Rock Mechanics and Rock Engineering

, Volume 52, Issue 11, pp 4217–4235 | Cite as

Experimental Study of Cracking Characteristics of Kowloon Granite Based on Three Mode I Fracture Toughness Methods

  • Louis Ngai Yuen Wong
  • Tian Yang GuoEmail author
  • Wing Ki Lam
  • Jay Yu Hin Ng
Original Paper


Mode I fracture toughness is an important material parameter of rock. To date, a number of laboratory methods have been developed to measure the mode I fracture toughness. Although the fracture toughness values measured by different methods have been compared in many previous studies, the effect of the specimen configuration and pre-existing notch shape on the fracture toughness value and the associated cracking characteristics have not been comprehensively studied. In the present study, the failure modes and mode I fracture toughness of Kowloon granite, a major type of granite in Hong Kong, are studied experimentally based on the chevron bend (CB), semi-circular bend (SCB) and cracked chevron notched semi-circular bend (CCNSCB) methods. The fracture toughness measured by the SCB test is much lower (56.5% lower) than that measured with the CCNSCB test. The measured CB fracture toughness is between the SCB and CCNSCB results. The failure modes of specimens containing the chevron notch (CB and CCNSCB specimens) are found to differ from those containing the straight-through notch (SCB specimens), especially with respect to the post-failure behavior. The cracking mechanism of the SCB and CCNSCB is studied macroscopically and microscopically. The results show that the straight-through notch and chevron notch, which are the most commonly used notch shapes adopted in various mode I fracture toughness tests, have significant effects on the cracking behavior and crack characteristics. Further investigation on the thin sections prepared from the specimens after the mode I fracture toughness tests provides us with new insights into the microscopic characteristics of tensile cracks in granite under mode I loading condition.


Fracture toughness Semi-circular bend specimens Cracking characteristics Microscopic investigation 

List of Symbols


Deviation area enclosed by the dominant crack profile and the central pre-existing notch line


Absolute deviation area of the dominant crack


Pre-existing notch length


Minimum chevron notch length


Maximum chevron notch length


Critical crack length in chevron notch ligament


Specimen thickness


Chervon bend specimen diameter


Deviation distance of the dominant crack


Maximum deviation distance of the dominant crack


Mode I fracture toughness


Chevron bend specimen length


Vertical length of studied dominant crack


Load applied on specimen


Peak load recorded in the fracture toughness test


Specimen radius


Saw blade radius


Relative deviation area of the dominant crack


Half span of the two supporting rollers


Notch width


Short rod specimen length


Minimum (i.e., critical) value of the dimensionless stress intensity factor


Normalized straight-through notch length


Normalized minimum chevron notch length


Normalized maximum chevron notch length


Normalized specimen thickness


Chevron angle


Parameter depends on β0 and βB


Parameter depends on β0 and βB



The first and second authors acknowledge the support from the HKU Start-up Fund, the General Research Fund 2017/18 (#17303917) of the Research Grants Council (Hong Kong), and the Hung Hing Ying Physical Sciences Research Fund 2017-18. The second author acknowledges the Postgraduate Scholarship at the University of Hong Kong. The authors would also like to thank Xinyu Xiao for her supportive work in experimental tests. MTR Corporation is acknowledged for providing the rock cores. The Public Works Central Laboratory (PWCL) of the Civil Engineering Development Department (CEDD) is acknowledged. The data for this paper are available by contacting the corresponding author at or the first author at


