## 4 Results of the Bridge Dynamic Responses
### Dynamic Vibration of the 192-m Span  
To monitor and evaluate the dynamic behavior of NDHRB, an ideal configuration would be to set the IBIS-S system at pier #7 or #8, aiming at the middle of the 336-m span. However, the bridge can only be accessed in the window time when there are no trains. Therefore, the Station S2 was chosen and the 192-m span was selected for the dynamic vibration monitoring. S2 was set at the south riverside, right underneath the bridge between piers #9 and 1#0. Two views (view S2a/b) were acquired: the radar signal of view S2a was transmitted through the archway of pier #9, aiming at studying the dynamic behavior of the 192-m span between piers #8 and #9. view S2b corresponds to the radar signal from the 108-m span between piers #9 and 1#0, aiming at monitoring the behavior of the beam end, where the telescopic devices are located. view S2b is analyzed in Section 4.3. A Trimble(tm) TX8 3D lidar--with maximum operating range of 340 m--was used for collecting the point clouds and supporting the geometric analysis of the radar measurements. The distances from S2 to pier #9 and 1#0 are 61 m and 47 m, respectively and the height to the bridge deck is 35 m.  
The view S2a observation geometry and the corresponding radar range profile are illustrated in Figure 7. In the view S2a campaign, the radar worked in the range 70-250 m. The sampling rate was 53.85 Hz, with 2.0-m resolution in range. The data acquisition started at 18:04, on 13 th July 2018 and lasted 26 min. Different loading cases were observed during the campaign. We selected six loading conditions described in Table 2 as representatives for the study of the bridge dynamic behavior. The measured LOS displacements, d\({}_{\text{LOS}}\), can be composed in a vertical displacement d\({}_{\text{V}}\) and an horizontal displacement \(d_{H}\), while the latter one can be decomposed into the longitudinal displacement d\({}_{\text{L}}\) and the lateral displacement d\({}_{\text{Lat}}\). The S2a acquisition geometry is almost perpendicular to the  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Cases** & **Track No. ** & **Direction** & **Carriages** & **Speed (km/h)** \\ \hline
**Case1** & \textbackslash{}  
lateral direction: this results in a negligible sensitivity to the lateral displacements. Considering the measurement geometry of view S2a, it is more sensitive to the longitudinal displacements than to the vertical ones. However, the longitudinal displacements are only present in some particular cases, such as nonuniform motions of the trains, irregularities at the wheel-to-rail interface and the centrifugal load on the curved movement path. Figure 8 shows the simultaneous displacement time series of the horizontal components measured by the bridge SHM system during the view S2a monitoring campaign. It can be seen that the lateral displacements (Figure 8a) in the middle of the 192-m span are within \(\pm\)0.1 mm, and the dynamic response of passing trains can be identified by the larger value magnitude. Variation of the longitudinal displacements at pier #8 (Figure 8b) are approximately 4 mm. It can be seen that the lateral displacement (less than 0.1 mm) is mainly affected by the train, while the longitudinal displacement (4 mm) is mainly affected by the ambient temperature variation (around 1 \({}^{\circ}\)C), which agrees with the calculated thermal expansion (4 mm) of the steel truss (coefficient of thermal expansion: \(13.0\times 10^{-6}\)/\({}^{\circ}\)C, length to the fixed pier #7: 336 m). No clear relation between the longitudinal displacements and passing trains was found. Thus, in the following, we neglect the horizontal displacement components, and the deformation is considered vertical. It is worth noting that the trend of the radar-measured displacements can be associated with a lowering of the of air temperature, which affected the radar phase measurement. Figure 9 shows the obtained vertical displacement time series in the middle of the 192-m span.