# Track Modulus Assessment of Engineered Interspersed Concrete Sleepers in Ballasted Track
## 2 Background and Theory  
Maintaining a consistent track modulus ensures that track performance meets the standard design and maintenance specifications (e.g., International Union of Railways (UIC) track performance evaluation criteria), and requires minimal maintenance interventions [13; 14]. Frohling [15] showed that vertical stiffness variations induce differential track settlements, resulting in accelerated deterioration of the railway track. Ensuring that sleeper support is consistent can also contribute to improved ride quality, and can minimize track and vehicle maintenance costs attributed to damage associated with variability in track stiffness. In this regard, stiffness transition zones are locations where abrupt changes in the track modulus occur due to a discontinuity in the track structure (e.g., between embankments and bridges or between different track configurations) [16], and a sizeable body of research has focused on providing a consistent track modulus to improve performance in these areas [17; 18]. For example, Korea Code 14080 (KR C-14080) provides guidance on the maximum allowable change in the track modulus in a transition zone section [19]. In this guideline, the variance in the track modulus at the transition zone must be within the allowable range, which is commensurate with the maximum allowable train speed (Figure 1). This method considers the following factors: vibration acceleration of vehicle body, wheel load fluctuation, yield stress of rail fatigue, and uplifting force [19]. While the change in stiffness in typical transition zones is more abrupt and disruptive than sleeper-to-sleeper variation (approximately 42% between timber and concrete sleepers, and as much as 73% between regular track and an average bridge deck [20]), the comparison to interspersed concrete sleepers in timber sleeper track is still applicable. Studies conducted on a Spanish high-speed line (HSL) indicate that maintenance at transitions to bridges or box culverts can be up to three to six times more frequent compared to open track [21]. This discontinuity at transitions can cause abnormal vibrations in both the vehicle and the track, which compromise ride comfort and safety due to the difference in the track impact factor [22]. Low track-support stiffness can result in the development of adverse track geometry. Under these conditions, the track structure is increasingly affected by vehicle loading, leading to loads that exceed the track strength and accelerate track deterioration [8; 23; 24]. Building on earlier findings in track transition areas, we investigated the difference in the track modulus due to the interspersed installation of EIC and timber sleepers. To mitigate the negative effects of train operation and maintenance, careful consideration should be given when designing the track with different track materials. Various methods have been used to gradually change the track modulus (e.g., reinforcement rail, substructure solidification, reinforced roadbed layer, and changes to the timber-sleeper length and cross-sectional area) [25]. While the applications are quite different from the current practice of interspersing concrete and timber sleepers (Figure 2), the objective is the same--to maintain a consistent track modulus to minimize excessive vehicle and track loads. Various methodologies for estimating a track's structural behavior have been developed and documented. [PERSON]'s method applies [PERSON]'s model to consider the foundation based on the upper and lower spring layers and the shear layer [26]. [PERSON]'s foundation model considers the effect of transverse shear deflection resulting from an error in shear force and moment distribution, which can become significant in  
Figure 1: The allowable ratio of the track modulus difference depending on train speed [19]. Figure 2: Installation of timber and engineered interspersed concrete (EIC) sleepers. foundation beams with a small length-to-depth ratio in closely spaced discrete column loads [27].