## 1 Introduction  
Cracking is a challenging topic which the researchers face. Insufficient and improper treatment of cracks often negatively impacts the pavement structure and its performance. Numerous studies on cracks' behavior have been conducted to reveal their influences on pavement performance. Initial cracks usually exist in the pavement structure in the form of micro-cracks, and these cracks grow due to temperature change, traffic loads, and other environmental factors. So, research on the mechanism of cracking growth will help monitor the cracks' behaviors from the beginning of their development and offer feasible ways of manufacturing and maintenance. Traditional fatigue methods explain the initiation and growth of cracks [1], but this only provides a rough approach that performs poorly while calculating longitudinal cracks. To solve this kind of problem, fracture mechanism theories were established. [PERSON] established the approximate equation of crack growth rate under repeated load [2]. [PERSON] expanded this theory, and normal forms of crack growth were obtained [3]. However, this equation needs four parameters related to material properties, which decrease its reliability and limit its usage. A life-related index was established based on engineering data, including traffic load, environment conditions, and embankment conditions [4]. Conditions included by this index are also limited, and it will take a long time to perform road surveys, which can be inconvenient. These methods are always based on numerous engineering data and cannot involve many working conditions. Correction factors are always acquired when using these methods, so a convenient way of researching crack behavior is needed. Conventional research on crack behavior heavily relies on laboratory-scale experiments, which require considerable time and effort. These experiments always focused on the final status of cracks and pavement, and the processes of cracks' growth were ignored due to testing methods. Over these years, the finite element method has become a popular approach to simulate the cracks' behavior during their life cycle. During their growth, every kind of cracks' behavior can be calculated using finite element software, requiring much less time than local experiments. The two-dimensional plane strain model was established by [PERSON] using finite element software ABAQUS [5]. This model revealed the growth of pre-set cracks under traffic loads and the direction of cracks' growth, which offered a mature way of pavement simulation. [PERSON] used the finite element method combined with fracture mechanics theory to investigate the cracking behavior of the orthogonal layered pavement, and uses the method of preset interlayer cracks to predict the cracking of each layer of the pavement during use. The results show that the cracking performance of the orthogonal layered pavement is largely affected by the initial shape and location of the cracks. These initial cracks mostly occur at the joints between layers, thinner layers and the free boundaries of each layer [6]. Results show that behaviors of crack growth are related to the viscoelasticity and creep properties of asphalt deeply. However, compared with two-dimensional models, three-dimensional models always perform better, especially when the process of crack growth was taken into consideration [5]. Parameters of crack growth and their time history curve can be calculated using the finite element method and predictions of pavement life, degree of damage can be drawn. Road workers can also choose the appropriate asphalt mixture based on the finite element calculation results, thus promoting the development of the asphalt mixture. J-integral and stress intensity factors are often used to describe the behaviors of crack growth, from which researchers can have a direct understanding of the process. [PERSON] developed a 3D model to compute the J-integral of large deformation solids [7].