## 4 Seismic Analysis
### Structural Finite Element Model
Concrete02 requires several parameters: concrete compressive strength (\(f_{\text{pc}}\)), strain at maximum strength (\(\epsilon_{\text{c0}}\)), strain at crushing strength (\(\epsilon_{\text{cu}}\)), ultimate compressive strength (\(f_{\text{pu}}\)), maximum tensile strength (\(f_{\text{ct}}\)), and the elastic modulus in tension for unconfined concrete (\(E_{\text{t}}\)), along with a parameter (\(\lambda\)) defining the ratio between unloading stiffness and initial stiffness in compression, which was set to 0.1. These values (Table 5) were calibrated to match the preliminary properties of the building using sensor data and construction documents, which may result in differences from the original hospital building documents. While the empirical factors and sensor data tuned the finite element model by aligning it with the observed dynamic characteristics in reality, uncertainties inherently reside in the collected data or the calibration process itself. These consist of noises within sensor records, environmental conditions during those times of collection, and approximations that come with the numerical models, such as ideal behaviours of materials, boundary conditions, and structural elements. Issues are mitigated by using the averages of multiple repeat measurements and the deployment of more than one sensor for the purpose of cross-verification. However, these could not fully eliminate uncertainties and other issues. Further studies shall make provisions for direct material tests and sensitivity analyses to obtain a comprehensive quantification of uncertainties; refined calibration, in turn, has to be used for arriving at robust evaluations. The value of \(\epsilon_{\text{cu}}\) was obtained from JSCE (2007) [32] specifications, while \(f_{\text{ct}}\) and \(E_{\text{t}}\) were defined based on [PERSON] and [PERSON] (1994) [33]. The confined concrete behaviour was modelled using the parameters by [PERSON] et al. (1988) [34], depending on the arrangement of longitudinal and transverse reinforcement. The Steel02 model is an elastic-plastic material with isotropic strain hardening based on the Giuffre-Menegotto-Pinto formulation [35; 36]. The same values for the Steel02 model are used across all structural elements, depending on the steel class. The steel model parameters, detailed in Table 6, include \(F_{\text{yst}}\) and \(E_{\text{st}}\), which represent the yield strength of the reinforcing steel and the modulus of elasticity, respectively. The parameter \(b\) defines the ratio between the post-yield tangent and the initial elastic tangent, while \(R_{0}\), \(CR_{1}\), and \(CR_{2}\) control the transition from elastic to plastic behaviour, as outlined by [PERSON] et al. (1983) [37] and [PERSON] (2014) [38]. The building features a 190 mm thick reinforced concrete (RC) slab on each floor, which acts as an in-plane diaphragm, providing restraint between the nodes in both the frame and wall directions. To capture the in-plane effects, a rigid diaphragm constraint was applied to the slab nodes. Additionally, the cast-in-place concrete slab, integrated with the beams, influences the flexural deformability of the beams by adding out-of-plane stiffness, thereby affecting their nonlinear behaviour. To incorporate this out-of-plane contribution in the model, nonlinear response envelopes were utilised for the beams, which were based on an equivalent beam section that includes both the RC beam cross-section and the contribution of the rectangular flange at the top edge with a thickness matching that of the slab and an effective width. RC walls are simulated by adopting a distributed plasticity approach via the force-based-column element with five integration points and the Gauss-Lobatto integration scheme. The impact of masonry infilled frames on the seismic response was also investigated. The infill panel was represented by two diagonal struts (one in each direction) modelled as truss elements using the Lowes-Mitra-Altoontash pinching material model.