PSI - Issue 78

Matilde Natalizi et al. / Procedia Structural Integrity 78 (2026) 449–456

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which represent about 60% of the building stock and are often built before the first Italian anti-seismic code (L.64/1974). In this context, assessing seismic vulnerability on a territorial scale is essential for planning effective seismic risk reduction strategies. Typological fragility curves, derived from actual damage data observed in buildings affected by earthquakes, are an efficient tool for rapidly estimating potential losses following seismic events. This approach is applied to the municipalities of Norcia and Arquata del Tronto, affected by the 2016 Central Italy earthquake. Despite geographical proximity and similar shaking intensity, the two municipalities reported different damages: Norcia was significantly less damaged. This difference is attributed to greater awareness of seismic risk and a long tradition of anti-seismic measures, consolidated over time thanks to historical earthquakes and local building regulations, such as the 18th-century building code wanted by Pope Pio IX (R.E. 1860). The results demonstrate that preventive measures can significantly reduce vulnerability, highlighting the need for tools that identify the most effective interventions and quantify their benefits. The AeDES forms (Baggio et al. 2007), from which the typological fragility curves are derived, classify buildings based on some structural parameters; if an intervention modifies one of these parameters, the building changes its structural typology and is therefore associated with a new fragility curve, which reflects a different expected seismic behavior. This enables a rapid assessment of the benefits of an intervention and supports the development of large-scale intervention plans that optimize the allocation of economic resources. 2. Methodologies of seismic risk and scenario analysis Seismic risk analysis allows for the quantification of economic losses of a specific structural typology by means of the combination of seismic hazard, vulnerability and exposure. Seismic vulnerability identifies the susceptibility of a structure to damage (Dolce et al., 2020), and can be expressed through fragility curves. These curves provide the probability of exceeding a certain damage level, conditioned to a specific intensity measure ( ), and are expressed by the following relationship: ( ≥ | ) = [ ( ) ] = 1,…,5 (1) where ( ≥ | ) representing the fragility curve, is the i-th damage level, defined according to the European Macroseismic Scale (EMS-98; Grünthal, 1998). Φ is the standard normal cumulative distribution, and are, respectively, the median and the standard deviation of the logarithm values of . As explained in Tatangelo et al. (2024), the fundamental parameters and can be derived using the Maximum Likelihood Estimation (MLE) method(Baker, 2013). This method maximizes the likelihood function, defined by the probability of observing a given sample realization, composed from the occurrence probability of the observed damage data. Therefore, the parameters and , for each fragility curve, are obtained by maximizing the logarithm of the likelihood function, which follows a binomial probability distribution. These parameters are derived as follows: ( 1 ,…, 5 , ) = ∑ ∑ 〈 ( )+ ∙ { [ ( ) ]}+( − ) ∙ { [ ( ) ]}〉 5 =1 = 1 (2) where ( 1 ,…, 5 , ) indicate, respectively, the median value and the standard deviation of the logarithmic values for each i . k j is the buildings number having a damage greater or equal than a specific damage level i , while z j is the buildings number in the j-th sub-sample having intensity measure . In order to evaluate economic losses, considering only direct costs, a procedure to derive the Expected Annual Loss ( ) is adopted (Tatangelo et al., 2023a-b). The average annual loss amount is calculated by integrating the loss curve, which considers the frequency and severity of various levels of seismic events.