# A Feasibility Study of the Drive-By Method for Damage Detection in Railway Bridges
## 4 Simulation Results
### Track Irregularities  
Simulations with track irregularity were carried out to assess the feasibility of the damage detection method when the vehicle modes of vibration are consistently excited, and the background acceleration level is increased. Figure 19a shows the vertical accelerations of the leading bogie of the TSR train, obtained with the first irregularity profile defined in Section 3.5 (i.e., RMS 2.1 mm in the 1-100 m wavelength range), for the case of bridge #2 (damage D40 and healthy), and a train speed of 120 km/h. Figure 19b shows the same signals filtered with a cut-off frequency of 2.95 Hz (i.e., 0.5 \(\times\)\(t_{\rm bridge}\)). In the figure, the distance covered by the train is reported in the bottom x-axis [m], and the corresponding time [s] in the top x-axis. Two dashed vertical lines report the bridge position, and the sections just before and after the bridge correspond to the ballasted track. Figure 17: Damage localization dependence on speed and damage entity. Train CSA type, bridge #2, damage located at the mid-span. Figure 18: Dependence of damage component on span length. CSA train at 100 km/h, damage located at the midspan. The variability of the filtered acceleration due to track irregularity (Figure 19b) is of the same order of amplitude of the acceleration related to bridge crossing (see Figures 11 and 12), and one order of magnitude higher than the difference between accelerations of the healthy and the damaged bridge. This means that the damage identification procedure would be definitely affected by an evolution of long waves irregularities. It is therefore fundamental that these irregularities, which evolve anyway in a slow process, are constantly monitored, and that the reference condition is updated. The carbody bounce and pitch natural frequencies, being usually lower than 2 Hz, and therefore lower than the cut-off frequency, are not filtered in the quasi-static procedure. For the TSR train model, these frequencies are equal, respectively, to 0.84 Hz and 1.22 Hz. Even if in the corresponding mode shapes the contribution of the bogie vertical motion is not negligible (15% of the carbody vertical motion for the bounce mode), the corresponding natural frequencies are not visible in Figure 19b to an extent which may affect the feasibility of the method. This is mainly due to the high non-dimensional dampings, which are equal to 22% for the carbody bounce and 32.9% for the carbody pitch, and it is an aspect in favor of the feasibility of the method. A persistence in the capability to identify the damage is confirmed when the healthy and the damaged bridge are simulated with different irregularities, to reproduce from a qualitative point of view the variation of short wavelenghts that may be generated by ballast degradation. The irregularity adopted for the healthy bridge (same as in Figure 19) was modified in the wavelength range from 1 to 6 m, by doubling the amplitudes and randomly shifting the phases, and then adopted for the simulation of the damaged bridge. Figure 20a reports the vertical accelerations of the leading bogie corresponding to the healthy and damaged bridge, whose differences are due to the different irregularity profiles. Figure 20b reports the damage signal, obtained as the difference of the filtered accelerations. The results of damage identification are positive and similar to the case with no irregularity, since the variations in vertical accelerations due to the change of irregularity profile are filtered in the quasi-static algorithm. Finally a modified finite element model was built by adopting, for the ballast on track sections out of the bridge, a vertical stiffness (\(\mathrm{k_{z}}=0.4540\times 10^{8}\) N/m) that was lower than the one that was adopted on the bridge (\(\mathrm{k_{z}}=0.6040\times 10^{8}\) N/m). This was aimed at simulating the increase of ballast stiffness, which may be found when the train enters the bridge, due to the lower height of the ballast subgrade and to the absence of soil.