# Dynamic Deflection Measurement on Stiff Bridges with High Piers by Preloaded Spring Method
## 4 Experimental Validation of Indoor and Field
### Field Experiment  
The Weihe River Bridge is a 4 \(\times\) 30 m precast concrete continuous box-girder bridge, located on the G70 Fuyin Expressway in Shaanxi Province. As shown in Figure 16, the height of the piers is 5 m. The second girder on the left side of the bridge was used as the test object. Two types of methods were used to measure the deflection of the mid-span section of the bridge under random-vehicle excitation, including contact (PSM, SHM, and SFM) and non-contact (vision-based optical method, abbreviated as VOM) methods. Dial gauges were used as reference sensors in the SFM. Figure 17a shows the camera utilized for the vision-based optical measurement, and Figure 17b shows the measurement process for the SFM, PSM, and SHM. Figure 17c shows a universal testing machine measuring the elastic modulus of a steel wire. In the tests, the diameter of the wire, obtained from vernier caliper measurements, was 1 mm, and the elasticity modulus \(E_{w}\)of the wire was determined to be 1.97 \(\times\) 10\({}^{5}\) MPa by the tensile test of the universal testing machine. In the SHM, the mass of the suspension hammer was 2 kg. In the PSM, the stiffness of the compression spring was 150 N/m, and the initial preload force was 20 N. The measurement process was carried out under windless conditions, and the environmental temperature was 24 \({}^{\circ}\)C. The entire measurement process lasted 10 min. Figure 18a-c presents the deflections of the bridges, collected three times, including dynamic deflections and static deflections. The quasi-static deflections of the bridge were obtained by low-pass digital filtering, and the related details can be found in [58]. The SFM can be used as a correction criterion for other methods because it is in rigid contact with the bottom of the girder, which can capture the real dynamic response of the bridge. \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Excitations**} & \multicolumn{2}{c}{**PSM Technique**} & \multicolumn{2}{c}{**Simulated by ANSYS**} \\ \cline{2-5}  & **APVE (\%)** & **NRMSE (\%)** & **APVE (\%)** & **NRMSE (\%)** \\ \hline Excitation 1 (3 Hz) & 0.64\% & 8.34\% & 0.34\% & 4.43\% \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison of the PSM measurement and simulation in 3 Hz excitation test. \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Excitations**} & \multicolumn{2}{c}{**PSM Technique**} & \multicolumn{2}{c}{**SHM Technique**} \\ \cline{2-5}  & **APVE (\%)** & **NRMSE (\%)** & **APVE (\%)** & **NRMSE (\%)** \\ \hline Excitation 2 (5 Hz) & 2.49\% & 9.27\% & 20.70\% & 34.66\% \\ \hline \end{tabular}
\end{table} 
Table 3: Comparison of different measurement methods in 5 Hz excitation test. Figure 16: Bridge profile (unit: cm). Figure 17: Field test and laboratory photos: **(a)** devices of the vision-based optical measurement (VOM); devices of **(b)** the contact type measurement and (c) tensile test of the steel wire. Notes: In the VOM, the target captured by the camera is a pasted marker (1 cm \(\times\) 1 cm) at the measurement point, the distance between the camera and the target is 8 m, the focal length of the camera is 483 mm, the sampling frequency of the camera is 60 frames per second (FPS), and the video resolution is 1280 \(\times\) 720 pixels; the object distance is calculated by the two-dimensional digital image correlation (2D-DIC) method. Figure 18: _Cont._  
close, with a maximum difference of 0.01, a maximum error of 6.02%, and an average error of 4.67%. The differences between the DLAs obtained by the SHM and the SFM are large, with a maximum difference of 0.07, a maximum error of 39.76%, and an average error of 29.14%. In three measurements, the maximum deflection error of the SHM was 5.7%, while the maximum error of the PSM was only 2.01%. In summary, the dynamic deflection of the bridge measured by the SHM differs considerably from that of the SFM and is subject to more external disturbances.