Acknowledgement
Supported by : Natural Science Fund of China
References
- Baker, G. (1996), "The effect of exposure to elevated temperatures on the fracture energy of plain concrete", RILEM Mater. Struct., 29(6), 383-388. https://doi.org/10.1007/BF02486347
- Bazant, Z.P. and Oh, B.H. (1983), "Crack band theory for fracture of concrete", RILEM Mater Struct, 16(93), 155-177.
- Bazant, Z.P. and Prat, P.C. (1988), "Effect of temperatures and humidity on fracture energy of concrete", ACI Mater. J., 85(4), 262-271.
- Bazant, Z.P. and Kazemi, M.T. (1990), "Determination of fracture energy, process zone length and brittleness number from size effect, with application to rock and concrete", Int. J. Fract., 44(2), 111-131. https://doi.org/10.1007/BF00047063
- Bretschneider, N., Slowik, V., Villmann, B. and Mechtcherine, V. (2011), "Boundary effect on the softening curve of concrete", Eng. Fract. Mech., 78(17), 2896-2906. https://doi.org/10.1016/j.engfracmech.2011.08.006
- Bueckner, H.F. (1970), "A novel principle for the computation of stress intensity factors", Z. Angew. Math. Mech., 50(2), 529-546.
- Bulletin D' Information (1993), CEB-Comite Euro-international du Beton-CEB-FIP Model Code 1990, Lausanne.
- Chen, H.H. and Su, R.K.L. (2013), "Tension softening curves of plain concrete", Constr. Build. Mater., 44(7), 440-451. https://doi.org/10.1016/j.conbuildmat.2013.03.040
- Glinka, G. and Shen, G. (1991). "Universal features of weight functions for cracks in Mode I", Eng. Fract. Mech., 40(6), 1135-1146. https://doi.org/10.1016/0013-7944(91)90177-3
- Gopalaratnam, V.S. and Shah, S.P. (1985), "Softening response of plain concrete in direct tension", ACI Mater. J., 82(3), 310-323.
- Hillerboerg, A., Modeer, M. and Peterson P.E. (1976), "Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements", Cement Concrete Res., 6(6), 773-782. https://doi.org/10.1016/0008-8846(76)90007-7
- Hilsdorf, H.K. and Brameshuber, W. (1991), Current Trends in Concrete Fracture Research. Springer, Netherlands.
- Hisham, A.F. and Sameer, A.H. (1997), "Variation of the fracture toughness of concrete with temperature", Constr. Build. Mater., 11(2), 105-108. https://doi.org/10.1016/S0950-0618(97)00005-6
- 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)
- Jenq, Y.S. and Shah, S.P. (1985b), "A fracture toughness criterion for concrete", Eng. Fract. Mech., 21(5), 1055-1069. https://doi.org/10.1016/0013-7944(85)90009-8
- Kumar, S. and Barai, S.V. (2012), "Size-effect of fracture parameters for crack propagation in concrete: a comparative study", Comput. Concr., 9(1), 1-19. https://doi.org/10.12989/cac.2012.9.1.001
- Kumar, S. and Barai, S.V. (2010), "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
- Kumar, S. and Barai, S.V. (2009), "Determining double-K fracture parameters of concrete for compact tension and wedge splitting tests using weight function", Eng. Fract. Mech., 76(7), 935-946. https://doi.org/10.1016/j.engfracmech.2008.12.018
-
Kumar, S. and Barai, S.V. (2008a), "Influence of specimen geometry and size-effect on the
$K_R$ -curve based on the cohesive stress in concrete", Int. J. Fract., 152(2), 127-148. https://doi.org/10.1007/s10704-008-9275-6 - Kumar, S. and Barai, S.V. (2008b), "Influence of specimen geometry on determination of double-K fracture parameters of concrete: a comparative study", Int. J. Fract, 149(1), 47-66. https://doi.org/10.1007/s10704-008-9227-1
- Kwon, S.H., Zhao, Z.F. 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(8), 1061-1069. https://doi.org/10.1016/j.cemconres.2008.03.014
- Nallathambi, P. and Karihaloo, B.L. (1986), "Determination of specimen-size independent fracture toughness of plain concrete", Mag. Concr. Res., 38(135), 67-76. https://doi.org/10.1680/macr.1986.38.135.67
- Nielsen, C.V. and Bicanic, N. (2003), "Residual fracture energy of high-performance and normal concrete subject to high temperatures", RILEM Mater. Struct., 36(8), 515-521. https://doi.org/10.1617/13880
- Petersson, P.E. (1981), Crack Growth and Development of Fracture Zones in Plain Concrete and Similar Materials, Division of Building Materials, Lund Institute of Technology, Report TVBM-1006, Sweden.
