PSI - Issue 78

Livio Pedone et al. / Procedia Structural Integrity 78 (2026) 1991–1998

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building-by-building vulnerability and loss assessment, adopting to the methodology illustrated in Fig. 3b. Operatively, the building footprints are first regularized, and a possible structural skeleton is assumed. Consequently, a “simulated design” procedure is implemented to define the complete structural system. Then, the building’s capacity curve is evaluated using the SLaMA (Simple Lateral Mechanism Analysis, NZSEE 2017; Pampanin, 2017) method. To account for missing data at this knowledge level, a parametric analysis is also implemented, considering differences in material properties and reinforcement/construction details. Results of the SLaMA method are then used to assess fragility relationships through simplified pushover-based methodologies (e.g., Kircher et al., 2006). Finally, similarly to “Level 0”, building -specific fragility relationships are used to define building-level vulnerability models. This procedure is implemented for each parametric SLaMA-based capacity curve, thus obtaining an expected range/domain of vulnerability relationships for each case-study building. Again, vulnerability models allow for the evaluation of the expected direct losses in scenario-based seismic risk assessment. For the WDN, when more information is available, a more detailed and refined approach is adopted. In this case, the required input data includes: (i) the network geometry (modelled as a graph in the code), (ii) the physical properties of the pipes (material, diameter, construction period), (iii) cost estimation for interventions (replacement and repair of the pipes), and (iv) the expected seismic intensity. The adopted procedure allows for finding critical segments of the network characterized by a higher probability of failure starting from a generic configuration of the water system, which includes pipes made of different materials (brittle or ductile). The adopted method - described exhaustively in Mazumder et al. (2020) - is characterized by four steps: (i) seismic intensity estimation; (ii) fragility analysis; (iii) damage and cost analysis; and (iv) a decision-making process depending on weights and importance assigned to each of the aspects of the vulnerability analysis. More details can be found in the cited papers. Results in terms of direct economic losses for the building stock and the WDN are shown in Fig. 4a and Fig. 4b, respectively. For both layers, a significant dispersion is observed in the results of the “Level 0” analysis, mainly due to the severe uncertainties related to this level of knowledge. Yet, Level 0 analysis still provides a quantitative assessment of the expected direct economic losses, which can represent valuable information for different end-users and stakeholders. By comparing the results of the “Level 1” analysis with those related to “Level 0”, a higher expected value is obtained for both layers. Yet, the expected value for direct losses of “Level 1” analysis is still included in the expected range obtained in the previous refinement level. Most importantly, moving from “Level 0” to “Level 1” allows for a reduction in the dispersion values, in line with the philosophy of the proposed framework.

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Fig. 4. Direct losses for (a) the building stock layer and (b) the water distribution network, according to Level 0 and Level 1 analyses.

3.3. Urban area loss assessment: indirect losses and layer interaction Results in terms of direct economic losses for each layer are used to evaluate the expected impact at the urban area scale. The first fundamental step consists of estimating the indirect economic losses, which can be related to a loss of functionality of a specific asset due to (i) the recovery time from direct earthquake damage and/or (ii) possible cascading effects, either intra-layer or inter-layer (Fig. 5a). Concerning the residential building stock, one of the main causes of indirect losses is the relocation cost of the displaced occupants during both the emergency