PSI - Issue 78

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

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The internal constraints on the half-joints and between pier caps and beams were modelled through the introduction of elastic links without rotational stiffness and a rigid configuration for the displacement. The concrete properties were calculated from in situ test in accordance with the formulations reported in NTC 2018 , assuming the compressive strengths listed in Table 1. The following elastic modulus values were considered: for the piers, E = 35072 MPa, for the longitudinal and transversal beams, E = 33019 MPa, and for the slab, E = 38987 MPa. The concrete mass density was assumed 2.4 t/m³. Non-structural masses, including the weight of the road pavement and barriers were included in the model. An eigenvalue analysis was performed, and the first five mode shapes are illustrated in Fig. 4.

Fig. 3. Ambient Vibration Test: (a) Setup 1; (b) Setup 2.

Fig. 4. 3D graphical representation of the numerical modal shapes for the first five modes identified: (a) 1st Mode — f = 5.116Hz; (b) 2nd Mode — f = 6.213Hz; (c) 3rd Mode — f = 8.164Hz; (d) 4th Mode — f = 15.541Hz; (e) 5th Mode — f = 10.645Hz.

2.5. Finite Element Model Updating Despite the availability of detailed information on geometry, structural details, and material properties, the modelling process remains affected by both epistemic and aleatory uncertainties. Epistemic uncertainties, in particular, are associated with the representation of structural details whose behavior is difficult to capture through continuous parameters. To address these uncertainties, alternative modelling assumptions were introduced. In this study, three main sources of epistemic uncertainty were investigated: the configuration of abutment restraints, half-joint constraints, and intermediate constraints above the piers. The specific configurations examined for each case are summarized in Table 2. For each configuration, an objective function quantifying the discrepancies between numerical and experimental modal properties was calculated. The objective function is defined as follows: (1) where, is the experimentally identified frequency of the ℎ mode, is the numerically calculated frequency of the ℎ mode, ( , ) is the Modal Assurance Criterion (Allemang and Brown 1982) index quantifying the correlation between experimental and numerical mode shapes for the ℎ mode, and is the total number of experimental modes equal to 5. The best configuration is identified as the one that minimizes the value of this objective function. ( ) exp mod mod exp exp 1 1 | | | , 1| num n es n es num i i i i i i i f f f MAC f   = = − = + −  