# Evaluating Collapse Fragility Curves for Existing Buildings Retrofitted Using Seismic Isolation
## 6 Conclusions  
The RINTC (Implicit Risk of code-conforming Italian buildings) research project [7], funded within the ReLuis/DPC 2015-2018 research program, investigated the collapse probabilities of different building typologies, included existing buildings retrofitted using seismic isolation, adopting pragmatic choices regarding the definition of the collapse conditions and the numerical non-linear modeling of the isolation system. In the present paper, developments in terms of non-linear modeling and collapse conditions have been proposed. In particular, an enhanced mechanical model for the description of the behavior of HDRBs is adopted to take into account the axial-shear load interactions (at small and large displacements) as well as P-delta effects due to post buckling behavior. Moreover, a less conservative and more rational criterion has been considered for the estimation of the buckling failure mode of the aforementioned devices. The revised model has been applied for the estimation of the CFFs of two case-studies representing typical existing buildings retrofitted using seismic isolation, located in two different sites, L'Aquila and Naples (characterized by medium and high seismicity). In particular, the existing building located in L'Aquila (high seismicity) was designed according to the pre-96 seismic code (SLD building) while that located in Naples (medium seismicity) was designed for gravity loads only (GLD building). A hybrid isolation system (HDRBs + FPBs) has been adopted for the retrofit intervention of both case-studies. For the SLD case-study building, despite a different seismic response of the isolation system is observed passing from the modeling approach adopted within RINTC project to that proposed herein, a limited variation (of the order of 10%) in terms of median collapse capacity (\(\text{S}_{\text{a,C}}\)) is obtained. On the other hand, for the GLD case-study building, the implementation of the Kikuchi bearing model and the adoption of a less prudential criterion for the buckling failure lead to more significant effects. As a matter of fact, a sensible reduction in terms of median collapse capacity (of the order of 30%) is observed. In both cases, slight variations of the record to record dispersion, \(\beta_{\text{RIR}}\), (lower than 10%) are obtained. It is worth noting that the derived dispersion values are in line with those proposed in literature [6]. Generally speaking, the preliminary results presented in this study outline that, in some cases, different choices in terms of failure conditions and modeling assumptions could sensibly affect the \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Case Study** & **HDRB Model** & **Median (g)** & **Dispersion** & **CMR** \\ \hline SLD & HDR & 0.219 & 0.200 & 1.24 \\  & Kikuchi & 0.243 & 0.185 & 1.37 \\ GLD & HDR & 0.190 & 0.271 & 2.04 \\  & Kikuchi & 0.133 & 0.238 & 1.43 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Collapse fragility function parameters and collapse margin ratio (CMR) values derived for the examined case-studies. collapse fragility. Further developments are needed to definitively assess the effect of such choices and to identify robust models and rational collapse criteria for each specific case. In this optic, new analysis considering more case-study buildings and isolation system typologies are in progress. In conclusion, the present study represents an improvement of the knowledge geared toward the refinement of the performance-based assessment and design procedures, providing helpful information for specific enhanced modeling assumptions. Conceptualization, A.F., G.P. and D.C.; Data curation, G.P. ; Formal analysis, A.F. ; Investigation, A.F. ; Methodology, A.F. and G.P. ; Validation, D.C.; Writing--original draft, A.F. and G.P. ; Writing--review and editing, A.F. All authors have read and agreed to the published version of the manuscript. This research was supported by the Italian Department of Civil Protection. This work has been carried out within the ReLuis RINTC 2019/21 research program.