# Qualitative Prediction Model for Dynamic Behavior of Ballasted Tracks
## 3 Field Measurements  
Field measurements of the dynamic response of a test track were then conducted, including the dynamic wheel load, rail and sleeper displacement, and rail bending stress. The studied ballasted railway line was an in-service straight and continuous welded rail (CWR) track weighing 60 kg located in the Republic of Korea. The design subgrade modulus was estimated according to the Korean standard KS F2310 for subgrade materials, which was adopted at the time of the construction [49; 50; 51]. Parameters and photographs of the test site are shown in Table 2 and Figure 2a,b, respectively, and the vehicle load composition during testing is shown in Figure 2c. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Properties** & **Rail (60 kg/m)** & **Prestressed Concrete Sleeper** \\ \hline \multirow{4}{*}{Section Properties} & Cross-sectional area (cm\({}^{2}\)) & 77.5 & 516.75 \\  & Moment of inertia (cm\({}^{4}\)) & 3090 & 16,375 \\  & Section modulus (cm\({}^{3}\)) & 396 & – \\  & Supported area & – & 3021 \\  & of half-sleeper (cm\({}^{2}\)) & – & \\ \hline \multirow{4}{*}{Material Properties} & Elastic modulus (kN/cm\({}^{2}\)) & 21,000 & 4000 \\  & Weight density (kN/cm\({}^{3}\)) & \(7.85\times 10^{-5}\) & \(2.5\times 10^{-5}\) \\ \cline{1-1}  & Poisson’s ratio (v) & 0.30 & 0.18 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Properties of the track components used in the proposed qualitative analysis. \begin{table}
\begin{tabular}{c c} \hline \hline
**Description** & **Properties** \\ \hline Track curvature (\(R\)) & \(\infty\) (Straight) \\ Cant & 0 mm \\ Substructure & Earthwork \\ Subgrade modulus a  & 0.15 N/mm\({}^{3}\) \\ Rail & 60 kg N, Continuous welded rail \\ Sleeper & 250 kg, Prestressed concrete sleeper \\ Sleeper spacing & 600 mm \\ Sleeper mass a  & 250 kg \\ Fastening type & Pandrol e-clip \\ Rail pad a  & Thermoplastic Polyurethane (TPU) pad \\ Rail pad stiffness a  & 400 kN/mm \\ Rail pad damping coefficient b  & 12.934 kNs/m \\ Ballast stiffness a  & 200 kN/mm \\ Ballast damping coefficient b  & 223.130 kNs/m \\ Ballast thickness (depth) & 300 mm \\ Ballast mat & – \\ Train type & EMU (electric multiple unit) \\ Wheelset mass (\(M_{\text{w}}\)) & 1025 kg \\ Static wheel load \(Q\) & 80 kN \\ Operational speed & Average 130 km/h \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the ballasted track used in the proposed qualitative analysis. The dynamic wheel load acting on the track segment subjected to the load of a passing train was measured by installing a two-axis strain gauge on the rail web between the two test sleepers [13]. The measured signal was recorded on a data acquisition system (MGC-Plus) and analyzed using the OriginTM program. To eliminate interference from other passing trains and obtain a reliable measure of the dynamic wheel load of the passing train, measurements were performed using a wheel load gauge wired to eight strain gauges at an angle of 45\({}^{\circ}\) and attached along the neutral axis of the rail web 100 mm from the center of the sleepers, as shown in Figure 3a. The vertical wheel loads were measured using shear strain gauges coupled to a full Wheatstone bridge circuit [52]. The strain gauge bridges were calibrated using a hydraulic ram and load cell to obtain measurements with an accuracy of 2% [13; 52]. To prevent data distortion and loss, the sampling rate was \(>\) 1 kHz. In Figure 3a, the strain gauge installed on the web of the rail is a sensor for measuring the wheel load. LVDT was used as a sensor to measure the displacement of rail and sleepers as shown in Figure 3b. The rail bending strain on the test track was measured using a one-axis strain gauge attached longitudinally to the bottom flange of the rail at the center of the sleepers, as shown in Figure 3a [13]. Figure 3: Photographs of wheel load sensor, strain gauges, and linear variable differential transformers (LVDTs) used to measure the (**a**) wheel load and rail bending stress; (**b**) rail and sleeper displacement.