# Interpretation of Bridge Health Monitoring Data from Satellite InSAR Technology
## 4 Results and Discussion
### Structural Interpretation of PS Deformation Velocity  
Using the MT-InSAR technique, we identified 8426 PSs on the bridge and in its surrounding area, and we extracted the time series of displacements along the LoS over eight years, from 2014 to 2021. Figure 10 shows the PSs' distribution in the case-study area, illustrated in a colour scale representing their displacement velocity along the satellite LoS. The velocity ranges from \(-13.21\) mm/year (away from the satellite, in red) to \(3.59\) mm/year (toward the satellite, in blue). The velocity of PSs has been calculated during the MT-InSAR data processing by fitting a linear function over the entire time series of displacement through the least-square analysis. The standard deviations of the estimated velocity range between \(0.21\) and \(0.56\) mm/year, depending on the considered PS.  
The PSs are mainly concentrated along the highway, within urban centres, and along local roads. As expected, the PSs are absent along the river and cultivated fields, except for four aligned PSs in the upper left corner, corresponding to high-voltage power line towers. Most PSs are coloured in green, indicating nearly negligible deformation velocity ranging between \(-1.5\) and \(+1.5\) mm/year. The road accessing the bridge from the south exhibits red and orange PSs, as does the road adjacent to the southern embankment of the river. The bridge is primarily covered by green PSs, with a small yellow portion--meaning deformation velocity between \(-3\) and \(-1.5\) mm/year--near Piers 10 and 11. These results suggest that the bridge experiences nearly negligible deformation velocity throughout its span, except for the portion that underwent significant erosion at the base of the piers and was retrofitted with backfill soil in 2012, as indicated by the yellow colour of PSs. This result may suggest the resumption of erosion phenomena at the base of the piers, which may have eroded the backfill soil after 2012.  
It is important to note that the deformation measurements obtained using the MT-InSAR technique from SAR satellite images are along the satellite LoS, i.e., from the sky to the ground and from right to left in this image. Negative values indicate displacements away from the satellite; therefore, negative velocities may result from a combination of downward and westward displacements.  
We focus on the deformation velocities ranging from \(0.5\) to \(-2.5\) mm/year to investigate the bridge displacements further; this allows for a better graphical representation  
Figure 10: Distribution of the PSs identified in the case-study area illustrated in a colour scale representing their displacement velocity along the satellite LoS.  
with greater details--of the PS displacements extracted along the bridge's LoS. Figure 11a shows the PSs on the bridge in a colour scale representing velocity with small ranges; Figure 11b shows the same PSs in a colour scale representing temporal coherence; as we can see, the temporal coherence of these PSs is mostly higher than 0.7, confirming the results' quality.  
Let us focus on Figure 11a. In the portion of the bridge over the floodplain, the deformation velocities are mainly between \(-0.5\) and \(-1\) mm/year. Conversely, in the portion of the bridge over the riverbed, the deformation velocities are close to 0 mm/year towards the north bank of the river and exceed \(-2\) mm/year near Piers 10 and 11. The velocities return to approximately \(-0.5\) mm/year after leaving the river's south bank. This result confirms the nearly negligible deformation velocity along most of the bridge but close to Piers 10 and 11.