# Track Modulus Assessment of Engineered Interspersed Concrete Sleepers in Ballasted Track
## 1 Introduction  
More than 94% of the world's railroad track infrastructure is ballasted [1], and 94% of the North American Class I rail network is ballasted track that is constructed with timber sleepers [2]. The current best practices for maintaining timber-sleeper track typically include either in-kind replacement with timber sleepers or out-of-face replacement with concrete sleepers. Each year, North American railroads undertake in-kind replacement of more than 12 million timber sleepers that have reached the end of their service lives [3]. The out-of-face replacement of timber sleepers with concrete sleepers is not regularly pursued because of the associated costs [4]. When properly manufactured, concrete sleepers have an expected lifespan of up to 45 years, several times that of the average timber sleeper [5]. Longer lifespans reduce the number of sleepers replaced each year, thus decreasing maintenance costs and delays due to track occupancy for maintenance activities.  
Despite the comparatively limited use of concrete sleepers in North America, they are often used in the most demanding service conditions for high-speed or heavy axle load (HAL) applications [6; 7; 8]. Additionally, as annual gross tonnages have increased on many routes that have been constructed with timber sleepers, there is a quantifiable benefit from the added strength of concrete sleepers. This is due in part to the properties of prestressed concrete, which is commonly used to withstand the demanding loading environment imparted by passing trains [9]. Prestressed concrete provides increased flexural strength, ductility, and resistance to cracking [10].  
As timber sleepers in ballasted track are replaced in kind by interspersing, the age and health of sleepers varies throughout the length of any given track segment. Given the benefits of concrete-sleeper track, the North American rail industry has made several attempts to intersperse concrete sleepers with timber as an incremental step to improve the strength of timber-sleeper track and gradually transition to concrete-sleeper track [11]. However, interspersing concrete with timber leads to spatial variation (heterogeneity) of the track stiffness, which leads to increases in the maximum rail stress and accelerates the rail fatigue process, and the rail-seat load applied to a given sleeper, which accelerates the ballast and substructure deterioration rates, which can lead to decreased track quality index (TQI) and ride quality [12]. Therefore, any effort to intersperse sleepers of different materials should consider the stiffness of each component and its effect on the track modulus.  
In this study, we quantified the track modulus of engineered interspersed concrete (EIC) sleepers that were installed in track to replace timber sleepers that had reached the end of their service lives. These EIC sleepers were designed to replicate timber's stiffness via an optimized structural design to reduce bending stiffness and construct an innovative engineered rail seat plate and pad system. The revenue-service vertical wheel loads and resulting sleeper vertical displacements were measured and used to determine the track modulus. The results provided an improved understanding of the ability of EIC sleepers in timber-sleeper track to provide consistent stiffness to the adjacent timber sleepers, and thus a consistent track modulus.