## 5 Numerical Analysis and Results  
In the first stage of the study, modal analysis was performed in order to examine the effect of seismic isolation on the free vibration behaviour of the structure and, as a result of the analysis, free vibration mode shapes and frequencies were obtained for each system (Figure 9). Performance limits were calculated according to TBEC 2018 (Turkish Building Earthquake Code-2018) (Table 5). Plastic rotations in construction elements were evaluated according to TBEC 2018 damage limits. As a result of the explosion analyses, the effect of explosives at different distances on the behaviour of the isolation units was also examined and the results were obtained comparatively. Isolator capacity is calculated as (D\({}_{\text{M}}\)) 0.778 m. When a vehicle with the effect of 227 kg TNT explodes at a distance of 5 m and 10 m, it is seen that the isolation unit  
Figure 8: (**a**) Explosion effects in structures with and without base isolation (**b**) Transferring the explosion load to the numerical model. Figure 9: Free vibration mode shapes and frequencies (**a**) Fixed Base; (**b**) Base Isolated. \begin{table}
\begin{tabular}{l l} \hline \hline
**Performance Limits** \\ \hline LS-1 (Immediate occupancy) & \(\theta_{\text{P}}=0\) \\ LS-2 (Life safety) & \(\theta_{\text{P}}=0.75\)\(\theta_{\text{P(LS-3)}}\) \\ LS-3 (Collapse Prevention) & \(\theta_{\text{P}}=(2/3(\theta_{\text{u}}-y)L_{\text{P}}\ (1-0.5\,\text{L}_{\text{P}}/\text{L}_{\text{s}})+4.5 \phi_{\text{u}}\text{d}_{\text{b}})\) \\ \hline LS: Limit state \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Performance damage limits for TBEC 2018 [31]. capacities targeted according to TBEC 2018 are exceeded and deformed, but if the same vehicle explodes at a distance of 15 m and 20 m, the isolation unit remains in the safe zone (Figure 10). In order to compare the building performances at different standoff distances, the shear forces occurring at the base of the building and the storey displacements were compared for the limit R\({}_{\text{G}}\) = 10 m where the islator capacity was exceeded, and the distance R\({}_{\text{G}}\) = 15 m where the isolation unit was in the safe zone. The reason for not making any comparison for R\({}_{\text{G}}\) = 5 m is the very high excess of the capacity. The high explosion pressure at 5 m, according to the data given in Table 2, also supports the analysis results. The time dependent variation of the base shear forces occurring in the structure as a result of the explosion at R\({}_{\text{G}}\) = 10 m and R\({}_{\text{G}}\) = 15 m is given comparatively in Figure 11 for base-isolated and non-isolated structures, considering the linear and nonlinear behaviour. The change of distance significantly differentiates the explosion effects occurring on the structure. It is seen that the base shear forces decrease in the building where seismic base isolation was applied. When linear analysis and nonlinear analysis methods are compared, nonlinear behaviour and permanent deformations occurred in the structure in large explosive effects (close standoff distance or increase in explosive amount) and smaller base shear forces occurred due to ductility according to linear analysis. Since it was estimated that two structures with and without seismic isolation would collapse for R\({}_{\text{G}}\) = 10 m, a detailed comparison of plastic hinge formations in the base-isolated and non-isolated structures was made for R\({}_{\text{G}}\) = 15 m, and the results are given in Figure 11. When Figure 12 is examined, although it was seen that there was a dense plastic hinge formation and some columns that became mechanisms in the seismic non-isolated state, the structural frame members in the isolated state were largely protected from explosion effects. In addition, there was no collapse at the ends of the structural frame members in seismic isolation. Figure 10: Comparison of hysteresis loops of the base isolators for different standoff distances under the blast load.