## 4 Results of the Bridge Dynamic Responses
### Dynamic Behavior at the Expansion joints
#### 4.3.2 View S3 and Results  
S3 was set perpendicular to the bridge longitudinal direction. This special setting provides high sensitivity to dynamic performance of the bridge deck in its lateral direction. This allowed distinguishing the vibration behavior due to trains running on different tracks and how the vibration affects the telescopic device at the expansion joints. The S3 dynamic mode sampled at a rate of 166.39 Hz, with 0.5-m resolution in the range, over a maximum measurement distance of 100 m.  
Figure 16 depicts the radar reflected signal and the bins selected for bridge displacement monitoring. Due to the short LOS distance (less than 80 m) and the corner reflector effect of the steel truss, the bridge deck has a very strong backscattering: the SNR of the radar signal scattered from the bridge deck is more than 60 dB. Eleven radar bins, excluding the two bins at the two sides of the structure (corresponding to the metro tracks, whose SNRs are less than 55 dB), were selected to estimate the dynamic behavior induced by high-speed train, running on all the different tracks, see Table 5.  
Figure 16: (**a**) Structure range profile of the bridge deck and the gray lines indicate the radar bins (numbers 87, 93, 98, 103, 108, 113, 119, 124, 127, 135, 142, 144 and 150) selected for estimating the deck displacement; (**b**) photograph from the view S3 in Figure 4, which shows the bottom of the bridge deck illuminated by the radar.  
Figure 15: Vertical displacement time histories of the four loading cases.  
Figure 17 depicts the vertical displacement map of the bridge deck which is near the expansion joint. The displacement induced by high-speed train mainly affects the swath where it is running. This phenomenon is clearer when the train is running on track 4 and track 5, e.g., in Case 1, Case 3 and the second part of Case 5. By contrast, in Case 2, Case 4, Case 6 and the first part of Case 5, where the trains were running on the track 3, there are also induced displacements in the other swaths. This phenomenon does not depend on the direction of the train and the load of the train. Therefore, it is necessary to inspect the structure of lane 3 to determine whether it affects the safety of the train. The vertical displacement map shows the space deformation of the bridge deck, especially along the lateral direction (30 m), which controls the running stability of high-speed trains.  
The vertical displacement time histories of the bridge deck at upstream and downstream swaths are compared in Figure 18. Although there is some slight difference between the displacement responses obtained from the six dynamic loading cases, the nature of the response curves is very  
Figure 17: Vertical displacement map of the bridge deck near the expansion joint.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Cases** & **Track No.** & **Direction** & **Carriages** & **Speed (km/h)** \\ \hline
**C1** & \�  
similar. The displacement is mainly caused by the train loading, and the duration of the displacement is related to the length of the train and its speed, as already commented for view S2b. It can be seen that the amplitude of the vibration is approximately 2 mm to the swath which has train loading, while the magnitude of the swath without loading is much smaller. This can be explained considering that the three main trusses have the effect of separating vibration induced by high-speed passing train.