## 5 Field Experiments  
The field experiments were undertaken in 2021 by the Shanxi Provincial Transportation Construction Engineering Quality Testing Center [20]. Practicing engineers employed two vehicles with weights of around 300 kN, each synchronously running through the bridge at different speeds (Figure 16). Four vehicle speed cases were utilized for the test, i.e., 20 km/h, 30 km/h, 40 km/h, and 50 km/h. According to Ref. [20], the vehicle drivers tried to keep the vehicles moving at the constant speeds. Although the statistics concerning the vehicle speed variations through the entire process were not measured, it was reported that vehicle speed was well controlled, and the effects of the vehicle speed variation on the excitation and the response were reduced to the minimum. For each vehicle speed case, two vertical accelerometers arranged at the mid-span of the third main span (measuring point 1) and the mid-span of the fourth main span (measuring point 2) were utilized to record the vehicle-induced structural velocity responses when the two vehicles ran  
Figure 14: Amplitude spectra of vertical acceleration time-histories calculated at the mid-span of the 3 rd main span in Cases 7–9. Figure 15: Maximum tensile stresses calculated for different cases. by them. The structural velocity response samples so obtained (Figures 17 and 18) were then transformed into power spectral densities (PSDs) using fast Fourier transformation (Figures 17 and 18). After that, the first-order natural frequency and the frequency of the forced vehicle excitation were identified from these PSDs via the peak picking method, and the results are listed in Table 3 for reference. According to Table 3, the most fundamental frequencies identified for Renyihe Bridge in different cases are at around 0.77 Hz, which is close to the numerical result presented in Table 1 (0.73 Hz), except for the result measured at the mid-span of the fourth main span in the 20 km/h vehicle speed case (0.82 Hz). The field test results and the numerical data are thereby validated by each other. According to Ref. [17], for bridges excited by passing vehicles, the natural frequencies of the actual system should be independent of excitations and measurements. The good agreements between the fundamental frequencies identified for Renyihe Bridge in different cases by the present study support the contention presented in Ref. [17]. The result measured at the mid-span of fourth main span in the 20 km/h vehicle speed case should also be close to the results measured for other cases. However, on-location physical tests suffer from inherent uncertainties and environmental interferences. Therefore, the field modal test results obtained for different cases might occasionally be different from each other. According to Ref. [19], the natural frequencies of the bridge structure measured are influenced by the velocity and mass weight of the vehicles, as the weight and location of the vehicle become part of some new system. Ref. [19] formulated an approach relying on a dynamic FE model updating to compensate for the deviation in the results of the modal experiment using vehicle excitations due to the adverse effects of running vehicles. In detail, the measurement change in the first modal frequency caused by the running vehicles was captured by on-location modal experiments using both ambient and vehicle excitations, and the equivalent vehicle weight was thereby identified via dynamic FE model updating. Using the updated numerical model, the measurement change in the high-order modal frequency due to the added equivalent vehicle weight was calculated, and the high-order modal frequency measured on location was then compensated for use. However, according to Table 3, the most fundamental frequencies identified for Renyihe Bridge in different cases are at around 0.77 Hz, suggesting that the effects of the velocity and mass weight of the vehicles on the natural frequencies of the bridge are similar for most vehicle speed cases.