## 4 Analysis of Bridge Deformation Characteristics
### Dynamic Deformation Characteristics of the Fenghuangshan Road Bridge Based on GB-RAR Technology
#### 4.1.1 Dynamic Deformation Characteristics of the Bridge with a 50 Hz Sampling Frequency  
Under a 50 Hz sampling frequency, the IBIS micro-deformation monitoring system was utilized to monitor the Fenghuangshan Road Bridge, and the monitoring time was  
Figure 8: Bridge spectrum diagram. (**a**) The monitoring frequency is 50 Hz; (**b**) the monitoring frequency is 50 Hz. 2272.59 s. Some of the monitoring data were extracted to draw the deflection deformation time series curve of the bridge at different positions (Figure 9). The analysis indicates that the bridge fluctuates up and down around a certain horizontal line at different positions, which is consistent with the motion characteristics of nonlinear elastic deformation. From Figure 10, it is observed that during the period from 7.940 s to 7.974 s at point A at the southern end of the bridge, the data fluctuate from the highest value (24.8 mm) to the lowest value (3.28 mm); the time is 0.035 s, the vibration period is 0.07 s, and the vibration frequency is 14.28 Hz. During the period from 279.40 s to 279.12 s, the deformation value changes from 30.5 mm to \(-\)3.4 mm; the time is 0.08 s, the vibration period is 0.16 s, and the vibration frequency is 6.25 Hz. From Figure 11a, it can be observed that the deformation value pertaining to point C of the northern 1/4 span of the bridge is \(-\)9.6 mm at 311.85 s and 38.0 mm at 311.96 s, with a 47.6 mm amplitude, a 0.22 s period, and a 4.5 Hz frequency. In Figure 11b, the initial deformation fluctuation range at point C is \(-\)6.5 mm to 5 mm, and it suddenly changes to \(-\)43.8 mm at 316.30 s.  
Figure 10: A 50 Hz sampling frequency: first monitoring results. (**a**) 7.90–8.05 s; (**b**) 279.35–279.50 s.  
Figure 9: Schematic diagram pertaining to the dynamic deformation characteristics of bridge with a 50 Hz sampling frequency. From Figure 12a, it can be observed that the southern 1/4 span at point E of the bridge deforms by 9.3 mm at 288.71 s and \(-\)16.8 mm at 288.59 s, with a 26.1 mm amplitude, a 0.24 s vibration period, and a 4.2 Hz vibration frequency. In Figure 12b, the point deforms by 3.5 mm at 311.42 s and 26.1 mm at 311.54 s, with a 22.6 mm amplitude, a 0.24 s vibration period, and a 4.2 Hz vibration frequency. From Figure 13, it can be observed that under the simultaneous action of vehicle dynamic load, different positions of the bridge exhibit different deformation characteristics. The deformation at point C is the largest, followed by point E; additionally, the deformation at point A is the smallest. The deformation of point C at 48.65 s is 11.4 mm, and the deformation in the reverse direction after 0.07 s is \(-\)19.2 mm. The time from adjacent wave peaks to troughs is approximately 0.07 s, the vibration period is 0.14 s, and the vibration frequency is 7.14 Hz. Additionally, the point deforms by 10.6 mm at 308.82 s and \(-\)38.3 mm at 308.89 s, with a 48.9 mm amplitude, a 0.14 s vibration period, and a 7.14 Hz vibration frequency. Figure 11: A 50 Hz sampling frequency: second monitoring results. (**a**) 311.8-312.1 s; (**b**) 316.1-316.4 s.  
Figure 12: A 50 Hz sampling frequency: second monitoring results. (**a**) 288.55–288.75 s; (**b**) 311.4-311.7 s.  
To describe the differences in movement characteristics at different bridge positions in detail, deformation data of the bridge from 1800 s to 1830 s during the monitoring period were extracted; a dynamic deformation trend comparison diagram was drawn at different bridge positions; the gravity direction was defined as the negative direction, and vice versa as the positive direction. From Figure 14, it can be observed that during this period, the deflection deformation trend at different bridge positions exhibits a \"V\" shape, first decreasing and subsequently increasing, among which the phenomenon is more apparent at 10 m, 20 m, 30 m, and 70 m, and the maximum deflection deformation values are \(-11.43\) mm, \(-8.22\) mm, \(-11.8\) mm, and \(-16.24\) mm, respectively.