Fracture model for predicting tensile strength and fracture toughness of concrete under different loading rates

For the sake of safety evaluation of concrete structures under dynamic loading conditions, the rate dependences of concrete fracture parameters are necessary to be elucidated rationally first. Therefore, the aim of this study is to develop a fracture model for determining the size-independent tensile strength (ft), the fracture toughness (KIC) and the fracture energy (GF) under different loading rates. The fracture mechanism was analyzed comprehensively using three-point bending tests on concrete beams with varied depths (h) and ratios of the initial crack length to the beam depth (a0/h). As the loading rate increases, the number of fractured coarse aggregates is increased, and the shape of the load–displacement curve around the maximum fracture load (Fmax) becomes sharper. Subsequently, a fracture model was proposed to predict the size-independent parameters ft, KIC and GF by incorporating the average aggregate size (davg) and a discrete coefficient (β) to indicate material heterogeneity and discontinuity, respectively. The critical effective crack length (Δac) was discretized and quantified as davg multiplied by β. Closed-form solutions of ft, KIC and GF were obtained using Fmax based on the boundary effect model. ft, KIC and GF can be explicitly predicted after determining Fmax from the fracture tests, and were generally irrelevant to h and a0/h under individual loading rates, indicating their size-independence. The scatters in the ft, KIC and GF values were determined using a statistical analysis. The rate dependences of the fracture parameters were clarified quantitatively through elucidating the variations in ft, KIC and GF with respect to the loading rate. Moreover, the predicted fracture parameters based on the proposed model were insensitive to the possible variations of davg and β. This study brings a new insight into the fracture behaviors of concrete under different loading rates and provides scientific guidance for the disaster prevention of concrete structures.