# Investigation of Geotechnical Seismic Isolation Systems Based on Recycled Tire Rubber-Sand Mixtures
## 3 Results and Discussions
### Ground Motions Selection
\begin{table}
\begin{tabular}{c c c c c} \hline \hline Shear Wave Velocity of Clay & & & 200 \\ Soil Layer (m/s) & & & & \\ \hline Profile Depth (m) & 20 & 19 & 18 & 17 \\ \hline Isolation (m) & 0 & 1 & 2 & 3 \\ \hline Shear Wave Velocity of & - & 243.15 & 243.15 & 243.15 \\ Isolation Layer (m/s) & - & 9.38 & 9.38 & 9.38 \\ \hline Initial Damping Ratio (\%) & - & 9.38 & 9.38 & 9.38 \\ \hline Natural Frequency (Hz) & 2.5 & 2.522 & 2.545 & 2.568 \\ \hline Natural Period (s) & 0.4 & 0.3965 & 0.3929 & 0.3894 \\ \hline \multirow{3}{*}{Earthquake} & \multirow{3}{*}{EL (Hz)} & \%0-100 kPa & \%0-100 kPa & \%0-100 kPa & \%0-100 kPa & \%0-100 kPa & \%0-100 kPa \\  & & 1 m Amp. & 2 m Amp. & 2 m Amp. & 3 m Amp. & \multirow{2}{*}{Ratio (\%)} \\  & Ratio (Hz) & & Ratio (Hz) & & Ratio (Hz) \\ \hline ChiChi & 3.702 & 3.206 & \(-13.40\%\) & 3.169 & \(-14.40\%\) & 3.106 & \(-16.10\%\) \\ \hline Coyote & 4.056 & 3.561 & \(-12.20\%\) & 3.530 & \(-12.97\%\) & 3.490 & \(-13.95\%\) \\ \hline Imp. Valley & 3.873 & 3.373 & \(-12.91\%\) & 3.339 & \(-13.79\%\) & 3.297 & \(-14.87\%\) \\ \hline Kocaeli & 4.200 & 3.745 & \(-10.83\%\) & 3.752 & \(-10.67\%\) & 3.738 & \(-11.00\%\) \\ \hline \multicolumn{3}{c}{Mean Value} & \multicolumn{3}{c}{\(\mathbf{-12.34\%}\)} & \multicolumn{3}{c}{\(\mathbf{-12.96\%}\)} & \multicolumn{3}{c}{\(\mathbf{-13.98\%}\)} \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Table of dominant frequencies based on the measured Fourier amplitude ratio for the isolation layer composed of sand containing 0% rubber content (\(\sigma_{0}\) = 100 kPa). Figure 20: Fourier amplitude ratio for the ChiChi, Coyote, Imperial Valley, and Kocaeli earthquakes with the isolation layer composed of sand containing 0% rubber content and subjected to a confining pressure of 100 kPa. Tables 4-15 were derived from a combination of numerical simulations and experimental data available in the literature. The response spectral accelerations, Fourier amplitude ratios, and damping behavior were computed using the frequency-domain analysis method, where acceleration time histories obtained from numerical simulations were transformed  
Figure 21: Fourier amplitude ratio for the ChiChi, Coyote, Imperial Valley, and Kocaeli earthquakes with the isolation layer composed of sand containing 0% rubber content and subjected to a confining pressure of 50 kPa. \begin{table}
\begin{tabular}{c c c c c c} \hline Shear Wave Velocity of Clay & & & & 200 & \\ Soil Layer (m/s) & & & & & \\ \hline Profile Depth (m) & 20 & 19 & 18 & 17 & \\ \hline Isolation (m) & 0 & 1 & 2 & 3 & \\ \hline Shear Wave Velocity of & - & 192.77 & 192.77 & 192.77 & 192.77 \\ Isolation Layer (m/s) & - & 6.23 & 6.23 & 6.23 & \\ \hline Initial Damping Ratio (\%) & 2.5 & 2.495 & 2.491 & 2.486 & \\ \hline Natural Frequency (Hz) & 0.4 & 0.4008 & 0.4015 & 0.4023 & \\ \hline \multirow{3}{*}{Earthquake} & \multirow{3}{*}{EL (Hz)} & \%0-50 kPa & Damping Ratio (\%) & \%0-50 kPa & Damping Ratio (\%) & \%0-50 kPa & Damping Ratio (\%) \\ \cline{1-1} \cline{3-5} ChiChi & 3.702 & 3.208 & \(-\)13.34\% & 3.164 & \(-\)14.53\% & 3.165 & \(-\)14.51\% \\ \hline Coyote & 4.056 & 3.563 & \(-\)12.15\% & 3.512 & \(-\)13.41\% & 3.511 & \(-\)13.44\% \\ \hline Imp. Valley & 3.873 & 3.375 & \(-\)12.86\% & 3.319 & \(-\)14.30\% & 3.316 & \(-\)14.38\% \\ \hline Kocaeli & 4.200 & 3.748 & \(-\)10.76\% & 3.738 & \(-\)11.00\% & 3.772 & \(-\)10.19\% \\ \hline \multicolumn{5}{c}{Mean Value} & \multicolumn{3}{c}{\(\mathbf{-12.28\%}\)} & \multicolumn{3}{c}{\(\mathbf{-13.31\%}\)} & \multicolumn{3}{c}{\(\mathbf{-13.13\%}\)} \\ \hline \end{tabular}
\end{table} 
Table 15: Table of dominant frequencies based on the measured Fourier amplitude ratio for the isolation layer composed of sand containing 0% rubber content (\(\sigma_{0}\) = 50 kPa). via Fast Fourier Transform (FFT). The Fourier amplitude ratio was then determined as the ratio of the spectral amplitudes at the surface to those at the base of the isolation layer.