# Behavior Characteristics of a Booted Sleeper Track System According to Substructure Deformation
## 2 Materials and Methods
### Finite Element Analysis  
The ANSYS Ver 17.2 [16] software package was used to conduct the 3D finite element (FE) analysis in this study by employing solid elements. The lower part of the concrete bed was fixed under supported conditions; the vertical load was considered as the displacement condition (5-40 mm). The edges of both ends of the lower part of the concrete bed were fixed. Further, both ends of the lower rail edges were fixed. The boundary condition of the rail support was applied with a roller condition. The load conditions were applied in the vertical and horizontal rail directions. The mesh of the track model contained 888,564 nodes and 437,264 elements. The FE model of the booted sleeper track was configured using the  
Figure 3: Field test setup and examples of collected data: (**a**) view of the test area; (**b**) measurement setup; (**c**) example of the measured dynamic wheel load; (**d**) example of the measured lateral wheel load; (**e**) example of the measured RC sleeper vertical displacement; (**f**) distribution of wheel load and RC sleeper displacement measurements. parameters shown in Figure 4. The solid components of the STEDEF system evaluated in this study included the rail, rail pad, RC sleeper, resilience pad, rubber boots, tie-bar, and concrete bed. The mechanical properties of these components are listed in Table 1.  
An FE analysis was first performed using the same conditions under which the field measurements were collected to verify the suitability of the model; then, various displacements were applied to the verified model to evaluate the resulting behavior of the sleeper track system. The load application and model boundary conditions used in the verification are illustrated in Figure 4a. For the boundary conditions of the full model, fixed support points were applied to both ends of the concrete bed and rail. The analysis domain for the rail was set to consider five rail support points beyond each end of the concrete bed. The full-scale model used to analyze the track deformation according to substructure uplift or subsidence is shown in Figure 4b. The length of the complete FE model was 20 m, and the rail was 20 m long for an analysis of rail deformation at the ends of the concrete bed. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Components**} & \multicolumn{3}{c}{**Properties**} \\ \cline{2-4}  & **Elastic Modulus (MPa)** & **Density (kN/m3)** & **Poisson’s Ratio (v)** \\ \hline Rail & 210,000 & 77.01 & 0.3 \\ Rail pad & 71.4 & 9.32 & 0.2 \\ RC block & 26,086 & 22.56 & 0.18 \\ Resilience pad & 0.9778 & 6.87 & 0.49 \\ Rubber boots & 21.6 & 7.85 & 0.2 \\ Concrete bed & 26,086 & 22.56 & 0.18 \\ Tie-bar & 200,000 & 77.01 & 0.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material properties of booted sleeper track (STEDEF) system components. Figure 4: FE model of the booted sleeper track system: (**a**) load and boundary conditions for model verification; (**b**) full model for substructure displacement analysis. The dynamic and lateral wheel loads from the field measurements (i.e., 80 kN and 40 kN, respectively) were applied to the rails in the model shown in Figure 4a as the load conditions for verification of the FE model of the track system. The accuracy of the model was then confirmed by comparing the RC sleeper vertical displacement obtained from the field measurements with the RC sleeper displacement obtained from the FE analysis. Figure 5 shows the FE analysis results for the vertical displacement of the RC sleeper. The RC sleeper vertical displacements obtained from the field measurement and FE analysis were approximately 2.78 mm (within a range of 2.05-3.86 mm) and 2.73 mm, respectively, as shown in Figure 5. Thus, the displacement obtained by the FE analysis was within approximately 1.8% of the field measurements.