DOI QR코드

DOI QR Code

Effect of shear-span/depth ratio on cohesive crack and double-K fracture parameters of concrete

  • Choubey, Rajendra Kumar (Department of Civil Engineering, Institute of Technology, Guru Ghasidas Vishwavidyalaya (A Central University)) ;
  • Kumar, Shailendra (Department of Civil Engineering, Institute of Technology, Guru Ghasidas Vishwavidyalaya (A Central University)) ;
  • Rao, M.C. (Department of Civil Engineering, Institute of Technology, Guru Ghasidas Vishwavidyalaya (A Central University))
  • 투고 : 2014.01.01
  • 심사 : 2014.11.07
  • 발행 : 2014.11.27

초록

A numerical study of the influence of shear-span/depth ratio on the cohesive crack fracture parameters and double - K fracture parameters of concrete is carried out in this paper. For the study the standard bending specimen geometry loaded with four point bending test is used. For four point loading, the shear - span/depth ratio is varied as 0.4, 1 and 1.75 and the ao/D ratio is varied from 0.2, 0.3 and 0.4 for laboratory specimens having size range from 100 - 500 mm. The input parameters for determining the double - K fracture parameters are taken from the developed fictitious crack model. It is found that the cohesive crack fracture parameters are independent of shear-span/depth ratio. Further, the unstable fracture toughness of double-K fracture model is independent of shear-span/depth ratio whereas, the initial cracking toughness of the material is dependent on the shear-span/depth ratio.

