## 3 Experimental Results  
### Seismic Soil-Foundation-Structure Interaction (SFSI)  
In the dynamic structural analyses, although free-field (FF) motion is considered as input motion [3; 4], acceleration recorded at the foundation called foundation input motion (FIM) usually differs from FF due to kinematic interaction of SFSI. Furthermore, inertial interaction due to inertial vibration of structure mass can cause difference between earthquake motion recorded at structure and FIM when it propagates from the foundation [13]. To eliminate effects of FF amplification, 5% response spectra of the foundation motion were normalized to those of FF as the ratio of response spectra (RRS\({}_{\text{FIM}}\)) [39] while the inertial interaction was assessed by ratio of response spectra (RRS\({}_{\text{II}}\)) of roof motion (RM) to that of FIM [40]. Figure 4 shows RRS\({}_{\text{FIM}}\) and RRS\({}_{\text{II}}\) of S1 structure with artificial earthquake at three different input intensities. It could be seen that foundation response was amplified at around 7 Hz (Figure 4a) which was close to the foundation sliding frequency. Moreover, FIM was slightly amplified at around 1 Hz as a result of inertial response from the lumped-mass. Base-slap averaging effects of kinematic interaction on foundation response were indicated by the below unity of RRS\({}_{\text{FIM}}\) values at the high-frequency range over the foundation sliding frequency [13] as shown in Figure 4a. In Figure 4b, RM was amplified at dominant peak frequency (i.e., flexible-base frequency, _fflex_) which was 1.6 Hz at L_Input, 1.3 Hz at M_Input, and 1.0 Hz at H_Input. These values were slightly lower than the fixed-base natural frequency (_f\({}_{\text{n}}\)_ = 2.19 Hz) of S1 structure indicating period lengthening or frequency shortening of SFSI [2; 13]. With increasing seismic loading, the maximum RRS of RM, the peak of response spectra ratio indicated by solid circles in Figure 4b, and _fflex_ decreased due to degradation in stiffness of soil beneath structures with an increase in earthquake motion or strain level [13; 40; 41]. RRS\({}_{\text{II}}\) of S2 and S3 structures were also defined and plotted in Figure 5 with artificial input at L_Input which indicated period lengthening effect in SFSI of the two structures. Moreover, the higher and more massive structure (i.e., S1 structure) exhibited higher Max.RRS\({}_{\text{II}}\) because it had higher inertial characteristics (i.e., height and mass). \begin{table}
\begin{tabular}{c|c c c|c} \hline \multirow{2}{*}{**Case**} & \multicolumn{3}{c|}{**Distance**} & \multirow{2}{*}{**Remark**} \\ \cline{2-2} \cline{4-5}  & **B** & **0.5B** & **0.03B** & \\ \hline Ref. S1, S2, S3 & \(-\) & \(-\) & \(-\) & Three reference tests for S1, S2, S3 \\ \hline S1-S2 & \(\surd\) & \(\surd\) & \(\surd\) & S1 + S2 structures \\ D (m) & 10.4 & 7.8 & 5.4 & S1 + S2 structures \\ \hline S1-S3 & \(\surd\) & \(\surd\) & \(\surd\) & S1 + S3 structures \\ D (m) & 8.8 & 6.3 & 3.8 & S1 + S3 structures \\ \hlineFigure 6 shows variations of observed flexible-base frequencies (\(f_{flex}\)) of S1, S2, and S3 structures with three different levels of input excitation. Markers of connected lines indicate the average \(f_{flex}\) values with error bars showing a difference in results between two input motions at each level. For all structures, a similar trend was observed: \(f_{flex}\) of all structures decreased with increasing intensity of input excitation. In addition, a structure with higher \(f_{n}\) had a higher \(f_{flex}\) regardless of the input intensity. However, with increasing input intensity, the difference in \(f_{flex}\) of three structures reduced and converged at the highest observed input levels, due to difference in aspect ratio value A (A = \(h/r_{f}\), where \(h\) was height and \(r_{f}\) was foundation equivalent radius as shown in Table 1).