Mathematical Modeling of Concrete Fracture Energy of Notched Specimens Using Experimental Evidence

The tensile stiffness of concrete is an important parameter for crack initiation. The microcrack initiation and propagation regulate the stress–strain behavior and the failure mode of concrete. Therefore, fundamental awareness of the fracture mechanism in terms of fracture energy is a requisite to comprehend concrete behavior. There is research consensus that fracture energy alone does not suffice to characterize the ductility/brittleness and also the size dependency of concrete. Therefore, it is necessary to evaluate the fracture energy and the characteristic length for a realistic assessment of the fracture behavior of concrete. Towards this objective, this study examined the fracture energy of concrete by experimentation, and the fracture energy proposed by various models in the literature. Further, the characteristic length proposed by Hillerborg which depicted both the material influence and the size effect, has been computed. Based on the RILEM—50 FM recommendations, 18 specimens with varying grades of concrete and notch depths have been tested and the fracture energy parameters have been evaluated. Also, two regression models with key fracture parameters as variables for two-notch ratios, have been formulated for the concrete fracture energy. The arguments have been supported by experimental evidence.