## 4 Seismic Analysis
### Structural Finite Element Model
This model effectively captures the nonlinear behaviour of the infill struts, which has been studied by various researchers employing different material models. Examples include the early version of the Ibarra-Medina-Krawinkler model [26], the concrete material model [39], the Kent-Scott-Park model [29; 31], and the Lowes-Mitra-Altoontash model [29; 40]. The Lowes-Mitra-Altoontash model was selected because it allows for adjusting pinching effects and cyclic degradation in the infill panel, and its suitability for modelling infill struts has been validated by [PERSON] et al. (2017) [29]. Figure 8 (adapted from [41]) provides a schematic representation of the Lowes-Mitra-Altoontash model, highlighting the parameters essential for the calibration process. These parameters are indicated in bold. The hysteretic response in the Lowes-Mitra-Altoontash model comprises a response envelope, an unload-reload path, and three damage rules. Specifically, the multi-linear response envelope (solid lines in Figure 8) is defined by eight points (16 parameters), while the unload-reload path (dashed lines in Figure 8) is determined by four points (six parameters). The degradation of unloading stiffness, reloading stiffness, and strength is characterised by five parameters each, estimating the damage index based on displacement history and energy accumulation. Further details of the model are available in [PERSON] et al. (2004) [41]. \begin{table}
\begin{tabular}{c c c c c c} \hline \(F_{\text{yst}}\) (MPa) & \(E_{\text{st}}\) (MPa) & \(b\) & \(R_{0}\) & \(CR_{1}\) & \(CR_{2}\) \\ \hline
460 & 210,000 & 0.5\% & 20 & 0.925 & 0.15 \\ \hline \end{tabular}
\end{table} 
Table 6: Calibrated parameter values for the uniaxial material model Steel02. \begin{table}
\begin{tabular}{c c c c c c} \hline \(f_{\text{pc}}\) (MPa) & \(\epsilon_{\text{col}}\) (\%) & \(f_{\text{pu}}\) (MPa) & \(\epsilon_{\text{cu}}\) (\%) & \(f_{\text{ct}}\) (MPa) & \(E_{\text{t}}\) (MPa) & \(\lambda\) \\ \hline
28 & 0.001 & 5.6 & 0.008 & 2.8 & 1400 & 0.1 \\ \hline \end{tabular}
\end{table} 
Table 5: Calibrated parameter values for the uniaxial material model Concrete02. To determine the model parameters for the Lowes-Mitra-Altoontash model, we employed empirical equations proposed by [PERSON] et al. (2020) [42], which relate each backbone parameter to various geometric and material properties of the infilled frame. Table 7 presents a comprehensive statistical summary of the key structural parameters associated with the masonry infill walls and their surrounding frame in the building. The column height (\(h_{\text{col}}\)) is measured from the top of the base to the beam centreline, while the beam span (\(l_{\text{beam}}\)) is measured to the column centreline. The height and length of the infill panel are denoted as \(h_{\text{w}}\) and \(l_{\text{w}}\), respectively, and its thickness is represented by \(t_{\text{w}}\). The column axial demand is defined as Equation (1):  
\[N=0.85A_{\text{g}}\cdot f_{\text{pc}} \tag{1}\]  
where \(f_{\text{pc}}\) is the characteristic compressive strength of the concrete, and \(A_{\text{g}}\) is the gross cross-sectional area. The coefficient of 0.85 was assumed based on gravity analysis. It is important to note that in real buildings, a portion of the gravitational load may be transferred from structural beams to the infill panels. The masonry prism strength is denoted as \(f_{\text{m}}\), and the masonry modulus of elasticity is represented by \(E_{\text{m}}\) (excluded from Table 5). When \(E_{\text{m}}\) is not available, as in this study, an empirical relationship (Equation (2)) is recommended, as suggested by [PERSON] et al. (2007) [43] and FEMA 306 [44]. \[E_{\text{m}}=550\cdot f_{\text{m}} \tag{2}\]  
Thus, a value of 1375 MPa was adopted for this parameter. Table 7 includes the minimum, maximum, median, and mean values for each parameter.