13th International Conference on Fracture June 16–21, 2013, Beijing, China -11- The validation of double-K fracture model to the post-fire concrete specimens is proved. In totally 45 effective specimens, the deviation between analytical value KI un-A and experimental KI un-E of 22 specimens is below 5%, and of 40 specimens is below 15%, account for 89% of total specimens. Accordingly, the number of specimens corresponding to the same deviation between KI un-W and KI un-E is 20 and 42, respectively. Meanwhile the weight function method agrees well with the analytical method, and the deviation below 5% accounts for 65% of total specimens. Acknowledgment The State Laboratory of Disaster Reduction in Civil Engineering (SLDRCE09-D-02) has supported this research. . Reference [1] HILLERBORG A., MODEER M. and PETERSON P.E. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cem Concr Res, 6(6), (1976) 773-782. [2] Bazant ZP, Oh BH. Crack band theory for fracture of concrete. Mater Struct, 16(93) (1983) 155-177. [3] Jenq YS, Shah SP Two parameter fracture model for concrete. J Engng Mech, ASCE, 111(10) (1985) 1227-1241. [4] Nallathambi P, Karihaloo BL. Determination of specimen-size independent fracture toughness of plain concrete. Mag Concr Res, 38(135) (1986) 67-76. [5] Bazant ZP, Kazemi MT. Determination of fracture energy, process zone length and brittleness number from size effect, with application to rock and concrete. Int J Fract, 44 ( 1990) 111-131. [6] Xu S, Reinhardt HW. Determination of double-K criterion for crack propagation in quasi-brittle materials, Part I: Experimental investigation of crack propagation. Int J Fract, 98 (1999) 111-149. [7] Xu S, Reinhardt HW. 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 (1999)151-177. [8] Xu S, Reinhardt HW. 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 (1999) 179-193. [9] Jenq YS, Shah SP. A fracture toughness criterion for concrete. Engng Fract Mech, 21(5) (1985) 1055-1069. [10] Kumar S, Barai SV. Determining the double-K fracture parameters for three-point bending notched concrete beams using weight function. Fatigue Fract Engng Mater Struct, 33(2010) 645-660. [11] Murakami. Stress Intensity factors handbook. London: Pergamon Press, 1987. [12] Shailendra Kumar, S. V. Barai. Influence of specimen geometry and size-effect on the KR-curve based on the cohesive stress in concrete. Inter J Fract, 152 (2008) 127-148. [13] Shailendra Kumar, S. V. Barai. Influence of specimen geometry on determination of double-K fracture parameters of concrete: a comparative study. Inter J Fract, 149 (2008) 47-66. [14] Karihaloo B L, Nallathambi P. Size effect prediction from the double-K fracture model for notched concrete. Materials and structures, 1990, 23: 178-185. [15] Zdenek. P. Bazant and Pere C. Prat: Effect of Temperatures and Humidity on Fracture Energy of Concrete. ACI Mater J, 85(4) (1988) 262-271.
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