## 4 Results of Vehicle-Bridge Coupling Analysis  
### Impact Analysis of Vehicle Parameters  
#### 4.1.1 Influence of Different Vehicle Speeds  
In the study of speed parameters, the 35 t spatial dual-axis vehicle model was adopted, and the analyzed speeds were 60 km/h, 80 km/h, 90 km/h, 100 km/h, and 120 km/h. The stiffness reduction coefficients were 1 (undamaged) and 0.76 (damaged), with a total of 10 working conditions. According to the discussion in Section 2, crack damage is realized by stiffness reduction. The positions of stiffness reduction are mid-span, one-third, and one-fourth of the middle span. When analyzing these conditions, the stiffness of the beam segment at the corresponding positions in the numerical model is multiplied by the stiffness reduction factor. Through the analysis of the dynamic response of the bridge under different vehicle speeds, the stress peak value of the concrete at the lower edge of the cross-section was extracted, and the change rule is shown in Figures 14 and 15. By comparing the stress values of the damaged bridges and undamaged bridges, it can be seen that the vehicle-bridge coupling vibration response of each section changes greatly after the bridge is damaged. Taking the maximum stress peak values of 80 km/h and 90 km/h as examples, the midspan stress increases by 84.71% and 107.89%, respectively. The stress of the one-fourth section of the midspan increases by 49.07% and 81.64%, respectively. The stress of the one-third section of the middle span increases by 40.07% and 68.39%, respectively. From the above data, it can be seen that the vehicle-bridge coupling vibration response of the damaged bridge is more significant. From Figure 14, the stress at the speed of 80 km/h is significantly greater than that of the other three speed conditions for any of  
Figure 13: Roughness sequence of three levels of pavement (bridge deck). the sections. Therefore, when the bridge is undamaged, the bridge response under vehicle-bridge coupling vibration is sensitive to the speed of 80 km/h. As can be seen in Figure 15, the peak value of the vehicle-bridge coupling vibration response is the highest when the vehicle speed is 90 km/h at the midspan and one-fourth section positions. However, at the one-third section of the midspan, the structural response is greater than that at the other speeds when the vehicle speed is 80 km/h, and the peak stress value is 2.14% larger than that at the 90 km/h speed. This indicates that although the dynamic response of the bridge at the one-third section of the midspan is the largest when the vehicle speed is 80 km/h, the dynamic response is also obvious at the 90 km/h speed. Taking the damaged bridge as the research object, the reduction coefficient is 0.76, and the other vehicle parameters remain unchanged. According to the above research on the relationship between the vehicle parameters and the damaged bridge, the vehicle speeds in this section are still 60 km/h, 80 km/h, 90 km/h, 100 km /h, and 120 km/h. The vehicle weight is 35 t, and the vehicle type is the spatial dual-axis model; the road roughness grade remains Class B, and the dynamic response of different vehicle speeds to the bridge is studied. Figures 16 and 17 show the variation diagrams of the peak displacement law and the impact coefficient. As shown in Figure 16, the dynamic response of each section of the middle span to the speed is different. For the damaged bridge, the fluctuation of the displacement curve of each section corresponds to the peak stress, reflecting the law that the peak displacement and peak stress increase and decrease at the same time. In combination with the vehicle speed, the peak displacement of both the midspan section and the midspan one-fourth section reaches its maximum when the vehicle speed is 90 km/h. At the one-third cross-section of the middle span, the displacement reaches the maximum when the speed is 80 km/h.