키워드

과제정보

연구 과제 주관 기관 : UGC

참고문헌

  1. Barenblatt, G.I. (1962), "The mathematical theory of equilibrium cracks in brittle fracture", Adv. Appl. Mech., 7(1), 55-129. https://doi.org/10.1016/S0065-2156(08)70121-2
  2. Bazant ZP (2002), "Concrete fracture models: testing and practice", Eng. Frac. Mech., 69, 165-205. https://doi.org/10.1016/S0013-7944(01)00084-4
  3. Bazant, Z.P. and Oh, B.H. (1983), "Crack band theory for fracture of concrete", Mater. Struct., 16(93), 155-177.
  4. Bazant, Z.P., Kim, J.K. and Pfeiffer, P.A. (1986), "Determination of fracture properties from size effect tests", J. Struct. Eng. ASCE, 112(2), 289-307. https://doi.org/10.1061/(ASCE)0733-9445(1986)112:2(289)
  5. Carpinteri, A. (1989), "Cusp catastrophe interpretation of fracture instability", J. Mech. Phy. Solids, 37(5), 567-582. https://doi.org/10.1016/0022-5096(89)90029-X
  6. Carpinteri, A., Cornetti, P., Barpi, F. and Valente, S. (2003), "Cohesive crack model description of ductile to brittle size-scale transition: dimensional analysis vs. renormalization group theory", Eng. Fract. Mech., 70, 1809-1839. https://doi.org/10.1016/S0013-7944(03)00126-7
  7. Carpinteri, A., Cornetti P. and Puzzi, S. (2006), "Scaling laws and multiscale approach in the mechanics of heterogeneous and disordered materials", Appl. Mech. Rev. ASME, 59, 283-305. https://doi.org/10.1115/1.2204076
  8. Cusatis, G. and Schauffert, E.A. (2009), "Cohesive crack analysis of size effect", Eng. Fract. Mech., 76, 2163-2173. https://doi.org/10.1016/j.engfracmech.2009.06.008
  9. De Borst, R. (2003), "Numerical aspects of cohesive-zone models", Eng Fract. Mech., 70, 1743-1757. https://doi.org/10.1016/S0013-7944(03)00122-X
  10. Dugdale, D. S. (1960), "Yielding of steel sheets containing slits", J. Mech. Phy. Solids, 8 (2), 100-104. https://doi.org/10.1016/0022-5096(60)90013-2
  11. Elices M., Guinea, G.V., Gomez, J. and Planas, J. (2002), "The cohesive cone model: advantages", limitations and challenges, Eng. Fract. Mech., 69, 137-163. https://doi.org/10.1016/S0013-7944(01)00083-2
  12. Elices, M. and Planas, J. (1996), "Fracture mechanics parameters of concrete an overview", Adv Cem Based Mater., 4, 116-127.
  13. Elices, M., Rocco, C. and Rosello, C. (2009), "Cohesive crack modeling of a simple concrete: Experimental and numerical results", Eng. Fract. Mech., 76, 1398-1410. https://doi.org/10.1016/j.engfracmech.2008.04.010
  14. Glinka, G. and Shen, G. (1991), "Universal features of weight functions for cracks in Mode I", Eng. Fract. Mech., 40, 1135-1146. https://doi.org/10.1016/0013-7944(91)90177-3
  15. Guinea, G.V. (1995), "Modelling the fracture of concrete: the cohesive crack", Mater. Struct., 28(4), 187-194. https://doi.org/10.1007/BF02473248
  16. Hillerborg, A., Modeer, M. and Petersson, P.E. (1976), "Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements", Cement Concrete Res., 6,773-782. https://doi.org/10.1016/0008-8846(76)90007-7
  17. Hu, S. and Lu, J. (2012), "Experimental research and analysis on Double-K fracture parameters of concrete", Adv. Sci. Lett., 12 (1), 192-195. https://doi.org/10.1166/asl.2012.2806
  18. Hu, S., Mi, Z. and Lu, J. (2012), Effect of crack-depth ratio on double-K fracture parameters of reinforced concrete", Appl. Mech. Mater., 226-228, 937-941. https://doi.org/10.4028/www.scientific.net/AMM.226-228.937
  19. Jenq, Y.S. and Shah, S.P. (1985a), "Two parameter fracture model for concrete", J. Eng. Mech. ASCE, 111(10), 1227-1241. https://doi.org/10.1061/(ASCE)0733-9399(1985)111:10(1227)
  20. Jenq, Y.S. and Shah, S.P. (1985b), "A fracture toughness criterion for concrete", Eng. Fract. Mech., 21, 1055-1069. https://doi.org/10.1016/0013-7944(85)90009-8
  21. Kaplan, M.F. (1961), "Crack propagation and the fracture of concrete", J. Am. Concrete Inst., 58(5), 591-610.
  22. Karihaloo, B.L. and Nallathambi, P. (1991), Notched Beam Test: Mode I Fracture Toughness, Fracture Mechanics Test methods for concrete, Report of RILEM Technical Committee 89-FMT (Edited by S.P. Shah and A. Carpinteri), Chamman & Hall, London, 1-86.
  23. Kim, J.K., Lee, Y. and Yi, S.T. (2004), "Fracture characteristics of concrete at early ages", Cement Concrete Res., 34, 507-519. https://doi.org/10.1016/j.cemconres.2003.09.011
  24. Kumar, S. and Barai, S.V. (2008a), "Influence of specimen geometry on determination of double-K fracture parameters of concrete: A comparative study", Int. J. Fract., 149, 47-66. https://doi.org/10.1007/s10704-008-9227-1
