PSI - Issue 78

Joud Habib et al. / Procedia Structural Integrity 78 (2026) 799–806

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3. Non-linear dynamic analysis 3.1. Number of records

This study employs Cloud Analysis using a dataset of 1,382 unscaled ground motion records to account for record-to-record variability. The use of a large dataset enhances the robustness of the probabilistic relationship between the IM and the (EDP), thereby increasing confidence in the results and reducing epistemic uncertainty. The records are primarily sourced from the Pacific Earthquake Engineering Research Center (PEER) database and the ITACA database. The peak ground acceleration (PGA) values of the selected records range from 0.026g to 2.2g. Fig. 2. (b) presents the distribution of records across different PGA intervals. 3.2. Considered Intensity Measures In seismic fragility analysis, the selection of an appropriate intensity measure (IM) is a critical step that directly influences the reliability and interpretability of the results. The choice of IM is typically guided by its sufficiency and efficiency, both of which are essential for accurately assessing structural performance. Prior studies by Baker et al. (2006) and Buratti (2012) have shown that IMs incorporating the spectral shape over a range of periods generally outperform single-spectral-ordinate IMs, especially at higher damage states. This improved performance is attributed to the damage-induced reduction in structural stiffness, which causes a shift in the natural period of the structure (i.e., period elongation). As a result, the structural response diverges from that of the undamaged configuration, highlighting the need for IMs that more comprehensively reflect this dynamic behaviour. In this study, the intensity measures considered for evaluating and selecting the most appropriate one for each structural typology include Peak Ground Acceleration (PGA) and the average elastic spectral acceleration over four different period ranges: 0.0–0.5 s, 0.3–0.6 s, 0.75–1.5 s, and 1.5–3.0 s. These ranges are selected to effectively capture the nonlinear dynamic response of the ESDoF systems and to reflect the diversity in elastic periods among the different structural typologies. The average spectral acceleration is computed using two approaches: i) Geometric mean, following Baker et al. (2006), as shown in Equation (1). In this equation, 1 ,…, represent the set of periods of interest, and ( ) is the spectral acceleration at each period : 1 ( 1 ,…, ) = [∏ ( ) = 1 ] 1/ (1) ii) mean value over a continuous period interval, based on the area under the spectral acceleration curve, as shown in Equation (2). Here, ( ) is the spectral acceleration at period , and the integral is evaluated from 1 to : 2 ( 1 , )= 1 − 1 ∫ ( ) 1 (2) The integral in Equation (2) is computed using trapezoidal rule. A preliminary Nonlinear Dynamic Analysis (NLDA) is performed in OpenSees, using each ground motion record from the set. This means that for every analysis, the model starts in an intact state with no initial damage. The NLDA captures the time history response in terms of displacement under the applied ground motion, allowing the computation of the Engineering Demand Parameter (EDP). For each typology, these preliminary analyses classify the records based on the resulting damage states in the model and generate a dataset of Intensity Measures and corresponding EDP values (IM, EDP) representing the cloud points. Since in these, the models always start from an undamaged condition, the resulting dataset is referred to as the dataset with no initial damage state 0 and is used in the traditional fragility assessment. The results of these analyses are then classified based on the damage state produced ( ). 3.3. Nonlinear dynamic analysis procedure