# Risk and Resilience Assessment of Lisbon's School Buildings Based on Seismic Scenarios
## 4 Seismic Risk and Resilience Assessment Methodology
The estimated loss values and the number of interdiction days associated with each limit state are shown in Table 5. These values are defined based on the literature and existing risk assessment frameworks [60; 61]. Moreover, expected losses and recovery times are also computed for seven different seismic scenarios, presented in Table 6, that vary in the moment magnitude scale (M\({}_{\text{w}}\)), between 5.3 and 7.1. All seismic scenarios considered in this research study are intraplate  
Figure 9: Seismic performance matrix with identification of the admissible and non-admissible zone (matrix of the school _[PERSON]_). seismic scenarios, which correspond to the most relevant types of scenarios, as demonstrated in previous LNEC studies [56; 60]. These intraplate seismic scenarios are based on earthquakes occurring along the Lower Tagus Valley, which corresponds to Lisbon's nearest seismogenic source [56; 62; 63; 64]. This approach provides results associated with different earthquake intensities and corresponding different probabilities of occurrence, which help stakeholders (in this case CML) to identify vulnerable assets that need to be strengthened and suggest potential leverage points for intervention useful for decision making and planning of emergency responses, depending on the earthquake intensity. It is worth noting that the estimates obtained for each scenario assume that all available resources are allocated, without any limitation, thus not depending on the socioeconomic and political context that affect the decision making in a post-earthquake scenario. As a consequence, these estimates only depend on the expected damage level and associated recovery times of the school building portfolio. Both the probabilistic seismic hazard analysis and the seismic scenarios defined in this study for CML's schools are based on a hazard model that integrates the seismogenic zones defined in the ERSTA project, Seismic and Tsunami Risk Study of Algarve [65]. The action determined for Lisbon is then amplified, taking into account the specific geotechnical characteristics of the soils where the CML schools are located. These ground characteristics are determined based on the soil map produced by LNEC [57], which was built using the systematization of hundreds of geotechnical surveys. The 32 schools being studied in this research work are thus assigned a given soil type, as shown in Figure 1. Among the total number of schools, 14 are located in soil type A, which corresponds to stiff rock foundation. The other 14 are located in soil type H, whereas 3 are located in soil type I. Finally, only one school is located in soil type V, which corresponds to one of the softest soils in LNEC's soil cartography. A detailed description of each soil type may be found in previous LNEC studies [22]. Based on the ground type associated with each school, the seismic action at the bedrock is propagated to the surface using equivalent linear stochastic analysis. The details of this procedure can be obtained in [66]. The surface response spectra, deduced through equivalent linear Frequency Response Functions (FRF), associated with the four ground types considered, are represented in Figure 10 for seismic scenario 5 (return period of 475 years). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Scenario** & **Return Period (Years)** & **Magnitude (M\({}_{w}\))** \\ \hline
1 & 20 & 5.3 \\
2 & 50 & 5.8 \\
3 & 100 & 6.1 \\
4 & 275 & 6.6 \\
5 & 475 & 6.8 \\
6 & 1100 & 7.0 \\
7 & 2200 & 7.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Magnitudes and return periods associated with seven intraplate seismic scenarios. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Limit State** & **EL1** & **EL2** & **EL3** & **EL4** & **Ref.** \\ \hline \(\text{DF}_{\text{ELi}}\) & 1\% & 10\% & 75\% & 100\% & Sousa and Campos Costa [60] \\ \(\text{RT}_{\text{ELi}}\) & 1 day & 60 days & 240 days & 720 days & HAZUS v.4.2.3 [61] \\ \hline \hline \end{tabular}
\end{table}