  25. Kumar, S. and Barai, S.V. (2008b), "Cohesive crack model for the study of nonlinear fracture behaviour of concrete", J. Inst. Engng. (India), CV 89 (Nov.), 7-15.
  26. Kumar, S. and Barai, S.V. (2009a), "Determining double-K fracture parameters of concrete for compact tension and wedge splitting tests using weight function", Eng. Fract. Mech., 76, 935-948. https://doi.org/10.1016/j.engfracmech.2008.12.018
  27. Kumar, S. and Barai, S.V. (2009b), "Influence of loading condition and size-effect on the KR-curve based on the cohesive stress in concrete", Int. J. Fract., 156, 103-110. https://doi.org/10.1007/s10704-009-9349-0
  28. Kumar, S. and Barai, S.V. (2009c), "Effect of softening function on the cohesive crack fracture parameters of concrete CT specimen", Sadhana-Acad. Proc. Eng. Sci., 36(6), 987-1015.
  29. Kumar, S. and Barai, S.V. (2010a), "Determining the Double-K fracture parameters for three-point bending notched concrete beams using weight function", Fatigue Fract. Eng. Mater. Struct., 33(10), 645-660. https://doi.org/10.1111/j.1460-2695.2010.01477.x
  30. Kumar, S. and Barai, S.V. (2010b), "Size-effect prediction from the double-K fracture model for notched concrete beam", Int. J. Damage Mech., 19, 473-497. https://doi.org/10.1177/1056789508101187
  31. Kumar, S. and Barai, S.V. (2012), "Effect of loading condition, specimen geometry, size-effect and softening function on double-K fracture parameters of concrete", Sadhana-Academy Proceedings in Engineering Science, 37 ( Part 1), 3-15.
  32. Kumar, S. and Pandey, S.R. (2012), "Determination of double-K fracture parameters of concrete using splittension cube test", Comput. Concr. An Int. J., 9(1), 1-19. https://doi.org/10.12989/cac.2012.9.1.001
  33. Kumar, S., Pandey, S.R. and Srivastava, A.K.L. (2013), "Analytical methods for determination of double-K fracture parameters of concrete", Adv. Concrete Constr., 1(4), 319-340. https://doi.org/10.12989/acc2013.1.4.319
  34. Kwon, S.H., Zhao, Z. and Shah, S.P. (2008), "Effect of specimen size on fracture energy and softening curve of concrete: Part II. Inverse analysis and softening curve", Cement Concrete Res., 38, 1061-1069. https://doi.org/10.1016/j.cemconres.2008.03.014
  35. Murakami, Y. (1987), "Stress Intensity Factors Hand Book", (Committee on Fracture Mechanics, The Society of Materials Science, Japan) Vol-1, Pergamon Press, Oxford.
  36. Murthy, A.R., Iyer N.R. and Prasad, B.K.R (2012), "Evaluation of fracture parameters by Double-G, Double-K models and crack extension resistance for high strength and ultra high strength concrete beams", Comput. Mater.Continua, 31(3), 229-252.
  37. Nallathambi, P. and Karihaloo, B.L. (1986), "Determination of specimen-size independent fracture toughness of plain concrete", Mag. Concrete Res., 38(135), 67-76. https://doi.org/10.1680/macr.1986.38.135.67
  38. Park, K., Paulino, G.H. and Roesler, J.R. (2008), "Determination of the kink point in the bilinear softening model for concrete", Eng. Fract. Mech., 7, 3806-3818.
  39. Petersson, P.E. (1981), "Crack growth and development of fracture zone in plain concrete and similar materials", Report No. TVBM-100, Lund Institute of Technology.
  40. Planas, J., Elices, M., Guinea, G.V., Gomez, F.J. Cendon, D.A. and Arbilla, I. (2003), Generalizations and specializations of cohesive crack models, Eng. Fract. Mech., 70, 1759-1776. https://doi.org/10.1016/S0013-7944(03)00123-1
  41. Planas, J. and Elices, M. (1991), "Nonlinear fracture of cohesive material", Int. J. Fract., 51, 139-157.
  42. Raghu Prasad, B.K. and Renuka Devi, M.V. (2007), "Extension of FCM to plain concrete beams with vertical tortuous cracks", Eng. Fract. Mech., 74, 2758-2769. https://doi.org/10.1016/j.engfracmech.2007.01.007
  43. Reinhardt, H.W., Cornelissen, H.A.W. and Hordijk, D.A. (1986), "Tensile tests and failure analysis of concrete", J. Struct. Eng., ASCE, 112(11), 2462-2477. https://doi.org/10.1061/(ASCE)0733-9445(1986)112:11(2462)
  44. RILEM Draft recommendation (50-FMC) (1985), "Determination of the fracture energy of mortar and concrete by means of three-point bend test on notched beams", Mater. Struct., 18, 285-290. https://doi.org/10.1007/BF02472917
  45. RILEM Draft Recommendations (TC89-FMT) (1990), "Determination of fracture parameters (KIcs and CTODc) of plain concrete using three-point bend tests", Mater. Struct., 23(138), 457-460. https://doi.org/10.1007/BF02472029
