A Weibull distribution-based method for the analysis of concrete fracture

Based on the design relation value of the variation dispersion coefficient beta at the notch tip in concrete specimens at the peak load P-max, a Weibull distribution method was employed to analyze the experimental data for different loading methods (3 PB, 4 PB, WS). The dispersion coefficient beta, which complies with the Weibull distribution for notched specimens, leads to a Weibull distribution of the tensile strength f(t) and fracture toughness K-IC. Furthermore, when the characteristic crack of concrete is alpha(ch)* = 1.0d(max) (or 1.5d(max)), the coefficient of variation for the Weibull distribution is the smallest in most cases. By adopting the simple relation alpha(ch)* = 1.0d(max) (or 1.5d(max)) and the fictitious crack growth, Delta alpha(f) = beta d(max), the fracture properties of concrete specimens with W/d(max) = 4-50 under different loading conditions (3 PB, 4 PB, WS) were investigated. Because of the scatter in the peak load P-max of the notched specimens and the variation in the fictitious crack growth Delta alpha(fici), a new statistical approach using the solution of the boundary effect model (BEM) was employed. The curves between the peak load P-max and specimen height W were predicted. The critical values of the peak load P-max and specimen height W were obtained, in which the notched specimen failure was controlled by the fracture toughness K-IC.