## 3 Numerical Evaluation
### Validation of Numerical Model: Comparison with Experimental Results
Furthermore, the difference between the simulation and experimental results became more pronounced as the PGA increased, primarily due to the progressive cracking and cumulative damage in the specimens, which introduced nonlinearities not fully reflected in the numerical model. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**PGA.** & **Specimen** & \multicolumn{2}{c}{**MWN**} & \multicolumn{2}{c}{**MWP2**} & \multicolumn{2}{c}{**MWPF5**} \\
**Strain** & \multicolumn{2}{c}{**Y-Axis Stress**} & \multicolumn{2}{c}{**Strain**} & \multicolumn{2}{c}{**Y-Axis Stress**} & \multicolumn{2}{c}{**Strain**} & \multicolumn{2}{c}{**Y-Axis Stress**} \\
**(MPa)** & **Max.** & 0.00008 & 0.22 & 0.00006 & 0.15 & 0.00008 & 0.20 \\
0.1 g & Min. & \(-\)0.00007 & \(-\)0.20 & \(-\)0.00007 & \(-\)0.20 & \(-\)0.00010 & \(-\)0.25 \\ \hline \multirow{2}{*}{0.2 g} & Max. & 0.00012 & 0.32 & 0.00008 & 0.21 & 0.00011 & 0.28 \\  & Min. & \(-\)0.00001 & \(-\)0.27 & \(-\)0.00014 & \(-\)0.36 & \(-\)0.00012 & \(-\)0.30 \\ \hline \multirow{2}{*}{0.3 g} & Max. & 0.00019 & \multirow{2}{*}{0.52} & 0.00011 & 0.28 & 0.00017 & \multirow{2}{*}{0.45} \\  & Max. & \(-\)0.00019 & & & & (Crack occurred) & \\  & Min. & (Crack occurred) & \(-\)0.51 & \(-\)0.00011 & \(-\)0.29 & \(-\)0.00015 & \(-\)0.37 \\ \hline \multirow{2}{*}{0.4 g} & Max. & 0.00024 & \multirow{2}{*}{0.66} & 0.00009 & 0.25 & 0.00012 & 0.31 \\  & Min. & \(-\)0.00027 & & \(-\)0.00017 & \(-\)0.49 & \(-\)0.00020 & \multirow{2}{*}{\(-\)0.51} \\  & Min. & (Crack occurred) & \(-\)0.75 & (Crack occurred) & & & \\ \hline \multirow{2}{*}{0.5 g} & Max. & & 0.00014 & 0.40 & 0.00022 & 0.30 \\  & Min. & & & \(-\)0.00020 & \(-\)0.55 & \(-\)0.00031 & \(-\)0.23 \\  & Min. & & (Crack occurred) & & (Crack occurred) & & \\ \hline \multirow{2}{*}{0.6 g} & Max. & & 0.00016 & 0.43 & 0.00021 & 0.56 \\  & Min. & & (Crack occurred) & & (Crack occurred) & & \\  & Min. & & (Crack occurred) & & (Crack occurred) & & \\ \hline \multirow{2}{*}{0.7 g} & Max. & & 0.00015 & 0.41 & 0.00027 & 0.68 \\  & Min. & & (Crack occurred) & & (Crack occurred) & & \\  & Min. & & & (Crack occurred) & & (Crack occurred) & \\ \hline \multirow{2}{*}{0.8 g} & Max. & & 0.00015 & \multirow{2}{*}{0.41} & 0.00030 & \multirow{2}{*}{0.76} \\  & Min. & & (Crack occurred) & & (Crack occurred) & & \\ \hline \multirow{2}{*}{0.9 g} & Max. & & 0.00032 & \multirow{2}{*}{0.90} & 0.99 \\  & Min. & & & (Crack occurred) & (Failure occurred) & \\  & Min. & & & & (Crack occurred) & (Failure occurred) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Numerical results of shaking table test. Figure 12: Stress contours at initial failure: (**a**) MWN at 0.4 g; (**b**) MWP2 at 0.7 g; (**c**) MWFP5 0.8 g.  
While the modal dynamics method provides useful insights into the overall displacement and strain behavior of the structure, it has limitations in capturing progressive damage and nonlinear failure mechanisms. These limitations become more evident as the PGA increases. To overcome this, future studies may incorporate dynamic/explicit analysis, which enables the modeling of crack propagation, stiffness degradation, and more accurate failure modes under severe seismic loading.