Bulletin of Engineering Geology and the Environment

, Volume 78, Issue 8, pp 5919–5936 | Cite as

Quantitative evaluation of rock brittleness based on crack initiation stress and complete stress–strain curves

  • Guoqing ChenEmail author
  • Wanzeng Jiang
  • Xiang Sun
  • Cong Zhao
  • Chang’An Qin
Original Paper


Brittleness is an important rock material property, and its accurate evaluation has guiding significance in construction as well as in disaster prevention and reduction. Considering the limitations of the existing brittleness indices, a new brittleness index based on the overall stress–strain process of a rock mass is established that considers both the stress growth rate between the peak stress and the crack initiation stress before the peak, as well as the stress descent rate after the peak. Uniaxial and triaxial compression tests were conducted to evaluate the new index. The results of the tests show that the new index can accurately determine the rock brittleness according to the prepeak stress–strain curve under uniaxial loading system conditions, which compensates for the limitation of inaccurate postpeak curves for brittle rock. Under triaxial compression conditions, the new index more clearly represents the influence of the confining pressure on the brittleness of marble. The reliability and comprehensiveness of the new index are verified, and these research results may improve the existing evaluation of rock brittleness.


Rock mechanics Brittleness index Stress–strain curve Crack initiation Influence of confining pressure 

List of symbols


Brittleness index


Major principal stress


Minor principal stress


Uniaxial compressive strength


Splitting tensile strength


Crack initiation stress


Peak compressive strength


Residual compressive strength


Peak strain


Residual strain


Axial strain

\( {\varepsilon}_c^p \)

Plastic strain necessary for cohesion loss

\( {\varepsilon}_f^p \)

Plastic strain necessary for frictional strengthening


Recoverable strain energy


Total strain energy


Elasticity modulus of prepeak


Poisson’s ratio


Elasticity modulus of postpeak


Stress slope of postpeak


Internal friction angle


Rock tenacity rating index


Stiffness factor


Texture factor


Foliation factor


Microhardness of rock


Macrohardness of rock


Fracture toughness


Proportion of detritus whose particle size is smaller than 11.2mm


Proportion of detritus whose particle size is smaller than 0.6mm


Maximum impact load


Penetration depth


Increment load


Attenuation load



This work is supported by the National Key R&D Program of China (2017YFC1501301) and the National Natural Science Foundation of China (grant nos. 41521002 and 41572283). This work is also supported by the Funding of Science and Technology Office of Sichuan Province (grant no. 2017TD0018) and the research fund of the State Key Laboratory of Geohazard Prevention and Geoenvironment Protection (no. SKLGP2018Z011).


