## 2 Analysis Conditions
### Holder Modeling  
Figure 6 shows a schematic diagram of the holder to be analyzed, and Table 2 lists its specifications. An analysis model was created based on these specifications; Figure 7 shows the finite element mesh diagram of the holder, and Table 3 lists the material constants of the holder, foundation, and pile. All structural members were modeled using hexahedral solid elements with a single-phase hypoelastic material [26]. As shown in Figure 6, the  
Figure 4: Undrained triaxial test of the Ylc layer (experimental and reproduction results): (**a**) Shear strain; (**b**) Mean effective stress.  
Figure 5: Dynamic deformation properties of the Ylc layer (experimental and reproduction results).  
Figure 3: Standard consolidation test of the Ylc layer (experimental and reproduction results).  
actual structure has four piles arranged per footing. Each footing was treated as a single unit in this analysis, and the four piles were modeled as a single solid element such that the flexural rigidity was equivalent to that of the actual product. The elastic modulus was set according to the actual material of the structural members other than the columns; however, the elastic modulus of the columns was set in consideration of the presence of the brace so that the natural period of the entire holder matched the actual value of 0.786 s (see Appendix A for the adjustment method). The piles were modeled as a bilinear elastic body by reducing the elastic modulus to 1/200 [27] when the relationship between the axial force N and bending moment M calculated from the solid elements exceeded the region of the M-N failure diagram [28] of the piles, as shown in Figure 8.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Items** & **Value** \\ \hline Nominal capacity & 200,000 m\({}^{3}\) \\ Design pressure & 0.83 MPa \\ Inner diameter of the spherical shell & 35.560 m \\ Inner diameter of the foundation & 35.330 m \\ Holder equatorial height & 19.000 m \\ Thickness of the spherical shell plate & 35.0 mm \\ Outer diameter, thickness, and number of column & \(\varphi\)600 mm \(\times\) 8 mm \(\times\) 14 pcs. \\ \multicolumn{2}{c}{High tensile steel} \\ Material of the spherical shell and columns & (DIS G3128; WEL-TENS70C) \\ Outer diameter of the braces & \(\varphi\)90 mm \\ Material of the braces & High strength steel \\ \multicolumn{2}{c}{(HBS G3102; HT690)} \\ \hline \hline \end{tabular}
\end{table}
Table 2: Holder specifications.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Unit Volume** & **Elastic Modulus** & \\  & **Weight (kN/m\({}^{3}\))** & **(kN/m\({}^{3}\))** & **Poisson’s Ratio** \\ \hline Footing, Core & 25.00 & 2.35 \(\times 10^{7}\) & 0.2 \\ Radial beam & 18.86 & \(1.07\times 10^{6}\) & 0.2 \\ Underground beam & 22.66 & \(1.85\times 10^{7}\) & 0.2 \\ Perimeter reinforcement beam & 15.09 & \(0.77\times 10^{7}\) & 0.2 \\ Column & 0.448 & \(1.70\times 10^{7}\) & 0.3 \\ Spherical shell & 3.953 & \(2.10\times 10^{8}\) & 0.3 \\ Pile under the column & 2.935 & \(3.19\times 10^{5}\) & 0.2 \\ Pile under the core & 2.390 & \(2.22\times 10^{5}\) & 0.2 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Holder foundation/body material constants.  
Figure 6: Spherical gas holder (analysis subject).  
The upper load acting on the ground (dead weight of the holder and pile) was shared by the bottom foundation (radiant and annular beams in this analysis), the tip-bearing force (axial force of the pile), and the frictional force on the peripheral surface of the pile. Assuming that the pile is solely responsible for the entire holder load of approximately 6800 kN, the axial force acting on each pile is approximately 240 kN. This is described in more detail later, but the axial force acting on a single pile at the time prior to the earthquake input is approximately one-half; thus, the difference is shared by the bottom foundation and the peripheral surface of the pile.