PSI - Issue 78

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

1997

phase and the repair/recovery time. Building upon the data collected on residential earthquake-damaged buildings after the 2009 L’Aquila earthquake in Italy, Di Ludovico et al. (2022) proposed empirical relationships between the direct costs for repair and population assistance. In this application, these formulations are adopted to assess the indirect losses due to earthquake-related damage to the building stock. The evaluation is performed for both “ Level 0 ” and “ Level ” 1 analyses, propagating the related uncertainties. Moving to cascading effects, at this stage of the research , only “inter - layer” effects are considered. The water distribution network is identified as a “master layer” for the building stock (“slave layer”) , i.e. a disruption to the water distribution network is expected to cause indirect losses for the building stock layer, even in the case of no damages to the structures. Some reasonable assumptions are made to estimate the possible impact of a disruption of the water distribution network: (i) a daily cost per person for water supply through alternative solutions (e.g., water tanker trucks) equal to = 5 €/( ∙ ) , (ii) a tributary area per person = 25 2 / (e.g., Calvi et al., 2021); a repair time for a node of the network equal to 21 days, with an upper bound of 90 days (e.g., Almufti and Willford, 2013). Moreover, it is also assumed that repairs may proceed in parallel or sequentially, leading to a range of possible recovery times and indirect losses. F or “Level 1” an alysis, the better estimation of damage to the water pipelines (break or leak) and the related decision-making process (repair vs. replacement) is also considered: 21 days is assumed for nodes where most pipes are repairable, and 90 days when replacement is needed. Results in terms of expected economic losses for the whole urban area are shown in Fig. 5b. As expected, moving from a lower level of analysis to a more refined one allows for a significant reduction in the dispersion value. Specifically, dispersion values are equal to 1.706 and 0.522 for Level 0 and Level 1 analyses, respectively. The reference value for economic losses from “ Level 1 ” analysis is slightly higher than the one from “ Level 0 ”, but still contained in the previous dispersion range. This suggests that stakeholders should conservatively consider the upper bound of expected losses when only basic urban data are available. Fig. 5b also highlights the contribution of each layer to the total loss of the urban area. In this virtual case study, repair costs of the water network are significant, mainly due to the low urban density assumed for illustration. More realistic results may be obtained by multiplying building stock losses by 5 – 10, which would also increase indirect losses from repair time and cascading effects.

(a)

(b)

Fig. 5. (a) Illustration of the evaluated indirect losses; (b) direct and indirect losses for the urban area, according to Level 0 and Level 1 analyses.

4. Conclusions This paper introduced an innovative framework for seismic vulnerability and risk assessment of urban areas. The proposed methodology employs a multi-scale approach, where loss analysis is performed starting from single assets/components (e.g., individual buildings, water pipelines), then moving to different clustered and interconnected layers (e.g., building stock, utility networks), and, finally, analyzing the whole urban area. Furthermore, the method relies on a multi-refinement level approach: alternative levels of analysis (from simplified to more refined) can be adopted depending on the quality and quantity of collected data (knowledge level). For each level of analysis, both expected and dispersion values are evaluated; uncertainties are propagated among the