# Fatigue Performance and Model of Polyacrylonitrile Fiber Reinforced Asphalt Mixture
## 1 Introduction  
The fatigue resistance of an asphalt mixture refers to its ability to withstand repeated bending without fracture. The fatigue in asphalt pavements mainly appears as cracking on the surface of the pavement. These fatigue cracks are usually a series of interconnecting cracks caused by fatigue failure of the asphalt surface under repeated traffic loading. These tensile cracks caused by repeated flexural stresses propagate and grow continuously. Finally, these cracks are interconnected, forming multi-sided, sharp-angled pieces, which develop a pattern resembling alligator skin. Fatigue cracking is considered one of the main structural distress modes in asphalt pavement. It is also essential to consider the loss of asphalt pavement serviceability in the performance-based design of asphalt mixtures and the structural design of flexible pavements [1; 2]. Some reports have revealed that the incorporation of fibers into asphalt mixture can improve the properties of the mixture to some extent [3; 4; 5; 6]. [PERSON] et al. [7] concluded that the reinforcing efficiencies of polyester and nylon fibers on the mechanical performance of asphalt concrete increased as the fiber content increased from 0.5% to 1.0%. [PERSON] et al. [8] found that basalt fiber, whose surface was modified by a silane coupling agent, had good interfacial compatibility with asphalt by the reaction with free silane groups. [PERSON] and [PERSON] [9] found that fracture behavior at low to medium temperaturesand rutting behavior was significantly improved by the addition of glass macro fibers and could reduce permanent deformation by up to 50% compared to a mixture without fibers. [PERSON] et al. [10] found that pavement overlays with a compound of polypropylene and aramid fiber modified hot mix asphalt can better resist reflective cracking and reduce rutting rate evolution. [PERSON] et al. [11] investigated the effect of phosphorus slag powder (PSP) and polyester fiber (PF) on the rheological properties of asphalt binder and the mechanical properties of the resultant mixture, and concluded that PSP in combination with PF can provide satisfactory rutting, moisture susceptibility, and low temperature cracking of the resultant mixture. [PERSON] et al. [12] found that the use of basalt fiber in a reinforced mixture with diatomic (which were of a higher stiffness) ended up doubling the fatigue life of the asphalt mixture. In this study, the composite of basalt fiber and diatomic was used to enhance the fatigue life and tensile strength of hot mix asphalt. [PERSON] and [PERSON] [13] evaluated the fatigue response of polyethylene terephthalate (PET) fiber modified asphalt specimens by a four-point bending test and found that PET fiber increased the fatigue life of hot mix asphalt (HMA) by up to 70%. [PERSON] et al. [14] found that aramid pulp fiber asphalt mixture had a lower fatigue life at high strain amplitudes (heavy truckloads). [PERSON] et al. [15] concluded that the use of 6% and 9% of amorphous polyolefin and a compound of low density polyethylene (LDPE) and ethylene/vinyl acetate (EVA), as well as cellulose and synthetic fibers, could improve the fatigue resistance of asphalt mixture and energetic methods can be effectively applied to data from indirect tensile fatigue tests. [PERSON] et al. [16] evaluated the effects of diamite and glass fiber on the properties of asphalt mixture using the statistical analysis of variance (ANOVA) method and statistical regression method. They found that diatomic and glass fiber can improve the rutting resistance and fatigue properties of asphalt mixture. Traditionally, fatigue models are proposed as a result of fitting laboratory test data. The fatigue characteristics are usually represented as relationships between the initial longitudinal stress and strain versus the number of load repetitions to failure. However, accurate description of the fatigue behavior of asphalt mixture is a difficult task due to the complexity of fatigue phenomenon under varying material, loading, and environmental conditions.