## 3 Simulation of Vehicle-Passing Scenarios  
On the MIDAS platform, we attempted to numerically simulate vehicle passing scenarios using the established FE model of Renyihe Bridge. Nine cases were set for the numerical simulations assuming a 30-ton vehicle running through the bridge at three vehicle speeds (20 km/h, 50 km/h, 90 km/h) considering three road surface roughness levels (smooth, slightly rough, severely rough). The reason we simulated three road surface roughness levels is that the road surface is smooth when the bridge is newly built, but the road surface roughness will increase over the years based on the basic rules of physics. With the detailed parameters listed in Table 2, numerical simulations of different vehicle passing cases were undertaken using the time-history analysis method. Taking Case 1 as an example, the vehicle load simulation at a certain point on the bridge deck is described in Figure 4. According to Figure 4, the vehicle load is assumed to be a single vertically downward concentrated force moving at the constant speed of 20 km/h (5.56 m/s). Since the vehicle action on a certain point is a transient impact load that disappears immediately in nature, it can be approximated as a triangular load with the maximum value occurring at the midpoint. As shown in Figure 5, the maximum value of the vehicle action at a certain point in the time domain is calculated as the linear superposition of the gravity of the vehicle body and the road-surface-roughness-induced dynamic action [18]. The road-surface-roughness-induced dynamic action can be calculated as the product of the elevation of the position relative to the initial point \(\Delta\) (=0 for Case 1) and the additive vertical stiffness of the four attempts (400 kN/m). According to Ref. [18], for a vehicle passing a bridge, it can be assumed that its tires keep contacting the road surface throughout the process, and the vehicle's dynamic action on the bridge can therefore be treated as the sum of the damping force and the elastic force induced by the road surface roughness. As it was found via calculations in Ref. [18] that the damping force is negligible compared with the elastic force, the total vehicle's dynamic action on the bridge roughly equals the elastic force induced by the rough surface roughness, which can be calculated using the method mentioned above. Although this vehicle-road coupling model is simple, its rationality has been proven in practical use [19]. The time-history analysis employed the mode superposition method. Since the accumulative modal participation mass of the 1 st-50 th modes reaches 96.89%, the main characteristics of the vehicle-induced vertical structural dynamic responses can be captured using the 1 st-50 th modes. As the natural period of the 50 th mode is around 0.05 s, the time-step was set to 0.005 s (=0.05 s/10) for the analysis. The total analysis time was set to 150 s, and the damping ratio was 0.05 for all modes. The vertical acceleration time-history calculated at the mid-span of the 2 nd main span in Case 1 and the corresponding amplitude spectrum are shown in Figures 6 and 7, respectively. In Figure 6, when the vehicle is close to the measuring point (70 s-85 s), the acceleration response is significantly amplified, which agrees with the basic rules of physics. As shown in Figure 7, a high peak and a low peak can be observed on the amplitude spectrum at around 1.0 Hz and 3.8 Hz, respectively. The high peak clearly is associated with the vehicle-induced structural resonance at the bridge's low-order natural frequency, while the low peak reflects the existence of the forced vehicle excitation at a high-frequency range. The local area under the high peak of the amplitude spectrum and that under the low peak are defined as the resonant response and the background response, respectively, both of which can be calculated via integration. Following the same principle, Cases 2-9 were simulated with the respective different road surface roughness levels.