# Fatigue Life Prediction of High Modulus Asphalt Concrete Based on the Local Stress-Strain Method
## 1 Introduction  
Fatigue damage refers to the accumulation of damage in asphalt concrete, causing cracks and fracture extensions, and ultimately resulting in loading failure. Fatigue failure includes the formation of the crack nucleation stage (fatigue), crack extension (stability) of crack growth, and fracture failure (unstable crack propagation). Because fracture failure happens rapidly, the fatigue life of pavement generally includes crack formation and propagation. The term \"stage of fatigue crack initiation\" usually refers to the fatigue crack nucleation and propagation, which require examination during engineering processes. In road engineering the period from crack nucleation to the crack reaching a length of 5 mm is treated as the life of the initiation of the fatigue crack. There are different approaches to quantify the fatigue crack process in asphalt concrete mixtures. Among the different approaches, practitioners primarily use the strain approach, which was first introduced by [PERSON], and the energy approaches because these approaches are simple andconsist of experimentally oriented procedures [1; 2; 3]. The most common fatigue model adopted by the Mechanistic Empirical Pavement Design Guide (MEPDG) is a strain approach that considers the material's properties using the value of dynamic modulus forms [4]. [PERSON] described the dissipated energy changes during loading and proposed four parameters to define fatigue performance for 13 mm dense-graded Hot Mix Asphalt (HMA) using bending beams at various strain amplitudes [5]. [PERSON] used continuum damage theory to characterize the fatigue properties of asphalt binders and their effect on fatigue resistance. This proposed model can be used as an alternative to time-consuming beam fatigue tests [6]. [PERSON] evaluated the Strategic Highway Research Program (SHRP) fatigue crack initiation life prediction model with crack measurements in laboratory slab fatigue tests. The study showed that the SHRP crack initiation life model significantly underestimates the fatigue crack initiation life for slabs [7]. [PERSON] developed a system for predicting the fatigue life of asphalt mixtures. This work indicates that the fatigue life of a mixture subjected to sinusoidal strain loading can be determined through the model's damage principles using IDT (indirect tensile test) test results [8]. [PERSON] employed a large scale experimental setup to examine the influence of the most important parameters on delaying reflection cracking in geogrid reinforced overlay in bending mode. Regression equations were developed to estimate fracture parameters which can be used to predict the crack growth rate in order to design asphalt overlay that is protected from reflective cracking [9]. One of the major achievements of the SHRP asphalt mix research projects is the development of a fatigue life prediction model based on the results of intensive bending beam fatigue tests. Several researchers have conducted fatigue testing on asphalt concrete in the laboratory to investigate fatigue life through bending beam fatigue tests [10; 11; 12; 13; 14; 15; 16]. Although this model covers a wide range of asphalt mix related fatigue variables, it has to apply a shift factor to deal with the stress concentration of cracks in High Modulus Asphalt Concrete (HMAC), including the state of stress. It would be helpful to determine how real stress state contributes to fatigue life, because local stress and direct tensile tests more realistically simulate the multiaxial state of stress and cracking in pavements than bending beam tests. A basic principle of the local stress-strain method is that the nominal stress and strain of a structure under various loadings are firstly converted into local stress and strain at the most unfavorable points (i.e., the stress concentration points) based on the stress-strain loop curve obtained from the fatigue test.