  1. Altindag R (2002) The evaluation of rock brittleness concept on rotary blast hold drills. J South Afr Inst Min Metall 102:61–66. Google Scholar
  2. Altindag R (2003) Correlation of specific energy with rock brittleness concepts on rock cutting. J South Afr Inst Min Metall 103:163–171. Google Scholar
  3. Altindag R (2010) Assessment of some brittleness indexes in rock-drilling efficiency. Rock Mech Rock Eng 43:361–370. CrossRefGoogle Scholar
  4. Baron LI, Loguntsov BM, Posin EZ (1962) Determination of properties of rocks. Gozgotekhizdat, Moscow (in Russian)Google Scholar
  5. Bishop AW (1967) Progressive failure with special reference to the mechanism causing it. In: Proceedings of the Geotechnical Conference, Oslo, Norway, pp 142–150Google Scholar
  6. Blindheim OT, Bruland A (1998) Boreability testing. In: Norwegian TBM tunnelling: 30 years of experience with TBMs in Norwegian tunnelling. Norwegian Soil and Rock Engineering Association, pp 21-27Google Scholar
  7. Coates DF, Parsons RC (1966) Experimental criteria for classification of rock substances. Int J Rock Mech Min Sci Geomech Abstr 3:181–189. CrossRefGoogle Scholar
  8. Copur H, Bilgin N, Tuncdemir H et al (2003) A set of indices based on indentation tests for assessment of rock cutting performance and rock properties. J South Afr Inst Min Metall 103(9):589–599. Google Scholar
  9. Diederichs MS (2003) Manuel rocha medal recipient rock fracture and collapse under low confinement conditions. Rock Mech Rock Eng 36(5):339–381. CrossRefGoogle Scholar
  10. Diederichs MS (2007) The 2003 Canadian Geotechnical Colloquium: mechanistic interpretation and practical application of damage and spalling prediction criteria for deep tunnelling. Can Geotech J 44(9):1082–1116. CrossRefGoogle Scholar
  11. Gong QM, Zhao J (2007) Influence of rock brittleness on TBM penetration rate in Singapore granite. Tunn Undergr Space Technol 22(3):317–324. CrossRefGoogle Scholar
  12. Hajiabdolmajid V, Kaiser P (2003) Brittleness of rock and stability assessment in hard rock tunneling. Tunn Undergr Space Technol 18:35–48. CrossRefGoogle Scholar
  13. Heidari M, Khanlari GR, Torabi-Kaveh M et al (2014) Effect of porosity on rock brittleness. Rock Mech Rock Eng 47:785–790. CrossRefGoogle Scholar
  14. Hetenyi M (1966) Handbook of experimental stress analysis. Wiley, New York, p 15Google Scholar
  15. Hoek E, Carranza-Torres CT, Corkum B (2002) Hoek–Brown failure criterion—2002 edition. In: Proceedings of the 5th North American Rock Mechanics Symposium and 17th Tunneling Association of Canada Conference, Toronto, Canada, July 2002.
  16. Honda H, Sanada Y (1956) Hardness of coal. Fuel 35:451–461Google Scholar
  17. Hucka V, Das B (1974) Brittleness determination of rocks by different methods. Int J Rock Mech Min Sci Geomech Abstr 11(10):389–392. CrossRefGoogle Scholar
  18. Kahraman S (2002) Correlation of TBM and drilling machine performances with rock brittleness. Eng Geol 65(4):269–283. CrossRefGoogle Scholar
  19. Lawn BR, Marshall DB (1979) Hardness, toughness, and brittleness: an indentation analysis. J Am Ceram Soc 62(7–8):347–350. CrossRefGoogle Scholar
  20. Li QH, Chen M, Jin Y et al (2012) Indoor evaluation method for shale brittleness and improvement. Chin J Rock Mech Eng 31(8):1680–1685 (in Chinese)Google Scholar
  21. 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. CrossRefGoogle Scholar
  22. Meng FZ, Zhou H, Zhang CQ et al (2015) Evaluation methodology of brittleness of rock based on post-peak stress–strain curves. Rock Mech Rock Eng 48:1787–1805. CrossRefGoogle Scholar
  23. Miskimins JL (2012) The impact of mechanical stratigraphy on hydraulic fracture growth and design considerations for horizontal wells. Bulletin 91(4):475–499Google Scholar
  24. Morley A (1954) Strength of materials, 11th edn. Longmans, Green, London, p 532Google Scholar
  25. Obert L, Duvall WI (1967) Rock mechanics and the design of structures in rock. Wiley, New York, p 278Google Scholar
