## 3 Numerical Evaluation
### Numerical Modeling of Shaking Table Test  
The finite element models of specimens MWN, MWP2, and MWPF5 using the simplified micro-method are summarized in Figure 9. Figure 9,c indicate that the STPU does not entirely cover the masonry wall. However, this is a visual result of modeling the STPU as a shell element such that it reinforces the entire surface of the masonry wall. The mesh size of the expanded unit is 50 mm with 8 nodes element type C3 DBR applied. For the reinforced materials (STPU and GFRP), 30 mm of mesh size and the S4R element type are applied. The mesh size of the expanded unit is 50 mm with 8 nodes element type C3D8R applied. For the reinforced materials (STPU and GFRP), 30 mm of mesh size and the S4R element type are applied. Prior to performing the main seismic analysis, a modal analysis was first conducted to determine the structure's natural frequencies and corresponding mode shapes. The first mode, with a natural frequency of approximately 8.0 Hz, was then adopted for the modal dynamics analysis. The seismic analysis used modal dynamics, and a 5% damping condition, which is used in general masonry wall structures, was applied. Although modal dynamics analysis does not allow direct observation of crack propagation or structural failure modes, it offers significant advantages in reducing computational time. Failure prediction was addressed indirectly by analyzing strain data at each PGA level and comparing it with the material's strain capacity. Although modal dynamics analysis typically involves combining multiple vibration modes, only the first mode was used in this study. This is because the first out-of-plane mode dominated the dynamic response of the masonry wall due to the structure's geometry, boundary conditions, and the frequency content of the input ground motion. The El Centro record used in this study has dominant frequency content near the first mode frequency (approximately 8.0 Hz), making the contribution of higher modes negligible. The boundary condition used in the actual experiment is similar to that employed in the simulation analysis. It is applied to the six degrees of freedom (DOF) of the bottom of the specimen as a fixed condition, as shown in Figure 10. The seismic load was applied to the bottom of the specimen in terms of acceleration, and the gravity load was employed to describe the action of inertia during the seismic load application. To ensure similarity between the experimental and simulation results, the analysis was performed using the acceleration data for each seismic load collected in the shaking table test. Table 4 presents the defined contact interface properties between the \begin{table}
\begin{tabular}{c c} \hline
**GFRP Elastic Property** & **Value** \\ \hline Density (kg/m\({}^{3}\)) & 1900 \\ Longitudinal modulus, \(E_{1}\) (GPa) & 73 \\ Transverse modulus, \(E_{2}\) (GPa) & 18 \\ In-plane Poisson’s ratio, \(\
u_{12}\) & 0.25 \\ In-plane shear modulus, \(G_{12}\) (GPa) & 9 \\ Transverse shear modulus, \(G_{13}\) (GPa) & 9 \\ Through-thickness shear modulus, \(G_{23}\) (GPa) & 7 \\ \hline \end{tabular}
\end{table} 
Table 2: Material properties of lamina type GFRP [41]. \begin{table}
\begin{tabular}{c c} \hline
**Fail Stress Property** & **Fail Stress** \\ \hline Tensile stress in fiber direction (MPa) & 1500 \\ Compressive stress in fiber direction (MPa) & \(-\)700 \\ Tensile stress in transverse direction (MPa) & 90 \\ Compressive stress in transverse direction (MPa) & \(-\)140 \\ Shear strength (MPa) & 6 \\ \hline \end{tabular}
\end{table} 
Table 3: Fail stresses of GFRP used in simulation [41]. expanded units, the STPU layer, and the laminated GFRP based on previous studies [37,41]. In the Abaqus simulation, the interface between the FRP and the masonry wall was defined using a surface-based cohesive contact. The damage-initiation criterion was set to the maximum nominal stress method, with critical values of 2.7 MPa for the normal direction and 0.88 MPa for both shear directions (Shear-1 and Shear-2).