## 2 Analysis Conditions
### Ground Modeling  
Figure 1[14] shows the soil boring log of the holder installation ground and the one-dimensional finite element mesh used in the analysis. The first two meters of the surface layer was sandy buried soil (F layer), which was approximately six meters of the alluvial (or Holocene) sand layer (Yus layer, GL \(-2\) m-8 m) and approximately 14 m of the alluvial (or Holocene) clay layer (Ylc layer, GL \(-9\) m-23 m). A hard diluvium (or Pleistocene layer) with a large N value was deposited in the deep layer. The F and Yus layers have low liquefaction resistance, which indicates a high risk of liquefaction. The Ylc was a layer in the soft state because it was not only mainly silt but also had an N value of almost zero, and there were concerns that the layer, despite being clayey soil, would decrease in rigidity owing to large vibrations [22]. Figure 1c shows a finite element mesh for 1D analysis to characterize the seismic response of the ground, as mentioned later. Figure 2 shows the three-dimensional finite element mesh of the ground and holder used in the analysis. The fine sand To-s2 layer in Figure 1a was set as the engineering bedrock, and the upper side was analyzed in this study. The foundation was set as a horizontal layer, with the surrounding boring data as a reference. Additionally, JGA guidelines [15] defined the input seismic motion in one specific direction, which was used in the seismic evaluation system. Therefore, in this study, the input was in one direction, and the 1/2 cross-section model (31,968 elements, 34,552 nodes) assumed symmetry. In addition, ground motion incoherence effects are not taken into account because the structure to be evaluated is small, and it is not considered in the design [15]. The hydraulic boundary at the ground surface was always set to zero excess pore water pressure such that the ground surface coincided with the groundwater level, and the lower end and sides were set to non-drainage conditions. Periodic boundaries were also set on each side. Figure 1: Soil boring log and 1D FE mesh with boundary conditions: (**a**) soil log; (**b**) shear wave velocity comparison; (**c**) FE mesh and BCs. Table 1 lists the elasto-plastic properties of the soils used in this analysis. The material constants and state quantities were determined using the SYS Cam-clay model [12] to reproduce various mechanical tests of undisturbed samples collected from the target points. This did not simply involve reproducing the mechanical test results but instead taking the state at the time of deposition as the initial state and numerically reproducing the series of processes from sampling, testing machine set, and then laboratory test. This allowed for the estimation of state quantities during deposition using inverse analysis through the reproduction of the mechanical test results [22]. Figures 3-5 show the standard consolidation test, undrained triaxial compression test, and deformation properties due to the repeated loading of the Ylc layer as an example of the reproduced results. All test results were reproduced with the same material constants and initial values. For the initial values of the ground, it was assumed that the specific volume (density), degree of structure, stress ratio, and degree of anisotropy were uniform within the same layer, and the overconsolidation ratio was distributed according to the overburden pressure [23, 24]. When the shear wave velocity \(V_{s}\) of each layer was calculated based on the elasto-plastic properties of the soil, the distribution of the initial values obtained by the calculation roughly agreed with the results of the field measurements, as shown in Figure 1b. In this elasto-plastic analysis, the damping factor used in the equivalent linear analysis [25] is not used, whereas the variation of equivalent shear stiffness \(G_{eq}\) is specifically considered. Figure 2: 3D FE mesh of ground and holder foundation. \begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline \hline  &