# Risk and Resilience Assessment of Lisbon's School Buildings Based on Seismic Scenarios
## 2 State of the Art on Seismic Risk Assessment and Mitigation for School Buildings
### Analytical Approaches for Risk and Vulnerability Assessment  
Analytical risk and vulnerability assessments are an alternative to overcome the limitations of empirical methods [43]. Ideally, these methods should include all the sources of uncertainty, e.g., geometry, material properties, static loads, ground motion, etc. [44]. However, analytical fragilities based on numerical analyses, such as Finite Element Method (FEM) analyses, are generally time consuming, as multiple FEM models need to be generated and analyzed to include aleatory uncertainty. Despite this negative aspect, the development of numerical models and analysis of the buildings allow for a deeper understanding of their performance and, therefore, for the development of more optimized retrofitting designs for mitigation of seismic risk. A recent research project entitled \"_Progetto Scuole_\", whose main objective was to assess the seismic risk of a number of representative school buildings, was carried out at the Eucentre Foundation (Pavia, Italy), in collaboration with the University School for Advanced Studies IUSS, in Pavia, Italy [45; 46]. Three schools, representative of the Italian school building portfolio, were selected to be analyzed in detail through advanced numerical models developed using information collected during in situ inspections and calibrated with the results of ambient vibration measurements. Two site locations were also chosen to perform probabilistic seismic hazard analysis and select hazard-consistent ground motion record sets adopting the seismicity model used for the calculation of the Italian national seismic hazard map. Expected Annual Losses (EAL), including both structural and non-structural building components, were estimated following the procedure proposed in FEMA P-58. Losses were then used as a performance parameter to quantify the seismic vulnerability of the school buildings. Table 1 reports the EAL obtained by [PERSON] et al. [46] for the three buildings under study, namely the Reinforced Concrete (RC), the Unreinforced Masonry (URM), and the Precast Concrete (PC) buildings. The EAL values computed following the FEMA P-58 methodology were below 1% for all typologies at the considered site locations. The authors stated that these loss values appear to be in line with typical values of recent quantification studies on existing Italian buildings. URM school buildings were demonstrated to be the most vulnerable, out of the three considered, when assessing the expected losses with respect to increasing seismic intensity. Moreover, the authors computed the damage to non-structural elements and showed that it tends to dominate the EAL, constituting between 70% and 90% of the total, depending on the structural typology. Additionally in Italy, the ASSESS project [47] defined a 3-level methodological approach for defining priorities in inspection and retrofitting school buildings in order to reduce seismic risk in the Friuli Venezia Giulia region (NE Italy). [PERSON] et al. [4] developed a seismic risk assessment and mitigation analysis of more than 1000 public school buildings in the Manila Metropolitan region in the Philippines. The authors quantified different risk contributions and identified cost-drivers that can be targeted for performance-based risk management of large school portfolios. [PERSON] et al. [48] proposed a cost-benefit index and an innovative resilience indicator that helps to identify the best prioritization strategy for retrofit interventions. [PERSON] and [PERSON] [49] also proposed a cost-benefit methodology, based on numerical analysis of the buildings, to assess possible interventions, such as retrofitting or reconstruction of structures focused on mitigation of direct physical losses due to seismic actions. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Expected Annual Loss Ratios (\%)** & **RC** & **URM** & **PC** \\ \hline High seismicity site & 0.35\% & 0.48\% & 0.30\% \\ Medium seismicity site & 0.28\% & 0.33\% & 0.13\% \\ \hline \hline \end{tabular}
\end{table}