Nondimensional size dependent fracture model of concrete based on boundary effect theory

The study presents a general fracture model of concrete linking the nondimensional nominal stress and equivalent crack size based on the boundary effect theory. The proposed model describes three typical fracture modes without introducing additional parameters: the strength theory for plain specimens, the linear elastic fracture model for specimens with long cracks and the quasi-brittle fracture model between these two classic limits. With a proper choice of stress distribution along the fracture process zone (FPZ) ahead of the crack tip, only the maximum load and necessary geometrical information of specimens are required to extract the fracture properties of concrete using the proposed model. The test data from three-point bending and wedge-splitting on concrete are reevaluated to justify the proposed model, where rectangular and trapezoidal stress distributions in the FPZ are assumed. The results show that the tensile strength and fracture toughness from geometrically similar specimens are consistent with those when specimens with different relative crack lengths are jointly considered. It is also found that the influence of stress distribution pattern along the FPZ is not significant. Rectangular stress distribution provides a simple relationship between the nominal stress and the equivalent crack length, which not only leads to a reliable estimation of the tensile strength and fracture toughness but also achieves a good agreement with the testing data.