PSI - Issue 84

Elisa Tomassini et al. / Procedia Structural Integrity 84 (2026) 288–295

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by four rectangular reinforced concrete piers founded on deep pile foundations. Pier heights vary according to the local terrain, with the second pier being the tallest (12.8 m), the adjacent piers approximately 10 m high, and the first pier significantly shorter. The monitoring system installed on the deck comprises 30 uniaxial MEMS accelerometers oriented along the gravity direction, with six sensors per span located at 1/4, 1/2, and 3/4 of each span length, as shown in Fig. 2(a). The target bridge is a continuous five-span post-tensioned concrete bridge with a total length of 122.5 m. The deck consists of a variable-depth box girder supported by four reinforced concrete piers with rectangular hollow cross-sections, founded on piles with pile caps. Two reinforced concrete abutments act as retaining walls. The monitoring system includes 10 uniaxial piezoelectric accelerometers oriented along the gravity direction, arranged as shown in Fig. 2(b).

Subsequently, the FEMs of both bridges were calibrated using experimental data. The calibration involved the stiffness and mass density of the concrete in the deck and piers, as well as the translational and rotational stiffness of the supports, modeled as springs. Both the deck and piers were represented by beam elements with cross-sections defined according to the design drawings. After calibration, eight vibration modes exhibiting similarity were identified between the two structures, as shown in Fig. 3, and quantitatively compared in Table 1. Mode selection was based on Modal Assurance Criterion (MAC) values and typological similarity of the calibrated experimental mode shapes (e.g., bending or torsional behavior). It can be noted that, while most transferred modes show satisfactory correlation, Mode 7 exhibits a relatively low MAC value. This discrepancy is attributed to structural differences between the bridges: the source bridge exhibits spatially localized torsional modes due to irregular pier heights, whereas the target bridge, characterized by uniform pier heights, develops more global torsional behavior. Despite this difference, Mode 7 was retained to assess the SM’s ability to generalize beyond structure-specific boundary conditions and capture broader dynamic behavior. This mode selection establishes a robust basis for effective knowledge transfer and cross-structure generalization of the surrogate model. Fig. 2. Geometry of the spans and control parameters of the FEMs of the (a) source and (b) target bridges. Black circles indicate the DOFs used for mode shape extraction in the FEM, while red arrows denote the locations of the accelerometric channels installed as part of the SHM system.

Mode id , , , − , MAC 1 0.88 2.87 -1.99 0.95

Table 1. Transferred mode shapes of the source and target bridges .

Description

1st order bending mode 1st order bending mode 1st order bending mode 2nd order bending mode 2nd order bending mode 1st order torsional mode 1st order torsional mode Lateral mode

2 3 4 5 6 7 8

3.76 5.05 4.53 6.42 6.81 5.31 6.14

-2.42 -3.22 -2.68 -3.74 -3.79 -0.32 -0.63

0.87 0.75 0.78 0.57 0.85 0.17 0.73

1.34 1.83 1.85 2.68 3.02 4.99 5.51