## 4 Analysis and Discussion
### Correlation Analysis  
#### 4.2.1 Automatic and Manual Test Scheme  
As shown in Figure 6, the detection vehicle equipped with the detection system passes through the bridge-road transition section and bridge section at a constant speed after acceleration, collects data and images, and stops after deceleration. Considering driving safety and reducing the influence of vehicle bumping on the test results, the vehicle runs at a constant speed of not more than 40 km/h after acceleration. Based on the built bridgehead settlement calculation model and algorithm, the data and images collected by the detection system are input. Then, the SPR of each test object will be obtained.  
Additionally, considering that the bridgehead settlement is caused by the uneven settlement between the road and bridge, the bridgehead settlement condition is described by measuring the longitudinal slope difference [28]. As shown in Figure 7, the leveler measured three elevation points at the bridge joint, the \(l_{0}\) distance before the bridge joint, and the \(l_{0}\) distance after the bridge joint.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Distance**} & \multicolumn{2}{c}{\(S_{AM}\)**/\%**} & \multicolumn{4}{c}{\(S_{\text{HMP}}\)**\%**} & \multicolumn{4}{c}{\(E_{\text{AF}}\)**/\%**} & \multicolumn{4}{c}{\(E_{\text{RF}}\)**/\%**} \\ \cline{2-10}  & **20 km/h** & **30 km/h** & **40 km/h** & **20 km/h** & **30 km/h** & **40 km/h** & **20 km/h** & **30 km/h** & **40 km/h** \\ \hline
50–60 & \(-\)10.32 & \(-\)10.49 & \(-\)10.25 & \(-\)10.42 & 0.10 & 0.07 & 0.17 & 0.93 & 0.64 & 1.62 \\
60–70 & \(-\)10.16 & \(-\)10.30 & \(-\)10.04 & \(-\)10.51 & 0.35 & 0.21 & 0.47 & 3.33 & 1.97 & 4.50 \\
70–80 & \(-\)10.02 & \(-\)9.96 & \(-\)9.92 & \(-\)10.10 & 0.08 & 0.14 & 0.18 & 0.82 & 1.43 & 1.83 \\
80–90 & \(-\)10.29 & \(-\)10.12 & \(-\)10.18 & \(-\)10.24 & 0.05 & 0.12 & 0.06 & 0.51 & 1.18 & 0.58 \\
90–100 & \(-\)9.98 & \(-\)9.74 & \(-\)9.97 & \(-\)10.12 & 0.14 & 0.38 & 0.15 & 1.42 & 3.74 & 1.52 \\
100–110 & \(-\)9.76 & \(-\)9.76 & \(-\)9.58 & \(-\)10.11 & 0.35 & 0.35 & 0.53 & 3.44 & 3.44 & 5.26 \\
110–120 & \(-\)9.99 & \(-\)10.02 & \(-\)9.95 & \(-\)10.22 & 0.23 & 0.20 & 0.27 & 2.29 & 1.99 & 2.68 \\
120–130 & \(-\)9.90 & \(-\)9.81 & \(-\)9.87 & \(-\)10.20 & 0.30 & 0.39 & 0.33 & 2.89 & 3.79 & 3.19 \\
130–140 & \(-\)9.63 & \(-\)9.43 & \(-\)9.61 & \(-\)10.17 & 0.54 & 0.74 & 0.56 & 5.32 & 7.32 & 5.52 \\
140–150 & \(-\)9.15 & \(-\)9.00 & \(-\)9.27 & \(-\)10.03 & 0.88 & 1.03 & 0.76 & 8.77 & 10.30 & 7.55 \\ \hline \hline \end{tabular}
\end{table}
Table 2: _Cont._  
Figure 6: Vehicular detection system collects longitudinal slope and pavement images. (**a**) Diagram of automatic test scheme. (**b**) Automatic test on site.  
Figure 7: Manual measurement of road longitudinal slope. (**a**) Diagram of manual test scheme. (**b**) Manual test on site.  
The longitudinal slope value and the absolute value of the difference between the transition section and the bridge section are calculated by Formula (20).  
\[\Delta S=\left|\frac{\frac{\Delta h_{1}}{d_{0}}}{\sqrt{1-\left(\frac{\Delta h_{1} }{d_{0}}\right)^{2}}}-\frac{\frac{\Delta h_{2}}{d_{0}}}{\sqrt{1-\left(\frac{ \Delta h_{2}}{d_{0}}\right)^{2}}}\right| \tag{20}\]  
where \(d_{0}\) denotes the front (rear) distance (m) of the bridge joint in the manual measurement of the longitudinal slope, which means the same as \(l_{0}\) in the above calculation model. \(\Delta h_{1}\) and \(\Delta h_{2}\) are the height (m) of the transition section and the bridge section, respectively. \(\Delta S\) is the absolute value (%) of the longitudinal slope difference before and after the bridge joint in manual measurement.