## 4 Numerical Results and Discussion
It is observed that the BI mitigates the superstructure dynamic responses by 80-90%, while the VCS reductions are in the range of 70-80%. Figure 8 presents the base relative displacements expressed as a percentage of the BI values. The VCS system manages to retain the \(u_{B}\) in the order of a few centimetres, 70-90% lower as compared to the BI. In Tables 2-4 are the main dynamic responses of the OS, BI and VCS for all the artificial accelerograms of the \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**OS**} & \multicolumn{2}{c}{**BI**} & \multicolumn{2}{c}{**VCS**} \\ \cline{2-9}  & \multicolumn{1}{c}{**Max(\(a_{S}\))**} & \multicolumn{1}{c}{**Max(\(d_{H}\))**} & \multicolumn{1}{c}{**Max(\(a_{S}\))**} & \multicolumn{1}{c}{**Max(\(d_{H}\))**} & \multicolumn{1}{c}{**Max(\(u_{B}\))**} & \multicolumn{1}{c}{**Max(\(a_{S}\))**} & \multicolumn{1}{c}{**Max(\(d_{H}\))**} & \multicolumn{1}{c}{**Max(\(u_{B}\))**} \\  & **(g)** & **(cm)** & **(g)** & **(cm)** & **(cm)** & **(cm)** & **(g)** & **(cm)** & **(cm)** \\ \hline acc \#1 & 1.93 & 5.08 & 0.25 & 0.76 & 31.20 & 0.54 & 1.44 & 7.89 \\ acc \#2 & 2.11 & 5.82 & 0.27 & 0.80 & 33.27 & 0.46 & 1.27 & 11.31 \\ acc \#3 & 2.11 & 5.82 & 0.27 & 0.80 & 33.27 & 0.46 & 1.27 & 11.31 \\ acc \#4 & 1.97 & 5.15 & 0.19 & 0.61 & 24.85 & 0.56 & 1.38 & 8.51 \\ acc \#5 & 1.97 & 5.15 & 0.19 & 0.61 & 24.85 & 0.56 & 1.38 & 8.51 \\ acc \#6 & 1.80 & 5.31 & 0.23 & 0.67 & 27.34 & 0.47 & 1.24 & 7.18 \\ acc \#7 & 2.48 & 6.36 & 0.23 & 0.72 & 30.11 & 0.46 & 1.24 & 6.54 \\ acc \#8 & 1.78 & 4.93 & 0.23 & 0.71 & 29.04 & 0.47 & 1.26 & 6.60 \\ acc \#9 & 1.78 & 4.93 & 0.23 & 0.71 & 29.04 & 0.47 & 1.26 & 6.60 \\ acc \#10 & 2.36 & 5.86 & 0.25 & 0.77 & 32.41 & 0.51 & 1.35 & 8.65 \\ \hline
**Average** & 2.03 & 5.44 & 0.23 & 0.72 & 29.54 & 0.50 & 1.31 & 8.31 \\ \hline
**Reduction** & \multicolumn{1}{c}{**-**} & \multicolumn{1}{c}{**-**} & \multicolumn{1}{c}{**88.7**} & \multicolumn{1}{c}{**86.8**} & \multicolumn{1}{c}{**-**} & \multicolumn{1}{c}{**75.4**} & \multicolumn{1}{c}{**75.9**} & \multicolumn{1}{c}{**71.9**} \\ \cline{2-9}
**(\%)** & \multicolumn{1}{c}{**-**} & \multicolumn{1}{c}{**-**} & \multicolumn{1}{c}{**88.7**} & \multicolumn{1}{c}{**86.8**} & \multicolumn{1}{c}{**-**} & \multicolumn{1}{c}{**75.4**} & \multicolumn{1}{c}{**75.4**} & \multicolumn{1}{c}{**75.9**} & \multicolumn{1}{c}{**71.9**} \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Main dynamic responses of the OS, the BI, and the VCS for the soft soil type (class D). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**OS**} & \multicolumn{2}{c}{**BI**} & \multicolumn{2}{c}{**VCS**} \\ \cline{2-9}  & \multicolumn{1}{c}{**Max(\(a_{S}\))**} & \multicolumn{1}{c}{**Max(\(d_{H}\))**} & \multicolumn{1}{c}{**Max(\(a_{S}\))**} & \multicolumn{1}{c}{**Max(\(d_{H}\))**} & \multicolumn{1}{c}{**Max(\(u_{B}\))**} & \multicolumn{1}{c}{**Max(\(a_{S}\))**} & \multicolumn{1}{c}{**Max(\(d_{H}\))**} & \multicolumn{1}{c}{**Max(\(u_{B}\))**} \\  & **(g)** & **(cm)** & **(g)** & **(cm)** & **(cm)** & **(cm)** & **(g)** & **(cm)** & **(cm)** \\ \hline acc \#1 & 0.66 & 1.46 & 0.05 & 0.16 & 6.91 & 0.19 & 0.43 & 1.06 \\ acc \#2 & 0.78 & 1.95 & 0.05 & 0.16 & 6.68 & 0.20 & 0.55 & 1.21 \\ acc \#3 & 0.67 & 1.76 & 0.06 & 0.17 & 6.65 & 0.22 & 0.59 & 1.07 \\ acc \#4 & 0.66 & 1.46 & 0.05 & 0.16 & 6.91 & 0.19 & 0.43 & 1.06 \\ acc \#5 & 1.24 & 3.2 The effectiveness of the VCS is examined also with real earthquakes. Two real ground motions are selected for each soil type. Chi-Chi and Niigata fall into the soft soil category, JMA and Northridge fall into the medium soil category, and Kocaeli and Tabas fall into the firm soil category. The categorization is based on the average shear-wave velocity for the upper 30-m depth of the station. The acceleration time histories are presented in Figure 9, and the details of the ground motions are presented in Table 5.  
Figures 10 and 11 and Table 6 present the controlled system main dynamic responses of the OS, BI, and VCS for the real earthquake records.