# Peridynamics for Fracture Analysis of Reflective Cracks in Semi-Rigid Base Asphalt Pavement
## 1 Introduction  
Asphalt pavement with a semi-rigid base is a widely used structure for high-grade highways due to a number of advantages, including high strength and stiffness, sound flatness, and good fatigue performance. However, this type of base course easily produces dry shrinkage cracks and low-temperature shrinkage cracks during its strength formation because of its sensitivity to changes in humidity and temperature. The repeated action of traffic load will lead to stress concentration at the crack tip, and further cracking will soon form and even propagate up to the flexible layer. Such a bottom-up crack is called a reflective crack. Reflective cracks by themselves may not have a serious impact on the structural bearing capacity of composite pavement. However, water infiltration through the reflective cracks at the joints, together with the heavy traffic movements, can accelerate structural pavement failure, greatly weakening the strength and stability of the subgrade, leading to early failure of the pavement and reducing the life of the pavement. Therefore, research on the mechanism of cracking growth will help monitor the cracks' behaviors from the beginning of their development and offer feasible methods manufacturing and maintenance. Many studies have been carried out to investigate cracking mechanisms [1; 2; 3; 4]. Conventional research on crack behavior relies heavily on laboratory-scale experiments, which require considerable time and effort. [PERSON] [5] and [PERSON] et al. [6] found that reflective cracks are produced under the joint action of temperature and traffic through a large number of experimental studies. [PERSON] et al. investigated the premature cracking distress in pavement by field tests that also involved destructive tests [7]. These experiments always focused on the final status of cracks and pavement, and the processes of crack growth wereignored due to testing methods. Over these years, advancements in computer technology have allowed realistic simulations of the performance of materials to be performed. The finite element method (FEM) has become a popular approach to simulate crack behavior during their life cycle. [PERSON] [3] established a two-dimensional plane strain model using the finite element software ABAQUS. The settlement results reveal the propagation law and direction of precast cracks under traffic loads, which provides a mature method for pavement simulation. [PERSON] [4] used the method of preset interlayer cracks to predict the cracking of each layer of pavement during the use. The results show that the initial cracks mostly occur at the joints between layers, the free boundaries of each layer, and the thinner layers. [PERSON] [8] found that top-down cracks in pavement structures can be broken down into I + II fractures by establishing a three-layer 3D model of asphalt pavement with top-down cracks, in which the working temperature and vehicle speed were assumed to be the changing working conditions of the pavement structure. Parameters of crack growth and their time history curve can be calculated using the finite element method and predictions of pavement life, and the degree of damage can be drawn. However, the finite element method is based on partial differential equations (PDEs) within the framework of classical continuum mechanics. All these methods within the scope of classical continuum mechanics suffer from the inherent limitation that the spatial derivatives required by the PDEs, by definition, may lose their meaning due to the presence of a discontinuity, such as a crack. To overcome this limitation, many special techniques within the framework of classical continuum mechanics have been developed, such as the cohesive zone model (CZM) [9] and the extended finite element method (XFEM) [10]. All these methods redefine a body in such a way as to exclude the crack and then apply conditions at the crack surfaces as boundary conditions. [PERSON] et al. [11] employed XFEM to investigate the fracture process of dowel bars in rigid pavement. [PERSON] et al.