PSI - Issue 84

Laura Dieci et al. / Procedia Structural Integrity 84 (2026) 591–598

597

that provides the best compromise between frequency and displacement residuals, ensuring that the model accurately captures both dynamic and static behavior. The calibration parameters have been searched in the ranges 800-50000 MPa, 1500-4500 kg/m 3 , and 10 3 - 10 8 kN/m for , and , respectively. Resulting optimal values are: = 9645 MPa, = 2466 kg/m 3 and =10 7.8 kN/m. The low value of the elastic modulus is related to the poor state of preservation of the concrete and the significant level of degradation observed in the elements, although they have been partially restored. With regard to the equivalent density of the slab, the estimated value was found to be comparable to that of reinforced concrete alone, possibly due to uncertainties about its actual thickness. The Pareto front obtained for varying values of α exhibits a nearly flat trend. This behavior stems from the different sensitivities of the residuals: while the frequency residual is influenced by both stiffness and mass parameters, the displacement residual is primarily governed by stiffness. This implies that once the optimal values for the stiffness related parameters are found, the frequency residual is heavily influenced by mass, unlike the displacement residual. Consequently, the optimal parameter set is found at α=0.90, where a higher weight is attributed to the frequency residual.

(a)

(b)

Fig. 5: Numerical mode shapes of (a) first flexural mode and (b) first torsional mode.

Table 2. Comparison between experimental and numerical natural modes. Mode ( ) ( ) First flexural mode 4.37 4.34

Relative error (%)

MAC (-)

0.69 -0.54

0.99 0.96

First torsional mode

9.27

9.32

5.2. Results The comparison between numerical and experimental modal properties focuses on the first bending and torsional modes, both in terms of mode shapes and natural frequencies. The numerical mode shapes are illustrated in Fig. 5, while Table 2 reports the corresponding numerical and experimental frequencies together with the relative errors and MAC values. A great correspondence between numerical and experimental results is observed, in terms of both natural frequencies, with discrepancy below 1%, and MAC values, higher than 0.96. In particular, the numerical frequency of the first bending mode is slightly lower than the experimental value, while for the first torsional mode the numerical frequency is slightly higher. Overall, the results indicate that the calibrated FE model accurately captures the dynamic behavior of the bridge, providing confidence in its use for subsequent assessment or monitoring interpretation. For the static behavior, the vertical deflections under the reference load configuration are compared between the calibrated FE model and the measurements obtained from the static load test. A summary of the comparison between measured and numerical deflections at midspan and at the Gerber saddle is reported in Table 3. The numerical model captures the general trend of the measured displacements: at the Gerber saddle, the numerical deflection is slightly lower than the measured value, while at midspan the calibrated model provides a displacement that is marginally higher than the experimental one. These differences remain below 3% and indicate a satisfactory agreement between numerical predictions and experimental observations.