## 4 Detrimental Effects of SSI  
### Data on Structures and Sites  
A further study on the time domain was performed on four buildings in California, USA, to investigate the possibility of SSI having detrimental effects. The parameters were selected from the published literature: the Hollywood Storage Building (California Strong Motion Instrumentation Program (CSMIP) station No. 24236) [32], the Millikan Library (National Strong Motion Project (NSMP) No. 5407) [33], a building in Sherman Oaks (CSMIP station No. 24322) and a building in Walnut Creek (CSMIP station No. 58364) [19]. These buildings have been used for strong-motion observations for decades, and their structural and site data are available, as well as earthquake records, which is helpful to establish proper SSI models. The details of the four buildings and the stratifications of the site can be found in our previous paper [34], and we list key information on the buildings in Table 1 and on the sites in Table 2, which are used to establish the SSI model. The influence of SSI is probably not taken into account in the seismic designs of the buildings. The fixed-base frequency \(\omega_{\rm b}/2\pi\) for the four buildings ranges from 0.83 Hz to 2.16 Hz, and the shear-wave velocity of the soil at the top of the site ranges from 184.7 m/s (soft soil) to 336 m/s (moderate rigid soil). A rough formula \(H_{e}=H/\sqrt{3}\) suggested in [35] is used as the effective height of the structures, since the structures are simplified to the equivalent SDOF oscillator. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & \begin{tabular}{c} **Hollywood** \\ **Storage Building** \\ \end{tabular} & **Millikan Library** & \
\begin{tabular}{c} **Sherman Oaks** \\ **Building** \\ \end{tabular} &
\begin{tabular}{c} **Walnut Creek** \\ **Building** \\ \end{tabular} \\ \hline \hline \(a\) (short side) & 7.77 m & 11.65 m & 18.15 m & 15.9 m \\ \hline \(b\) (long side) & 33.15 m & 12.55 m & 28.8 m & 22.6 m \\ \hline \(c\) & 8.74 m & 4.30 m & 16.10 m & 4.20 m \\ \hline \(H\) & 45.6 m & 43.9 m & 50.0 m & 39.2 m \\ \hline \(H_{e}\) & 26.3 m & 25.3 m & 28.9 m & 22.6 m \\ \hline \(M_{0}\) (kg) & \(1.38\times 10^{7}\) kg & \(1.43\times 10^{6}\) kg & \(4.57\times 10^{7}\) kg & \(1.43\times 10^{6}\) kg \\ \hline \(M_{\text{b}}\) & \(1.17\times 10^{7}\) kg & \(1.07\times 10^{7}\) kg & \(1.66\times 10^{7}\) kg & \(1.07\times 10^{7}\) kg \\ \hline \(M_{\text{b}}/M_{0}\) & 0.85 & 7.48 & 0.24 & 7.48 \\ \hline \(\tilde{\xi}_{\text{b}}\) & 2\% & 2\% & 2\% & 2\% \\ \hline \multirow{7}{*}{NS} & \(b/a\) & 4.27 & 0.93 & 1.59 & 1.42 \\ \cline{2-5}  & \(c/a\) & 1.12 & 0.34 & 0.89 & 0.26 \\ \cline{2-5}  & \(H_{e}/a\) & 3.38 & 2.17 & 1.59 & 1.42 \\ \cline{2-5}  & \(\omega_{\text{b}}/\pi\beta_{1}\) & 0.070 & 0.168 & 1.10 & 0.14 \\ \cline{2-5}  & \(\omega_{\text{b}}/2\pi\) & 0.83 Hz & 2.16 Hz & 1.54 Hz & 1.52 Hz \\ \cline{2-5}  & \(\tilde{\omega}_{\text{b}}/2\pi\) & 0.78 Hz & 1.86 Hz & 1.38 Hz & 1.40 Hz \\ \cline{2-5}  & \(\tilde{\omega}_{\text{b}}/\omega_{\text{b}}(\tilde{\eta}_{\text{b}}/\eta_{ \text{b}})\) & 0.93 & 0.84 & 0.90 & 0.92 \\ \hline \multirow{7}{*}{EW} & \(a/b\) & 0.23 & 1.08 & 0.63 & 0.70 \\ \cline{2-5}  & \(c/b\) & 0.26 & 0.37 & 0.56 & 0.186 \\ \cline{2-5}  & \(H_{e}/b\) & 0.79 & 2.02 & 1.00 & 1.00 \\ \cline{2-5}  & \(\omega_{\text{b}}a/\pi\beta_{1}\) & 0.72 & 0.11 & 0.61 & 0.28 \\ \cline{2-5}  & \(\omega_{\text{b}}/2\pi\) & 2.00 Hz & 1.26 Hz & 1.69 Hz & 2.10 Hz \\ \cline{2-5}  & \(\tilde{\omega}_{\text{b}}/2\pi\) & 1.78 Hz & 1.20 Hz & 1.55 Hz & 1.88 Hz \\ \cline{2-5}  & \(\tilde{\omega}_{\text{b}}/\omega_{\text{b}}(\tilde{\eta}_{\text{b}}/\eta_{ \text{b}})\) & 0.89 & 0.94 & 0.92 & 0.89 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Buildings for case studies.