# Bridge Expansion Joint in Road Transition Curve: Effects Assessment on Heavy Vehicles
## 3 Methodology and Case of Study
### 3D Finite Element Model  
In addition to the in situ measurements, a simulation model was implemented. In particular, a 3D model of the asphalt concrete pavement and the seismic BEJ was developed using LS-DYNA. It allowed evaluating the stress magnitude on the test heavy vehicle mechanical components (Figure 6) due to the vertical irregularity that characterizes the BEJ. For this reason, the vehicle is modeled in detail, while for the BEJ, a simple geometry, able to describe the unevenness, was considered. In addition, only the concrete slab was modeled to reduce the computational burden, its bottom surface being fully constrained.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Test Number** & **Speed (km/h)** & **Speed (m/s)** & **Load Blocks** & **Total Load (t)** \\ \hline
1 & 107 & 29.72 & C1, C2 and C3 & 22.08 \\
2 & 84 & 23.33 & C1, C2 and C3 & 22.08 \\
3 & 103 & 28.61 & C3 & 18.22 \\
4 & 85 & 23.61 & C3 & 18.22 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Considered load-speed combinations.  
Figure 5: Geometric (in cm) and load characteristics of the test vehicle.  
The pavement is a three-layer (two asphalt concrete and one cement concrete) 22.4 m long and 4 m-wide model. The BEJ is located at the middle of the strip (Figure 7), where there is a 0.8-m hole in the lower layer, while the two upper layers are interrupted by the BEJ (2.00 m long). The joint surface is 3 cm lower than the rolling surface, thus the upper pavement layers have a transition zone of 1.60 m before and after the joint to reach the appropriate height. The pavement/joint model consists of 15,540 8-node brick (solid) elements. Mechanical characteristics of the materials are linear-elastic for the bottom layer (concrete slab-structure) and viscoelastic for the two upper layers.  
With respect to the boundary conditions adopted in the model, the horizontal displacements on the sides of the model were restrained to represent the confinement due to the presence of the surrounding portion of pavement.  
The test vehicle model (Figure 8) was initially built to perform roadside hardware crash test simulations [35; 36; 37]. It is the IVECO FIAT 180 NC, IVECO (Group CNH Industrial), Torino, Italy, 4-axle heavy goods vehicle, with a net mass of 10,560 kg and a total mass of about 30,000 kg. Its model consists of about 12,000 shell, 150 solid and 100 beam elements (in total, about 15,000 elements).  
Figure 8: FE model of the 30-ton truck.  
Figure 6: LS-DYNA 3D model.  
Figure 7: Pavement and BEJ model (detail of the BEJ zone).  
The whole suspension system of the vehicle test was modeled to reproduce the dynamic effects and the vehicle behavior during the test, as shown in Figure 9. The reference truck has an old type of suspension (leaf springs), with elastic steel beams packed over each axle, and hydraulic dampers.  
These elements were reproduced with a variable thickness shell beam, while the axles are steel beams. The main parts of the vehicle's structure have an elastic-plastic behavior. The loads are accurately transferred to the pavement because this vehicle is equipped with inflated tires and rolling wheels, as shown in Figure 10. A contact surface with a Coulomb-like friction ensures the interface between the two bodies (tire-rubber and pavement).  
The model was validated and then used to calculate the stress, strain and acceleration of each element of the pavement, joint and vehicle. These data are useful, for example, to verify the fatigue damage of the vehicle structure, estimating the effects of an uneven surface as the BE) examined.