Geotechnical and Geological Engineering

, Volume 32, Issue 2, pp 525–546 | Cite as

A Review of the Tensile Strength of Rock: Concepts and Testing

  • Matthew A. Perras
  • Mark S. Diederichs
Original paper


A review of the tensile strength of rock was conducted to determine the relationship between direct tensile strength (DTS) and Brazilian tensile strength (BTS) and to examine the validity of estimating tensile strength from other measured properties, such as the crack initiation (CI) threshold. A data set was gathered from the existing literature where tensile values could be reliably correlated with unconfined compressive strength or CI values. It was determined that the BTS obtained in standard testing is generally greater than the equivalent DTS and that this relationship is rock type dependent. CI yields a reasonable estimate of tensile strength and this correlation is improved when the BTS values are reduced to DTS values by rock type specific correlations. The factor f, in DTS = f BTS, can be considered to be approximately 0.9 for metamorphic, 0.8 for igneous and 0.7 for sedimentary rocks. The relationships presented demonstrate that there is wide scatter in the available data for estimating tensile strength likely due to both specimen variability and testing configuration, including platen geometry and relative stiffness. Estimates of tensile strength should only be used for preliminary design purposes and measurements should be made to confirm preliminary assumptions for each design.


Laboratory testing Direct tensile Indirect tensile Brazilian tensile Unconfined compressive strength Crack initiation 



The authors would like to thank the Nuclear Waste Management Organization (NWMO) of Canada and the Natural Sciences and Engineering Research Council (NSERC) of Canada for funding this review. Special thanks is due to Dr. Evert Hoek for use of testing data and for discussions related to this paper.


