PSI - Issue 78

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

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3.2. Model Updating

Table 3 resents the objective -function values for each modelling configuration addressing the main epistemic uncertainties. For the abutment constraints, two modelling strategies were explored due to the lack of as-built drawings: a point-constrained model, where translational spring stiffnesses ( , ) were treated as aleatory variables, and a detailed abutment model, with explicitly modelled abutments derived from a similar bridge. Regarding the half joint constraints, the “all - rotations released” co nfiguration was selected for rotations, confirming the expected Gerber joint behavior. For translations, the best-fitting model released only the transverse displacement on one side of the drop-in span. Although the release of longitudinal displacement was expected, field observations revealed that a poorly executed expansion joint repair had unintentionally restrained movement. For the intermediate constraints, the “all released” configuration was preferred for rotations despite a slightly higher objective function, as the “fixed” setup yielded a MAC value below 0.70 for mode 5. For translations, the “fixed” configuration provided the best fit. Fig. 6a provides a summary of the epistemic uncertainties assumed for the point-constrained model, while Fig. 6b summarizes the epistemic uncertainties assumed for the detailed abutment model. Aleatory uncertainties included Young’s modulus and mass density, with reference values from experimental tests (Section 2.4). For the point -constrained model, the spring stiffnesses and were also treated as aleatory. Young’s modulus varied from – 30% to +0%, reflecting potential stiffness reduction due to observed damage such as cracking, spalling, and reinforcement corrosion. Mass density ranged from 2.20 t/m³ and 2.60 t/m³ (Neville and Brooks 2010) . The point-constrained model was calibrated first. Elements were grouped by structural components (piers, transverse beams, longitudinal beams, slabs), with further distinction between internal and external decks. For each group, both modulus and density were calibrated. Table 4 summarized the updated parameter values. The updated model exhibits a ~30% reduction in stiffness for most components, except the central beams, and an increase in mass density. Spring stiffnesses were also significantly reduced. In the detailed abutment model, and were replaced by the abutments’ Young’s modulus and density. As shown in Table 5, stiffness reductions were again concentrated in longitudinal beams, internal slabs, and transverse beams, while the other components changed by smaller amounts. Most densities decreased, except for the abutments, whose higher calibrated density likely compensates for soil loading effects not explicitly modelled due to missing construction details. Table 6 provided the results of both calibration processes. The calibration processes resulted in a significant reduction in the discrepancy between the experimental and numerical frequencies. The MAC index values indicate a strong correlation between the experimental and numerical mode shapes, with the objective function reaching a value of 0.561, for the point-constrained model, and 0.684, for the detailed abutment model. The better results of the point-constrained model can be attributed to the translational springs, which implicitly account for additional soil structure interaction effects and compensate for the uncertain geometry of the abutments, factors that the detailed abutment model cannot capture. Table 4. Objective function value for each configuration. Epistemic uncertainties Objective function value for each configuration i ii iii iv v Abutment constraint 2.178 2.353 1.384 2.455 0.910 Half joint constraint (rotation) 2.178 2.197 2.179 2.257 - Half joint constraint (translation) 2.178 2.254 2.163 2.239 - Intermediate constraint (rotation) 2.106 2.103 2.117 2.119 2.178 Intermediate constraint (translational) 2.178 2.339 2.238 2.322 -