## 4 Parametric Study
### Analysis Results  
Figures 11 and 12 show typical analysis results of the CWR track on ab open-deck steel plate girder bridge for \(R\) = 1500 m and \(R\) = 300 m, respectively, where PLR represents the peak lateral resistance of the girder-sleeper fastener. Note that in both figures PLR is  
Figure 10: Comparison results with LONGSTAB (track on the embankment region): (a) rail temp. vs. lateral disp. ; (b) comparison of buckling shape. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Range** & **Remarks** \\ \hline Length of girder, \(L_{G}\) (m) & 9, 15.2, and 30 & 3 cases \\ Curve radius, \(R\) (m) & 1500, 700, and 300 & 3 cases \\ Lateral disp. of the girder, \(\epsilon_{G}\) & 0, \(L_{G}\)/1500, and \(L_{G}\)/1000 & 3 cases \\ Lateral resistance of girder-sleeper & 14–22 & 5 cases \\ fastener, P.L.R. (kN/m/track) & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Analysis parameters. \(14\) kN/m/track, span length, \(L_{G}\), is \(30\) m, and lateral displacement of girder, \(e_{G}\), is equal to \(0\). The difference between \(T_{b,max}\) and \(T_{b,min}\) of a model with \(R=1500\) m is larger than that of the model with \(R=300\) m. This means that the CWR buckling behavior is changed from snap-through buckling to progressive buckling by decreasing the curve radius. Generally, if \(T_{b,max}-T_{b,min}\) is large, the track is categorized into a \"strong track\" while the track becomes \"weak\"to the buckling with decreasing the value of \(T_{b,max}-T_{b,min}\). The similar behaviors are also observed in this analysis. Furthermore, it can be seen that the buckling shape is changed with decreasing the curve radius, from \(3\) half waves to \(1\) half wave, as shown in Figures 11b and 12b. If \(T_{b,max}-T_{b,min}\) is smaller than \(5\)\({}^{\circ}\)C, \(T_{b,min}\) has to be adjusted as \(T_{b,min}-5\)\({}^{\circ}\)C for the calculation of critical buckling stress, \(f_{b,min}\), according to UIC code [19] and this method is also used in this study to calculate \(f_{b,min}\). After \(f_{b,min}\) is obtained from the analysis, allowable additional axial compressive stress, \(f_{all}\), can be calculated using Equation (1), where \(\Delta T_{R}\) is set as \(35\)\({}^{\circ}\)C.\(f_{all}\) is plotted in Figures 13-15 to examine the effect of girder length, curve radius, and lateral displacement of the girder on \(f_{all}\), respectively. Figure 11: Analysis results (\(R=1500\) m): (**a**) rail temp. vs. lateral disp. ; and (**b**) buckling shape. Figure 12: Analysis results (\(R=300\) m): (**a**) rail temp. vs. lateral disp. ; and (**b**) buckling shape. From Figures 13-15, it can be found that \(f_{all}\) increases with increasing PLR. In Figure 13, the \(x\) and \(y\) axes denote girder length and \(f_{all}\), respectively. It can be seen that the variation of \(f_{all}\) with girder length is negligible for all considered girder lengths, as shown in Figure 13a-c. In the case of the curve radius, \(f_{all}\) decreases with decreasing curve radius, \(R\) (refer to Figure 14). The maximum reduction of \(f_{all}\) is almost 49% by decreasing \(R\) from 1500 m to 300 m. This case is the model with PLR = 14 kN/m/track, \(e_{G}\) = \(L_{G}\)/1000, and \(L_{G}\) = 9 m. Figure 15 shows the effect of the lateral displacement of the girder, \(e_{G}\). By increasing \(e_{G}\), \(f_{all}\) is decreased. The average and the maximum reduction of \(f_{all}\) are 5% and 39%, respectively. The maximum reduction is observed among \(R\) = 300 m models and the effect of \(e_{G}\) becomes more critical with decreasing \(R\). In summary, it can be observed that the effect of girder length is negligibly small. On the other hand, the effect of the curve radius and lateral displacement of the girder should be considered to determine \(f_{all}\), since \(f_{all}\) is reduced by 49% and 39% due to the effect of \(R\) and \(e_{G}\), respectively.