  1. Akazawa T (1943) New test method for evaluating internal stress due to compression of concrete: the splitting tension test. J Japan Soc Civil Eng 29:777–787Google Scholar
  2. Alehossein H, Boland JN (2004) Strength, toughness, damage and fatigue of rock. In: Atrens A, Boland JN, Clegg R, Giffiths JR (eds) Proceedings of the international conference on structural integrity and fracture. Brisbane, Australia, SIF 836. Accessed 13 Oct 2013
  3. Andreev GE (1991a) A review of the Brazilian test for rock tensile strength determination. Part I: calculation formula. Min Sci Technol 13(3):445–456. doi: 10.1016/0167-9031(91)91006-4 CrossRefGoogle Scholar
  4. Andreev GE (1991b) A review of the Brazilian test for rock tensile strength determination. Part II: contact conditions. Min Sci Technol 13(3):457–465. doi: 10.1016/0167-9031(91)91035-G CrossRefGoogle Scholar
  5. ASTM (2008a) D2936-08: standard test method for direct tensile strength of intact rock core specimens. ASTM International, West ConshohockenGoogle Scholar
  6. ASTM (2008b) D3967-08: standard test method for splitting tensile strength of intact rock core specimens. ASTM International, West ConshohockenGoogle Scholar
  7. Bell FG (1981) A survey of the physical properties of some carbonate rocks. Bull Int Assoc Eng Geol 24:105–110. doi: 10.1007/BF02595261 CrossRefGoogle Scholar
  8. Berrenbaum R, Brodie I (1959) Measurement of the tensile strength of brittle materials. Brit J Appl Phys 10:281–286. Accessed 14 Dec 2012
  9. Betournay M (1983) Examinatin of URL-1, URL-2, and URL-5 Uniaxial compressive and tensile test data. Canadian Centre for Mineral and Energy Technology, Mining Research Laboratories Division Report, ERP/MRL 83-26(TR)Google Scholar
  10. Bieniawski ZT (1967) Mechanism of brittle fracture of rock: part I—theory of the fracture process. Int J Rock Mech Min Sci Geomech Abs 4(4):395–406. doi: 10.1016/0148-9062(67)90030-7 CrossRefGoogle Scholar
  11. Brace WF (1964) Brittle fracture of rocks. In: Judd WR (ed) Proceedings of the International Conference on State of Stress in the Earth’s Crust. Elsevier, New York, pp 111–174Google Scholar
  12. Brace WF, Paulding B, Scholz C (1966) Dilatancy in the fracture of crystalline rocks. J Geophys Res 71:3939–3953. doi: 10.1029/JZ071i016p03939 CrossRefGoogle Scholar
  13. Cai M (2010) Practical estimates of tensile strength and the Hoek-Brown strength parameter m i of brittle rocks. Rock Mech Rock Eng 43:167–184. doi: 10.1007/s00603-009-0053-1 CrossRefGoogle Scholar
  14. Carneiro FLLB (1943) A new method to determine the tensile strength of concrete. In: Proceedings of the 5th Meeting of the Brazilian Association for Technical RulesGoogle Scholar
  15. Colback PSB (1966) An analysis of brittle fracture initiation and propagation in the Brazilian test. 1st ISRM congress. Lisbon, Portugal, 1CONGRESS-1966-066Google Scholar
  16. Coviello A, Lagioia R, Nova R (2005) On the measurement of the tensile strength of soft rocks. Rock Mech Rock Eng 38(4):251–273. doi: 10.1007/s00603-005-0054-7 CrossRefGoogle Scholar
  17. Crouch SL (1970) Experimental determination of volumetric strains in failed rock. Int J Rock Mech Min Sci Geomech Abs 7(6):589–603. doi: 10.1016/0148-9062(70)90020-3 CrossRefGoogle Scholar
  18. Dan DQ, Konietzky H, Herbst M (2013) Brazilian tensile strength tests on some anisotropic rocks. Int J Rock Mech Min Sci 58:1–7. doi: 10.1016/j.ijrmms.2012.08.010 Google Scholar
  19. Diedeirchs MS (1999) Instability of hard rockmasses: the role of tensile damage and relaxation. PhD Thesis, Department of Civil Engineering, University of Waterloo, Waterloo, Canada, pp 566Google Scholar
  20. Diederichs MS (2003) Rock fracture and collapse under low confinement conditions. Rock Mech Rock Eng 36(5):339–381. doi: 10.1007/s00603-003-0015-y CrossRefGoogle Scholar
  21. 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 44:1082–1116. doi: 10.1139/T07-033 CrossRefGoogle Scholar
  22. Diederichs MS, Kaiser PK (1999) Tensile strength and abutment relaxation as failure control mechanics in underground excavations. Int J Rock Mech Min Sci 36:69–96. doi: 10.1016/S0148-9062(98)00179-X CrossRefGoogle Scholar
