## 1 Introduction  
Nowadays, adding a paving asphalt layer on cracked cement concrete pavement is a widespread construction measure. Due to defects in the cement concrete layer, the bearing capacity of the structure decreases over time. As the pavement temperature increases, the effects of the interface bonding on the overlay response amplify [1], and reflection cracks are more prone to occur in the overlay subjected to temperature change and loading; however, study has shown that glass fiber reinforced modified asphalt could strengthen the bonding and mitigate cracking of the overlay [2]. In order to delay the development of reflection cracks, the stress-absorption layer has been adopted domestically, and some experiments have been carried out to validate the effects of anti-crack performance. The stress-absorption layer, set between the cement concrete layer and the asphalt layer, can delay the occurrence of a reflection crack, because the deformation and the ability of elastic recovery of the layer reduces the stress concentration [3]. The stress-absorption layer is good at fatigue resistance,because the layer dissipates the concentrated stress and prevents the emergence of fatigue cracks in it, and consequently, it slows down the speed of propagation of the reflection crack, and thus attains the objectives of preventing and controlling the cracks. Nowadays, the theories and methods of fatigue fracture mechanics have been used to study the cracks of asphalt pavement. The nonlinear X-SBFEM (which is the extended proportional boundary finite element method) is capable of modeling the nonlinear fracture propagation process while taking into account the effects of cohesive interactions [4], because the main reason for the failure of the asphalt pavement is fatigue failure under the persistent actions of traffic load and temperature load. Therefore, research of the fatigue crack propagation law of the asphalt pavement is important. The fatigue failure of asphalt pavement can be divided into two stages: The fatigue-initiation stage and the fatigue fracture stage. Some experience has been accumulated in the study of the fatigue initiation stage, and the results have been used so far. The study of the fatigue fracture stage showed that the fractured area increased significantly as the interface bonding strength decreased. On the contrary, the fractured area decreased slightly as the interface stiffness decreased [5]. In the past, model I cracks were researched mainly through fatigue fracture tests for asphalt-overlay composite pavement. In fact, I-II composite cracks have existed extensively in pavement structures, but few experiments have been conducted [6; 7; 8; 9; 10; 11]. The propagation behavior of composite cracks was previously simulated through the uniaxial compression experiment using a notched beam, but the cyclic loading was not applied, and the type of crack and the trend of the crack propagation were also lacking [12]. Test simulations of the propagation process of load reflective cracking and temperature reflective cracking have been carried out to evaluate the cracking resistance of the stress-absorption layer, and it has been proven that paving of the stress-absorption layer is a good method to delay reflection cracks; however, only the influence of loading and temperature on the stress-absorption layer was tested, the material of the stress-absorption layer and the crack were not included [13]. The effects of the thickness of the stress-absorption layer on the speed of the propagation of the reflection crack have also been investigated, but the mechanism of the stress-absorption layer was not quite clear [14; 15; 16; 17]. With the increase of the thickness of the stress-absorption layer, the speed of the propagation of the reflection crack would decrease, but the flexural and tensile effects of the overlay would increase, and also the cost [18; 19; 20]. It has been verified by engineering that the optimal thickness of the interlayer is 20-40 mm [9; 10; 21].