Micro-failure Analysis of Direct and Flat Loading Brazilian Tensile Tests

  • Yan-Sheng Wang
  • Jian-Hui DengEmail author
  • Lin-Rui Li
  • Zheng-Hu ZhangEmail author
Original Paper


The difference between rock tensile strength measured by a direct tensile test and a Brazilian test is always attributed to external testing conditions and the natural heterogeneity of rock. There are few studies focusing on achieving a substantial understanding and quantifiable analysis of this difference. Methodologically, the relationship between the dominant frequency characteristics of acoustic emission and micro-failure has been preliminarily verified in the direct tensile test. To further explore the relationship between micro-failure types and dominant frequency characteristics and to quantitatively study the relationship between micro-failure and macro-mechanical behaviour, direct tensile tests and Brazilian disc tests were carried out to determine rock tensile strength. Furthermore, the acoustic emission technique was used to monitor the micro-failure of rock during the loading process. Detailed temporal and spatial distribution, as well as spectrum analyses of the acoustic emission signals, were conducted. Based on the statistical analysis of dominant frequency of AE signals, comparisons were made in rock tensile strength and micro-failure components from direct tensile tests and Brazilian tests. Then, a new parameter of strength factor was established to evaluate the contribution of micro-cracks produced by micro-tensile and micro-shear failures to the strength indirectly. The parameter also reflects the statistical relationship between micro-failure events and macro-failure process. By virtue of this parameter, it has been demonstrated that the difference between direct tensile strength and Brazilian splitting strength results from the higher proportion of micro-shear failure in the Brazilian test. Finally, the “ideal” tensile strength under the specific condition was obtained based on the statistical relationship between the strength and micro-failure component and suggested as a conservative design parameter for rock engineering.


Rock tensile strength Direct tensile test Brazilian test Acoustic emission Statistical analysis Micro-failure 



Tensile strength


Applied peak load


Cross-sectional area of the cylinder


Diameter of the Brazilian disk


Thickness at the centre of the Brazilian disk




Proportion of micro-tensile failure events


Proportion of micro-shear failure events


Total strength factor


Strength factor of micro-tensile failure


Strength factor of micro-shear failure



This study is financially supported by the National Key Research and Development Programme of China (no. 2016YFC0600702).


