## 7 Conclusions  
This paper presents the results of an ongoing RINTC research project investigating the global collapse (GC) and the usability preventing damage (UPD) limit states of reinforced concrete (RC) buildings with isolation systems based on double concave curved surface sliders (DCCSS). Starting from the same 6-storey prototype building, four case studies of isolation systems have been designed considering two different sites, characterised by medium and high seismicity, and including two existing structures retrofitted through the base isolation technique. Bi-directional nonlinear dynamic analyses considering twenty natural earthquakes for ten increasing seismic intensity levels have been carried out. The numerical model includes the nonlinear behaviour of the superstructure elements and the infill panels considered as drift-sensitive non-structural components. An advanced non-linear model of the DCCSS over-stroke capacity calibrated with specific experimental tests conducted on similar bearings is adopted. The model can describe the DCCSS behaviour when the displacement exceeds the maximum geometric capacity and a limit associated with the loss of vertical support due to overturning mechanisms of the inner slider is reached. The influence of the contact pressure on the sliding material degradation has been considered for the estimation of the limit displacement of DCCSS bearings. High values of contact pressure in the sliding material, due to the decreasing contact area between the housing plates and the slider, reduce the ultimate over-stroke displacement of the bearing. Results show the isolation systems efficiency in limiting non-structural damage for seismic intensities even higher than the design one and also point out their little margin toward collapse for these intensity levels. In cases of retrofitted buildings, the superstructure failure has shown to be the main failure mode, especially for the case of the building designed without seismic rules due to the deformability of the structure. Differently, the isolation system collapse is always the prevalent failure mode for new base-isolated buildings mainly due to the generally low design margin of isolation devices. The influence of different procedures assumed for the design of seismic isolators for new and existing buildings is negligible. Compared with the results obtained in previous works considering the unlimited elasto-plastic behaviour modelling of isolation systems, the probability of reaching the GC limit state reduces to values comparable with the UPD limit state when over-stroke capacity is considered. Further research should be carried out on the topic, from a two-fold point of view: many other case study structures need to be numerically investigated, to generalise the drawn conclusions also considering the responses of acceleration-sensitive non-structural components and building contents; additional experimental testing campaigns should be performed to evaluate possible dependencies of the over-stroke effect of DCCSS devices \begin{table}
\begin{tabular}{c c c} \hline \hline
**Case\_ID** & **Limit State** & **Annual Rate of Failure \(\mathbf{\lambda_{\mathrm{f}}}\)** \\ \hline \multirow{2}{*}{AQ\_New} & UPD & \(8.7\times 10^{-4}\) \\  & GC & \(7.0\times 10^{-4}\) \\ \hline \multirow{2}{*}{NA\_New} & UPD & \(1.1\times 10^{-4}\) \\  & GC & \(1.1\times 10^{-4}\) \\ \hline \multirow{2}{*}{AQ\_LSD} & UPD & \(9.8\times 10^{-4}\) \\  & GC & \(6.6\times 10^{-4}\) \\ \hline \multirow{2}{*}{NA\_GLD} & UPD & \(5.4\times 10^{-4}\) \\  & GC & \(1.5\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Annual rates of failure for the analysed cases. on some response parameters, such as vertical load and sliding velocity, or the number of subsequent cycles which can be run without significant cumulative damage. Conceptualization, A.D.C., F.C.P. and A.P. ; methodology, A.D.C. and A.T.; numerical analysis, M.F. and A.T.; data processing, A.T. and M.F. ; project administration, F.C.P. and A.P. ; writing original draft, A.T. and M.F.