PSI - Issue 84

Enrique García-Macías et al. / Procedia Structural Integrity 84 (2026) 837–844

843

From a computational standpoint, the proposed approach provides a substantial reduction in execution time. For the case shown in Fig. 4, the reference semi-analytic and HT time-stepping evaluation required 16.97 s and 18.43 s, respectively, whereas the proposed approach completed the maximum identification in 2.11 s, yielding a speed-up of approximately one order of magnitude. In terms of accuracy, the displacement maxima obtained with both approaches are virtually identical, with values of 3.37615 mm for both the reference solution and the proposed method, the relative difference being negligible. For the acceleration response, the reference maximum of 0.1609 m/s 2 is closely approximated by the proposed method, which yields a value of 0.1588 m/s 2 .

4.2. Case study II: concrete box girder bridge, the viaduct of Rodenillo.

Fig. 5. Lateral view and FEM of the viaduct of Rodenillo (a), and first eight vibration modes (b). This case study considers the Rodenillo viaduct, a double-track, cast-in-place post-tensioned concrete box-girder bridge on the Madrid–Valencia HSR line, comprising five continuous spans with a total length of 207 m (two 36 m outer spans and three 45 m central spans; Fig. 5a). The viaduct was modelled in the commercial FEM code SAP2000 (refer to García-Macías and Martínez-Castro (2020) for further details). The modal features of the bridge have been obtained by linear modal analysis of the FEM, finding a total of 123 modes of vibration with resonant frequencies below 30 Hz that must be considered in the subsequent dynamic analyses. Figure 5 (b) shows the first eight modes of vibration. A constant modal damping ratio of ζ =2 % is selected in the dynamic analyses.

Fig. 6. Displacement (a) and acceleration (b) time-series at the edge of the ballast layer at mid-span of the central span of the Rodenillo viaduct (A1 train; =307 km/h; semi- analytic: ∆t = 1 ms ; HT: 10 Hz cut-off frequency, (6m)/ reduced Hilbert integral, ∆t = 2 ms) . Figure 6 shows the displacement and acceleration time-series at the edge of the ballast layer at mid-span of the central span of the Rodenillo viaduct for the A1 train travelling at 307 km/h. The reference semi-analytic response, computed with a uniform time step of 1 ms, is compared with the proposed maximum identification framework at a