  23. Diederichs MS, Martin CD (2010) Measurement of spalling parameters from laboratory testing. In: Zhao J, Labiouse V, Dudt JP, Mathier JF (eds) Proc of Eurock 2010. Lausanne, SwitzerlandGoogle Scholar
  24. Eberhardt E, Stead D, Stimpson B, Read RS (1998) Identifying crack initiation and propagation thresholds in brittle rock. Can Geotech J 35:222–233. doi: 10.1139/t97-091 CrossRefGoogle Scholar
  25. Efimov VP (2009) The rock strength in different tension conditions. J Min Sci 45(6):569–575. doi: 10.1007/s10913-009-0071-0 CrossRefGoogle Scholar
  26. Eloranta P (2006) Posiva laboratory testing report WR-2006-80.
  27. Eloranta P, Hakala M (1998) Posiva laboratory testing report WR-98-49.
  28. Eloranta P, Hakala M (1999) Posiva laboratory testing report WR-99-47.
  29. Erarslan N, Williams DJ (2012) Experimental, numerical and analytical studies on tensile strength of rocks. Int J Rock Mech Min Sci 49(1):21–30. doi: 10.1016/j.ijrmms.2011.11.007 CrossRefGoogle Scholar
  30. Fairhurst C (1961) Laboratory measurements of some physical properties of rock. In: Proceedings of the fourth symposium on rock mechanics. Pennsylvania, USAGoogle Scholar
  31. Falls S (1993) Ultrasonic imaging and acoustic emission studies of microcrack development in lac du bonnet granite. PhD Thesis, Queens University, Kingston, CanadaGoogle Scholar
  32. Franklin JA, Dusseault MB (1989) Rock engineering. McGraw-Hill, New York, p 600Google Scholar
  33. Ghazvinian E, Diederichs M, Archibald J (2011) Challenges related to standardized detection of crack initiation thresholds for lower-bound or ultra-long-term strength prediction of rock. In: Proceedings of the Pan-Am CGS Geotechnical Conference. Toronto, CanadaGoogle Scholar
  34. Golder (2011) Geotechnical data report: geotechnical and hydrogeological investigation—Ottawa light rail transit (OLRT) tunnel (segment 2). Ottawa, Ontario. Report Number 10-1121-0222Google Scholar
  35. Gorski B (1993) Tensile testing apparatus. United States Patent, 5193396Google Scholar
  36. Gorski B, Yu YS (1991) Tensile strength tests on URL rock specimens from borehole 401-009-HF1. CANMET Mining Research Laboratories report MRL 91-080(TR)Google Scholar
  37. Gorski B, Conlon B, Ljunggren B (2007) Forsmark Site investigation—Determination of the direct and indirect tensile strength on cores from borehole KFM01D. SKB P-07-76,Svensk ärnbränslehantering ABGoogle Scholar
  38. Gorski B, Anderson T, Conlon T (2009) DGR site characterization documents, technical reports TR-07-03 and TR-08-11.
  39. Gorski B, Anderson T, Conlon T (2010) DGR site characterization documents, technical reports TR-08-24 and TR-08-36.
  40. Gorski B, Rodgers D, Conlon B (2011) DGR site characterization document, technical report TR-09-07
  41. Grasle W, Plischke I (2010) LT experiment: mechanical behavior of Opalinus clay, final report from Phases 6-14. Mont Terri Project Technical Report 2009–07Google Scholar
  42. Graue R, Siegesmund S, Middendorf B (2011) Quality assessment of replacement stones for the Cologne Cathedral: mineralogical and petrophysical requirements. Environ Earth Sci 63:1799–1822. doi: 10.1007/s12665-011-1077-x CrossRefGoogle Scholar
  43. Griffith AA (1921) The phenomena of rupture and flow in solids. Philos Trans R Soc Lond 221A:163–198CrossRefGoogle Scholar
  44. Griffith AA (1924) Theory of rupture. In: Proceedings of the 1st international congress on applied mechanics. Delft, pp 55–63Google Scholar
  45. Haimson BC, Cornet FH (2003) ISRM suggested methods for rock stress estimation—Part 3: hydraulic fracturing (HF) and/or hydraulic testing of pre-existing fractures (HTPF). Int J of Rock Mech Min Sci 40:1011–1020. doi: 10.1016/j.ijrmms.2003.08.002 CrossRefGoogle Scholar
  46. Hakala M, Heikkila E (1997) Posiva laboratory testing reports WR-97-04, WR-97-07e.
  47. Hansen FD, Vogt TJ (1987) Thermo mechanical properties of selected shales. Oak Ridge National Laboratory Report ORNL/Sub/85-97343/2 (RSI-0305)Google Scholar
