## 1 Introduction
EN1991-2 [2] defines specific values for this additional damping of the bridge as a function of the bridge span length which some authors considered to be non-conservative [23]. Inclusively, [PERSON] [24] shows that the additional damping can assume negative values, which implies influx instead of dissipation of energy. This situation occurs when the mass of the wheels cannot be neglected in comparison to the bridge mass, and for specific locations of the vehicle over the bridge. In relation to the experimental damping estimation, several strategies are available depending on the type of test adopted, namely, the ambient vibration tests [25; 26], the forced vibration tests [18; 27], and the dynamic test under traffic actions [28; 29]. In many works, the damping estimations are performed under ambient vibration conditions [30; 31]. However, this scenario of low vibration amplitude is not representative of the real loading conditions of a train crossing a bridge, particularly in terms of amplitude of vibration, as well as considering the train-bridge interaction and eventual non-linear incursions at the bearings and track-deck interface. Thus, the use of forced vibration tests, resorting to an external controlled excitation by means of dedicated equipment, constitutes a partial solution, since, even in these circumstances, the vibration amplitude is not necessarily representative of the amplitudes induced by real traffic loads [18]. In addition, the test setups are usually complex, time consuming and costly, and in some situations may require the temporary occupation of the track corridor. Therefore, the most used strategy to estimate the damping ratios is based on dynamic tests under traffic actions, particularly using time records collected during or after the train passage [1; 16]. [PERSON] et al. [9; 19] used a large-scale test facility to simulate a dynamic test under traffic loads and quantifiedthe ballasted track's damping properties under vertical excitations. These authors proved that in a ballasted track, the damping values are frequency-dependent and approximately linear amplitude-dependent. Based on the results of a dynamic test under traffic loads on a steel-concrete composite bridge, [PERSON] & [PERSON] [32] also verified that the damping ratios increased with increasing amplitude of vibration. Focusing on the dynamic tests under traffic actions, there are several methodologies to calculate the damping ratios, mostly based on the free vibration response after the train passage [26; 28; 29; 33], as well as during the train passage [1]. Considering the free vibration responses, the mostly used techniques resort to the Logarithmic Decrement (LD) method [26], Autoregressive models [1], Prony-Pisarenko method [34], Hilbert transform [35], Kalman filters [36], and Continuous Wavelet Transforms (CWT) [32]. The LD method is particularly efficient in situations where the free vibration records are predominantly influenced by non-coupled modes of vibration, where the application of pass-band filters can efficiently separate the contribute from one mode in relation to the others [25; 37]. [PERSON] et al. [10] performed an extensive damping measurement campaign in a multi-girder RC simply supported viaduct using the free vibration parts of the vertical acceleration records for the passage of ETR500/1000 high-speed trains. The authors used the LD method resulting in damping ratios for the vertical bending mode between 2.76% and 3.70%. These values were considerable higher in comparison to the damping ratio of 1% provided by EN1991-2 [2], which confirms the conservative lower bound damping ratios provided by the norm and depicted by several other authors [16; 18; 25; 26; 28; 29; 33]. [PERSON] et al. [26] applied the LD method to estimate the damping coefficients of local modes of vibration of the upper slab of a RC box-girder viaduct.