Analytical method for predicting mode I crack propagation process of concrete under low-cycle fatigue loading

The fatigue failure of concrete structures is preceded by the formation of microcracks and the propagation of macrocracks. Therefore, the fatigue fracture properties of concrete should be investigated thoroughly to guarantee the safety of structures. In this paper, an analytical method for predicting the mode I crack propagation in concrete under low-cycle fatigue loading is proposed according to the fictitious crack model, where the fatigue tension-softening constitutive relationship is introduced, and the initial fracture toughness-based crack propagation criterion is applied. The fatigue crack propagation process can be determined by solving two governing equations. To validate the effectiveness of the method, the fatigue crack propagation in threepoint bending (TPB) beams is calculated, and the results are compared with the simulated and experimental results. It is shown that, although the linearization assumption of the crack opening displacement (COD) along the depth direction leads to slight differences between the analytical and simulated results, there is still a reasonable agreement between the analytical and experimental results. The effectiveness of the analytical method is verified. Therefore, when Young's modulus, initial fracture toughness, and fatigue tension-softening constitutive relationship are determined, the mode I fatigue crack propagation in concrete can be predicted based on the analytical method. It is expected that the method will contribute to the safety assessment of concrete structures under low-cycle fatigue loading.