## 4 Numerical Results
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Earthquake** & **Recording Station** & \(M_{w}\) & \(\Delta\)**[km]** & \(PGA_{H}\)**[m/s\({}^{2}\)]** & \(PGA_{V}\)**[m/s\({}^{2}\)]** \\ \hline Chi-Chi (Taiwan, 1999) & TCU059 & 7.6 & 17.1 & 1.24 & 0.64 \\ Chi-Chi (Taiwan, 1999) & TCU065 & 7.6 & 0.6 & 7.93 & 2.58 \\ Chi-Chi (Taiwan, 1999) & TCU068 & 7.6 & 2.2 & 4.59 & 5.20 \\ Northridge (USA, 1994) & Newhall-Fire St. & 6.7 & 5.9 & 6.83 & 5.38 \\ Northridge (USA, 1994) & Rinaldi & 6.7 & 6.5 & 8.63 & 9.40 \\ Northridge (USA, 1994) & Pico-Canyon & 6.7 & 5.5 & 4.07 & 2.91 \\ Imperial Valley (USA, 1999) & El Centro D.A. & 6.5 & 5.1 & 3.45 & 7.55 \\ Imperial Valley (USA, 1999) & El Centro Array\#5 & 6.5 & 0.6 & 3.75 & 5.83 \\ Imperial Valley (USA, 1999) & El Centro Array \#7 & 6.5 & 4.0 & 4.58 & 5.67 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Main features of the selected near-fault EQs (PEER database) [37]. After some preliminary results presented in [38], the accuracy of the CM2 CR model is tested by examining the seismic response of superstructures and isolators of the test buildings. As first step, the ductility demands of beams and columns provided by the CM2 CR model are compared with those obtained by less sophisticated HDRBs models (i.e., VEL, CM1, CM1C). To this end, the results are plotted as a function of the submultiple \(\alpha\) of the peak ground acceleration of the selected EQ (i.e., \(a_{g}=PGA\times\alpha\)), for each test structure, storey, nominal stiffness ratio and HDRB model. More specifically, three different values of the nominal stiffness ratio \(\alpha_{K0}\) (i.e., 400, 1200, 2400) and three different near-fault EQs, one with prevailing horizontal component (i.e., Chi-Chi EQ), one with prevailing vertical component (i.e., Imperial Valley EQ), and one with comparable horizontal and vertical components (i.e., Northridge EQ), are considered in the IDA of three--(i.e., B3), seven--(i.e., B7) and ten--(i.e., B10) storey buildings. For the sake of brevity, ductility demands of the B3 structure corresponding to nominal stiffness ratio \(\alpha_{K0}=1200\) are plotted in Figure 4 with reference to the Imperial Valley EQ. These figures show that the different HDRB models provide overlapping results until the coefficient \(\alpha\) attains a specific value, different for each storey. Once exceeded such threshold, the different models continue to provide similar results except for the first storey (Figure 4a-c) where the ductility demands corresponding to the CM2 CR model are lower than those provided by the other models, with a percentage reduction compared to the VEL model reaching \(-110.9\%\) and \(-156.4\%\) at the end sections and mid-span sections of the beams, respectively, when the maximum value of the acceleration ratio (i.e., \(\alpha\) = 0.71) is attained (Figure 4a,b). Moreover, the highest ductility demands in the mid-span section of beams are recorded at the third storey (Figure 4h), where a significant contribution of the vertical component of the selected earthquake is expected. In order to better understand the response of the superstructure, main parameters of the base-isolation systems are shown in Figure 5a-c with reference to the most stressed isolator (see isolator n.9 in Figure 2a): i.e., the maximum shear strain of the elastomer due to seismic displacements (\(\gamma_{s,max}\)), the maximum total shear strain (\(\gamma_{tot,max}\)) and the ratio (\(N/N_{cr}\)) between the maximum and critical axial loads. As can be observed, the base-isolation system presents a behavior opposite to that of the superstructure, with the CM2 CR model highlighting the most conservative results, contrary to the other models which correspond to the lower-bound values of \(\gamma_{s,max}\) (i.e., an increase of about \(+25\%\) with reference to the VEL model in Figure 5a) and \(\gamma_{tot,max}\) (i.e., an increase of about \(+32\%\) with reference to the VEL model in Figure 5b) and \(N/N_{cr}\) (i.e., an increase of about \(+52.8\%\) with reference to the VEL model in Figure 5c).