## 6 Results  
Figure 11 shows the results in terms of top acceleration spectra for the selected 10 input motions, for the two models (SSI and EQ model). SSI is the finite element model described in Section 3, while the EQ model is the equivalent fixed-based model with fundamental period 0.80 s and 11.5% damping. It is worth noting that the peak values occur at the fundamental period of the system, demonstrating that both models work properly. Moreover, SSI model results are conservatively smaller than those calculated for the EQ model with a range of 84.0% for BOL and 95.5% for MUL. In particular, the shape of the spectra for many input motions is close between the two models, especially for FF input motions. It is important to notice that the application of the damping (11.5%) and thus the reduction of the input motion by the parameter \(\eta\) allows us to obtain realistic values of the spectra. In only two cases (PER and YER) the values are larger than those calculated by the SSI model. In particular, for these input motions, the differences occur for PGA \(>\) 1 g. In one case (BRN), for some values EQ results are not conservative, if compared with SSI cases, and this may be due to the effects of soil non-linear mechanisms that cannot be included in the equivalent fixed model. However, the general trends of the EQ spectra are similar and demonstrate that the proposed methodology is able to represent the amplifications due to site and basin effects. In this regard, five input motions (ERZ, ATM; BOL, CHY and YER) show amplifications at higher periods that are conservatively represented by the EQ spectra in a close way. For RRS, the site effects are represented but with a delay: the peak value for the SSI model (4.97 m/s\({}^{2}\)) occurs for 1.7 s, while the peak one for EQ is 6.40 m/s\({}^{2}\), occurring at 1.9 s, with a delay of 0.2 s. Moreover, it is worth noting that for FF cases, the EQ model seems to be more representative than for the cases of NF, where the differences between the two models are more significant. Overall, the proposed EQ model that implements Equations (20) and (28), is shown to be conservatively correct to represent the complex mechanism due to the SSI between the structure and the soil.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Input Motions** & **Name** & **PGA (g)** & **PGV (cm/s)** & **PGD (cm)** \\ \hline NF & Superstition Hills & BPT & 0.45 & 112.05 & 52.49 \\ \hline NF & Loma Prieta & BRN & 0.48 & 55.78 & 11.69 \\ \hline NF & Erzincan & ERZ & 0.52 & 84.00 & 27.68 \\ \hline NF & Cape Mendocino–Petrolia & PET & 0.59 & 48.35 & 21.99 \\ \hline NF & Northridge & RRS & 0.83 & 160.40 & 29.72 \\ \hline FF & Friuli Tolmezzo & ATM & 0.45 & 30.82 & 5.08 \\ \hline FF & Duzce–Bolu & BOL & 0.46 & 56.53 & 23.09 \\ \hline FF & Chy Chy & CHY & 0.18 & 115.09 & 68.81 \\ \hline FF & Northridge BH & MUL & 0.27 & 58.99 & 13.16 \\ \hline FF & Landers–Yermo & YER & 0.24 & 51.48 & 43.83 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Input motion characteristics.  
Figure 11: _Cont._  
Figure 11: (**a**) Results (near-field (NF) motions): comparison between top spectra: SSI model and EQ model. (**b**) Results (far-field (FF) motions): comparison between top spectra: SSI model and EQ model.