Structural Engineering and Mechanics

  • 제66권3호
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  • Pages.379-386
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  • 2018
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

The discrete element method simulation and experimental study of determining the mode I stress-intensity factor

  • Shemirani, Alireza Bagher (Department of Civil Engineering, Sadra Institute of Higher Education) ;
  • Haeri, Hadi (Young Researchers and Elite Club, Bafgh Branch, Islamic Azad University) ;
  • Sarfarazi, Vahab (Department of Mining Engineering, Hamedan University of Technology) ;
  • Akbarpour, Abbas (Department of Civil Engineering, South Tehran Branch, Islamic Azad University) ;
  • Babanouri, Nima (Department of Mining Engineering, Hamedan University of Technology)
  • 투고 : 2017.09.14
  • 심사 : 2018.02.08
  • 발행 : 2018.05.10
⟨ 이전 논문 다음 논문 ⟩

초록

The present study addresses the direct and indirect methods of determining the mode-I fracture toughness of concrete using experimental tests and particle flow code. The direct method used is compaction tensile test and the indirect methods are notched Brazilian disc test, semi-circular bend specimen test, and hollow center cracked disc. The experiments were carried out to determine which indirect method yields the fracture toughness closer to the one obtained by the direct method. In the numerical analysis, the PFC model was first calibrated with respect to the data obtained from the Brazilian laboratory test. The crack paths observed in the simulated tests were in reasonable accordance with experimental results. The discrete element simulations demonstrated that the macro fractures in the models are caused by microscopic tensile breakages on large numbers of bonded particles. The mode-I fracture toughness in the direct tensile test was smaller than the indirect testing results. The fracture toughness obtained from the SCB test was closer to the direct test results. Hence, the semi-circular bend test is recommended as a proper experiment for determination of mode-I fracture toughness of concrete in the absence of direct tests.

