# Possibility of Bridge Inspection through Drive-By Vehicles
## 4 Drive-By Inspection through 3D Virtual Simulations  
Following a previous study [22; 25], a 3D vehicle model based on a real truck HS20-44 was created. The model uses the same vehicle properties as [PERSON] et al. [25] did, including mass, spring stiffness, damping, and body rotary inertias. The needed vehicle parameters are shown in Figure 11. Its specific parameters are given in Table 4. The first seven natural frequencies and relative mode shapes are extracted and compared in ABAQUS (Figure 12). Figure 10: Comparison of STFT results of bridge accelerations with multiple damages. Figure 9: Comparison of STFT results of bridge accelerations with different damage levels. Figure 11: Truck model: (**a**) side view, (**b**) rear view. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Element** & **Notation** & **Value** \\ \hline \multicolumn{3}{c}{**Stiffness(N/m)**} \\ \hline Rear wheels & K\({}_{\text{t1}}\), k\({}_{\text{t2}}\) & \(1.57\times 10^{6}\) \\ Front wheels & K\({}_{\text{t3}}\), k\({}_{\text{t4}}\) & \(7.85\times 10^{5}\) \\ Rear suspensions & K\({}_{\text{s1}}\), k\({}_{\text{s2}}\) & \(3.73\times 10^{5}\) \\ Front suspension & K\({}_{\text{s3}}\), k\({}_{\text{s4}}\) & \(1.16\times 10^{5}\) \\ \hline \multicolumn{3}{c}{**Dampings (N*/m)**} \\ \hline Rear wheels & C\({}_{\text{t1}}\), C\({}_{\text{t2}}\) & 200 \\ Front wheels & C\({}_{\text{t3}}\), C\({}_{\text{t4}}\) & 100 \\ Rear suspensions & C\({}_{\text{s1}}\), C\({}_{\text{s2}}\) & 35,000 \\ Front suspension & C\({}_{\text{s3}}\), C\({}_{\text{s4}}\) & 25,000 \\ \hline \multicolumn{3}{c}{**Masses (Kg)**} \\ \hline Rear axle & m\({}_{\text{ra}}\) & 1000 \\ Front axle & m\({}_{\text{fa}}\) & 600 \\ Body & m\({}_{\text{b}}\) & 17,000 \\ \hline \multicolumn{3}{c}{**Rotatory Inertias (kg*m2)**} \\ \hline Rear axle (roll) & I\({}_{\text{a,ra}}\) & 600 \\ Front axle (roll) & I\({}_{\text{a,fa}}\) & 550 \\ Body (roll) & I\({}_{\text{a,b}}\) & 13,000 \\ Body (pitch) & I\({}_{\text{Y,b}}\) & 90,000 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The mechanical parameters of the vehicle. Figure 12: _Cont._Figure 12: _Cont._  
In the ABAQUS model, all truck bodies are assumed rigid and modeled using element type R3D4 with a mesh size of 0.1 m, since the vibration caused by external forces is concerned, and the deformation of the truck body itself is small and could be neglected. The rigid body needs to have a reference point, which is set as the geometry center of each part. Figure 12: Cont. The rotatory inertias are attached to the reference point of the body part. However, the axle parts could not simply attach the mass and rotatory inertia on the reference point since this will make the axle only have vertical displacement but no rotation. In solving this issue, the axle mass is divided into four-point masses, and the locations can be calculated to meet the given rotatory inertia. Through these implementations, the ABAQUS truck model's frequency analysis results are quite the same as those by [PERSON] et al. [25]. Comparing these frequencies in [PERSON] et al. [25], the current results are shown in Figure 12.  
A 3D multiple-span bridge was also created based on previous research [22] and used to test the drive-by inspection hypothesis. Shell element type S4R was adopted. The bridge is 79.2 m long in total, with three 26.4 m spans. The width is 10.7 m, and the depth is 0.95 m. [PERSON]'s modulus is 14.54 \(\times\) 10\({}^{10}\) N/m\({}^{2}\), [PERSON]'s ratio is 0.3, and the density of the bridge material is 2375 kg/m\({}^{3}\). The vehicle crosses the bridge with its right tires at a distance of 1 m from the bridge's right span edge. The bridge's left boundary is fixed, while the two intermediate supports and the right boundary only have the lateral movement allowed. A similar mesh size sensitivity study was conducted and shown in Figure 13. The results suggest that mesh size under 0.1 is adequate and convergent in capturing bridge displacement. In the later simulations of this model, 0.1 m was chosen as the mesh size.