PSI - Issue 78

Andrea Pozè Falet et al. / Procedia Structural Integrity 78 (2026) 325–332

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(a) (b) Fig. 6. Example of identifications from the first run of acquisitions on span 3. (a) stabilisation diagram with stables (red circles) and unstable (black crosses) poles; (b) mode shape corresponding to the first mode. 3.2. Comparison with Previous Identifications Two sets of comparisons can be made for each mode of interest. First, it is possible to compare the identified modal parameters (and especially the mode shapes) ‘spatially’ – in the sense, at the same instant over the different, independent, and nominally identical spans – to evaluate any potentially damage- (more correctly here, scour-) related anomaly. Second, these can also be compared ‘temporally’, focusing on the same span in the 2003, 2004, and 2024 campaigns. That allows tracking time-dependent changes, such as the retrofitting of Pier P2 (clearly visible in Figures 7.a and 7.c, where the asymmetries of the first mode shape almost disappear after retrofitting) and the potential changes due to scour at Pier P3. For brevity, Figure 7 only reports the first mode (the first vertical bending one), as previously highlighted in Figure 6.b. Please note that, for the 2003 and 2004 campaigns (Figure 7.a to 7.d), a denser sensor layout was used, by combining in post-processing via the PoSER technique (Döhler et al., 2011) the identifications of multiple setups, totaling 26 vertical channels per span, equally spaced on both sides. It is important to note that the differences in sensor layout across the three monitoring campaigns prevent a direct comparison of the mode shapes. However, although not addressed in detail in this short contribution, an interpolation scheme has been employed to enhance the comparability of mode shapes despite the varying spatial densities of the measurement channels. This scheme, represented as a curved surface in all figures and applied wherever possible (i.e. not at the two extreme spans in the 2024 campaign), will be further discussed in future work. In the following, Tables 1 to 3 report the quantitative metrics for comparing the different spans throughout the same campaign. The subscript 1b indicates the first bending mode, while stands for natural frequency, in Hz, and for damping ratio, in absolute value. The last two columns represent, respectively, the mean and standard deviation of f 1b and 1b, calculatedconsidering all spans. Lastly, the Modal Assurance Criterion (MAC) (Allemang & Brown, 1982) is reported. In all cases, the first bending mode shape is used, comparing the several spans (C1 to C5, indicated generally by the writing ,∎ ) against the first one ( , ). Table 1. Modal parameters (first bending mode), 2003 (pre-retrofitting), for all bridge spans C1 C2 C3 C4 C5 1 [Hz] 4.68 4.52 4.67 4.69 4.91 4.69 ± 0.14 1 [-] 4.80 ∙ 10 −2 1.81 ∙ 10 −2 4.09 ∙ 10 −2 3.62 ∙ 10 −2 5.40 ∙ 10 −2 3.94 ∙ 10 −2 ± 1.37 ∙ 10 −2 MAC( , , ,∎ ) 1.0000 0.9785 0.9984 0.9992 0.9788 - - By comparing Table 1 and Table 2, the natural frequencies undergo some changes. These variations are generally small, although a significant reduction (up to almost 6%) occurs for the first bending mode frequency on span C3. This lower natural frequency may be a consequence of the deformability of the new pier cap installed during the retrofit intervention (Figure 1c). More significant differences are detected in the mode shapes: while it was found