# Fast Falling Weight Deflectometer Method for Condition Assessment of RC Bridges
## 2 Methods of Analysis
### Numerical Simulations  
The FE model was developed in ANSYS(tm) Mechanical (see Figure 8). The mesh is made of SHELL181 Elements for the concrete beams and SOLID187 Tetrahedral Elements for the concrete slab and the asphalt roadbed. The characteristic size of each finite element is 0.15 m.  
Concrete, asphalt and steel properties are reported in Table 1. Moreover, the Rayleigh damping coefficients values are \(\alpha=53.66\) and \(\beta=0.0069\).  
A first static analysis was performed, to check the reliability of the model, and the contour of vertical displacements can be seen in Figure 9. The bridge is simply supported by the abutments on the longer side; thus, the vertical displacement peak can be found, at midspan, in most external lateral edges. Then, the basin shape profile was simulated through a static analysis of the loading scenario corresponding to point 48 (Figure 7). For the sake of brevity, just three geophones (1, 2 and 4 in Figure 4) were considered in the analysis.  
A static load of 91.74 kN was applied to point 48, and the deflection in the location of each geophone was calculated and reported in Figure 10. The envelope of the maximum deflection of each geophone during the dynamic experimental test is also reported in Figure 10, confirming the accuracy of the numerical model. In addition, the maximum displacement is located near the loading plate, and the deflection is reduced as the distance from the loading plate is increased.  
Figure 8: (a) Elements merging nodes with the ones belonging to the surface of the asphalt. (b) Thus, a rigid contact between the loading plate and asphalt is developed during the whole loading time.  
A transient analysis was able to represent the Fast-FWD dynamic load on the structure. The load is applied as a transient force on the loading plate, and the time-history of the deflection recorded in the positions of each geophone is recorded (Figure 11). The selected time step is \(\Delta t\) = 1 ms. It represents the best compromise between accuracy and computational costs reduction; indeed, with an i9-x series processor with 48 cores and 128 Gb of RAM, it is possible to obtain the transient results in 25 min.  
Figure 10: Comparison between experimental and numerical basin shape profile for load point 48.  
Figure 9: Contour of vertical displacement under inertia loads.  
Figure 11: Vertical displacement at (a) t = 3.5 ms, (b) t = 26 ms and (c) t = 55 ms for the load at point 48.  
For the sake of synthesis, in the following, we consider just the loading condition in which the Fast-FWD load plate is in point 48. The contour of the vertical displacements at different time steps is shown in Figure 12. It can be seen how the load wave is moving from the loading plate to the positions of the geophones. A first comparison between the deflection measured by the geophones in the field and the corresponding simulation is shown in Figure 12. The general trend of the FE results is almost similar to the experimental ones. However, in dynamic analysis, it is possible to highlight a difference in the amplitude and a time lag in maximum point. Figure 13 shows a significant diversion in the peak than in the relative abscissa. The structural behavior of the bridge is not straightforward, considering that the damages present in the bridge strongly affect its performance. More accurate models will be developed in the future, considering also the data coming from the Fast-FWD.