## 2 Model Preparation and Testing Procedure
### Experimental Program  
#### 2.2.1 Structure and Soil Modeling  
Three model buildings named S1, S2, and S3 with different masses and heights were designed to simulate theSSI effects between various structures in a megacity environment. Structure models were made as SDOF building composed of two thin plates and a lumped mass at the top. Aluminum was used because it was challenging to construct model structures with concrete. Table 1 shows dimensions of prototype structures with considering scaling laws. Foundation dimensions with equivalent radius (\(r_{f}=\sqrt{BL/\pi}\), where \(B=\) width and \(L=\) length of the foundation) were selected considering the size of each model, the size of the ESB container, and centrifugal acceleration. Height (\(h\), from bottom to center of lumped mass) of the structure was 9.4 m for S1, 8.25 m for S2, and 2.97 m for S3. Mass ratio (\(\psi=\mathrm{mass_{adjacent}}/\mathrm{mass_{reference}}\)) and height ratio (\(\chi=h_{adjacent}/h_{reference}\)) between adjacent and reference buildings are influential factors controlling SSSI phenomena [16; 17; 18; 30; 32]. In this study, to explore the effects of mass between adjacent buildings on SSSI phenomena, the mass of S1, the most massive structure, was pre-designed to be approximately 1.5 times larger than the mass of S2 and 15.3 times larger than that of S3. The mass ratio (\(\psi_{1.2}=\mathrm{m_{S1}}/\mathrm{m_{S2}}\)) between S1 and S2 was 1.5, while the mass ratio (\(\psi_{1.3}=\mathrm{m_{S1}}/\mathrm{m_{S3}}\)) between S1 and S3 was 15.3. Also, to investigate the effect of height ratio between adjacent structures, height ratios were pre-defined to be \(\chi_{1.2}=h_{\mathrm{S1}}/h_{\mathrm{S2}}=1.14\) for S1 and S2 structures and 3.16 for S1 and S3 (i.e., \(\chi_{1.3}=3.16\)). Therefore, in a tested case composed of S1 and S2 structures, the mass ratio \(\psi_{2.1}\) and height ratio \(\chi_{2.1}\) for S1 structure were 0.67, and 0.88 respectively, while these values were inversely calculated for S2 structure as \(\psi_{1.2}=1.5\) and \(\chi_{1.2}=1.14\). Similarly, for a series of tests with a configuration of S1 and S3 structures, the mass ratio \(\psi_{3.1}\) was 0.07 and the height ratio \(\chi_{3.1}\) was 0.32 for the S1 structure. For the S3 structure, \(\psi_{1.3}\) was 15.3 and \(\chi_{1.3}\) was 3.16. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Structures** & **S1** & **S2** & **S3** \\ \hline Dimensions at prototype scale (m) (Dimensions at 1 g) (mm) & & & \\ \hline Foundation dimensions: Width (\(B\)) & & & \\ \(\times\) Length (\(L\)) \(\times\) Thickness (\(T\)) (m) & & & \\ Foundation equivalent radius, \(r_{f}\) (m) & & & \\ Height, \(h\) (m) & & & \\ Mass at 1 g, \(m\) (kg) & & & \\ \(f_{n,modt}\) at 1 g, (Hz) (hammer test) & & & \\ \(f_{n}\) at 45 g, (Hz) & & & \\ Mass ratio, \(\psi=m_{\mathrm{S1}}/m\) & & & \\ Height ratio, \(\chi=h_{\mathrm{S1}}/h\) & & & \\ Factor of safety, \(F_{\mathrm{S}_{0}}\) & & & \\ \hline \hline \end{tabular} Note: \(r_{f}=\sqrt{BL/\pi};f_{n}=\) structural fixed-base frequency; \(T_{n}=\) structural fixed-based period.  
\end{table} 
Table 1: Dimensions and characteristics of structural models. Fixed-base natural frequencies of small-scale structure models (\(f_{\rm n,model}\)) were measured by the impact hammer test on fixed-based small-scale models and calculated by the fast Fourier transform (FFT) analysis from measured results. With reference to the scaling law [37], fixed-base natural frequencies (\(f_{\rm n}\)) of the prototype structures were calculated to be 2.19 Hz for S1, 1.82 Hz for S2, and 7.05 Hz for S3. [PERSON] et al. [16] have reported beneficial SSSI effects on structural response when the adjacent structure is shorter or has a higher fixed-base frequency. Since the S1 building was taller, but has higher stiffness and fixed-base frequency compared to the S2 structure, the influence of height ratio or fixed-base frequency ratio on SSSI could be differentiated between the S1 and S2 structures.