  1. Aker E, Kühn D, Vavryčuk V, Soldal M, Oye V (2014) Experimental investigation of acoustic emissions and their moment tensors in rock during failure. Int J Rock Mech Min Sci 70:286–295CrossRefGoogle Scholar
  2. ASTM (2008) D3967-08: standard test method for splitting tensile strength of intact rock core specimens. ASTM International, West ConshohockenGoogle Scholar
  3. Bykov II, Beloivan AF (1973) Tensile strength of cast stone. Strength Mater 5(2):262–264CrossRefGoogle Scholar
  4. Cai M, Kaiser PK (2004) Numerical simulation of the Brazilian test and the tensile strength of anisotropic rocks and rocks with pre-existing cracks. Int J Rock Mech Min Sci 41(3):450–451CrossRefGoogle Scholar
  5. Chen CS, Pan E, Amadei B (1998) Determination of deformability and tensile strength of anisotropic rock using brazilian tests. Int J Rock Mech Min Sci 35(1):43–61CrossRefGoogle Scholar
  6. Chou YC, Chen CS (2010) Determining elastic constants of transversely isotropic rocks using brazilian test and iterative procedure. Int J Numer Anal Methods 32(3):219–234CrossRefGoogle Scholar
  7. Claesson J, Bohloli B (2002) Brazilian test: stress field and tensile strength of anisotropic rocks using an analytical solution. Int J Rock Mech Min Sci 39(8):991–1004CrossRefGoogle Scholar
  8. Dan DQ, Konietzky H, Herbst M (2013) Brazilian tensile strength tests on some anisotropic rocks. Int J Rock Mech Min Sci 58:1–7CrossRefGoogle Scholar
  9. Diederichs MS, Kaiser PK (1999) Tensile strength and abutment relaxation as failure control mechanisms in underground excavations. Int J Rock Mech Min Sci 36(1):69–96CrossRefGoogle Scholar
  10. Exadaktylos GE, Kaklis KN (2001) Applications of an explicit solution for the transversely isotropic circular disc compressed diametrically. Int J Rock Mech Min Sci 38(2):227–243CrossRefGoogle Scholar
  11. Fahimifar A, Malekpour M (2012) Experimental and numerical analysis of indirect and direct tensile strength using fracture mechanics concepts. B Eng Geol Environ 71(2):269–283CrossRefGoogle Scholar
  12. 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
  13. Hoek E (1964) Fracture of anisotropic rock. J S Afr I Min Metall 64(10):501–518Google Scholar
  14. Ishiguro S, Nakaya M (1985) Direct tensile strength of steel fiber reinforced concrete by using clamping grips. Bull Univ Osaka Pref Ser B Agric BIOL Osaka (Pref) Daigaku 37:69–73Google Scholar
  15. ISRM (1978) Suggested methods for determining tensile strength of rock materials. Int J Rock Mech Min Sci Geomech Abstr 15(3):99–103CrossRefGoogle Scholar
  16. Kawasaki Y, Wakuda T, Kobarai T, Ohtsu M (2013) Corrosion mechanisms in reinforced concrete by acoustic emission. Constr Build Mater 48:1240–1247CrossRefGoogle Scholar
  17. Li LR (2017) Dominant frequencies and their mechanical mechanism of acoustic emissions in rock failures. PhD Thesis, Sichuan UniversityGoogle Scholar
  18. Li LR, Deng JH, Zheng L, Liu JF (2017) Dominant frequency characteristics of acoustic emissions in white marble during direct tensile tests. Rock Mech Rock Eng 50:1–10CrossRefGoogle Scholar
  19. Liu J, Chen L, Wang C, Man K, Wang L, Wang J et al (2014) Characterizing the mechanical tensile behaviour of beishan granite with different experimental methods. Int J Rock Mech Min Sci 69(3):50–58CrossRefGoogle Scholar
  20. Liu J, Li Y, Xu S, Xu S, Jin C (2015) Cracking mechanisms in granite rocks subjected to uniaxial compression by moment tensor analysis of acoustic emission. Theor Appl Fract Mec 75:151–159CrossRefGoogle Scholar
  21. Ohno K, Ohtsu M (2010) Crack classification in concrete based on acoustic emission. Constr Build Mater 24(12):2339–2346CrossRefGoogle Scholar
  22. Ohtsu M (1991) Simplified moment tensor analysis and unified decomposition of acoustic emission source: application to in situ hydrofracturing test. J Geophys Res Sol Earth 96(B4):6211–6221CrossRefGoogle Scholar
  23. Ohtsu M, Okamoto T, Yuyama S (1998) Moment tensor analysis of acoustic emission for cracking mechanisms in concrete. ACI Struct J 95(2):87–95Google Scholar
  24. Perras MA, Diederichs MS (2014) A review of the tensile strength of rock: concepts and testing. Geotech Geol Eng 32(2):525–546CrossRefGoogle Scholar
  25. Shiotani T, Ohtsu M, Ikeda K (2001) Detection and evaluation of AE waves due to rock deformation. Constr Build Mater 15(5):235–246CrossRefGoogle Scholar
  26. Sondergeld CH, Estey LH (1981) Acoustic emission study of microfracturing during the cyclic loading of Westerly granite. J Geophys Res Sol Earth 86(B4):2915–2924CrossRefGoogle Scholar
  27. 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):641–653CrossRefGoogle Scholar
  28. Toutanji HA, Liu L, El-Korchi T (1999) The role of silica fume in the direct tensile strength of cement-based materials. Mater Struct 32(3):203–209CrossRefGoogle Scholar
  29. Wijk G, Rehbinder G, Lögdström G (1978) The relation between the uniaxial tensile strength and the sample size for bohus granite. Rock Mech 10(4):201–219CrossRefGoogle Scholar
  30. Wong LNY, Ming CJ (2015) Study of the water effects on the tensile strength and cracking processes of molded gypsum. The Engineering Geology for Society and Territory, vol 5. Springer, BerlinGoogle Scholar
  31. Xie HP, Ju Y, Li LY (2005) Criteria for strength and structural failure of rocks based on energy dissipation and energy release principles. Chin J Rock Mech Eng 24(17):3003–3010 (in Chinese) Google Scholar
  32. Yin T, Li X, Cao W, Xia K (2015) Effects of thermal treatment on tensile strength of laurentian granite using brazilian test. Rock Mech Rock Eng 48(6):2213–2223CrossRefGoogle Scholar
  33. Yu Y (2005) Questioning the validity of the Brazilian test for determining tensile strength of rocks. Chin J Rock Mech and Eng 24(7):1150–1157 (in Chinese) Google Scholar
  34. Zang A, Wagner C, Stanchits F, Dresen S, Andresen GR, Haidekker MA (1998) Source analysis of acoustic emissions in Aue granite cores under symmetric and asymmetric compressive loads. Geophys J Int 135(3):1113–1130CrossRefGoogle Scholar
  35. Zhang ZH, Deng JH, Zhu JB, Li LR (2018) An experimental investigation of the failure mechanisms of jointed and intact marble under compression based on quantitative analysis of acoustic emission waveforms. Rock Mech Rock Eng 51(7):2299–2307CrossRefGoogle Scholar
  36. Zhao J, Li HB (2000) Experimental determination of dynamic tensile properties of a granite. Int J Rock Mech Min Sci 37(5):861–866CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resources and HydropowerSichuan UniversityChengduChina
  2. 2.Centre for Rock Instability and Seismicity Research, School of Civil EngineeringDalian University of TechnologyDalianChina

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