  26. Protodyakonov MM (1963) Mechanical properties and drillability of rocks. In: Proceedings of the 5th Symposium on Rock Mechanics, University of Minnesota, May 1962, pp 103–118Google Scholar
  27. Quinn JB, Quinn GD (1997) Indentation brittleness of ceramics: a fresh approach. J Mater Sci 32(16):4331–4346. CrossRefGoogle Scholar
  28. Ramsey JG (1967) Folding and fracturing of rocks. McGraw-Hill, London, p 289Google Scholar
  29. Reichmuth DR (1967) Point load testing of brittle materials to determine tensile strength and relative brittleness. In: Proceedings of the 9th US Symposium on Rock Mechanics (USRMS), Golden, Colorado, April 1967. American Rock Mechanics Association (ARMA), pp 134–159Google Scholar
  30. Rickman R, Mullen MJ, Petre JE et al (2008) A practical use of shale petrophysics for stimulation design optimization: all shale plays are not clones of the Barnett shale. In: Proceedings of the SPE Annual Technical Conference and Exhibition, Denver, Colorado, September 2008. Society of Petroleum Engineers.
  31. Rybacki E, Reinicke A, Meier T et al (2015) What controls the mechanical properties of shale rocks?—Part I: strength and Young’s modulus. J Pet Sci Eng 135:702–722. CrossRefGoogle Scholar
  32. Rybacki E, Meier T, Dresen G (2016) What controls the mechanical properties of shale rocks?—Part II: brittleness. J Pet Sci Eng 144:39–58. CrossRefGoogle Scholar
  33. Singh SP (1986) Brittleness and the mechanical winning of coal. Min Sci Technol 3(3):173–180. CrossRefGoogle Scholar
  34. Suorineni FT, Chinnasane DR, Kaiser PK (2009) A procedure for determining rock-type specific Hoek–Brown brittle parameters. Rock Mech Rock Eng 42(6):849–881. CrossRefGoogle Scholar
  35. Tarasov BG, Potvin Y (2012) Absolute, relative and intrinsic rock brittleness at compression. Min Technol 121(4):218–225. CrossRefGoogle Scholar
  36. Tarasov B, Potvin Y (2013) Universal criteria for rock brittleness estimation under triaxial compression. Int J Rock Mech Min Sci 59:57–69. CrossRefGoogle Scholar
  37. Wang Y, Li X, Wu YF et al (2014) Research on relationship between crack initiation stress level and brittleness indices for brittle rocks. Chin J Rock Mech Eng 33(2):264–275 (in Chinese). CrossRefGoogle Scholar
  38. Xia YJ, Li LC, Tang CA et al (2016) Rock brittleness evaluation based on stress dropping rate after peak stress and energy ratio. Chin J Rock Mech Eng 35(6):1141–1154 (in Chinese). CrossRefGoogle Scholar
  39. Xia YJ, Li LC, Tang CA et al (2017a) A new method to evaluate rock mass brittleness based on stress–strain curves of class I. Rock Mech Rock Eng 50:1123–1139. CrossRefGoogle Scholar
  40. Xia YJ, Li LC, Tang CA et al (2017b) Experiment and numerical research on failure characteristic and brittleness index for reservoir sandstone. Chin J Rock Mech Eng 36(1):10–28 (in Chinese). CrossRefGoogle Scholar
  41. Yagiz S (2006) An investigation on the relationship between rock strength and brittleness. In: Proceedings of the 59th Geological Congress of Turkey, Ankara, Turkey, March 2006. MTA General Directory Press, p 352Google Scholar
  42. Yagiz S (2009) Assessment of brittleness using rock strength and density with punch penetration test. Tunn Undergr Space Technol 24(1):66–74. CrossRefGoogle Scholar
  43. Yarali O, Kahraman S (2011) The drillability assessment of rocks using the different brittleness values. Tunn Undergr Space Technol 26(2):406–414. CrossRefGoogle Scholar
  44. Yilmaz NG, Karaca Z, Goktan RM et al (2009) Relative brittleness characterization of some selected granitic building stones: influence of mineral grain size. Constr Build Mater 23(1):370–375. CrossRefGoogle Scholar
  45. Yuan JL, Deng JG, Zhang DY et al (2013) Fracability evaluation of shale-gas reservoirs. Acta Pet Sin 3(1):523–527 (in Chinese)Google Scholar
  46. Zhang J, Ai CH, Li YW et al (2017) Brittleness evaluation index based on energy variation in the whole process of rock failure. Chin J Rock Mech Eng 36(6):1326–1340 (in Chinese). CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Geohazard Prevention and Geoenvironment ProtectionChengdu University of TechnologyChengduChina

Personalised recommendations