## 3 Numerical Study
### Time History Analyses: Ground Motions Considered  
The numerical models representing the above prototypes were subjected to ground acceleration recorded during 20 near-field earthquakes, and the response was obtained through nonlinear time history analyses. The ground acceleration records were scaled to match (with a tolerance of \(\pm\)2%) the \(V_{D}\) considered for designing the dampers: \(V_{D}\) = 1.08 m/s, \(V_{D}\) = 0.97 m/s and \(V_{D}\) = 0.927 m/s for prototypes N3, N6 and N9, respectively. Table 4 shows the properties of the ground motion records used in the analysis, where \(M_{w}\) is the magnitude moment, \(R_{jp}\) is the closest horizontal distance to rupture plane and PGV is the peak ground velocity. The signals were selected from the Pacific Earthquake Engineering Research Center Ground motion database [30; 31]. Table 4 also shows the scale factor employed for each record and prototype building, \(\lambda_{N3}\), \(\lambda_{N6}\) and \(\lambda_{N9}\). Figure 5 shows the unscaled \(S_{A}\)-\(T\) and \(S_{V}\)-\(T\) spectra of the records used, together with the mean value (bold line). Figure 4: Shear force versus inter-story drift curve for the first story: (**a**) N3, (**b**) N6 and (**c**) N9. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Name of the** & **Station** & **Comp** & \(M_{w}\) & \(R_{jb}\) & **Soil** & **PGA** & **PGV** & \(\lambda_{\text{N3}}\) & \(\lambda_{\text{N6}}\) & \(\lambda_{\text{N9}}\) \\
**Earthquake** & & & & **(km)** & & **(cm/s\({}^{2}\))** & **(cm/s)** & & \\ \hline \hline Coyote Lake, 1979 & Gilroy Array & 50 & 5.74 & 8.47 & Stiff & 187.13 & 10.27 & 3.46 & 3.14 & 4.14 \\  & Parkfield- & & & & & & & & \\ Parkfield 02, 2004 & Stone Corral & 360 & 6.00 & 2.85 & Stiff & 816.7 & 39.78 & 1.63 & 5.76 & 4.35 \\  & 1E & & & & & & & & \\ Duzce, Turquia, 1999 & IRIGM 487 & NS & 7.14 & 2.65 & Very dense & 297.5 & 38.93 & 1.42 & 1.99 & 1.62 \\ Kobe, Japan, 1995 & Takatori & 90 & 6.90 & 1.46 & Stiff & 658.08 & 122.92 & 0.96 & 2.31 & 2.44 \\ Kobe, Japan, 1996 & Takarazuka & 0 & 6.90 & 0 & Stiff & 683.86 & 68.38 & 1.29 & 4.82 & 3.04 \\ Kocaeli, Turquia, 1999 & Izmit & 180 & 7.51 & 3.62 & Rock & 161.95 & 22.32 & 3.33 & 2.46 & 2.20 \\ Kocaeli, Turquia, 2000 & Arcelik & 90 & 7.51 & 10.56 & Very dense & 131.6 & 40.05 & 4.40 & 3.46 & 4.14 \\ Tabas, Iran, 1978 & Tabas & L & 7.35 & 1.79 & Rock & 837.47 & 98.81 & 0.59 & 2.93 & 2.93 \\ Tabas, Iran, 1979 & Tabas & T & 7.35 & 1.79 & Rock & 845.1 & 123.36 & 0.62 & 3.14 & 2.57 \\ Chi-Chi, Taiwan, 1999 & NIST & E & 7.62 & 38.36 & Very dense & 306.1 & 20.88 & 2.34 & 4.40 & 3.67 \\  & Saratoga- & & & & & & & & \\ Loma Prieta, 1989 & Aloha & 0 & 6.93 & 7.58 & Very dense & 504.51 & 41.56 & 1.26 & 3.09 & 2.88 \\  & Avenue & & & & & & & & \\  & Saratoga- & & & & & & & & \\ Loma Prieta, 1990 & Aloha & 90 & 6.93 & 7.58 & Very dense & 319.92 & 45.96 & 2.70 & 4.87 & 5.40 \\  & Ave & & & & & & & & \\ Imperial Valley 06, 1979 & Holtville Post & 315 & 6.53 & 5.35 & Stiff & 217.17 & 51.44 & 2.39 & 2.25 & 2.73 \\  & Office & & & & & & & & \\ Irpinia, Italy 01, 1980 & Sturno (STN) & 270 & 6.90 & 6.78 & Very dense & 314.32 & 71.93 & 1.87 & 2.46 & 2.62 \\ Irpinia, Italy 01, 1981 & Sturno (STN) & 0 & 6.90 & 6.78 & Very dense & 222.28 & 36.97 & 2.25 & 1.78 & 1.41 \\  & Pacoima Dam & & & & & & & & \\ San Fernando, 1971 & (upper left & 164 & 6.61 & 0 & Rock & 1195.47 & 114.43 & 0.73 & 3.88 & 3.25 \\  & abut) & & & & & & & & \\  & Geetech & & & & & & & & \\ San Salvador, 1986 & Investig & 90 & 5.80 & 2.14 & Very dense & 690.62 & 79.9 & 1.14 & 3.62 & 3.67 \\  & Center & & & & & & & & \\  & LA Dam & 64 & 6.69 & 0 & Very dense & 418.06 & 74.82 & 1.85 & 3.20 & 2.73 \\  & Centerville & & & & & & & & \\ Cape Mendocino, 1992 & Beach Naval & 360 & 7.01 & 16.44 & Very dense & 468.41 & 51.17 & 1.53 & 3.77 & 3.04 \\  & Face & & & & & & & & \\ Christchurch, New & Panges Road & & & & & & & & \\ Zealand, 2011 & Pumping & & & & & & & & \\  & Station & & & & & & & & \\ \hline \hline \end{tabular}
\end{table}