  1. Aliha MRM, Sistaninia M, Smith DJ, Pavier MJ, Ayatollahi MR (2012) Geometry effects and statistical analysis of mode I fracture in guiting limestone. Int J Rock Mech Min Sci 51:128–135CrossRefGoogle Scholar
  2. Aliha MRM, Hosseinpour GR, Ayatollahi MR (2013) Application of cracked triangular specimen subjected to three-point bending for investigating fracture behavior of rock materials. Rock Mech Rock Eng 46(5):1023–1034CrossRefGoogle Scholar
  3. Aliha MRM, Mahdavi E, Ayatollahi MR (2017) The influence of specimen type on tensile fracture toughness of rock materials. Pure Appl Geophys 174(3):1237–1253CrossRefGoogle Scholar
  4. Amrollahi H, Baghbanan A, Hashemolhosseini H (2011) Measuring fracture toughness of crystalline marbles under modes I and II and mixed mode I-II loading conditions using CCNBD and HCCD specimens. Int J Rock Mech Min Sci 48(7):1123–1134CrossRefGoogle Scholar
  5. Ayatollahi MR, Mahdavi E, Alborzi MJ, Obara Y (2016) Stress intensity factors of semi-circular bend specimens with straight-through and chevron notches. Rock Mech Rock Eng 49(4):1161–1172CrossRefGoogle Scholar
  6. Barry NW, Raghu NS, Gexin S (1992) Rock fracture mechanics principles design and applications. Elsevier, AmsterdamGoogle Scholar
  7. Chen F, Sun Z, Xu J (2001) Mode I fracture analysis of the double edge cracked Brazilian disk using a weight function method. Int J Rock Mech Min Sci 38(3):475–479CrossRefGoogle Scholar
  8. Chen CH, Chen CS, Wu JH (2008) Fracture toughness analysis on cracked ring disks of anisotropic rock. Rock Mech Rock Eng 41(4):539–562CrossRefGoogle Scholar
  9. Chong KP, Kuruppu MD (1984) New specimen for fracture toughness determination of rock and other materials. Int J Fract 26:R59–62CrossRefGoogle Scholar
  10. Cui ZD, Liu DA, An G, Sun B, Zhou M, Cao F (2010) A comparison of two ISRM suggested chevron notched specimens for testing mode-I rock fracture toughness. Int J Rock Mech Min Sci 47(5):871–876CrossRefGoogle Scholar
  11. Dai F, Xu Y, Zhao T, Xu NW, Liu Y (2016) Loading-rate-dependent progressive fracturing of cracked chevron-notched Brazilian disc specimens in split Hopkinson pressure bar tests. Int J Rock Mech Min Sci 88:49–60CrossRefGoogle Scholar
  12. Fowell RJ (1995) ISRM commission on testing methods. Suggested method for determining mode I fracture toughness using cracked chevron notched Brazilian disc (CCNBD) specimens. Int J Rock Mech Min Sci Geomech Abstr 32(1):57–64CrossRefGoogle Scholar
  13. Franklin JA, Sun ZQ, Atkinson BK, Meredith PC, Rummel F, Mueller W, Bobrov GF (1988) Suggested methods for determining the fracture toughness of rock. Int J Rock Mech Min Sci Geomech Abstr 25(2):71–96Google Scholar
  14. Funatsu T, Shimizu N, Kuruppu M, Matsui K (2015) Evaluation of mode I fracture toughness assisted by the numerical determination of K-resistance. Rock Mech Rock Eng 48(1):143–157CrossRefGoogle Scholar
  15. Gonçalves da Silva B (2016). Fracturing processes and induced seismicity due to the hydraulic fracturing of rocks. PhD thesis, Massachusetts Institute of TechnologyGoogle Scholar
  16. Guo H, Aziz NI, Schmidt LC (1993) Rock fracture-toughness determination by the Brazilian test. Eng Geol 33(3):177–188CrossRefGoogle Scholar
  17. Iqbal MJ, Mohanty B (2007) Experimental calibration of ISRM suggested fracture toughness measurement techniques in selected brittle rocks. Rock Mech Rock Eng 40(5):453–475CrossRefGoogle Scholar
  18. ISRM (2007) The complete ISRM suggested methods for rock characterization, testing and monitoring: 1974–2006. In: Ulusay R, Hudson JA (eds) Suggested methods prepared by the commission on testing methods. International Society for Rock Mechanics, Compilation Arranged by the ISRM Turkish National Group, Ankara, TurkeyGoogle Scholar
  19. Kataoka M, Obara Y, Kuruppu M (2015) Estimation of fracture toughness of anisotropic rocks by semi-circular bend (SCB) tests under water vapor pressure. Rock Mech Rock Eng 48(4):1353–1367CrossRefGoogle Scholar
