# Seismic Fragility for a Masonry-Infilled RC (MIRC) Building Subjected to Liquefaction
## 2 Case Study
### Structural Model  
The benchmark MIRC structure was calibrated to be representative of a residential 3-storey concrete building with masonry walls and previously modeled [20] as Building 1 (B1) that is built up with three floors (3.4 m each, total height: 10.2 m), 4 columns in longitudinal direction (8 m spaced) and 2 ones in transversal direction (10 m spaced). The columns and the beams were modeled with fiber sections, by applying Concrete02 material for the core and the cove (Figure 5a,b and Table 3). The unloading slope (at maximum strength) and the initial slope are related with a ratio of 0.1. The bars were represented by Steel02 material (see Table 4) and 0.01 was chosen as the ratio between post-yield tangent and initial elastic tangent (Figure 6). Following [38], the transition parameters were: R0 = 15, CR1 and CR2 = 0.925 and 0.15, respectively, as suggested by [38]. Figure 7 shows the diagram moment-curvature of the section. Table 5 shows the characteristics of the elements in terms of cross sections and reinforcement details. Diagonal elasticBeamColumn elements [38] were used to model the masonry walls (both longitudinally and transversally) and with selected properties taken from Table C8A2.1 [42] and described in Table 6. In this regard, this may be considered a limited assumption since the interaction between frame and infill walls depends on the model adopted to simulate the infill wall behavior. In particular, this is due to the complexity of the problem and the computational burden required to complete the analyses, generally simplified models are employed to account for the nonlinear behavior of the superstructure, as shown in [43].  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Core** & **Cover** \\ \hline Compressive strength at 28 days (kPa) & \(-4.63\times 10^{4}\) & \(-2.76\times 10^{4}\) \\ Strain at maximum strength (\%) & \(-3.484\times 10^{-3}\) & \(-2.00\times 10^{-3}\) \\ Crushing strength (kPa) & \(-4.66\times 10^{4}\) & 0 \\ Strain at crushing strength (\%) & \(-3.57\times 10^{-3}\) & \(-6.00\times 10^{-3}\) \\ Tensile strength (kPa) & \(4.68\times 10^{3}\) & \(3.86\times 10^{3}\) \\ Tension softening stiffness (kPa) & \(1.86\times 10^{6}\) & \(1.93\times 10^{6}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Concrete02 (Core and Cover) characteristics.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Mass density (kN/m\({}^{3}\)) & 19.58 \\ Reference shear modulus (kPa) & \(5.80\times 10^{4}\) \\ Reference bulk modulus (kPa) & \(7.90\times 10^{4}\) \\ Shear wave velocity (m/s) & 173 \\ Friction angle (\({}^{\circ}\)) & 30 \\ Permeability (m/s) & \(10^{-8}\) \\ Peak angle (\({}^{\circ}\)) & 30 \\ c\({}_{1}\) & 0.07 \\ d\({}_{1}\) & 0.4 \\ d\({}_{2}\) & 2 \\ l\({}_{1}\) & 10 \\ l\({}_{2}\) & 0.01 \\ l\({}_{3}\) & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 2: 20 m soil parameters.  
Figure 5: Shear stress vs. shear strain relationship for (**a**) Concrete02: Cover; (**b**) Concrete02: Core.  
Figure 6: Shear stress vs. shear strain relationship for Steel02: Bars.