  48. Hardy HR, Jayaraman NI (1970) An investigation of methods for the determination of the tensile strength of rock. In: Proceedings of the 2nd congress international society for rock mechanics, Belgrade, vol 3, pp 85–92Google Scholar
  49. Heikkila E, Hakala M (1998) Posiva laboratory testing reports WR-98-06e, WR-98-21e.
  50. Hoek E (1964) Fracture of anisotropic rock. J S Afr Inst Min Metall 64(10):501–518.
  51. Hoek E, Brown T (1997) Practical estimates of rock mass strength. J Rock Mech Min Sci 34(8):1165–1186.
  52. Hondros G (1959) The evaluation of Poisson’s ratio and the modulus of materials of a low tensile resistance by the Brazilian (indirect tensile) test with particular reference to concrete. Aust J Appl Sci 10(3):243–268Google Scholar
  53. ISRM (1978) Suggested methods for determining tensile strength of rock materials. Int J Rock Mech Min Sci Geomech Abstr 15(3):99–103. doi: 10.1016/0148-9062(78)90003-7 CrossRefGoogle Scholar
  54. Jacobsson L (2004) Site investigation reports. Swedish nuclear fuel and waste management Co. Technical Reports P-04-170, P-04-172, P-04-173, P-04-174, P-04-223, P-04-225, and P-04-226.
  55. Jacobsson L (2005) Site investigation reports. Swedish nuclear fuel and waste management Co. Technical Reports P-05-97, P-05-98, P-05-120, P-05-121, P-05-211, and P-05-212.
  56. Jacobsson L (2006) Site investigation reports. Swedish nuclear fuel and waste management Co. Technical Reports P-06-37, P-06-38, P-06-73, P-06-74, P-06-270, P-06-271, P-06-299, and P-06-300.
  57. Jacobsson L (2007) Site investigation reports. Swedish nuclear fuel and waste management Co. Technical Reports P-07-142, P-07-143, P-07-145, P-07-146, and P-07-207.
  58. Jaeger JC (1967) Failure of rocks under tensile conditions. Int J Rock Mech Min Sci Geomech Abstr 4(2):219–227. doi: 10.1016/0148-9062(67)90046-0 CrossRefGoogle Scholar
  59. Jaeger JC, Cook NGW (1969) Fundamentals of rock mechanics. Methuen and Co Ltd., London, p 513Google Scholar
  60. Jaeger JC, Hoskins ER (1966) Rock failure under the confined Brazilian test. J Geophys Res 71:2651–2659. doi: 10.1029/JZ071i010p02651 Google Scholar
  61. Klanphumeesri S (2010) Direct tension testing of rock specimens. Masters of Engineering Thesis, Suranaree University of TechnologyGoogle Scholar
  62. Lajtai EZ, Lajtai VN (1974) The evolution of brittle fracture in rocks. J Geo Soc 130(1):1–16. doi: 10.1144/gsjgs.130.1.0001 CrossRefGoogle Scholar
  63. Lama RD, Vutukuri VS (1978) Handbook on mechanical properties of rocks—testing techniques and results 3(1). Trans Tech Publications, ClausthalGoogle Scholar
  64. Langford JC (2013) Application of reliability methods to the design of underground structures. PhD Thesis, Queen’s University, Kingston, Ontario, CanadaGoogle Scholar
  65. Lee MY, Haimson BC (1993) Laboratory study of borehole breakouts in Lac du Bonnet Granite: a case of extensile failure mechanism. Int J Rock Mech Min Sci Geomech Abstr 30(7):1039–1045CrossRefGoogle Scholar
  66. Li D,Wong LNY (2012) The Brazilian disc test for rock mechanics applications: review and new insights. Rock Mech Rock Eng May. doi: 10.1007/s00603-012-0257-7
  67. Lim SS, Martin CD (2010) Core disking and its relationship with stress magnitude for Lac du Bonnet granite. Int J Rock Mech Min Sci 47: 254-264. doi: 10.1016/j.ijrmms.2009.11.007
  68. Lo KY, Hori M (1979) Deformation and strength properties of some rocks in Southern Ontario. Can Geotech J 16:108–120. doi: 10.1139/t79-010 CrossRefGoogle Scholar
  69. Lockner D (1993) The role of acoustic emission in the study of rock. Int J Rock Mech Min Sci Geomech Abstr 30(7):883–899. doi: 10.1016/0148-9062(93)90041-B CrossRefGoogle Scholar
  70. Luong MP (1990) Tensile and shear strengths of concrete and rock. Eng Fract Mech 35(1,2,3):127–135. doi: 10.1016/0013-7944(90)90190-R
  71. Markides CF, Pazis DN, Kourkoulis SK (2011) Influence of friction on the stress field of the Brazilian tensile test. Rock Mech Rock Eng 44:113–119. doi: 10.1007/s00603-010-0115-4 CrossRefGoogle Scholar
