## 2 Field Measurements
### Track Support Stiffness  
Track support stiffness (TSS) is used as a quality index of railway tracks to assess their performance and bearing capacity [4,10]. The track support stiffness is measured in terms of the amount of deformation in tracks subjected to a passing train load [4,10]. The track support stiffness directly depends on the elastic stiffness of the elastic track components and the structural characteristics of the track system [4,10]. Therefore, the track support stiffness directly depends on the variations in the dynamic wheel load and deflections in the tracks [4,10,16,17]. Furthermore, the TSS values vary with the track structure (e.g., ballasted and slab tracks) and the structural characteristics of the slab track (elastic fastening system, rail floating system, sleeper floating system, and direct fixation track system) [4,10,16,17]. Track support stiffness is an indicator of track performance that provides a quality assessment indicating the bearing capacities of the track structure [2,4]. The analytical model of a general track structure is a linear spring model wherein each track component is connected to spring elements having different spring stiffnesses [4,10]. The stiffness of the track components such as rails and sleepers was excluded from the calculations of the elastic stiffness of the track structure; only the configuration of elastic-resilience materials was considered [4,10]. Several researchers have assumed that k can be expressed as a series of linear spring elements with different spring stiffnesses placed at the rail supporting point composed of a rail pad, sleeper, and roadbed (subsoil) connected in series following Equation (1) [4,10]. As shown in Equation (1), larger spring stiffness, such as that in the direct fixation track system of the Yeongjong Grand Bridge, is insignificantly affected by changes in track support stiffness. \[k=\frac{1}{\frac{1}{k_{p}}+\frac{1}{k_{b}}+\frac{1}{k_{s}}}, \tag{1}\]  
where, \(k_{p}\): rail pad stiffness, \(k_{b}\): ballast stiffness, and \(k_{s}\): subsoil stiffness. The track support stiffness of a direct fixation track supported by track girders has been found to be directly affected by the bending stiffness of the track girders [2]. [PERSON] et al. [2] proposed an analytical model of the direct fixation track of the Yeongjong Grand Bridge that considers the equivalent spring stiffness as shown in Figure 13[2]. Figure 13: Spring stiffness model of a direct fixation track at the rail supporting points [2]. The measured track support stiffness is the ratio of the maximum measured wheel load to the maximum vertical displacement of the rail; it can reflect the track support stiffness in the in-service condition [2,4,10]:  
\[k=\frac{F_{\mathrm{rail\;mid\;mid\;mid}}}{d_{\mathrm{rail\;mid\;mid}}}, \tag{2}\]  
where \(k\) is the measured track support stiffness (kN/mm), \(F_{\mathrm{rail\;mid\;mid}}\) is the maximum wheel load (kN) at the center between the rail supporting points, and \(d_{\mathrm{rail\;mid}}\) is the maximum rail displacement (mm) at the center between the rail supporting points [2,4,10]. In this study, the measured dynamic wheel loads on the measurement section were calculated and correlated to the rail displacement before and after rail pad replacement for each train type. Figure 14 shows the dynamic wheel loads of all trains passing through the measurement section correlated to the rail displacements before and after rail pad replacement. Using the measured load-displacement data, the dynamic wheel load and displacement range for each train type in the measurement section was identified. Figure 15 shows the track support stiffness calculated based on the load-displacement measurements in Figure 14 before and after rail pad replacement. The results in Figure 15 show that there was no clear change in the track support stiffness and no clear difference in the dynamic track support stiffness under different train speeds or before and after rail pad replacement.