## 3 Sensitivity Study on Vertical Seismic Isolation Performance with VIF  
In principle, the basic concept of seismic isolation design is to design an appropriate seismic isolation frequency to avoid resonance with input earthquakes by moving the natural frequency of the superstructure in the frequency range of a strong earthquake to a sufficiently low frequency using a seismic isolator. In general, the vertical natural frequency of a nuclear power plant building is around 10-20 Hz, which is out of the range of peak spectral frequency band, 3 Hz to 10 Hz in the US NRC RG-1.60 design ground-response spectrum [22]. However, there is possibility of resonance seismic response if the earthquake level increases enough to invoke severe cracks in the nuclear power plant building structures. In this case, the spectral peak frequencies of the response spectrum at the floor where the nuclear power plant equipment is seismically isolated may be shifted to a lower region due to the decrease of the structural stiffness of the nuclear power plant building. This situation can cause severe vertical seismic response amplification in nuclear power plants. Therefore, in the vertical seismic isolation design of nuclear power plants against a large earthquake, it is very important to determine the \begin{table}
\begin{tabular}{c c c} \hline \hline
**Design VIF** & \
\begin{tabular}{c} **Required Vertical** \\ **Stiffness** \\ **(kN/m)** \\ \end{tabular} &
\begin{tabular}{c} **Static Disp. for 10 kN** \\ **(mm)** \\ \end{tabular} \\ \hline
1.0 & 39.5 & 253.3 \\
2.0 & 157.9 & 63.3 \\
2.5 & 246.7 & 40.5 \\
3.0 & 355.3 & 28.1 \\
3.5 & 483.6 & 20.7 \\
4.0 & 631.7 & 15.8 \\
5.0 & 987.0 & 10.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameter values for simple seismic analysis model. Figure 2: Schematics of 3D seismic isolator’s motions: (**a**) Without loads; (**b**) with vertical static load; (**c**) with horizontal and vertical seismic loads. design VIF that can deviate from the floor-response spectrum peak frequency band and the resonant frequency of the upper structure. In this study, a remote shutdown console (RSC), which is installed at elevation of 136 ft of an actual nuclear power plant building, is chosen as one of the target 3D seismic isolation equipment. To investigate the sensitivity of the VIF, the vertical seismic isolation performance analyses are carried out with the preliminary specified design parameters of the vertical seismic isolation device, as shown in Table 3.  
Figure 3 presents the input earthquake used in the design of the vertical seismic isolation device in this study. Figure 3a is the vertical floor-response spectrum at 136 ft of the auxiliary building, corresponding to the peak ground acceleration, PGA = 0.5 g, which is 1.67 times the Safe Shutdown Earthquake (PGA = 0.3 g). We can see that the peak spectral frequency band exists at 10 Hz to 16 Hz and the peak spectral acceleration is large at about 40 g. As shown in Figure 3b,c, the zero-period acceleration (ZPA) value is 1.2 g, and the peak/valley displacements are \(-\)211 mm/+176 mm. Figure 4 presents the simple seismic analysis model used for the sensitivity of the vertical seismic isolation performance on the VIF. For the transient seismic time history analysis, a commercial finite element program ANSYS [23] was used. As shown in Figure 4a, the vertical spring is modeled by a simple stiffness-damping element (COMBIN14), and the vertical damper is model with a bilinear force-displacement element (COMBIN40), reflecting the hysteretic characteristics of the steel damper. It was assumed that the inertia mass of the superstructure acts as a concentrated mass (MASS21) at node 3. Figure 4b shows the concept of the bilinear model of the steel damper. Figure 3: Used vertical seismic input motion (PGA = 0.5 g): (**a**) Floor response spectrum; (**b**) acceleration time history; (**c**) displacement time history.