  72. Markides CF, Pazis DN, Kourkoulis SK (2012) The Brazilian disc under non-uniform distribution of radial pressure and friction. Int J Rock Mech Min Sci 50(1):47–55. doi: 10.1016/j.ijrmms.2011.12.012 CrossRefGoogle Scholar
  73. Martin CD (1994) The strength of massive Lac du Bonnet Granite around underground openings. PhD Thesis, University of ManitobaGoogle Scholar
  74. Mellor M, Hawkes I (1971) Measurement of tensile strength by diametral compression of discs and annuli. Eng Geol 5(3):173–225. doi: 10.1016/0013-7952(71)90001-9 CrossRefGoogle Scholar
  75. Mishra DA, Basu A (2012) Use of the block punch test to predict the compressive and tensile strengths of rocks. Int J Rock Mech Min Sci 51:119–127. doi: 10.1016/j.ijrmms.2012.01.016 CrossRefGoogle Scholar
  76. Murrell SAF (1963) A criterion for brittle fracture of rocks and concrete under triaxial stress and the effect of pore pressure on the criterion. In: Fairhurst (ed) Rock mechanics. Proceedings of the fifth rock mechanics symposium, University of Minnesota, Oxford, Pergamon, pp 563–577Google Scholar
  77. Myer LR, Kemeny JM, Zheng Z, Suarex R, Ewy RT, Cook NGW (1992) Extensile cracking in porous rock under differential compressive stress. In: Li LY (ed) Micromechanical modeling of quasi-brittle materials behaviour. Applied Mechanics Reviews, 45(8):263–280. doi: 10.1115/1.3119757
  78. Pandey P, Singh DP (1986) Deformation of a rock in different tensile tests. Eng Geol 22(3):281–292. doi: 10.1016/0013-7952(86)90029-3 CrossRefGoogle Scholar
  79. Perras MA (2009) Tunnelling in horizontally laminated ground: the influence of lamination thickness on anisotropic behaviour and practical observations from the Niagara Tunnel Project. Masters Thesis, Queen’s University, Kingston, Ontario, CanadaGoogle Scholar
  80. Perras MA, Langford C, Ghazvinian E, Diederichs MS (2012) Numerical delineation of the excavation damage zones: from rock properties to statistical distribution of the dimensions. In: Proceedings of the Eurock, Stockholm, SwedenGoogle Scholar
  81. Perras MA, Besaw D, Diederich MS (2013) Geological and geotechnical observations from the Niagara Tunnel Project. Submitted to the Bulletin of Engineering Geology and the Environment, BOEG-D-12-00133R1Google Scholar
  82. Perras MA, Ghazvinian E, Amann F, Wannenmacher H, Diederichs MS, (2013b) Back analysis of rock mass behavior of the Quintner Limestone at the Gonzen mine near Sargans, Switzerland. In: The proceedings of Eurock 2013, Wroclaw, PolandGoogle Scholar
  83. Pestman BJ, Van Munster JG (1996) An acoustic emission study of damage development and stress-memory effects in sandstone. Int J Rock Mech Min Sci 33(6):585–593. doi: 10.1016/0148-9062(96)00011-3
  84. Ramana YV, Sarma LP (1987) Split-collar tensile test grips for short rock cores. Eng Geol 23:255–261. doi: 10.1016/0013-7952(87)90092-5 CrossRefGoogle Scholar
  85. Scholz CH (1968) Microfracturing and the inelastic deformation of rock in compression. J Geophy Research 73(4):1417–1432. doi: 10.1029/JB073i004p01417
  86. Stacey TR (1981) A simple extension strain criterion for fracture of brittle rock. Int J Frac 18:469–474. doi: 10.1016/0148-9062(81)90511-8 Google Scholar
  87. Taponnier P, Brace WF (1976) Development of stress-induced microcracks in Westerly granite. Int J Rock Mech Min Sci and Geomech Abstr 13(4):103–112. doi: 10.1016/0148-9062(76)91937-9 CrossRefGoogle Scholar
  88. Tavallali A, Vervoort A (2010) Failure of layered sandstone under Brazilian test conditions: effect of micro-scale parameters on macro-scale behaviour. Rock Mech Rock Eng 43(5):641–653. doi: 10.1007/s00603-010-0084-7 CrossRefGoogle Scholar
  89. Vutukuri VS, Lama RD, Saluja SS (1974) Handbook on mechanical properties of rocks. Series on rock and soil mechanics 2(1), Trans Tech Publications, Ohio, USAGoogle Scholar
  90. Zhang L (2005) Engineering properties of rocks (pp: 175-202). Elsevier. Online version available at: Accessed 15 Dec 2012

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Queen’s UniversityKingstonCanada

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