# Risk and Resilience Assessment of Lisbon's School Buildings Based on Seismic Scenarios
## 4 Seismic Risk and Resilience Assessment Methodology  
In terms of assessing the seismic performance of buildings and their structural and non-structural elements, one of the most comprehensive performance-based earthquake engineering (PBEE) methodologies was initially conceived by [PERSON] and [PERSON] [27] and then adopted by the Pacific Earthquake Engineering Research (PEER) Center. The PEER PBEE framework includes a number of analysis stages and variables, illustrated in Figure 4. Firstly, hazard analysis is conducted based on the rupture and local site details D, yielding the definition of the intensity measure IM to be used in the subsequent analysis. Secondly, structural analysis is carried out, relating the intensity measure of the seismic action to the structural response, which is characterized by an engineering demand parameter EDP. Thirdly, damage analysis allows for the definition of a relationship between structural response (EDP) and a damage measure DM. Finally, loss analysis is conducted to provide information for a final consequence analysis of performance measures referred to as decision variables (DV), such as the expected losses and probability of collapse. In this work, the analysis of the seismic performance of schools and the definition of an intervention plan to mitigate the seismic risk is based on the following fundamental steps, illustrated in Figure 5. First, the main buildings of the school under analysis are characterized according to the previously mentioned structural typologies, creating groups that differ in the type of structural analysis to be carried out. Second, seismic action is characterized, based on a probabilistic study of the seismic hazard [56], at each school location taking into account site effects due to soil conditions, which are quantified based on the available information at LNEC [57]. Afterwards, seismic response assessment is  
Figure 3: Total number of schools in each structural typology (total: 32 schools) (**left**); total number of main buildings in each structural typology (total: 85 main buildings) (**right**). performed using different numerical modeling procedures. Nonlinear numerical models of two of the schools, represented in Figure 6, are developed in the Seismosoft's SeismoStruct software, Version 2021--Release 3 [24], allowing for the evaluation of the structural behavior and the nonlinear response of each main building for different seismic intensity levels, which serves to calculate the expected losses in terms of the school's built-up area and recovery times (number of days of interdiction). Figure 4: Illustration of the four stages of the PEER PBE framework (adapted from [27]). Figure 5: Overview of the assessment methodology employed for the Lisbon City Council school building portfolio. Numerical models of RC buildings are based on force-based beam-column frame elements with fiber-discretized sections. Each beam-column element has seven integration points along its length and 150 uniaxial fibers defined in their cross sections, which are assigned stress-strain phenomenological models. Concrete fibers are assigned the model proposed by [PERSON] et al. [58], while fibers associated with reinforcing steel bars are assigned the Giuffre-Menegotto-Pinto [59] model. The confinement effects provided by the lateral transverse reinforcement are incorporated through the rules proposed by [PERSON] et al. [58] whereby constant confining pressure is assumed throughout the entire stress-strain range. In what concerns composite structures, masonry piers and spandrels are modeled through equivalent nonlinear frame elements with fiber sections. The uniaxial masonry fiber response is based on the Seismostruct parabolic masonry model, which consists of a uniaxial material model for masonry that is based on the hysteretic rules of the constant confinement concrete model [58]. Material parameters assumed for the aforementioned models vary among schools. Whenever possible, material parameters are taken from the school project drawings or complementary information.