키워드

참고문헌

  1. Akbas, S.D. (2016), "Analytical solutions for static bending of edge cracked micro beams", Struct. Eng. Mech., 59(3), 579-599. https://doi.org/10.12989/sem.2016.59.3.579
  2. Aliha, M.R.M., Sistaninia, M., Smith, D.J., Pavier, M.J. and Ayatollahi, M.R. (2012), "Geometry effects and statistical analysis of mode I fracture in guiting limestone", Int. J. Rock Mech. Min. Sci., 51, 128-35. https://doi.org/10.1016/j.ijrmms.2012.01.017
  3. Amrollahi, H., Baghbanan, A. and 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), 1123-1134. https://doi.org/10.1016/j.ijrmms.2011.06.015
  4. Atkinson, C., Smelser, R.E. and Sanchez, J. (1982), "Combined mode fracture via the cracked Brazilian disk test", Int. J. Fract., 18(4), 279-291. https://doi.org/10.1007/BF00015688
  5. Bagher Shemirani, A., Haeri, H., Sarfarazi, V. and Hedayat, A. (2017), "A review paper about experimental investigations on failure behaviour of non-persistent joint", Geomech. Eng., 13(4), 535-570.
  6. Bagher Shemirani, A., Naghdabadi, R. and Ashrafi, M. (2016), "Experimental and numerical study on choosing proper pulse shapers for testing concrete specimens by split Hopkinson pressure bar apparatus", Constr. Build. Mater., 125, 326-336. https://doi.org/10.1016/j.conbuildmat.2016.08.045
  7. Bagher Shemirani, A., Sarfarazi, V., Haeri, H., Marji, M. and Hosseini, S. (2018), "A discrete element simulation of a punchthrough shear to investigate the confining pressure effects on the shear behaviour of concrete cracks", Comput. Concrete, 21(2), 189-197. https://doi.org/10.12989/CAC.2018.21.2.189
  8. Chang, S.H., Lee, C.I. and Jeon, S. (2002), "Measurement of rock fracture toughness under modes I and II and mixed-mode conditions by using disc-type specimens", Eng. Geol., 66(1-2), 79-97. https://doi.org/10.1016/S0013-7952(02)00033-9
  9. Chen, R., Xia, K., Dai, F., Lu, F. and Luo, S.N. (2009), "Determination of dynamic fracture parameters using a semicircular bend technique in split Hopkinson pressure bar testing", Eng. Fract. Mech., 76(9), 1268-1276. https://doi.org/10.1016/j.engfracmech.2009.02.001
  10. Chong, K. and Kuruppu, M.D. (1984), "New specimen for fracture toughness determination for rock and other materials", Int. J. Fract., 26(2), R59-62. https://doi.org/10.1007/BF01157555
  11. Cundall, P.A. and Strack, O.D.L. (1979), "A discrete numerical model for granular assemblies", Geotech., 29(1), 47-65. https://doi.org/10.1680/geot.1979.29.1.47
  12. Cundall, P.A. and Strack, O.D.L. (1999), Particle Flow Code in 2 Dimensions, Itasca Consulting Group, Inc.
  13. Dai, F., Chen, R., Iqbal, M.J. and Xia, K. (2010a), "Dynamic cracked chevron notched Brazilian disc method for measuring rock fracture parameters", Int. J. Rock Mech. Min. Sci., 47(4), 606-13. https://doi.org/10.1016/j.ijrmms.2010.04.002
  14. Dai, F., Wei, M.D., Xu, N.W., Ma, Y. and Yang, D.S. (2015), "Numerical assessment of the progressive rock fracture mechanism of cracked chevron notched Brazilian disc specimens", Rock Mech. Rock Eng., 48(2), 463-479. https://doi.org/10.1007/s00603-014-0587-8
  15. Dai, F., Xia, K., Zheng, H. and Wang, Y.X. (2011), "Determination of dynamic rock mode-I fracture parameters using cracked chevron notched semi-circular bend specimen", Eng. Fract. Mech., 78(15), 2633-2644. https://doi.org/10.1016/j.engfracmech.2011.06.022
  16. Fowell, R.J. (1995), "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, 57-64. https://doi.org/10.1016/0148-9062(94)00015-U
  17. Guo, C., Jiang, F., Liu, R. and Yang, Y. (2011), "Size effect on the contact state between fracture specimen and supports in Hopkinson bar loaded fracture test", Int. J. Fract., 169(1), 77-84. https://doi.org/10.1007/s10704-011-9588-8
  18. Haeri, H. (2015g), "Propagation mechanism of neighboring cracks in rock-like cylindrical specimens under uniaxial compression", J. Min. Sci., 51(3), 487-496. https://doi.org/10.1134/S1062739115030096
  19. Haeri, H. (2015h), "Simulating the crack propagation mechanism of pre-cracked concrete specimens under shear loading conditions", Strength Mater., 47(4), 618-632. https://doi.org/10.1007/s11223-015-9698-z
  20. Haeri, H., Khaloo, A. and Marji, M.F. (2015c), "Experimental and numerical simulation of the microcracks coalescence mechanism in rock-like materials", Strength Mater., 47(1), 740-754. https://doi.org/10.1007/s11223-015-9711-6
  21. Haeri, H., Khaloo, A. and Marji, M.F. (2015d), "A coupled experimental and numerical simulation of rock slope joints behavior", Arab. J. Geosci., 8(9), 7297-7308. https://doi.org/10.1007/s12517-014-1741-z
  22. Haeri, H., Khaloo, A. and Marji, M.F. (2015e), "Fracture analyses of different pre-holed concrete specimens under compression", Acta Mech. Sinic., 31(6), 855-870. https://doi.org/10.1007/s10409-015-0436-3
