## 5 NTHA Results  
Nonlinear Time History Analyses were performed by considering a set of 200 ground motions, consisting of 20 records for each intensity measure level (IM), as reported in Table 2. The GC limit is explained in Figure 11 where an example of force vs. displacement behaviour and displacement orbit of the corner DCCSS device at IM6 (Earthquake number 2) for the case of the existing isolated building located in L'Aquila is reported, together with the ultimate displacement (orange continuous line) and the displacement capacity (orange dashed line). As can be observed from Figure 11a) the numerical model well describes the over-stroke displacement. The collapse of the DCCSS is attained when isolators displacement \(\mathrm{d}>\mathrm{d_{lim}}\), as shown in Figure 11b).  
Figure 10: Limit displacement function of the contact pressure of DCCSS sliding material for the GC performance level.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Limit State** & **EDP** & **Failure Conditions** & **Case ID** & **Limit Value** \\ \hline \multirow{3}{*}{UPD} & \multirow{3}{*}{Superstructure global drift\({}_{\mathrm{lim}}\)} & End of the elastic branch on & AQ\_New & 0.32\%; 0.31\% \\  & & pushover curves for & NA\_New & 0.32\%; 0.31\% \\  & & directions X and Y & AQ\_LSD & 0.27\%; 0.34\% \\  & & & NA\_GLD & 0.20\%; 0.26\% \\ \hline \multirow{3}{*}{GC} & \multirow{3}{*}{Maximum displacement of isolators \(\mathrm{d_{lim}}\)} & Vertical instability or contact & AQ\_New & 414 mm \\  & & pressure of the & NA\_New & 290 mm \\ \cline{1-1}  & & sliding material & AQ\_LSD & 420 mm \\ \cline{1-1}  & & NA\_GLD & 342 mm \\ \hline \hline \end{tabular}
\end{table}
Table 5: Definition of the performance levels for the isolated buildings.  
Figure 12 shows the results about the GC performance level in terms of the number of records vs. IM for which the EDP limit is attained. Results show the AQ_New case study is characterised by the highest number of failures. Furthermore, for the cases located in the site of L'Aquila, the isolation system failure is attained for seismic intensities close to the design one (IM6-CLS), while for Naples cases, this condition is only reached for high seismic intensities.  
The results in terms of UPD performance level are reported in Figures 13-16 in terms of D/C ratios vs IM. The total number of failure cases (D/C \(\geq\) 1) is shown on top of the charts, red dots represent the superstructural UPD failure cases, while the cases in which isolation system failure (GC) is registered are represented with a blank dot, for these records the UPD performance level is considered attained too, regardless of the D/C ratio. As can be seen, in accordance with the GC results, a significant number of failures is only registered for intensities higher than the IM6 for the site of L'Aquila. For the NA_New case, the EDP limit is attained for IM10 only, this effect is due to the updated superstructure design and the lower seismic hazard of the site. Moreover, an average value of 0.2 for the D/C ratio is recorded at IM2 (DLS) for both the New construction buildings,  
Figure 11: Results for an LLS (IM 6; EQ no. 2) intensity accelerogram on a force vs displacement diagram (**a**) and in plan view (**b**).  
Figure 12: GC results for the four case studies analysed.