## 4 Definition of Performance Levels  
The engineering demand parameters (EDP) defined to control the seismic performance of isolated buildings are the superstructure global drift and the isolation system displacement for the attainment of the Limit State corresponding to the Usability-Preventing Design (UPD) and the Global Collapse (GC), respectively. The UPD is defined as the performance level in which the structure, with its structural and nonstructural elements, undergoes a damage level that does not expose its occupants to any risk and does not compromise the strength and stiffness of the structural elements; the structure is immediately accessible even if some equipment is not fully operational. A multi-criteria approach has been adopted to define the limit value of drift \(drift_{lim}\) for UPD level combining conditions related to easy non-structural components reparability and no service interruption with the conditions of protecting structural members from damage for frequent earthquakes [42]. The UPD failure condition is attained when the superstructure global drift corresponding to the end of the elastic branch on pushover curves is reached. Figure 9 sums up the threshold values of the top displacements found on the pushover curves for the case studies carried out on the fixed-based superstructures, with a force \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Case\_ID**} & \(\mathbf{d_{c}}\) & \(\mathbf{d_{u}}\) & \(\mathbf{K_{p}}\) & \(\mathbf{K_{2}}\) & \(\Delta\mu\) \\ \cline{2-6}  & **[mm]** & **[mm]** & **[kN/mm]** & **[kN/mm]** & **-** \\ \hline AQ\_New & \(\pm\)330 & 430 & 0.240 & 2.50 & 0.02 \\ NA\_New & \(\pm\)165 & 290 & 0.172 & 2.50 & 0.02 \\ AQ\_LSD & \(\pm\)330 & 430 & 0.174 & 2.50 & 0.02 \\ NA\_GLD & \(\pm\)275 & 355 & 0.372 & 2.50 & 0.02 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Over-stroke parameters of the isolation system. Figure 8: Maximum geometric (**a**) and ultimate (**b**) displacement of DCCSS Isolators. distribution proportional to the storey masses using a barycentric node in the top floor as control node [20; 21; 43]. The GC is defined as the performance level in which one DCCCS device reaches the limit displacement \(\mathrm{d}_{\mathrm{lim}}\) in the over-stroke regime, mainly dependent on the contact pressure and sliding material degradation. It has been observed that the limit displacement \(\mathrm{d}_{\mathrm{lim}}\) is related to the contact pressure supported by the sliding material and to the number of cycles over in the over-stroke regime. The area of contact between the plates surfaces and the inner slider reduces and a peak in contact pressure can be reached. When the inner slider runs on the edge of the sliding surfaces the friction coefficient increases and the sliding material suffers some damage. For the case studies, a Polytetrafluoroethylene (PTFE)-based sliding material with a maximum contact pressure of 60 MPa has been assumed and a number of two over-stroke cycles has been allowed. Depending on the thickness of the inner slider, the covered area at the sliding interfaces or the overlapped area  
Figure 9: Limit values of top displacement associated with the attainment of the Usability-preventing Performance Level, as derived from Pushover analysis for new construction buildings (**a**), and existent buildings in the sites of L’Aquila (**b**) and Naples (**c**). between the backing plates can be considered for the computation of the average contact pressure: if the thickness is enough to ensure a proper vertical stress distribution the former can be adopted, otherwise the latter represents a more correct parameter. Figure 10 shows the ratio between the limit displacement \(\mathrm{d_{lim}}\) and maximum capacity displacement \(\mathrm{d_{c}}\) corresponding to the maximum contact pressure on the covered area of the slider for each case study. For three case studies (AQ_new, AQ_LSD and NA_GLD) the contact pressure limit is reached before the ultimate displacement \(\mathrm{d_{u}}\).