  23. Haeri, H., Khaloo, A. and Marji, M.F. (2015f), "Experimental and numerical analysis of Brazilian discs with multiple parallel cracks", Arab. J. Geosci., 8(8), 5897-5908. https://doi.org/10.1007/s12517-014-1598-1
  24. Haeri, H., Marji, M.F. and Shahriar, K. (2015b), "Simulating the effect of disc erosion in TBM disc cutters by a semi-infinite DDM", Arab. J. Geosci., 8(6), 3915-3927. https://doi.org/10.1007/s12517-014-1489-5
  25. Haeri, H., Shahriar, K., Marji, M.F. and Moarefvand, P. (2013), "Modeling the propagation mechanism of two random micro cracks in rock Samples under uniform tensile loading", Proceedings of the 13th International Conference on Fracture, Beijing, China.
  26. Haeri, H., Shahriar, K., Marji, M.F. and Moarefvand, P. (2014a), "On the cracks coalescence mechanism and cracks propagation paths in rock-like specimens containing pre-existing random cracks under compression", J. Centr. South Univ., 21(6), 2404-2414. https://doi.org/10.1007/s11771-014-2194-y
  27. Haeri, H., Shahriar, K., Marji, M.F. and Moarefvand, P. (2014b), "Investigating the fracturing process of rock-like Brazilian discs containing three parallel cracks under compressive line loading", Strength Mater., 46(3), 133-148.
  28. Haeri, H., Shahriar, K., Marji, M.F. and Moarefvand, P. (2015a), "The HDD analysis of micro cracks initiation, propagation and coalescence in brittle substances", Arab. J. Geosci., 8(5), 2841-2852. https://doi.org/10.1007/s12517-014-1290-5
  29. He, M.Y., Cao, H.C. and Evans, A.G. (1990), "Mixed-mode fracture: The four-point shear specimen", Acta Metallurg. Mater., 38(5), 839-846. https://doi.org/10.1016/0956-7151(90)90037-H
  30. Huang, Y.H., Yang, S.Q., Tian, W.L., Zeng, W. and Yu, L.Y. (2015), "An experimental study on fracture mechanical behavior of rock-like materials containing two unparallel fissures under uniaxial compression", Acta Mech. Sinic., 1-14.
  31. Karfakis, M.G. and Akram, M. (1993), "Effects of chemical solutions on rock fracturing", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 30, 1253-1259. https://doi.org/10.1016/0148-9062(93)90104-L
  32. Kataoka, M. and Obara, Y. (2013), "Estimation of fracture toughness of different kinds of rocks under water vapor pressure by SCB test", J. MMIJ, 129, 425-432. https://doi.org/10.2473/journalofmmij.129.425
  33. Khan, K. and Al-Shayea, N.A. (2000), "Effect of specimen geometry and testing method on mixed mode I-II fracture toughness of a limestone rock from Saudi Arabia", Rock Mech. Rock Eng., 33(3), 179-206. https://doi.org/10.1007/s006030070006
  34. Kuruppu, M., Obara, Y. and Kataoka, M. (2010), Determination of Fracture Toughness of Anisotropic Rocks under Water Vapour Pressure by Semi-Circular Bend Test.
  35. Kuruppu, M.D., Obara, Y., Ayatollahi, M.R., Chong, K.P. and Funatsu, T. (2013), ISRM-Suggested Method for Determining the Mode I Static Fracture Toughness Using Semi-Circular Bend Specimen, The ISRM Suggested Methods for Rock Characterization, Testing and Monitoring, Springer.
  36. Lee, S., Lee, S.H. and Chang, Y.S. (2015), "Evaluation of RPV according to alternative fracture toughness requirements", Struct. Eng. Mech., 53(6), 1271-1286. https://doi.org/10.12989/sem.2015.53.6.1271
  37. Lim, I.L., Johnston, I.W. and Choi, S.K. (1993), "Stress intensity factors for semi-circular specimens under three-point bending", Eng. Fract. Mech., 44(3), 363-382. https://doi.org/10.1016/0013-7944(93)90030-V
  38. Lim, I.L., Johnston, I.W., Choi, S.K. and Boland, J.N. (1994), "Fracture testing of a soft rock with semi-circular specimens under three-point bending. Part 1-mode I", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 31(3), 185-197. https://doi.org/10.1016/0148-9062(94)90463-4
  39. Maccagno, T.M. and Knott, J.F. (1989), "The fracture behaviour of PMMA in mixed modes I and II", Eng. Fract. Mech., 34(1), 65-86. https://doi.org/10.1016/0013-7944(89)90243-9
  40. Mahajan, R.V. and Ravi-Chandar, K. (1989), "An experimental investigation of mixed-mode fracture", Int. J. Fract., 41(4), 235-252. https://doi.org/10.1007/BF00018856
  41. Molenaar, A.A.A., Scarpas, A., Liu, X. and Erkens, S. "Semicircular bending test; simple but useful?", J. Assoc. Asph. Pav. Technol., 71.
  42. Morozov, N., Petrov, Y. and Smirnov, V. (2009), "Dynamic fracture of rocks", Proceedings of the 7th EUROMECH Solid Mechanics Conference, Lisbon, Portugal.
  43. Mosabepranah, M.A. and Eren, O. (2016), "Statistical flexural toughness modeling of ultra high performance concrete using response surface method", Comput. Concrete, 17(4), 477-488. https://doi.org/10.12989/cac.2016.17.4.477
  44. Obara, Y., Sasaki, K. and Yoshinaga, T. (2007), "Estimation of fracture toughness of rocks under water vapor pressure by semicircular bend (SCB) test", J. MMIJ, 123(4-5), 145-151. https://doi.org/10.2473/journalofmmij.123.145
