# Perspectives on the Structural Health Monitoring of Bridges by Synthetic Aperture Radar
## 3 Analyses of Structural Integrity of Bridges from SAR
### Study Case 2  
The \"Celico\" bridge is built in reinforced concrete and has a maximum height of 120 m and a length of 1182 m. The bridge consists of three main spans, and at its ends there are two semi-arches anchored to the ground. In the past the bridge has suffered an accident because one of the three spans collapsed during the renovation work, causing the death of four people. Figure 11a,b show the magnitude of the SLC SAR ROI and the superimposed estimated vibration map, respectively. From Figure 11b, it is possible to observe the joint dilations of the horizontal load-bearing components composing the roadway deck. From this observation geometry, it is possible to count six joints, all numbered and indicated by the yellow arrows drawn on Figure 11b. Joint dilatations from 1 to 3 are confirmed by optical images in Figure 12a-c, respectively, while, joint dilatations from 4 to 6 are confirmed by optical images in Figure 13a-c, respectively.  
Figure 10: SAR reflectivity profiles (energy): (**a**): Full resolution. (**b**): Half resolution.  
Figure 9: SAR images: (**a**): Full resolution. (**b**): Half resolution.  
The time domain vibration plot is reported in Figure 14, where 5 s of observations are reported. Hereafter, the vibration plots are depicted in the time domain. Specifically, the satellite at full spatial resolution in azimuth, takes a certain amount of time for image formation which, for the cases at hand, is 5-6 s. In order to estimate the vibrational micro-motion information of the bodies, it is necessary to synthesize multiple images, with multiple spatial resolution in azimuth, and refocused according to the Doppler sub-aperture strategy of Figure 3. Notice that the rigid sliding of the filters generates the temporal dimension.  
Figure 11: (**a**) Celico bridge, SAR SLC magnitude, (**b**) Vibration map of the Celico bridge.  
Figure 12: Optical representation of dilatation joints: (**a**) Joint number 1, (**b**) Joint number 2, (**c**) Joint number 3.  
Figure 13: Optical representation of dilatation joints: (**a**) Joint number 4, (**b**) Joint number 5, (**c**) Joint number 6.  
Figure 15a,b represent the vibration spectrum in the linear and logarithm scales, respectively. The spectrum has a low-pass characteristic and has three low oscillation energy singularities, the first singularity is located at about 80 Hz, (indicated by the purple arrow (1), the second is located at about 380 Hz, (indicated by the purple arrow (2) the last at about 820 Hz, (indicated by the purple arrow (3). The most energetic harmonics are localized at 75 Hz, then others are present at near 180 Hz. We can also observe sources of vibration harmonics at higher frequencies, localized around 600 Hz.  
This case study shows the possibility to measure the vibrations of a bridge with a single SAR observation. In particular, we point out that it is possible to monitor the vibrations of the horizontal beams constituting the road surface of the bridge, through the observation of the singularities generated by the cuts constituting the dilation joint.