## 1 Introduction
Results show that J-integral is unconditionally path independent, reflecting that it is not very important to set a specific path while simulating cracks using J-integral, thus decreasing the difficulties. Moreover, energy can be used to calculate the J-integral. [PERSON] added the strain energy density into the J-integral formulation to calculate the deformation histories of the specimen [7]. [PERSON] proposed a new model of calculating J-integral based on the energy density equivalence by introducing 3D constraint functions to describe the relationships between J-integral and load in mode-I cracks [8]. [PERSON] compared two criteria of stress intensity factor and fracture energy to investigate the behavior of asphalt mixtures under combined tensile shear loadings [9]. The SCB (Semi-Cycle Bending Test) fracture test results show that the fracture behavior of asphalt mixtures is significantly dependent on testing temperature and loading rate, which can reflect the working conditions of asphalt mixtures during engineering construction. Moreover, finite element calculation was conducted to verify the correctness of SCB tests. As for pavement structure, J-integral and stress intensity factors can be different from theoretical calculations and mechanical experiments due to the structural differences between theoretical calculation models or mechanical specimens and pavement structure. Researchers often use elastic layered continuum theory to describe the structure of asphalt pavement. [PERSON] established a three-layer 3D model of asphalt pavement with top-down cracks [10]. Working temperature and vehicle speed were assumed to be the changing working conditions of the pavement structure. Results show that top-down cracks in pavement structure can be broken down into I + II fracture, and J-integral can be used to describe stress intensity on the crack tip. [PERSON] developed a wave propagation-based analytical solution to calculate the mechanical responses of transversely isotropic viscoelastic multi-layered asphalt pavement subject to moving harmonic load [11]. This solution can be used for asphalt pavement design and analysis with consideration of realistic load and material parameters. However, a specimen of asphalt mixtures can only reveal the crack resistance of the material, but the mixtures' behaviors in pavement structure are not widely studied. J-integral and stress intensity factors on the crack tip in pavement structures have not been researched systematically. Mechanical responses during the crack growth need to be calculated using the finite element method. The research described in this paper is aimed to reveal the cracks' behaviors during the pavement's life cycle and under different working situations. The effects of traffic loads and Young's modulus of layers on the crack extension were investigated. This paper uses finite element software ABAQUS to simulate the pre-set crack's growth during the pavement's life cycle. J-integral, stress intensity factors, absolute stress, and strains were calculated to describe how the cracks extend while working. Moreover, the entropy method was used to analyze the relationship between these influencing factors aiming to help to deal with cracking problems efficiently.