# Investigation of Load Environment and Bending Load Capacities of Aged Prestressed Concrete Sleepers
## 2 Investigation of Load Environment of PC Sleepers
### Investigation Results  
#### 2.2.1 Measured Wheel Loads and Bending Moments of PC Sleepers  
Figure 7 shows the measured wheel loads and bending moments. The maximum wheel load was 79.51 kN, and the maximum bending moment at the rail seat section of the PC Sleeper was 3.81 kN\(\cdot\)m. The maximum wheel load and bending moment are the largest wheel load and bending moment generated by each axle of one train set. Each value was compared with the corresponding design value. The measured values were smaller than the design values. The wheel load was 49.7% of the design wheel load of 160 kN, and the bending moment was 34.7% of the design decompression moment (DDM) of 10.95 kN\(\cdot\)m. In addition, neither the wheel load nor the bending moment depended on speed. The reasons for the margin between the measured and design values included the fact that the actual wheel load was smaller than the design wheel load, the consideration of the variable wheel load coefficient, and the conservative assumption for the design's lateral force and sleeper support condition. \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Constant** \\ \hline Train speed (km/h) & 200, 250, 270, 300, 320 \\ Vehicle occupancy rate (\%) & 50, 100, 200 \\ \hline Spring constant of track pad (MN/m) & 50, 100, 150, 250 \\ \hline Spring constant of ballast (MN/m) & 10, 30, 50, 100, 200 \\ \hline Rail surface roughness & None, original (measured on-site), three times the original, and five times the original \\ \hline Support condition of PC Sleeper & Uniform support with reduced spring constant (\(\alpha\times D_{\text{B}}\)) (support condition R) \\ Center support (\(\alpha\times D_{\text{B}}\)) (support condition C) \\ \(\alpha\) = 1/100, 1/10, 1/2, 4/5 \\ \hline \end{tabular}
\end{table} 
Table 2: Analysis cases. Figure 6: Rail surface roughness at rail joint of conventional line. 2.2 Numerical Analysis Verification Results of Effects of Various Parameters on Bending Moments of PC Sleepers  
Figure 8 shows a comparison of the analyzed and measured bending moments at the rail seat sections of the PC sleepers. The bending moment obtained from the data of 337 measurements was approximately 2.0 kN\(\cdot\)m, which is the average value shown in Figure 7, at a train speed of 300 km/h. As can be seen in Figure 8, the analysis and measurement results were generally identical, and the actual average phenomenon was reproduced using the material constants in Table 1.  
Figure 9 shows the numerical analysis results of the effects of the parameters on the positive bending moments at the rail seat sections. Figure 9a-g show the effects of each parameter on the basic case. The yellow plot in the figure is the basic case. According to Figure 9, similar to the measurement results, the bending moment did not depend on the train speed and increased with the vehicle occupancy rate, the spring constants of the track pad and ballast, and the rail surface roughness. In addition, when the support spring constant of a PC Sleeper decreased, the adjacent PC Sleeper bore the load, so the bending moment of the PC Sleeper decreased. Figure 10 shows the numerical analysis results of the effects of the parameters on the negative bending moments at the center sections. Only the results of the support conditions of the PC sleepers are shown here. The descriptions of the other parameters are omitted because they are similar to those shown in Figure 9. Figure 10a shows the result of a PC Sleeper with a uniform support with a reduced spring constant; the trend is almost the same as that in Figure 9f. Figure 10b shows the result of the center support, where the negative bending moment at the center section of the PC Sleeper greatly increased. Specifically, when the support spring constants at the rail seat section were 1/2, 1/10, and 1/100 of the constant at the center section, the bending moments at the center sections were approximately doubled, approximately quintupled, and approximately nonupled, respectively.