# Fast Falling Weight Deflectometer Method for Condition Assessment of RC Bridges
## 2 Methods of Analysis  
### Fast Falling Weight Deflectometer (Fast-FWD)  
The deflections induced by Fast-FWD were obtained by a series of impulses from a repeated falling load. The deflectometric data registered by Fast-FWD data acquisition system were processed to assess deflection basin parameters and pavement layers stiffness through ELMOD 6 software [39] developed by Dynatest [40]. The load is pushed by a circular steel plate of diameter 300 mm. The plate is segmented in four angular sectors, to better match the shape of the tires footprint. Twelve velocity transducers (geophones) are along a line radiating out from the load plate to a max distance of 2100 (Figure 3). The geophone numbers 11 and 12 were placed in approximately symmetric position with respect to the geophone numbers 2 and 3, to check the deflection basin nearest to the impact point. The impulse was given in correspondence with the measurement axis, aligned with the geophones zero. The measurement axis was moved along all the bridge deck during the experimental campaign. In this experimental campaign, the geophone bar was moved alongside the road axis; so, for each drop, longitudinal deflection is measured. The weight and the drop height of the falling mass can be modified: The weighting mass range is 50-350 kg, while the drop height is from 50 to 390 mm, so the impulse load can range from 40 to 120 kN, acting on mass and drop height. The duration of the impulse load ranges from 25 to 30 ms. For each drop, the system samples the load and measures the time history of the deflection in a period of 60 ms. The load is applied by a falling mass with a fixed height drop and is verified with a Dynamometer. The kind of pavement can influence the local pressure, but the axial load is fixed. The standard test comprises three repeated drops with the same load or through progressive impulse with growing stress. It is useful to perform the test with three different vertical stresses, to investigate if the response of the system is linear with respect to the intensity of the impulse. Figure 3 shows a typical deflection basin measured by the geophones after the impulsive load. The deflection profile is influenced by the properties of the pavement layers, as well of the magnitude and frequency of the loading [31]. The largest deflection is in correspondence of the loading point, measured by the D\({}_{1}\) and D\({}_{11}\) geophones. The amplitude and the shape of the basin contain information about the stiffness of the layers of the pavement; the time history of the deflection contains information about the dynamic properties of the underlying layers. From this data, some synthetic indicators can be drawn. Conventional stiffness values were obtained by dividing the applied load with the displacement obtained measured by the axial geophone \(D_{0}\). \[K=\frac{F}{D_{0}} \tag{1}\]  
where \(F\)--impulsive load and \(D_{0}\)--maximum deflection measured at the center of the plate. Figure 3: Basin shape profile, number and position of the Geophone. In addition, the analysis of the basin shape furnishes some indicators called \"Basin Indexes\". These are defined in References [41; 42]. The more relevant ones in the analysis of the concrete deck are defined in Equations (2)-(6) and described below. The radius of curvature (RC) defines the average radius of curvature of the deflection basin related to the radius of the load plate. The Surface Condition Index (SCI), Base Distress Index (BDI), and Deep Condition Index (DCI) are defined as the difference of the deflection at different distance from the load points. Rectangular Area (RA) indicator is a synthetic that considers the summation of all the displacements related to \(D_{1}\).