## 4 Discussion  
### Effects of Distance Between Structures  
Figure 9a,b show averaged trends of \(\Delta\)PSD for S1 structure installed with S2 structure, and S3 structure at various distances, respectively. Average trends of \(\Delta\)PSD for S2, and S3 structures with S1 are plotted in Figure 9c,d, respectively. Error bars show a variation in results of the two input motions that indicates the similar trends, were observed for two input motions. The dashed line at zero \(\Delta\)PSD implies unchanged total power spectral density of structure due to SSSI effects. A negative value of \(\Delta\)PSD indicates that SSSI phenomena decrease the structure response. The \"unfavorable distance,\" ranging from \(\lambda/4\) to \(\lambda/2\) proposed by [PERSON] et al. [34], was also marked in Figure 8, where \(\lambda\) was soil wavelength induced by adjacent structure vibration during an earthquake. For example, when considering SSSI effects on S1 structure with S2 structure (Figure 9a), \(\lambda_{\text{S2}}\) was plotted. The \(\lambda\) value (=vs. \(\text{FF}\times\tilde{\text{T}}\)) is related to the free-field shear wave velocity (V\({}_{\text{s-FF}}\)) and the fundamental period of soil-foundation-structure systems (\(\tilde{\text{T}}\)), which can be defined from \(f_{flex}\) in Figure 6. Furthermore, [PERSON] et al. [33] have reported that versus \(\text{FF}\) is approximately 0.4 times of shear wave velocity measured at ground surface by in-flight bender elements array because shear modulus of soil will decrease with increasing shear strain. Note that the center-to-center distance between foundations defined in Table 3 was taken into comparison with the \"unfavorable distance\" range [34]. As shown in Figure 9, SSSI effects appeared at all tested distances between two structures regardless of input intensity. The response of S1 structure was reduced compared to reference motion because of interaction with S2 or S3 structures (Figure 9a,b respectively). The most significant reduction in response of S1 structure (i.e., the most considerable SSSI effect on S1 structure) was observed at B distance, which was approximately one-half of the wavelength (\(\lambda/2\)) or the lowest peak of the wave radiated from the adjacent structures (i.e., S2 or S3). When the distance decreased to \(\lambda/4\) or to the middle point of the radiation wave amplitude expected to have the lowest influence of radiation wave, the \(\Delta\)PSD value of S1 structure increased and approached zero value indicating SSSI effects on S1 structure decrease. In contrast to S1 structure behavior, SSSI effects increased the total power spectral density of S2 and S3 structures as illustrated in Figure 9c,d. Also, S2 and S3 structures experienced the lowest increment in response, at a distance of \(\lambda_{\text{S1}}/2\), with interacting S1 structure, while \(\Delta\)PSD of S2 and S3 structures surged when the distance between structures decreased. The reduction of S3 response at \(\lambda/4\) distance in case of S1-S3 (Figure 9d) could be attributed to two reasons: (1) AN increase in soil stiffness below S3 structure, due to closeness to a much heavier structure (i.e., S1), and (2) SSSI effects diminished with increasing height ratio between structures [32]. However, observed results for S1 and S2 structures in the S1-S2 case at H_Input level, with both input motions (i.e., dash-dot blue lines in Figure 9a,c still followed the above trend, although the most significant structure response was obtained at a distance of 0.5B. Due to the reduction in \(f_{flex}\) of these structures at H_Input level (Figure 6), compared to that at lower input intensities, adjacent structure vibrated with longer wavelength, causing peak response of S1 or S2 structure at a distance of 0.5B.