PSI - Issue 78

Simone Reale et al. / Procedia Structural Integrity 78 (2026) 1657–1664

1662

4.4. Fragility Analysis

Four Damage States (DS), namely Slight (DS1), Moderate (DS2), Extensive (DS3) and Complete (DS4) Damage, have been considered. The thresholds used in the fragility analysis have been reported in Table 3, based on (Cardone, 2014). Fragility curves for each DS have been obtained through the Maximum Likelihood Estimation (MLE) method (Baker, 2015). The total dispersion of each fragility curve β tot is estimated as per Equation (19): =√ 2 + 2 + 2 (19) Where β gm is the dispersion component associated with record-to-record variability, β mod is the component associated with modeling uncertainty and β ds is the uncertainty in the DS definition. β gm is estimated through the MLE method, β mod is computed according to the FEMA P-58 (FEMA, 2012) and β ds is defined as per (Stefanidou et al., 2022). System fragility functions P(F system ) have been defined based on the probability of exceeding a given DS for the i-th component P(F i) taking the upper bound of Equation (20), as per (Nielson and DesRoches, 2007): =1 [ ( )] ≤ ( ) ≤ 1 − ∏ [1 − ( )] =1 (20) The effects of different corrosion damage modeling strategies can be efficiently discussed by considering the reduction of the IM value corresponding to the median of the system fragility curve for DS4, as reported in Table 4. It can be observed that the values tend to decrease over time, in significantly more pronounced way as more details are included in the corrosion damage modeling strategies. The divergence between the four strategies increases as time passes. While for t=20 years the discrepancy is not pronounced, from t=40 years onwards the difference between the strategies becomes not negligible, with relevant effect on the subsequent phases of seismic risk assessment.

Table 3. Thresholds for each component and for each DS.

Component

EDP

DS1

DS2

DS3

DS4

Piers

Displacement

Δ y +0.5( Δ u - Δ y )

Δ y +2/3( Δ u - Δ y )

Δ y

Δ u

Bearings Backwall

Shear deformation 150%

200%

300%

Unseating

Displacement

Δ y +2/3( Δ u - Δ y )

d gap

d y,ab

d u,ab

Table 4. Evolution of DS4 median IM values for each modeling strategy. The values between branches represent the ratio between median IMat a given time and its initial value.

Modeling Strategy Initial

20 years

40 years

60 years

80 years

1 2 3 4

0.638 (-) 0.638 (-) 0.638 (-) 0.615 (-)

0.638 (1.000) 0.634 (0.993) 0.617 (0.967) 0.594 (0.967)

0.634 (0.993) 0.6151 (0.964) 0.583 (0.914) 0.558 (0.908)

0.634 (0.993) 0.594 (0.930) 0.573 (0.898) 0.521 (0.847)

0.631 (0.989) 0.583 (0.913) 0.557 (0.873) 0.504 (0.820)

4.5. Seismic Risk Assessment Seismic Risk Assessment is performed by computing the failure rate λ f according to Equation (21): = ∫ ( | = )| ( > )| 0 ∞

(21)