# Fast Falling Weight Deflectometer Method for Condition Assessment of RC Bridges
## 2 Methods of Analysis
### Description of the Structure  
The bridge is an in situ cast reinforcement concrete bridge. The crossing girders have comparable dimensions and are joined with a reinforcement concrete deck. This makes the structure near to the so-called \"plate-behavior\". The limited length, related to the width of the deck, makes an analysis with the Plate Theory or a Finite Element (FE) analysis an effective way to estimate the structural behavior, since simplified beam models, such as the [PERSON]'s one, are not valid for it. The considered bridge structure is composed of a concrete deck with trellis girders measuring 11.86 m (length) and 15.45 m (width). The thickness of the deck, also considering that the road pavement, is 45 cm. The intradoses cross-beam are casted on site. In Figure 4 is drawn the planimetric view and the structural cross-section of the deck. This is characterized by eight primary bearing beams (in Section B-B) and four diaphragms in the transverse section (Section A-A), with the support diaphragm of double thickness, as compared to the central ones. The primary beams are of T-shape with an overall height of about 90 cm and a thickness of 35 cm. The transverse girders are 90 per 30 cm (60 cm the ones placed on the side). The bridge was preliminarily investigated with pull out, sclerometer and coring tests, to assess the concrete compression strength. The asphalt was similarly assessed: Mechanical data of the numerical model are summarized in Table 1.  
The visual inspection of concrete (Figure 5) revealed a high level of spalling, whilst the steel rebars revealed a high level of corrosion. The original shear strength was made by stirrups and longitudinal profiled ties. A relevant number of cracked stirrups (on the combined effect of load and aggressive environmental conditions) highlighted a relevant risk of brittle shear failure. The Fast-FWD tests campaign was performed in May 2019, in one single hour. In Figure 6, an aerial view shows the bridge road and the testing site. On each of the 48 testing points, three load impulses were applied with increasing contact pressure, respectively, of 1300, 1400 and 1500 kPa. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Concrete**} & \multicolumn{2}{c}{**Asphalt**} & \multicolumn{2}{c}{**Steel**} \\ \hline \(\mathbf{E_{c}}\) (\(\mathbf{GPa}\)) & \(\mathbf{\mathit{v_{c}}}\) & \(\mathbf{E_{a}}\) (\(\mathbf{GPa}\)) & \(\mathbf{\mathit{v_{a}}}\) & \(\mathbf{E_{s}}\) (\(\mathbf{GPa}\)) & \(\mathbf{\mathit{v_{s}}}\) \\ \hline
10.52 & 0.35 & 1.50 & 0.35 & 206 & 0.20 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mechanical properties for the Finite Element (FE) model. Before tests, a geometric grid was established on the deck of the bridge, whose origin of the reference system is in Figure 6. Testing-point positions are in Figure 7 and the positions of the geophones are in Figure 7. Comparing Figure 7 with Figure 4, it is evident that the test net is different from the structural net of girders. This is motivated by the fact that test net is established with the criteria to measure equally spaced points on all the bearing surface of the bridge, aside from the actual position of the bearing element. This is done in order to validate the method, also in the case of lack of knowledge of the structural net that is sustaining the deck. Figure 4: View of the deck: (**a**) planimetric view of the trellis girder and (**b**) longitudinal and transversal sections. Figure 5: Picture of the bridge, showing significant corrosion: (**a**) lateral view of the deck and (**b**) view of the intrados of the beam. The Fast-FWD Load Cell is a low-profile shear web designed with strain gauges. Despite its high range of 250 kN, it features a height of only 45 mm. Due to design specifications, the cell will deflect less than 30 microns at peak load. Nominal sensitivity is approximately 16 uV/V/kN. Figure 6: Aerial view of the testing site. Figure 7: Survey grid and schematic position of the station points.