Geomechanics and Engineering

  • 제24권4호
  • /
  • Pages.349-358
  • /
  • 2021
  • /
  • 2005-307X(pISSN)
  • /
  • 2092-6219(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Estimation of tensile strength and moduli of a tension-compression bi-modular rock

  • Wei, Jiong (Department of Engineering Mechanics and CNMM, School of Aerospace Engineering, Tsinghua University) ;
  • Zhou, Jingren (State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resources and Hydropower, Sichuan University) ;
  • Song, Jae-Joon (Department of Energy Resources Engineering, Research Institute of Energy and Resources, Seoul National University) ;
  • Chen, Yulong (State Key Laboratory of Coal Resources and Safe Mining, China University of Mining and Technology) ;
  • Kulatilake, Pinnaduwa H.S.W. (School of Resources and Environmental Engineering, Jiangxi University of Science and Technology)
  • 투고 : 2020.08.03
  • 심사 : 2021.01.29
  • 발행 : 2021.02.25
⟨ 이전 논문 다음 논문 ⟩

초록

The Brazilian test has been widely used to determine the indirect tensile strength of rock, concrete and other brittle materials. The basic assumption for the calculation formula of Brazilian tensile strength is that the elastic moduli of rock are the same both in tension and compression. However, the fact is that the elastic moduli in tension and compression of most rocks are different. Thus, the formula of Brazilian tensile strength under the assumption of isotropy is unreasonable. In the present study, we conducted Brazilian tests on flat disk-shaped rock specimens and attached strain gauges at the center of the disc to measure the strains of rock. A tension-compression bi-modular model is proposed to interpret the data of the Brazilian test. The relations between the principal strains, principal stresses and the ratio of the compressive modulus to tensile modulus at the disc center are established. Thus, the tensile and compressive moduli as well as the correct tensile strength can be estimated simultaneously by the new formulas. It is found that the tensile and compressive moduli obtained using these formulas were in well agreement with the values obtained from the direct tension and compression tests. The formulas deduced from the Brazilian test based on the assumption of isotropy overestimated the tensile strength and tensile modulus and underestimated the compressive modulus. This work provides a new methodology to estimate tensile strength and moduli of rock simultaneously considering tension-compression bi-modularity.

