Modified Paris law for mode I fatigue fracture of concrete based on crack propagation resistance

To characterize mode I fatigue fracture of concrete, the Paris law has been widely applied. However, due to the quasi-brittle properties of concrete, it has been found that the empirical constants in the model are dependent on the size of the specimen and the level of the fatigue load. In addition, the crack propagation resistance under cyclic loading introduced in the existing modified Paris law is difficult to determine. In this study, the crack propagation resistance of concrete under static loading is introduced into the Paris law, and a new modified Paris law is proposed. The validity of the model is confirmed by the reasonable correspondence between the prediction of the mode I fatigue lives of TPB beams and the experimental data. The proposed model offers several advantages. First, the empirical constants remain independent of the specimen depth, initial crack length to depth ratio, and fatigue load level. Additionally, the introduced crack propagation resistance is easier to determine. The study concludes that if the initial fracture toughness, unstable fracture toughness, and empirical constants in the model are predetermined, it can forecast the mode I fatigue fracture life of concrete with diverse geometric dimensions and fatigue load levels. This prediction contributes to the overall safety assessment of concrete structures subjected to fatigue loading.