PSI - Issue 78

Andrea Nettis et al. / Procedia Structural Integrity 78 (2026) 1404–1411

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through two force-based beam–column elements. The lower segment (10% of the total height) captures the plastic hinge region and incorporates the effects of corrosion-induced deterioration. The remaining 90% represents the elastic portion of the column. Concrete was modeled using Concrete01 for both the core and cover, while longitudinal reinforcement was simulated using ReinforcingSteel . Bearing devices were introduced as linear elastic springs via twoNodeLink elements, accounting for shear stiffness proportional to the material shear modulus. In this study, a uniform corrosion scenario is assumed, in which all faces of the pier are equally affected. Consequently, it is considered that all cross-sections along the lower element of the pier exhibit uniform corrosion, with the same intensity class predicted for each photo corresponding to each face. As a result, the entire lower element is assigned a single, consistent predicted corrosion class. The adopted modeling strategy for the corroded lower element involves the following steps applied to the sections: (1) removal of cover concrete fibers; (2) assignment of corroded steel constitutive laws and reduction of reinforcement cross-sectional areas for the longitudinal bars; and (3) modeling of confined concrete using a corrosion-adjusted version of the Mander model. 3.3. Methodology for fragility analysis and loss assessment A cloud-based fragility analysis is conducted following the methodology of Jalayer et al. (2017) and Nettis et al. (2021), using natural, unscaled ground-motion records. Seismic intensity is quantified by an intensity measure (IM), typically the spectral acceleration at the fundamental period of the structure. In this study, the spectral acceleration at the first mode period of the pier, Sa(T 1 ), is adopted as the IM. Nonlinear time history analyses (NLTHAs) are performed, and structural response is recorded in terms of an engineering demand parameter (EDP), specifically the pier drift. This is defined as the relative displacement between the top and bottom nodes of the pier, normalized by its height, resulting in a dimensionless quantity. Prior to fragility assessment, a static pushover analysis is conducted to determine EDP thresholds for both pristine and corroded conditions across all realizations. Based on HAZUS guidelines (FEMA, 2012), four damage states (DS) are defined, each corresponding to a specific physical damage level, repair strategy, and associated Repair Cost Ratio (RCR), as summarized in Table 1.

Table 1. Damage States definition.

Damage State

Damage Level

EDP Threshold (Cardone et al., 2014 )

Repair Actions

RCR (FEMA,2012)

DS1

Slight

Δ y

Repair minor concrete cracking/spalling at the column (e.g., epoxy injection, concrete patch). Repair moderate concrete cracking/spalling at the column; possible repair of some reinforcing bars (e.g., concrete patch, reinforce and recast). Severe damage requiring expensive interventions (e.g., shear failure/strength degradation without collapse, significant residual movements). Replace or reuse of the column-base system after repairs; reconstruction of the whole bridge.

0.03

DS2

Moderate

Δ y + ( Δ u - Δ y )/2

0.08

DS3

Extensive

Δ y +2( Δ u - Δ y )/3

0.25

DS4 Near Collapse

Δ u

1.00

Given the distribution of EDPs for each IM, fragility curves are developed to express the probability of exceeding a particular damage state. To capture record-to-record variability, a suite of 100 natural ground motions is selected from the SIMBAD database (Smerzini et al., 2014), covering a wide intensity range (0.16 g to 1.77 g in terms of peak ground acceleration). For each structural realization, 100 NLTHAs are performed, forming the basis for deriving the fragility curves. Based on these fragility curves, the vulnerability function is developed according to the approach proposed by Nettis et al. (2023), which relates the expected loss ratio to corresponding IM values. By combining the vulnerability