  20. Keles C, Tutluoglu L (2011) Investigation of proper specimen geometry for mode I fracture toughness testing with flattened Brazilian disc method. Int J Fract 169(1):61–75CrossRefGoogle Scholar
  21. Kranz RL (1983) Microcracks in rocks: a review. Tectonophysics 100(1–3):449–480CrossRefGoogle Scholar
  22. Kuruppu MD (1997) Fracture toughness measurement using chevron notched semi-circular bend specimen. Int J Fract 86(4):L33–L38Google Scholar
  23. Kuruppu MD, Obara Y, Ayatollahi MR, Chong KP, Funatsu T (2014) ISRM-suggested method for determining the mode I static fracture toughness using semi-circular bend specimen. Rock Mech Rock Eng 47(1):267–274CrossRefGoogle Scholar
  24. Mahanta B, Singh TN, Ranjith PG (2016) Influence of thermal treatment on mode I fracture toughness of certain Indian rocks. Eng Geol 210:103–114CrossRefGoogle Scholar
  25. Markides CF, Kourkoulis SK (2015) The finite circular disc with a central elliptic hole under parabolic pressure. Acta Mech 226(6):1929CrossRefGoogle Scholar
  26. Miller JT (2008) Crack coalescence in granite. SM thesis, Massachusetts Institute of TechnologyGoogle Scholar
  27. Mostafavi M, McDonald SA, Mummery PM, Marrow TJ (2013) Observation and quantification of three-dimensional crack propagation in poly-granular graphite. Eng Fract Mech 110:410–420CrossRefGoogle Scholar
  28. Ouchterlony F (1982) Review of fracture toughness testing of rock: SveDeFo. Stiftelsen Svensk Detonikforskning 7:131–211Google Scholar
  29. Schmidt RA (1976) Fracture-toughness testing of limestone. Exp Mech 16(5):161–167CrossRefGoogle Scholar
  30. Szendi-Horvath G (1980) Fracture toughness determination of brittle materials using small to extremely small specimens. Eng Fract Mech 13(4):955–961CrossRefGoogle Scholar
  31. Tang TX, Bažant ZP, Yang SC, Zollinger D (1996) Variable-notch one-size test method for fracture energy and process zone length. Eng Fract Mech 55(3):383–404CrossRefGoogle Scholar
  32. Thiercelin M (1989) Fracture toughness and hydraulic fracturing. Int J Rock Mech Min Sci Geomech Abstr 26(3–4):177–183CrossRefGoogle Scholar
  33. Tutluoglu L, Keles C (2011) Mode I fracture toughness determination with straight notched disk bending method. Int J Rock Mech Min Sci 48(8):1248–1261CrossRefGoogle Scholar
  34. Wei MD, Dai F, Xu NW, Liu JF, Xu Y (2016a) Experimental and numerical study on the cracked chevron notched semi-circular bend method for characterizing the mode I fracture toughness of rocks. Rock Mech Rock Eng 49(5):1595–1609CrossRefGoogle Scholar
  35. Wei MD, Dai F, Xu NW, Zhao T, Xia KW (2016b) Experimental and numerical study on the fracture process zone and fracture toughness determination for ISRM-suggested semi-circular bend rock specimen. Eng Fract Mech 154:43–56CrossRefGoogle Scholar
  36. Wei MD, Dai F, Xu NW, Zhao T, Liu Y (2017) An experimental and theoretical assessment of semi-circular bend specimens with chevron and straight-through notches for mode I fracture toughness testing of rocks. Int J Rock Mech Min Sci 99:28–38CrossRefGoogle Scholar
  37. Xu SL, Malik MA, Li QH, Wu Y (2016) Determination of double-K fracture parameters using semi-circular bend test specimens. Eng Fract Mech 152:58–71CrossRefGoogle Scholar
  38. Xu Y, Dai F, Xu NW, Zhao T (2016) Numerical investigation of dynamic rock fracture toughness determination using a semi-circular bend specimen in split Hopkinson pressure bar testing. Rock Mech Rock Eng 49(3):731–745CrossRefGoogle Scholar
  39. Zhang ZX, Kou SQ, Yu J, Yu Y, Jiang LG, Lindqvist PA (1999) Effects of loading rate on rock fracture. Int J Rock Mech Min Sci 36(5):597–611CrossRefGoogle Scholar
  40. Zhou YX, Xia K, Li XB, Li HB, Ma GW, Zhao J, Zhou ZL, Dai F (2012) Suggested methods for determining the dynamic strength parameters and mode-I fracture toughness of rock materials. Int J of Rock Mech Min Sci 49:105–112CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Department of Earth SciencesThe University of Hong KongHong KongChina

Personalised recommendations