## 1 Introduction
The authors used the free vibration response of a deck slab considering the time lapse between the successive groups of axles, revealed as sufficient to have several free vibration responses periods. ERRI D214/RP3 [1] proposed a specific procedure to estimate the damping in railway bridges. First, isolate the free vibration part of the record based on the exact identification of the time when the train leaves the bridge using the so-called multiple-impulse method. Second, estimate the damping using one of the reference methods, which are Prony-Pisarenko or Auto-Regressive methods. Additionally, this Committee proposed to evaluate the non-linearity of the damping ratio using a strategy consisting of, first, evaluating the damping based on the initial four cycles in free vibration, and then, moving forward one cycle and calculating again the damping. This would allow one to show the eventual dependency of the damping with the variation of the amplitude of vibration. More recent methods propose evaluating the damping during the train passage, which are revealed to be particularly efficient in situations close to resonance. ERRI D214/RP3 [1] adopted the ARX method (Auto Regressive with eXogenous inputs) which is a non-linear time series model able to reproduce the dynamic response of the bridge based on previous responses (outputs) and previous forces (inputs). The application of the method requires the reconstitution of the excitation model of the moving train based on multiple-impulse decomposition and application of perceptual filters [1]. However, this method proposed by the ERRI D214 Committee has not yet a widespread use and requires new enhancements in further studies. Thus, this study aims to give clear contributions in relation to some aspects that presently, according to the authors' knowledge, are not sufficiently addressed in the existent literature, particularly:  
* To provide reliable estimates for the damping ratios of railway bridges, which typologies are not sufficiently covered by EN1991-2 [2] and previous studies of Committee D214 from ERRI [1], particularly the filler-beam type. For this purpose, a set of dedicated experimental campaigns were performed in a significant number of filler-beam bridges belonging to the Portuguese railway network. The information derived from this study, framed in the Shift2 Rail EU Projects In2 track2 [38] and In2 track3 [39], can be certainly valuable for the future revisions of the norm EN1991-2 [2]. To propose a consistent methodology for estimation of the damping ratios envisaging the short/medium span filler-beam railway bridges, in which, mostly, exists coupling between the bending and torsion fundamental modes, and therefore, the classical LD method presents limitations. - Application of the Prony method as the reference method to efficiently estimate the damping ratios in filler-beam railway bridges with coupled and closely spaced fundamental modes of vibration. Since the precursors studies of the Committee ERRI D214, at the end of the 1990s, this method has been very rarely used in studies involving railway bridges. In most situations, the authors insistently remain using the LD method. Additionally, a numerical validation of the Prony method is performed based on a 3D Finite element (FE) model of a filler-beam bridge, in which a set of predefined damping ratio values were defined, and, posteriorly, based on the free vibration responses under traffic actions, the damping estimates were confirmed. - To propose a simple methodology to precisely estimate the exact time step when the last train axle no longer influences the dynamic response of the bridge, and therefore, it initiates the free vibration movement.