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

Abstract

Based on the design relation value of the variation dispersion coefficient β at the notch tip in concrete specimens at the peak load Pmax, a Weibull distribution method was employed to analyze the experimental data for different loading methods (3 PB, 4 PB, WS). The dispersion coefficient β, which complies with the Weibull distribution for notched specimens, leads to a Weibull distribution of the tensile strength ft and fracture toughness KIC. Furthermore, when the characteristic crack of concrete is αch∗=1.0dmax (or 1.5dmax), the coefficient of variation for the Weibull distribution is the smallest in most cases. By adopting the simple relation αch∗=1.0dmax (or 1.5dmax) and the fictitious crack growth, Δαf=βdmax, the fracture properties of concrete specimens withW/dmax = 4–50 under different loading conditions (3 PB, 4 PB, WS) were investigated. Because of the scatter in the peak load Pmax of the notched specimens and the variation in the fictitious crack growth Δαfici, a new statistical approach using the solution of the boundary effect model (BEM) was employed. The curves between the peak load Pmax and specimen height W were predicted. The critical values of the peak load Pmax and specimen height W were obtained, in which the notched specimen failure was controlled by the fracture toughness KIC.