PSI - Issue 84

Lorenzo Sangiuliano et al. / Procedia Structural Integrity 84 (2026) 1326–1333

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For the numerical analysis, a single span was modeled, consistent with its simply supported scheme. The box girder was represented by three longitudinal beams connected to diaphragms via rigid links. The model was defined through a set of primary geometric parameters—namely span length, load path discretization, and slab dimensions—while secondary elements were automatically derived. In particular, diaphragm spacing was calibrated and scaled proportionally to maintain consistency with the real structure. Cross-sections were defined through closed-curve geometries. The mechanical properties assigned to the model included material stiffness, damping, support stiffness, and a longitudinal spring representing slab continuity effects due to track–ballast interaction, along with the distributed mass. Finally, the analysis setup comprised train velocities ranging from 6 km/h to 350 km/h, train geometry and mass imported from external data (CSV), post-passage simulation time, damping ratio, and time integration parameters, including step size and number of increments. The validation of the numerical model was carried out by comparing the natural frequencies of the structure obtained in situ through Operational Modal Analysis with those calculated via the Finite Element Model. In particular, the comparison focused on the first two flexural modes and the first two torsional modes, as these represent the most significant dynamic characteristics for the case under consideration, as previously discussed. The results presented in Table (Table 2) show that the frequencies predicted by the numerical model are in very close agreement with the numerical find by the solid model of PhD thesis of Giuseppe Chellini, thereby confirming the adequacy of the modelling approach.

Table 2: Comparison between solid and three beam model Type Frequence of solid model [Hz]

Frequence of three beam model [Hz]

I vertical flexural

3.817 8.529 10.723 14.33

3.81254 5.4675 11.69696 13.33576

I torsional

II vertical flexural

II torsional

An additional verification was performed by comparing the acceleration time histories measured by the monitoring system with those simulated by the model during train passages. As illustrated in Figures 4 and 5, the peak accelerations obtained from the numerical analysis closely match the experimental records, and the maximum accelerations associated with different train speeds also show good consistency between experimental and simulated data, as shown in Figure 5.