PSI - Issue 78

Joud Habib et al. / Procedia Structural Integrity 78 (2026) 799–806 803 This classification is used in order to perform analyses with a sequence of two records; the first record is from the set that causes the initial damage state while the second is from the whole set of used records. The results of the second record, in terms of intensity measure (IM) and engineering demand parameter (EDP), are saved. Since structural damage is generally considered irrecoverable, a model starting from a given damage state can only transition to the same or a higher damage state. This means that if the EDP resulting from the second record corresponds to a lower damage state, the model is considered to have remained in its initial state. For each record that causes the initial damage state , the model is analyzed with every record from the full dataset as the second input. This results in multiple (IM, EDP) pairs for each , forming the dataset with initial damage used for state-dependent fragility assessment. Where represents the initial damage state (slight 1 , moderate 2 and extensive 3 ) that can reach a higher damage state. To ensure consistency across all models and for computational efficiency, a maximum number of records causing damage is used in the analysis: 80 records causing 1 , 60 records causing 2 and 40 records causing 3 . 3.4. Selection of the most suitable intensity measure To identify the most appropriate intensity measure (IM) for representing the structural response of each typology, a systematic statistical methodology based on the analysis of efficiency is adopted. This evaluation is performed using the datasets corresponding to the undamaged condition, obtained through the analysis procedure described earlier. Specifically, the method applies linear regression to relate the natural logarithm of the structural response to the standardized form of each IM. The quality of this relationship is evaluated based on the regression coefficient (slope), which indicates the predictive strength of the intensity measure (IM), and the residuals, which reflect the dispersion of the observed responses around the predicted values. For each structural typology, the most suitable IM is the one that results in a strong correlation and minimal residual scatter — characterized by a steep slope and a low residual standard deviation — indicating a reliable prediction of structural response across a range of ground motions. Fig. 3. presents an example of this methodology applied to the CDL-H4-5 typology, demonstrating the dispersion of data points around the regression line for three different intensity measures.

Based on the slope and residual standard deviation, the most effective IM for all one-story typologies is 1 (0−0.5s) . For two-story typologies and the CDL-H3-10 typology, the best-performing IM is 1 (0.3− 0.6s) , while for the remaining structural typologies, 1 (0.75 − 1.5s) results in the lowest dispersion and highest correlation. Fig. 3. Standardized IM and the regression line for CDL-H4-5; a) IM=PGA; b) IM= 1 (0−0.5s) ; c) IM= 1 (0.75 − 1.5s) .