PSI - Issue 78

Parvane Rezaei Ranjbar et al. / Procedia Structural Integrity 78 (2026) 615–622

621

y = 1.1202x - 4.0765 R² = 0.9563 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 Ln(Maximum Drift Ratio) Ln(S a ) Y-Direction -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 Ln(Maximum Drift Ratio) Ln(S a ) Y-Direction y = 1.1837x - 4.9273 R² = 0.8637

y = 0.9394x - 3.6458 R² = 0.9367 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 Ln(Maximum Drift Ratio) Ln(S a ) X-Direction -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 Ln(Maximum Drift Ratio) Ln(S a ) X-Direction y = 1.0781x - 5.0425 R² = 0.8927

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(c) (d) Fig. 5. Linear regression analysis: (a) Existing Structure - X-Direction; (b) Existing Structure - Y-Direction; (c) Retrofitted Structure - X-Direction; (b)Retrofitted Structure - Y-Direction.

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(d) Fig. 6. Fragility curves: (a) Existing Structure - X-Direction; (b) Existing Structure - Y-Direction; (c) Retrofitted Structure - X-Direction; (b)Retrofitted Structure - Y-Direction. Sa (g) Sa (g)

The results also highlight direction-dependent vulnerability, with the Y-direction showing a more favorable response. This is reflected in the steeper slope of the fragility curves along the X-axis, indicating higher fragility for all damage states, as defined by the HAZUS criteria. The fragility curve can be interpreted by identifying the spectral acceleration correspond ing to the building’s location and then evaluating the probability that the structure will exceed a specific damage state at that intensity level. For instance, in the X direction, the fragility curve of the existing building shows that at a spectral acceleration of S a ( T 1 =0.743 s)=0.657g, which corresponds to the Life Safety (LS) limit state, the probabilities of exceeding each damage state are: 100% for slight damage; 100% for moderate damage; 100% for extensive damage; 39.7% for complete damage. According to the Italian Seismic Code (NTC-Guidelines, 2018), the LS limit state - corresponding to extensive damage - should not exceed a 10% probability of occurrence over the building’s reference life ( V R ). The existing structure significantly exceeds that threshold, emphasizing the need for seismic retrofitting. For the retrofitted building in the X-direction, the spectral acceleration is S a ( T 1 =0.325s)=0.801g, and the probabilities of exceeding each damage state are: 100% for slight damage; 91.4% for moderate damage; 8.96% for extensive damage; 0.006% for complete damage. The retrofitted structure does not exceed the 10% threshold for extensive damage, confirming the effectiveness of the proposed retrofit strategy.