키워드

참고문헌

  1. Cai, M. and Kaiser, P.K. (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), 450-451. http://doi.org/10.1016/j.ijrmms.2003.12.111.
  2. Carneiro, F.L.L.B. (1943), "A new method to determine the tensile strength of concrete", Proceedings of the 5th Meeting of the Brazilian Association for Technical Rules, Sao Paulo, Brazil.
  3. Chen, C.S., Pan, E. and Amadei, B. (1998), "Determination of deformability and tensile strength of anisotropic rock using Brazilian tests", Int. J. Rock Mech. Min. Sci., 35(1), 43-61. https://doi.org/10.1016/S0148-9062(97)00329-X.
  4. Chen, Y. and Irfan, M. (2018), "Experimental study of kaiser effect under cyclic compression and tension tests", Geomech. Eng., 14(2), 203-209. https://doi.org/10.12989/gae.2018.14.2.203.
  5. Chen, Y., Zuo, J., Liu, D. and Wang, Z. (2019), "Deformation failure characteristics of coal-rock combined body under uniaxial compression: Experimental and numerical investigations", B. Eng. Geol. Environ., 78(5), 3449-3464. https://doi.org/10.1007/s10064-018-1336-0.
  6. Cho, J.W., Kim, H., Jeon, S. and Min, K.B. (2012), "Deformation and strength anisotropy of Asan gneiss, Boryeong shale, and Yeoncheon schist", Int. J. Rock Mech. Min. Sci., 50, 158-169. https://doi.org/10.1016/j.ijrmms.2011.12.004.
  7. Claesson, J. and 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), 991-1004. http://doi.org/10.1016/S1365-1609(02)00099-0.
  8. Fairhurst, C. (1964), "On the validity of the 'Brazilian' test for brittle materials", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 1(4), 535-546. http://doi.org/10.1016/0148-9062(64)90060-9.
  9. Gong, F.Q., Li, X.B. and Zhao, J. (2010), "Analytical algorithm to estimate tensile modulus in Brazilian disk splitting tests", Chin. J. Rock Mech. Eng., 29(5), 881-891.
  10. 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", Austr. J. Appl. Sci., 10(3), 243-268.
  11. Hudson, J.A., Brown, E.T. and Rummel, F. (1972), "The controlled failure of rock discs and rings loaded in diametral compression", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 9(2), 241-248. http://doi.org/10.1016/0148-9062(72)90025-3.
  12. Jaeger, J.C., Cook, N.G.W. and Zimmerman, R. (2007), Fundamentals of Rock Mechanics, 4th Edition, Wiley-Blackwell.
  13. Liang, Z.Z., Xing, H., Wang, S.Y., Williams, D.J. and Tang, C.A. (2012), "A three-dimensional numerical investigation of the fracture of rock specimens containing a pre-existing surface flaw", Comput. Geotech., 45, 19-33. https://doi.org/10.1016/j.compgeo.2012.04.011.
  14. Liu, C. (2010), "Elastic constants determination and deformation observation using Brazilian disk geometry", Exp. Mech., 50(7), 1025-1039. https://doi.org/10.1007/s11340-009-9281-2.
  15. Liu, Y., Dai, F., Xu, N., Zhao, T. and Feng, P. (2018), "Experimental and numerical investigation on the tensile fatigue properties of rocks using the cyclic flattened Brazilian disc method", Soil Dyn. Earthq. Eng., 105, 68-82. https://doi.org/10.1016/j.soildyn.2017.11.025.
  16. Ning, Y.J., Yang, J., An, X.M. and Ma, G.W. (2011), "Modelling rock fracturing and blast-induced rock mass failure via advanced discretisation within the discontinuous deformation analysis framework", Comput. Geotech., 38(1), 40-49. http://doi.org/10.1016/j.compgeo.2010.09.003.
  17. Park, B., Min, K.B., Thompson, N. and Horsrud, P. (2018), "Three-dimensional bonded-particle discrete element modeling of mechanical behavior of transversely isotropic rock", Int. J. Rock Mech. Min. Sci., 110, 120-132. https://doi.org/10.1016/j.ijrmms.2018.07.018.
  18. Patel, S. and Martin, C.D. (2018), "Evaluation of tensile Young's modulus and Poisson's ratio of a bi-modular rock from the displacement measurements in a Brazilian test", Rock Mech. Rock Eng., 51(2), 361-373. https://doi.org/10.1007/s00603-017-1345-5.
  19. Perras, M.A. and Diederichs, M.S. (2014), "A review of the tensile strength of rock: Concepts and testing", Geotech. Geol. Eng., 32(2), 525-546. https://doi.org/10.1007/s10706-014-9732-0.
  20. Roy, D.G. and Singh, T.N. (2016), "Effect of heat treatment and layer orientation on the tensile strength of a crystalline rock under Brazilian test condition", Rock Mech. Rock Eng., 49(5), 1663-1677. https://doi.org/10.1007/s00603-015-0891-y.
  21. Stimpson, B. and Chen, R. (1993), "Measurement of rock elastic moduli in tension and in compression and its practical significance", Can. Geotech. J., 30(2), 338-347. https://doi.org/10.1139/t93-028.
  22. Sundaram, P.N. and Corrales, J.M. (1980), "Brazilian tensile strength of rocks with different elastic properties in tension and compression", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 17(2), 131-133. https://doi.org/10.1016/0148-9062(80)90265-X.
  23. Timoshenko, S.P. and Goodier, J.N. (2013), Theory of elasticity, Beijing Higher Education Press.
  24. Ulusay, R. and Hudson, J.A. (2007), The Complete ISRM Suggested Methods for Rock Characterization, Testing and Monitoring: 1974-2006, Commission on Testing Methods, International Society for Rock Mechanics.
  25. Wang, Q.Z., Jia, X.M., Kou, S.Q., Zhang, Z.X. and Lindqvist, P.A. (2004), "The flattened Brazilian disc specimen used for testing elastic modulus, tensile strength and fracture toughness of brittle rocks: Analytical and numerical results", Int. J. Rock Mech. Min. Sci., 41(2), 245-253. http://dx.doi.org/10.1016/S1365-1609(03)00093-5.
  26. Wei, J., Niu, L.L., Song, J.J. and Xie, L.M. (2019), "Estimation of rock tensile and compressive moduli with Brazilian disc test", Geomech. Eng., 19(4), 353-360. https://doi.org/10.12989/gae.2019.19.4.353.
  27. Wei, M.D., Dai, F., Xu, N.-W., Zhao, T. and 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, 28-38. https://doi.org/10.1016/j.ijrmms.2017.09.004.
  28. Wijk, G. (1978), "Some new theoretical aspects of indirect measurements of the tensile strength of rocks", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 15(4), 149-160. http://doi.org/10.1016/0148-9062(78)91221-4.
  29. Ye, J.H., Wu, F.Q. and Sun, J.Z. (2009), "Estimation of the tensile elastic modulus using Brazilian disc by applying diametrically opposed concentrated loads", Int. J. Rock Mech. Min. Sci., 46(3), 568-576. http://doi.org/10.1016/j.ijrmms.2008.08.004.
  30. Ye, J.H., Wu, F.Q., Zhang, Y. and Ji, H.G. (2012), "Estimation of the bi-modulus of materials through deformation measurement in a Brazilian disk test", Int. J. Rock Mech. Min. Sci., 52, 122-131. https://doi.org/10.1016/j.ijrmms.2012.03.010.
  31. Yu, Q.L., Zhu, W.C., Tang, C.A. and Yang, T.H. (2014), "Impact of rock microstructures on failure processes - Numerical study based on DIP technique", Geomech. Eng., 7(4), 375-401. http://doi.org/10.12989/gae.2014.7.4.375.
  32. Yu, Y., Yin, J. and Zhong, Z. (2006), "Shape effects in the Brazilian tensile strength test and a 3D FEM correction", Int. J. Rock Mech. Min. Sci., 43(4), 623-627. https://doi.org/10.1016/j.ijrmms.2005.09.005.
  33. Yuan, R. and Shen, B. (2017), "Numerical modelling of the contact condition of a Brazilian disk test and its influence on the tensile strength of rock", Int. J. Rock Mech. Min. Sci., 93, 54-65. https://doi.org/10.1016/j.ijrmms.2017.01.010.
  34. Zhou, G.L., Xu, T., Heap, M.J., Meredith, P.G., Mitchell, T.M., Sesnic, A.S.Y. and Yuan, Y. (2020), "A three-dimensional numerical meso-approach to modeling time-independent deformation and fracturing of brittle rocks", Comput. Geotech., 117, 103274. https://doi.org/10.1016/j.compgeo.2019.103274.