PSI - Issue 78

Andrea Gennaro et al. / Procedia Structural Integrity 78 (2026) 663–670

669

Fig. 6. Summary of the epistemic uncertainties assumed (a) for the point-constrained model; (b) detailed abutment model.

Table 5: Comparison between the parameters of the FE model before (Ref. value) and after updating (Upd. value) for point model. Group Description Ref. Value Upd. Value Δpar [%] Units Spring stiffnesses Translational spring stiffness (x, y) 1.0×10⁷ / 1.0×10⁷ 6.9×10⁶ / 1.1×10⁶ – 30.81 / – 88.66 kN/m Elastic modulus Piers, Ext. & Int. Long. Beams, Transv. Beam, Ext. & Int Slabs 35.7/33.0/33.0/ 33.0/39.0/39.0 24.5/23.1/23.1/ 31.9/27.3/27.3 – 30.00 to – 3.22 GPa

Piers, Ext. & Int. Long. Beams, Transv. Beam, Ext. & Int Slabs

2.4/2.4/2.4/2.4/ 2.4/2.4

2.6/2.6/2.36/2.6/ 2.6/2.6

+8.33

t/m³

Mass densities

Table 6: Comparison between the parameters of the FE model before (Ref. value) and after updating (Upd. value) for abutment model. Group Description Ref. Value Upd. Value Δpar [%] Units Elastic modulus – 30.00 to +0.00 GPa

Abutments Piers, Ext. & Int. Long. Beams, Transv. Beam, Ext. & Int Slabs Abutments, Piers, Ext. & Int. Long. Beams, Transv. Beam, Ext. & Int Slabs

36.2/35.7/33.0/ 33.0/33.0/39.0/39.0

36.2/35.2/25.2/ 23.1/23.1/39.0/30.7

2.4/2.4/2.4/2.4/ 2.4/2.4/2.4

2.6/2.2/2.6/2.2/ 2.6/2.2/2.2

-8.33 to +8.33 t/m³

Mass densities

Table 7: Comparison between experimental and numerical modal characteristics of the updated FE models. Mode Exp freq. [Hz] Initial FEM Point-constrained Detailed abutment. Δf [%] MAC Δf [%] MAC Δf [%] MAC 1 3.678 51.69 0.927 5.91 0.976 9.65 0.974 2 5.082 22.26 0.975 8.10 0.977 -9.08 0.973 3 6.447 26.63 0.965 8.76 0.968 -12.82 0.961 4 9.068 71.38 0.972 2.83 0.978 9.24 0.972 5 11.888 -10.46 0.868 7.24 0.888 5.16 0.895 f (f, MAC) 2.178 0.561 0.684

4. Conclusion In this paper a finite element model updating based on ambient vibration test for a Gerber half-joints bridge was present. The AVT tests provided five experimental frequencies and mode shapes, revealing large discrepancies with the dynamic behavior of the initial FE model. Epistemic uncertainties (abutment constraints, half joint constraint, Intermediate constraint and slab modeling) were explored, and two abutments modeling strategies were defined: a point-constrained model with translational springs and a detailed abutment model with assumed geometry. For each strategy, the aleatory variables of Young’s modulus, material density, and translational spring stiffnesses (for the point‑constrained model) were calibrated through Bayesian Parameter Estimation. Bo th calibration processes produced a marked reduction in the misfit between numerical and experimental modal properties. Nevertheless, the