# Investigation of the Fatigue Life of Bottom-Up Cracking in Asphalt Concrete Pavements
###### Abstract  
Traditionally, fatigue cracking in asphalt pavement means fatigue failure, which is the basis for controlling the design thickness of asphalt pavements. In fact, the fatigue failure of asphalt pavements includes three stages: fatigue cracking, crack expansion, and structural failure. Therefore, this paper aims to investigate the fatigue life of the bottom-up cracking of asphalt concrete (AC) pavements considering the different stages of fatigue failure. The dynamic modulus of AC of different grades was experimentally determined. The tensile stresses at the bottom of the AC layer were evaluated by embedding the tested dynamic modulus into a numerical simulation, which can be used to calculate the fatigue cracking life. Then, overlay tests (OTs) at different temperatures were conducted to obtain the fracture parameters \(A\) and \(n\) from the asphalt mixture. The crack propagation life was calculated via the Paris formula based on the fracture parameters \(A\) and \(n\). The analysis results showed that an increase in AC thickness could effectively improve the fatigue crack life of the pavement structure, and the proportion of crack propagation life to fatigue crack life at different temperatures varied significantly. Therefore, when analyzing and calculating the fatigue life of pavement structures, besides the fatigue cracking life, the crack propagation life after cracking should also be considered, which is very important for accurately calculating the entire fatigue life of asphalt pavement structures. This will offer guidance for asphalt pavement thickness design. b 2  
life in terms of potential fatigue cracking is crucial for pavement design, maintenance, and rehabilitation. To this end, some researchers have conducted many studies to predict fatigue cracking. [PERSON] et al. [1] investigated the fatigue cracking of expressway asphalt pavement, which highlighted that asphalt pavement is subjected to repeated actions of driving loads and temperature loads. When the action times reached a certain number, fatigue cracking would occur. However, cracks are hard to spot until they reach the surface of the road. Therefore, it is very difficult to study the characteristics of fatigue cracks on the actual pavement. With the development of computer technology, it is possible for researchers to study fatigue cracking by numerical analysis. Due to the singularity of the crack tip, the results calculated from the traditional strength theory are unreasonable. Therefore, fracture mechanics can be introduced to study the fractures. [PERSON] et al. [2] obtained the stress intensity factor (SIF) at the crack tip based on fracture mechanics, and used SIF to reflect the stress distribution at the crack tip. [PERSON] et al. [3] presented a mechanistic model for predicting the performance of asphalt mixtures in terms of crack propagation rate, fatigue life assessment, and permanent deformation characteristics. [PERSON] et al. [4] used the neural networks (NN) approach to model the SIF as cracks grow upward through a hot-mix asphalt (HMA) overlay because of both the load and thermal effects with and without the reinforcing interlayers. Several cases under both thermal loading and traffic loading were considered, and the NN models had significantly higher accuracy in predicting the SIFs compared with the nonlinear regression approach. Based on seminal investigations of the integer transform, [PERSON] et al. [5] proposed the modelling tensile strain response in asphalt pavements in bottom-up and/or top-down fatigue crack initiation. The Texas A&M Transportation Institute developed a correlation between the number of cycles to failure and the fracture energy index using overlay tests (OTs) [6; 7]. [PERSON] and [PERSON] et al. [6] summarized how crack initiation is related to crack propagation and provided both the theory and validation for the usefulness of OT to assess fatigue cracking.