## 3 Numerical Modelling  
Nonlinear models have been developed in OpenSEES [34], including the superstructure (Figure 7a) and the isolation system with over-stroke capacity (Figure 7b,c). To correctly predict the effects of the superstructural inelastic behaviour on the seismic response of base-isolated buildings, a lumped plasticity model has been implemented for the main elements of the superstructures. The flexural behaviour of the plastic hinges for beams and columns critical cross-sections, considering axial load interaction effects, has been assumed with the Ibarra-Medina-Krawinkler [35] model. The model includes staircase knee beams and cantilever steps modelled as non-linear elements. To take into account and model the possible onset of non-ductile failure modes in elements expected to experience a shear failure, prior to or following flexural yielding, such as staircase short columns structural members, the ultimate rotation capacity of plastic hinges has been defined through empirical models providing the expected deformation capacity at shear and axial failures [21; 22]. A modified version of the Decanini model [36] has been used for masonry infill panels modelled with an equivalent compression-only strut considering a proper reduction of strength and lateral stiffness due to openings influence and potential premature out-of-plane collapse. In this study, 5% Rayleigh damping is used to model the viscous damping of the superstructure. Previous studies have shown that this approach could result in fictitiously large damping forces in base-isolated buildings resulting in underestimation of the first-mode and higher mode responses. Future studies focusing on the topic of the present manuscript should also consider alternative approaches proposed in the literature for modelling the viscous damping of the superstructure [37; 38; 39]. Reference to [17; 18; 19; 21; 22] can be made for further modelling details. The finite element friction-pendulum isolator (SingleFPEearing) was used for the DCCSS isolator modelling in numerical nonlinear analyses. The cyclic nonlinear behaviour shows an initial stiffness \(\text{K}_{\text{i}}\) before sliding, with a quasi-rigid behaviour, and a restoring stiffness \(\text{K}_{\text{p}}~{}=~{}\text{N}/\text{R}_{\text{e}}\), as shown in Figure 7c). As generally supposed by manufacturers, the isolation devices maximum geometric capacity displacement is \(\text{d}_{\text{c}}=\text{d}_{\text{max}}\cdot\)1.1 as shown in Figure 8a). The velocity dependence of the friction coefficient \(\upmu\) is modelled as described in [37]. High values for initial and vertical stiffness have been used (\(\text{K}_{\text{i}}~{}=~{}5.0~{}\text{kN}/\text{mm}\); \(\text{K}_{\text{V}}~{}=~{}1.5~{}\text{e}6~{}\text{kN}/\text{mm}\)). In the present work, the dependency of the friction coefficient on the applied contact pressure \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{**Case**} & \(\mathbf{R_{e}}\) & \(\upmu\) & \(\mathbf{K_{e}}\) & \(\mathbf{T_{e}}\) & \(\mathbf{\xi_{e}}\) & \(\mathbf{d_{Ed}}\) & \(\mathbf{\Phi}\) & \(\mathbf{d_{max}}\) \\ \cline{2-10}
**Study** & **[mm]** & **[\%]** & **[kN/mm]** & **[sec]** & **[\%]** & **[mm]** & **[mm]** & **[mm]** \\ \hline AQ\_New & 3700 & 2.5 & 0.357 & 3.17 & 21 & 237 & 200 & \(\pm 300\) \\ NA\_New & 2500 & 2.5 & 0.560 & 2.53 & 23 & 134 & 250 & \(\pm 150\) \\ AQ\_LSD & 3700 & 2.5 & 0.296 & 2.97 & 26 & 216 & 200 & \(\pm 300\) \\ NA\_GLD & 4500 & 2.5 & 0.303 & 3.01 & 28 & 125 & 165 & \(\pm 250\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Geometric characteristics and main design parameters of the isolation system at the CLS. Figure 7: (**a**) Schematical representation of the base-isolated prototype building. DCCSS isolators: (**b**) numerical models and (**c**) constitutive law. and the temperature rise has been neglected, to better highlight the direct consequences of the over-stroke response.