The use of asphalt mixtures in railway tracks provides a positive contribution to the bearing capacity, stability, durability and more importantly damping properties of the railway structure particularly for the new generation of low-vibration-railway track systems. However, one of the main concerns in the use of asphalt mixtures in railways is their fatigue cracking caused by the repeated traffic loading. The present study focused on the fatigue damage behavior of asphalt mixtures in the railways through using the viscoelastic continuum damage theory. Three experiments of creep compliance, constant crosshead rate and cyclic fatigue tests were carried out on some asphalt mixtures with different air void contents and aging conditions. Based on the results obtained, the crumb rubber modification of railways asphalt mixtures at low stress levels increases the fatigue life of asphalt up to 7.2 times while this increase is at the most 3.6 for the highway asphalt mixture. Furthermore, reducing the air void content from 4% to 2% for the crumb rubber modified asphalt mixture increases the fatigue life by 9.4 times at high stress levels and 18.2 times at low stress levels, which is a great improvement. It was shown that the lowest fatigue life is obtained in the aged crumb rubber modified mixture (i.e., 20 percent of unmodified asphalt mixture).
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Introduction

Railway transportation system is usually preferred over other modes of transportations because of its higher speed, better safety, and less environmental negative impacts. In recent years, with the development of high-speed tracks, this transport system has been given more attention. High-speed tracks require a safer and more reliable railway structure with lower maintenance operations [1,2]. Furthermore, transmission of vibrations to surrounding structures in the urban railways is a serious concern. A very effective solution that improves both the stability and the durability of the structure, contributes to the reduction of need for maintenance operations, and reduces the induced railway vibrations is the use of asphalt mixture in the railway construction [2–۶]. Moreover, the use of asphalt mixture makes the possibility of reducing the railway height, and in turn provides great advantages in the construction of tunnels with smaller diameter or lighter bridges. Asphalt mixtures can be used as the ballast layer (Fig. 1a) or the subballast layer (Fig. 1b) in the railway system. According to the literature, the behavior of the overall structure can be improved by using the asphalt mixture as a sub-ballast layer in the track-bed [3]. Also replacing the ballast layer by an asphalt layer can cause more elasticity of the track support system as well as easier construction and maintenance (i.e., easier geometry deviations corrections) [3]. Asphalt underlayment design and construction standards for railways typically follow the recommendations set forth by the Asphalt Institute [7]. It is generally agreed that fatigue cracking, rutting, and lowtemperature cracking are the three principal types of distress considered in the flexible pavement design [8]. However, rutting of the asphalt mixture is not a serious concern in the track-bed, since the pressures are applied through the ballast over a wide area [9] and also the temperatures are not sufficiently high to promote rutting [7]. Bleeding is also of little concern since there is not a direct contact between the wheels and the asphalt layer [9]. However, cracking caused by the fatigue due to repetitive nature of train loads is important in asphalt pavements of railways [10]. This is noteworthy mentioning that the vertical stress levels on the top of the hot mix asphalt (HMA) layer in the railway track-bed are much less than (about one-third of) the one in the highway asphalt layer even with the heavy tonnage of railroad loadings [3,11]. This is due to the wider load distribution of the sleepers on the underneath layer [3]. In 2007, the Design Standard for Railway Structures used by Japanese railway organizations was revised in order to consider the fatigue life of the railway track pavement as it is greatly influenced by the number of passing trains [3,9,12].