  46. Roesler J., Paulino, G.H., Park, K. and Gaedicke, C. (2007), "Concrete fracture prediction using bilinear softening", Cement Concrete Compos., 29, 300-312. https://doi.org/10.1016/j.cemconcomp.2006.12.002
  47. Tada, H., Paris, P.C. and Irwin, G. (2000), The Stress Analysis of Cracks Handbook, Paris Productions Incorporated, St. Louis, Missouri, USA.
  48. Xu, S. and Reinhardt, H.W. (1998), "Crack extension resistance and fracture properties of quasi-brittle materials like concrete based on the complete process of fracture", Int. J. Fract., 92, 71-99. https://doi.org/10.1023/A:1007553012684
  49. Xu, S. and Reinhardt, H.W. (1999a), "Determination of double-K criterion for crack propagation in quasibrittle materials, Part I: Experimental investigation of crack propagation", Int. J. Fract., 98, 111-149. https://doi.org/10.1023/A:1018668929989
  50. Xu, S. and Reinhardt, H.W. (1999b), "Determination of double-K criterion for crack propagation in quasibrittle materials, Part II: analytical evaluating and practical measuring methods for three-point bending notched beams", Int. J. Fract., 98, 151-77. https://doi.org/10.1023/A:1018740728458
  51. Xu, S. and Reinhardt, H.W. (1999c), "Determination of double-K criterion for crack propagation in quasibrittle materials, Part III: compact tension specimens and wedge splitting specimens", Int. J. Fract., 98, 179-193. https://doi.org/10.1023/A:1018788611620
  52. Xu, S. and Reinhardt, H.W. (2000), "A simplified method for determining double-K fracture meter parameters for three-point bending tests", Int. J. Fract., 104, 181-209. https://doi.org/10.1023/A:1007676716549
  53. Xu, S. and Zhang, X. (2008), "Determination of fracture parameters for crack propagation in concrete using an energy approach", Eng. Fract. Mech., 75, 4292-4308. https://doi.org/10.1016/j.engfracmech.2008.04.022
  54. Xu, S. and Zhu, Y. (2009), "Experimental determination of fracture parameters for crack propagation in hardening cement paste and mortar", Int. J. Fract., 157, 33-43. https://doi.org/10.1007/s10704-009-9315-x
  55. Yu, K. and Lu, Z. (2013), "Determining residual double-K fracture toughness of post fire concrete using analytical and weight function method", Mater. Struct., DOI 10.1617/s11527-013-0097-2.
  56. Zhang, X. and Xu, S. (2011), "A comparative study on five approaches to evaluate double-K fracture toughness parameters of concrete and size effect analysis", Eng. Fract. Mech., 78, 2115-2138. https://doi.org/10.1016/j.engfracmech.2011.03.014
  57. Zhang, X., Xu, S. and Zheng, S. (2007), "Experimental measurement of double-K fracture parameters of concrete with small-size aggregates", Front. Archit. Civ. Eng. China, 1(4), 448-457. https://doi.org/10.1007/s11709-007-0061-8
  58. Zhao, Y. and Xu, S. (2002), "The influence of span/depth ratio on the double-K fracture parameters of concrete", J China Three Georges Univ. (Nat. Sci.), 24(1), 35-41.
  59. Zhao, Z., Kwon, S.H. and Shah, S.P. (2008), "Effect of specimen size on fracture energy and softening curve of concrete: Part I. Experiments and fracture energy", Cement Concrete Res., 38, 1049-1060. https://doi.org/10.1016/j.cemconres.2008.03.017
  60. Zi. G. and Bazant, Z.P. (2003), "Eignvalue method for computing size effect of cohesive cracks with residual stress, with application to kink-bands in composites", Int. J. Eng. Sci., 41, 1519-1534. https://doi.org/10.1016/S0020-7225(03)00033-8

피인용 문헌

  1. Modeling of fracture parameters for crack propagation in recycled aggregate concrete vol.106, 2016, https://doi.org/10.1016/j.conbuildmat.2015.12.101
  2. Effect of cracks on concrete diffusivity: A meso-scale numerical study vol.108, 2015, https://doi.org/10.1016/j.oceaneng.2015.08.054
  3. Failure Behavior of Tunnel Lining Caused by Concrete Cracking: A Case Study vol.19, pp.4, 2014, https://doi.org/10.1007/s11668-019-00718-7
  4. Fracture behaviors of tunnel lining caused by multi-factors: A case study vol.8, pp.4, 2014, https://doi.org/10.12989/acc.2019.8.4.269
  5. A parametric shear constitutive law for reinforced concrete deep beams based on multiple linear regression model vol.8, pp.4, 2014, https://doi.org/10.12989/acc.2019.8.4.285
  6. Shear Behaviour of RC Beams Strengthened by Various Ultrahigh Performance Fibre-Reinforced Concrete Systems vol.2020, pp.None, 2020, https://doi.org/10.1155/2020/2139054