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