# Peridynamics for Fracture Analysis of Reflective Cracks in Semi-Rigid Base Asphalt Pavement
## 1 Introduction
[12] developed an XFEM model of a semicircular bending test to simulate crack propagation and compared it with a laboratory semicircular bending test. [PERSON] et al. [13; 14; 15] studied the reflective crack propagation of asphalt pavement under single temperature and circle temperature loads and studied the reflective crack propagation under the action of temperature-traffic coupling dynamics with XFEM. However, within these methods, the continuity and the discontinuity of a solid body are described by different governing equations, which means external criteria are needed to define the onset of crack growth, the direction, and the speed of crack propagation, and even to answer whether the crack should turn, branch, oscillate, arrest, etc. Peridynamics (PD), proposed by [PERSON] et al. [16; 17; 18], is a nonlocal theory of mechanics that replaces spatial derivatives with an integral operator and introduces a new definition for damage. The PD theory avoids singularities at the crack tip because it introduces a length-scale, the size of the nonlocal region. Meshfree discretization methods for PD models (based on midpoint integration of the integral operator) can simulate the natural evolution of damage and fracture seamlessly. Such models have natural theoretical advantages in analyzing crack propagation and severe damage of solids under dynamic loading such as impact [19; 20; 21], in which the crack nucleation and crack propagation are spontaneously simulated by applying a simple bond damage criterion without any additional criterion for judging whether the crack propagates. PD theory has been widely used by scholars to analyze the fracture of different types of material. [PERSON] et al. [22] studied the elastic wave dispersion, propagation, and impact damage of the concrete Brazilian disc in the split Hopkinson pressure bar (SHPB) test based on a PMB (Prototype Microelastic Brittle) peridynamics model. [PERSON] et al. [23] applied an intermediately homogenized peridynamics (IH-PD) model of concrete to numerically investigate the dynamic failure behavior in concrete. [PERSON] et al. [24] established a micro-calculation model of concrete by the MATLAB-ABAQUS co-simulation method based on the PD theory, and the evolution law of fracture reflects the micro-characteristics and macro-evolution law of fracture well. [PERSON] et al. [25] established a numerical model of asphalt mixtures based on PD theory, analyzed the stress state and energy changes in specimens during the semicircular bending test, and analyzedthe effects of coarse aggregates, voids, and microcracks on the low-temperature cracking of asphalt mixtures by using a two-dimensional micronumerical model. [PERSON] et al. [26; 27] used the numerical method of PD theory to simulate the crack branching stage of a cylindrical asphalt mixture used in the laboratory under a compression load. In view of the advantages of PD theory in dealing with discontinuous problems, many scholars have devoted themselves to the study of PD theory in recent years, and PD theory has good development prospects. However, there are few studies on semi-rigid multilayer pavement based on this theory. In this paper, the theory of peridynamics is briefly described, and the peridynamics algorithm program is compiled by MATLAB. After that, the correctness of the written program is verified by several typical examples. Then, the pavement model of the multilayer structure is built, the crack propagation trajectory of different positions under load is obtained through simulation calculation, and the influence of loads at different positions on the expansion of existing reflective cracks in the semi-rigid base is analyzed. On this basis, the calculation model is simplified to simulate the reflective crack propagation under different thicknesses of asphalt overlay, and the influence of asphalt overlay on reflective crack cracking is analyzed.