## 5 Results and Discussion  
SFSI analyses are performed for different foundation block sizes (\(2a\times 2b\)) with dimensions of (10 m \(\times\) 10 m), (20 m \(\times\) 20 m), and (30 m \(\times\) 30 m) to examine the effect of foundation block size on the dynamic behavior of the superstructures. The mass density of the foundation block, with a constant height of \(h=1\) m, is \(\rho_{\textit{filled}}=2.5\) t/m\({}^{3}\). In the analyses, the height of the superstructures is kept constant at \(H=14\) m.  
In the interaction between the soil and the superstructure, reducing the foundation block size causes significant changes in SD values (Figure 7). When the analyses are conducted for a foundation block of (10 m \(\times\) 10 m), SD values vary according to soil type. As shown in Figure 7, the SD values for superstructures interacting with hard soils (such as ZB and ZC) are higher compared to those on soft soils (such as ZD and ZE). This difference arises because the equivalent earthquake loads are reduced by the increased flexibility and damping in soil-interacting structures on relatively soft soils. This result is consistent with findings from published studies [28; 29; 30; 31]. It is observed that this flexibility is more pronounced in buildings with smaller foundations situated on soft soils. As the foundation block dimensions increase from (10 m \(\times\) 10 m) to (20 m \(\times\) 20 m) and (30 m \(\times\) 30 m), the spectral displacement (SD) values for each soil type converge for all superstructure systems \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Soil Type**} & \multirow{2}{*}{\begin{tabular}{c} **Mass Density** \\ \(\rho\) **(kg/m\({}^{3}\))** \\ \end{tabular} } & \begin{tabular}{c} **Horizontal Translation:** \\ **Shear Waves** \\ **Velocity (\(c_{s}\))** \\ **(m/s)** \\ \end{tabular} & \begin{tabular}{c} **Rocking:** \\ **Dilatational Waves** \\ **Velocity (\(c_{p}\))** \\ **(m/s)** \\ \end{tabular} & \
\begin{tabular}{c} **Constrained** \\ **Elastic Modulus** \\ **(\(E_{c}\)) (N/m\({}^{2}\))** \\ \end{tabular} &
\begin{tabular}{c} **Shear Modulus** \\ **(G) (N/m\({}^{2}\))** \\ \end{tabular} \\ \hline ZB & 2200 & 1130 & 2260 & \(1.124\times 10^{10}\) & \(2.809\times 10^{9}\) \\ ZC & 2000 & 560 & 1120 & \(2.509\times 10^{9}\) & \(6.272\times 10^{8}\) \\ ZD & 1900 & 270 & 540 & \(5.54\times 10^{8}\) & \(1.385\times 10^{8}\) \\ ZE & 1800 & 90 & 180 & \(5.832\times 10^{7}\) & \(1.458\times 10^{7}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Soil characteristics. Figure 6: The north–south acceleration component of the 1940 El Centro earthquake. (Figures 8 and 9). For superstructures with larger foundation blocks, the response values increase regardless of soil type. The primary reason for this increase is the higher mass of the foundation block, which results in larger earthquake forces. This increase suppresses the damping effect of the soil and causes the structure to behave like a fixed-base structure. In soil-interacting structures, the system's flexibility increases compared to a fixed-base structure, altering the natural vibration periods of the structures. Analyzing the spectral acceleration (SA) values for a structure with a smaller foundation size (10 m \(\times\) 10 m) shows that as the soil becomes softer, the spectral characteristic periods (or corner periods, \(T_{A}\) and \(T_{B}\)), which define the boundary values of the plateau region in the acceleration response spectra, increase (Figure 10). Moreover, for systems with small foundations on soft soils, the plateau region of the spectrum is extended compared to that of the non-interacting system (represented by the thick continuous line in Figure 10). This extension implies that the period value used in the design of the non-interacting system would fall within the plateau region of the soft-soil interacting system. Figure 8: Effect of soil type on the SD response of structures with (20 m \(\times\) 20 m) foundation blocks.