Fitting the fracture curve of concrete as a density function pertaining to the generalized extreme value family

Abstract

The load-displacement (P-δ) curve, recorded during the fracture process of concrete in three-point bending tests, is supposed to depict a fracture phenomenon of statistical character that can be suitably described by a density function pertaining to the generalized extreme value family, which proves to be maximal Fréchet, as a particular case of heavy tail distributions. Since the proposed analytical function fits the test record throughout, the non-measured fracture work, corresponding to the upper asymptotic tail of the fracture curve P-δ, is expected to be measured in a more reliable and accurate way than using other methods currently recommended to evaluate the total fracture energy of concrete. The general scale parameter Ω, identified as the area under the fracture curve, and the three parameters of the Fréchet density function are estimated by fitting the recorded data to the experimental P-δ curve using a specific Matlab program. The model is applied to fit experimental fracture curves from an ample 3-PB test program on notched specimens for different self-compacting concrete mixes. The results obtained for the size-independent specific fracture energy are compared with those provided by other well-established conventional approaches. In both instances, the suitability of the proposal is confirmed.