%0 Journal Article
%A WANG Zhan-ke
%A GAO Hong-bo
%A HAN Xiao-yan
%A MA Peng
%T Analytical Calculation Method for Unstable Toughness of Double-<i>K</i> Fracture Model
%D 2019
%R 10.11988/ckyyb.20171144
%J Journal of Yangtze River Scientific Research Institute
%P 106-109
%V 36
%N 6
%X An analytical method which merely needs the axial compressive strength  <i>f</i><sub>c</sub> of concrete to calculate the unstable toughness <i>K</i><sup>un</sup><sub>Ic</sub> of double-<i>K</i> fracture model is proposed in this paper. Massive experimental data indicate that the ratio of critical crack propagation length Δ<i>a</i><sub>c</sub> to ligament length (<i>h-a</i><sub>0</sub>) tends to be a constant. According to this regularity and on the basis of the bilinear constitutive relationship of the fictitious crack model, the maximum load <i>P</i><sub>max</sub> of three-point bending notched beam is calculated under  equilibrium condition. Then the calculated result of  <i>P</i><sub>max</sub>  is substituted to the formula and the unstable toughness <i>K</i><sup>un</sup><sub>Ic</sub>  of double-<i>K</i> fracture model is calculated. The calculated results of <i>P</i><sub>max</sub> and <i>K</i><sup>un</sup><sub>Ic</sub> are compared with those of test values to verify the accuracy of the method. Results conclude that the calculated results of <i>P</i><sub>max</sub> and <i>K</i><sup>un</sup><sub>Ic</sub>  agree well with test values for relatively big size concrete specimens with maximum aggregate size not greater than 40  mm. The maximum load <i>P</i><sub> max</sub> and the unstable toughness <i>K</i><sup>un</sup><sub>Ic</sub> can be predicted by the proposed analytical method.
%U http://ckyyb.crsri.cn/EN/10.11988/ckyyb.20171144