  45. Potyondy, D.O. and Cundall, P.A. (2004), "A bonded-particle model for rock", Int. J. Rock Mech. Min. Sci., 41, 1329-1364. https://doi.org/10.1016/j.ijrmms.2004.09.011
  46. Potyondy, D.O., Cundall, P.A. and Lee, C.A. (1996), "Modelling rock using bonded assemblies of circular particles", Proceedings of the 2nd North American Rock Mechanics Symposium, American Rock Mechanics Association.
  47. Rajabi, M., Soltani, N. and Eshraghi, I. (2016), "Effects of temperature dependent material properties on mixed mode crack tip parameters of functionally graded materials", Struct. Eng. Mech., 58(2), 217-230. https://doi.org/10.12989/sem.2016.58.2.217
  48. Ramadoss, P. and Nagamani, K. (2013), "Stress-strain behavior and toughness of high-performance steel fiber reinforced concrete in compression", Comput. Concrete, 11(2), 149-167. https://doi.org/10.12989/cac.2013.11.2.149
  49. Sarfarazi, V., Haeri, H. and Bagher Shemirani, A. (2017a), "Direct and indirect methods for determination of mode I fracture toughness using PFC2D", Comput. Concrete, 20(1), 39-47. https://doi.org/10.12989/CAC.2017.20.1.039
  50. Sarfarazi, V., Haeri, H., Bagher Shemirani, A. and Zhu, Z. (2017b), "The effect of compression load and rock bridge geometry on the shear mechanism of weak plane", Geomech. Eng., 3(3), 57-63.
  51. Sarfarazi, V., Haeri, H., Bagher Shemirani, A., Hedayat, A. and Hosseini, S. (2017c), "Investigation of ratio of TBM disc spacing to penetration depth in rocks with different tensile strengths using PFC2D", Comput. Concrete, 20(4), 429-437.
  52. Sato, K. and Hashida, T. (2006), "Fracture toughness evaluation based on tension-softening model and its application to hydraulic fracturing", Rock Dam. Flu. Transp., 1073-1089.
  53. Shiryaev, A.M. and Kotkis, A.M. (1983), "Methods for determining fracture toughness of brittle porous materials", Indust Lab, 48(9), 917-918.
  54. Singh, R.N. and Sun, G. (1990), "A numerical and experimental investigation for determining fracture toughness of Welsh limestone", Min. Sci. Technol., 10(1), 61-70. https://doi.org/10.1016/0167-9031(90)90850-R
  55. Suresh, S., Shih, C.F., Morrone, A. and O'Dowd, N.P. (1990), "Mixed mode fracture toughness of ceramic materials", J. Am. Ceram. Soc., 73(5), 1257-1267. https://doi.org/10.1111/j.1151-2916.1990.tb05189.x
  56. Tang, C. and Xu, X. (1990), "A new method for measuring dynamic fracture toughness of rock", Eng. Fract. Mech., 35(4-5), 783-791. https://doi.org/10.1016/0013-7944(90)90162-A
  57. Tutluoglu, L. and Keles, C. (2011), "Mode I fracture toughness determination with straight notched disk bending method", Int. J. Rock Mech. Min. Sci., 48(8), 1248-1261. https://doi.org/10.1016/j.ijrmms.2011.09.019
  58. Wang, Q.Z., Feng, F., Ni, M. and Gou, X.P. (2011), "Measurement of mode I and mode II rock dynamic fracture toughness with cracked straight through flattened Brazilian disc impacted by split Hopkinson pressure bar", Eng. Fract. Mech., 78(12), 2455-2469. https://doi.org/10.1016/j.engfracmech.2011.06.004
  59. Wang, Q.Z., Zhang, S. and Xie, H.P. (2010), "Rock dynamic fracture toughness tested with holed-cracked flattened Brazilian discs diametrically impacted by SHPB and its size effect", Experiment. Mech., 50(7), 877-885. https://doi.org/10.1007/s11340-009-9265-2
  60. Wei, M.D., Dai, F., Xu, N.W. and Zhao, T. (2016), "Stress intensity factors and fracture process zones of ISRM-suggested chevron notched specimens for mode I fracture toughness testing of rocks", Eng. Fract. Mech., 168, 174-189. https://doi.org/10.1016/j.engfracmech.2016.10.004
  61. Wei, M.D., Dai, F., Xu, N.W., Zhao, T. and Xia, K.W. (2016), "Experimental and numerical study on the fracture process zone and fracture toughness determination for ISRM-suggested semicircular bend rock specimen", Eng. Fract. Mech., 154, 43-56. https://doi.org/10.1016/j.engfracmech.2016.01.002
  62. Xu, N.W., Dai, F., Wei, M.D., Xu, Y. and Zhao, T. (2016), "Numerical observation of three dimensional wing cracking of cracked chevron notched Brazilian disc rock specimen subjected to mixed mode loading", Rock Mech. Rock Eng., 49(1), 79-96. https://doi.org/10.1007/s00603-015-0736-8
  63. Yu, K. and Lu, Z. (2015), "Influence of softening curves on the residual fracture toughness of post-fire normal-strength concrete", Comput. Concrete, 15(2), 199-213. https://doi.org/10.12989/cac.2015.15.2.199
  64. Zhou, Y.X., Xia, K., Li, X.B., Li, H.B., Ma, G.W., Zhao, J., Zhou, J.L. and Dai, F. (2012), "Suggested methods for determining the dynamic strength parameters and mode-I fracture toughness of rock materials", Int. J. Rock Mech. Min. Sci., 49, 105-112. https://doi.org/10.1016/j.ijrmms.2011.10.004