# Investigation of the Fatigue Life of Bottom-Up Cracking in Asphalt Concrete Pavements
###### Abstract
[PERSON] and [PERSON] [8] proposed the new mechanics-based thermal cracking performance model, and the calibrated model can be used to establish performance-based specification limits based on material properties or the parameters determined from the new mixture test. At present, the fatigue crack growth formula proposed by [PERSON] and [PERSON] [9] based on experiments was the most widely used formula to study fatigue crack growth life, which was also known as the famous Paris formula. In the 1970s, [PERSON] et al. [10; 11] introduced the principle and method of fracture mechanics into the study of pavement structure cracking. [PERSON] et al. [12] applied fracture mechanics to qualitatively analyze the mechanism of geotextiles for preventing crack propagation. [PERSON] [13] presented the fracture properties of asphalt concrete under fatigue loading and illustrated the thermal contraction conditions and the way it is altered by the addition of geotextiles. [PERSON] and [PERSON] [14] predicted the number of cycles that cause fracturing in hot-mix asphalt (HMA) based on the number of cycles upon which the slope of the accumulated strain switched from a mode of decreasing to increasing and evaluated the effect of aggregate gradation and temperature on fatigue behaviors of hot-mix asphalt. [PERSON] et al. [15] developed a numerical prediction model for fatigue life by modifying the crack growth rate using the Paris law with the horizontal deformation rate to compare the relative performance of the material based on experimental test results. [PERSON] et al. [16] proposed an accurate and efficient model using the discrete element method and the digital image processing technique to investigate the fracture evolution of an asphalt mixture at low temperatures, which was well compared and verified via acoustic emission activities. Additionally, the fatigue crack life of asphalt pavements has also been investigated by many researchers. [PERSON] et al. [17] used some index parameters as the main prediction variables of asphalt pavement fatigue cracking modeling and obtained the prediction model for fatigue cracking life. [PERSON] et al. [18] proposed a method to predict the pavement fatigue crack initiation life and the fatigue life of a typical high modulus asphalt concrete (HMAC) overlay pavement, which runs the risk of bottom-up cracking; this was predicted and validated. Obviously, concealed failures (e.g., bottom-upcracks) are, by definition, difficult to identify and localize. In order to identify the concealed cracks (particularly bottom-up cracks) and monitor their growth over time, a supervised machine learning (ML)-based method for the identification and classification of the SHS of a differently cracked road pavement based on its vibroacoustic signature was set up [19]. The stress intensity principle was used to determine the locations and lengths of the cracks, and the hidden bottom-up cracks were detected, which has significantly impacted the current pavement detection practice [20]. From the above literature analysis, researchers have carried out extensive studies on the crack initiation and propagation prediction of asphalt pavement. However, these studies have generally focused on crack initiation or propagation for predicting fatigue cracking. In fact, the fatigue failure of asphalt pavement includes three stages: fatigue cracking, crack expansion, and structural failure. Therefore, the pavement structure design should fully consider the different stages of fatigue failure. In view of the above reasons, this paper aimed to obtain the fatigue life of bottom-up cracks in asphalt pavements, including fatigue cracking and crack propagation. OTs at different temperatures were conducted to obtain the fracture parameters \(A\) and \(n\) of the asphalt mixture, and crack propagation life was further calculated via the Paris formula.