## 2 Model Preparation and Testing Procedure
### Soil Models  
Three ground models were prepared, including uniform (Uni) and two layered soil profiles (L1 and L2), as shown in Figure 1. Considering the scaling law [18], the total thickness of the prototype ground was equivalent to 27 m. The layered profiles included a relatively thin low stiffness layer laid over a higher stiffness layer, and a uniform profile contained only the low stiffness layer. The thickness of the low stiffness upper layer (T) was 2.6 m for profile L1, 5.2 m for L2, and 27 m for the Uni profile, which is approximately 0.5, 1.0, and 5.0 times the foundation width (B) of the S1 structure. Figure 1 shows the cross-sections of ground soils modeled in the ESB container at a prototype scale for the centrifuge experiments. Two types of soil were used in this study, a poor-graded silica sand for preparing the low stiffness layer and a mixture of small pebbles with weathered soil to simulate the high stiffness layer. An air-pluviation method was used to prepare the low stiffness layer that uses the silica sand with a relative density (\(D_{r}\)) of about 80%, corresponding to a dry density (\(\rho\)) of 1.54 t/m\({}^{3}\). The high stiffness soil was prepared by mixing soil with a weight ratio of 45% pebbles and 55% weathered soil at the optimum water content (\(\omega_{opt}\)) to obtain its maximum dry unit weight and shear stiffness (\(G\)). Note that \(\omega_{opt}\) of the mixture was defined as approximately 10.5% based on standard compaction test results. The high stiffness layer was divided into several thin layers (i.e., the thickness of 5 cm in model scale) and was carefully tamped until reaching the pre-determined unit weight. The resonant column (RC) tests were performed on the soil samples under the same conditions (i.e., \(D_{r}\), unit weight, and water content) as the soil in the models to find the variation of shear modulus degradation and damping curves of the two soils under different confinements.  
An array of bender elements (BE) was placed in the ESB container to measure the shear wave velocity profile of the ground at the given centrifugal acceleration. The shear wave profiles measured for Uni, L1, and L2 profiles are plotted in Figure 1. The measured V\({}_{\rm s}\) profile for the silica sand layer matched the results of the resonant column (RC) tests well on specimens with the same conditions as the soils in the ESB container. The measured Vs  
Figure 1: Three soil profiles with an in-flight bender element, accelerometer (left), and shear wave velocity (V\({}_{\rm s}\)) profile (right) at (**a**) Uni: uniform ground, (**b**) L1: ground with 2.6 m soft above layer, and (**c**) L2: ground with 5.2 m soft above layer. Unit: m.  
for the high stiffness layer shows relatively high values compared to the low stiffness layer. The free-field shear wave velocity (V\({}_{\rm{s,FF}}\)) was measured to be about 95 m/s for all three soil profiles. The estimated shear modulus suggested that the shear stiffness of the stiff lower layer was approximately 3.9 times that of the soft upper layer (\(G_{2}/G_{1}\) = 3.9, as shown in Figure 1). Note that the dashed lines in the figure were calculated by a power function of mean effective stress, which increased with model depth [19]. The site fundamental frequencies (\(f_{\rm{G}}\)), which can be calculated from the V\({}_{\rm{s}}\) profile, were 2.02 Hz, 2.60 Hz, and 2.50 Hz for Uni, L1, and L2 profiles, respectively [20].