# Bridge Expansion Joint in Road Transition Curve: Effects Assessment on Heavy Vehicles
## 4 Test Results and Discussion  
The geometric-topographic measurements permitted plotting the level curves of the surveyed pavement area, which is characterized by the presence of three BEJs marked as BEJ1, BEJ2 and BEJ3 (Figure 12). In particular, three different longitudinal alignments, highlighted in Figure 12, were examined. In Figure 13, the location of all three examined BEJs along the alignments is depicted. The most critical BEJ, close to which many accidents were localized, is BEJ1, which is in a sag section (Figure 13). Figure 12: Level curves (in m) of the surveyed road. Figure 13: Road longitudinal profiles and the BEJs’ location. In the examined portion of the road, a rotation of the carriageway takes place, and BEJ1 is placed in correspondence with the transition curve, while the other two (i.e., BEJ2 and BEJ 3) are located in the circle arc. Applying a high-pass Butterworth filter with cut-off spatial frequency equal to 0.05 cycles/m (wavelength of 20 m) to the three 500 m-long alignments, it was found that the most significant irregularities were placed in correspondence to the three BEJs compared to the elevations in the remaining part of the pavement profiles (Figure 14). Moreover, Figure 14 shows that the unevenness caused by the expansion joint in the road transition curve (i.e., BEJ1) is much greater than the other two BEJs. For this reason, further analyses were specifically carried out for BEJ1 (Figure 13). From the inspection survey, the largest pavement deformation was found 25 m after the joint location. Other pavement unevenness characterized by wavelengths of about 15 m occurred after the BEJ1. They are linked to the dynamic load applied to vehicles bumping on the joint with a speed of 90-110 km/h and the principal oscillation frequency of about 2 Hz (body bounce). The roughness assessment of the survey road section was performed calculating the most worldwide used roughness evaluation criteria [38]: the International Roughness Index (IRI). This approach [39] is based on a mathematical model (quarter-car), whose mechanical parameters (also known as golden-car) are listed in Table 4.  
Its calculation is performed using Equation (7):  
\[IRI=\frac{1}{I}\int\limits_{0}^{1/p}\left|\dot{x}_{s}-\dot{x}_{u}\right|\cdot dt \tag{7}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline \(m_{s}\) (sprung mass) & 9000 kg \\ \(m_{u}\) (unsprung mass) & 1350 kg \\ \(k_{s}\) (suspension spring constant) & 569.7 kN/m \\ \(k_{t}\) (tire spring constant) & 5877 kN/m \\ \(c_{s}\) (suspension viscous damping constant) & 54 kN s/m \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Golden-car mechanical parameters for the IRI quarter-car model. Figure 14: Filtered longitudinal profile: Alignment 2.  
where \(l\) is the length of the profile in km, \(v\) is the simulated speed equal to 80 km/h, \(\dot{x}_{s}\) is the time derivative of vertical displacement of the sprung mass in m and \(\dot{x}_{u}\) is the time derivative of vertical displacement of the unsprung mass in m. The final value is expressed in slope units (e.g., m/km or mm/m). IRI was developed in order to assess not only the ride quality on road pavements, but also other detrimental effects, such as dynamic load increment (on both vehicle and pavement) induced by road pavement irregularities. The algorithm to be used for its calculation is provided in [40]. The Italian highway road agency requires calculating IRI on a segment of 10 m, admitting in general values lower than 1.8 m/km [38]. In the case of short span bridges and when joints are present on road pavement surface, IRI values until 2.5 m/km are tolerated [41]. According to Figure 15, all examined alignments have IRI values greater than the threshold limit suggested by [41] in the area across BEJ1, while close to the other two BEJs (i.e., BEJ2 and BEJ3) and in the remaining part of the profiles, the IRI values are lower than the threshold value. The only exception is Alignment 2 across BEJ3 (IRI = 3.55 m/km).