## 4 Detrimental Effects of SSI
### Case Studies
\begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{**Earthquake**} & \multirow{2}{*}{**Year**} & \multicolumn{4}{c}{**Time History \(\tilde{u}_{\text{b}}(t)\)**} & \multicolumn{2}{c}{**RS(\(\tilde{u}_{\text{b}}\))**} \\ \cline{3-8}  & & \multicolumn{2}{c}{**Maximum (g)**} & \multicolumn{2}{c}{**Mean (g) \(\times\)10\({}^{-2}\)**} & \multicolumn{2}{c}{**Maximum (g)**} \\ \cline{3-8}  & & **SSI System** & **Fixed-Base** & **SSI System** & **Fixed-Base** & **SSI System** & **Fixed-Base** \\ \hline \multicolumn{8}{c}{Hollywood Storage Building (EW)} \\ \hline Kern County & 1952 & 0.44 & 0.32 & 7.84 & 7.02 & 2.39 & 2.50 \\ \hline San Fernando & 1971 & 0.38 & 0.19 & 4.01 & 3.17 & 1.45 & 1.36 \\ \hline Whittier Narrow & 1987 & 0.49 & 0.53 & 8.60 & 15.42 & 2.09 & 4.69 \\ \hline Northridge & 1994 & 0.45 & 0.32 & 6.60 & 4.15 & 3.11 & 1.95 \\ \hline Chino Hills & 2008 & 0.35 & 0.41 & 5.52 & 6.45 & 1.94 & 3.14 \\ \hline Encino & 2014 & 0.19 & 0.25 & 2.88 & 3.67 & 0.88 & 1.48 \\ \hline \multicolumn{8}{c}{Millikan Library (EW)} \\ \hline Lytle Creek & 1970 & 0.39 & 0.49 & 9.47 & 15.44 & 2.37 & 3.77 \\ \hline San Fernando & 1971 & 0.20 & 0.19 & 6.65 & 7.74 & 1.35 & 1.53 \\ \hline Whittier Narrow & 1987 & 0.27 & 0.34 & 5.53 & 6.36 & 1.30 & 1.80 \\ \hline Yorba Linda & 2002 & 0.107 & 0.105 & 2.62 & 3.54 & 0.56 & 0.70 \\ \hline San Simeon & 2003 & 0.44 & 0.55 & 11.74 & 14.90 & 3.13 & 4.19 \\ \hline \multicolumn{8}{c}{Sherman Oaks Building (EW)} \\ \hline Lander & 1992 & 0.19 & 0.27 & 5.20 & 8.10 & 1.20 & 1.99 \\ \hline Whittier Narrow & 1987 & 0.20 & 0.26 & 2.95 & 5.50 & 0.87 & 1.64 \\ \hline Northridge & 1994 & 0.187 & 0.190 & 2.91 & 3.11 & 1.13 & 1.15 \\ \hline Chatsworth & 2007 & 0.055 & 0.106 & 0.060 & 0.087 & 0.19 & 0.43 \\ \hline Chino Hills & 2008 & 0.20 & 0.24 & 3.58 & 5.18 & 1.46 & 1.63 \\ \hline Encino & 2014 & 0.061 & 0.12 & 0.053 & 0.06 & 0.18 & 0.33 \\ \hline \multicolumn{8}{c}{Walnut Creek Building (NS)} \\ \hline Livermore & 1980 & 0.28 & 0.37 & 6.25 & 8.17 & 2.07 & 2.42 \\ \hline Livermore & 1980 & 0.14 & 0.17 & 2.75 & 3.27 & 0.85 & 1.01 \\ \hline Loma Prieta & 1989 & 0.14 & 0.20 & 3.09 & 2.94 & 0.96 & 1.33 \\ \hline Alamo & 2008 & 0.13 & 0.19 & 1.11 & 2.15 & 0.36 & 0.59 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Dynamic responses of structures in the time domain of target buildings in the YOZ-plane. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{**Earthquake**} & \multirow{2}{*}{**Year**} & \multicolumn{4}{c}{**Time History \(\tilde{u}_{\text{b}}(t)\)**} & \multicolumn{2}{c}{**RS(\(\tilde{u}_{\text{b}}\))**} \\ \cline{3-8}  & & \multicolumn{2}{c}{**Maximum (g)**} & \multicolumn{2}{c}{**Mean (g) \(\times\)10\({}^{-2}\)**} & \multicolumn{2}{c}{**Maximum (g)**} \\ \cline{3-8}  & & **SSI System** & **Fixed-Base** & **SSI System** & **Fixed-Base** & **SSI System** & **Fixed-Base** \\ \hline \multicolumn{8}{c}{Walnut Creek Building (EW)} \\ \hline Livermore & 1980 & 0.33 & 0.34 & 4.94 & 6.20 & 1.32 & 1.48 \\ \hline Livermore & 1980 & 0.27 & 0.39 & 4.33 & 7.84 & 1.50 & 2.37 \\ \hline Loma Prieta & 1989 & 0.24 & 0.33 & 4.54 & 5.83 & 1.19 & 1.68 \\ \hline Alamo & 2008 & 0.10 & 0.12 & 1.25 & 1.77 & 0.30 & 0.45 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._Figure 7 illustrates the ratio of the three responses (maximum response in the time history, mean response in the time history, and maximum response spectrum of structure acceleration response) of the SSI system to those of the fixed-base oscillator. The \(x\)-axis corresponds to each event in Tables 3 and 4, and the \(y\)-axis is the percentage value. The symbol \"FB\" represents a \"fixed-base oscillator\". A value larger than 100% on the \(y\)-axis indicates that the dynamic response of the SSI system is larger than that of the corresponding fixed-base oscillator, or that SSI amplifies the dynamic response of the structure and has a detrimental effect on the seismic designs. As shown in the figure, about 15-20% of the 42 selected earthquakes on four buildings' events had detrimental effects.