- Park, K., Paulino, H.G. and Roesler, J.R. (2008), "Determination of the kink point in the bilinear softening model for concrete", Eng. Fract. Mech., 75(13), 3806-3818. https://doi.org/10.1016/j.engfracmech.2008.02.002
- Phillips, D.V. and Zhang, Z. (1993), "Direct tension tests on notched and un-notched plain concrete specimens", Mag. Concr. Res., 45(162), 25-35. https://doi.org/10.1680/macr.1993.45.162.25
- Prokopski, G. (1995), "Fracture toughness of concretes at high temperature", J Mater. Sci., 30(6), 1609-1612. https://doi.org/10.1007/BF00375272
- 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)
- Roesler, J., Paulino, G.H., Park, K. and Gaedicke, C. (2007), "Concrete fracture prediction using bilinear softening", Cement Concrete Compos., 29(4), 300-312. https://doi.org/10.1016/j.cemconcomp.2006.12.002
- Tada, H., Paris, P.C. and Irwin, G. (1985), The stress analysis of cracks handbook. Paris Productions Incorporated, St. Louis, Paris, France.
- Xu, S. and Reinhardt, H.W. (1999a), "Determination of double-K criterion for crack propagation in quasi-brittle materials, Part I: Experimental investigation of crack propagation", Int. J. Fract., 98(2), 111-149. https://doi.org/10.1023/A:1018668929989
- Xu. S and Reinhardt, H.W. (1999b), "Determination of double-K criterion for crack propagation in quasi-brittle materials, Part II: Analytical evaluating and practical measuring methods for three-point bending notched beams", Int. J. Fract, 98(2), 151-177. https://doi.org/10.1023/A:1018740728458
- Xu, S. and Reinhardt, H.W. (1999c), "Determination of double-K criterion for crack propagation in quasi-brittle materials, Part III: Compact tension specimens and wedge splitting specimens", Int. J. Fract., 98(2), 179-193. https://doi.org/10.1023/A:1018788611620
- Yu, J.T., Yu, K.Q. and Lu, Z.D. (2012), "Residual fracture properties of concrete subjected to elevated temperatures", RILEM Mater. Struct., 45 (8), 1155-1165. https://doi.org/10.1617/s11527-012-9823-4
- Yu, K.Q. and Lu, Z.D. (2014), "Determining residual double-K fracture toughness of post-fire concrete using analytical and weight function method", RILEM Mater. Struct., 47(5), 839-852. https://doi.org/10.1617/s11527-013-0097-2
- Zhang, B., Bicanic, N., Pearce, C.J. and Balabanic, G. (2000), "Residual fracture properties of normal and high-strength concrete subject to elevated temperatures", Mag. Concr. Res., 52(2), 123-136. https://doi.org/10.1680/macr.2000.52.2.123
-
Zhang, B. and Bicanic, N. (2006), "Fracture energy of high-performance concrete at high temperatures up to
$450^{\circ}C$ : the effects of heating temperatures and testing situations (hot and cold)", Mag. Concr. Res., 58(5), 277-288. https://doi.org/10.1680/macr.2006.58.5.277 - Zhang, B., Bicanic, N., Pearce, C.J. and Phillips, D.V. (2002), "Relationship between brittleness and moisture loss of concrete exposed to high temperatures", Cement Concrete Res., 32(3), 363-371. https://doi.org/10.1016/S0008-8846(01)00684-6
- Zhang, B., Bicanic, N., Pearce, C.J. and Balabanic, G. (2000), "Assessment of toughness of concrete subjected to elevated temperatures from complete load-displacement curve- Part I: General introduction", ACI Mater., 97(5), 550-555.
- Zhang, B., Bicanic, N., Pearce, C.J. and Balabanic, G. (2000), "Assessment of toughness of concrete subjected to elevated temperatures from complete load-displacement curve- Part II: Experimental Investigation", ACI Mater., 97(5), 556-566.
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