## 4 Non-Linear Numerical Modelling and Structural Analysis  
In the next section, the assumptions adopted to define the numerical models [25] and to perform the NL dynamic simulations of the investigated RC building are listed in agreement with [26], Refs. [39; 40] and also with reference to the characterization of ground motion inputs. Definition of the NL Numerical Models Related to RC Framed Building including Infills for Base-Fixed and Base-Isolated Structure  
The RC-framed building under investigation has been numerically reproduced in line with the geometrical and material characteristics introduced in the previous sections using SAP2000 [25]. As for the modeling of the RC columns, it has been performed with the assumption of full restraint at the level of the rigid inverted RC beams that constitute the foundations of the building. Furthermore, the behavior of the stiff fields of \"latero-cement\" floors has been reproduced by appropriate membrane constraints in SAP2000 [25]. As introduced in previous sections, the building, up to the level of story 1, is surrounded by an embankment of soil. The presence of the latter has been included within the numerical representation of the structures, accounting for its restraining effect for in-plane (i.e., X and Y directions) displacements of story 1 [26]. Concerning the modeling of the main structural elements, characterized by RC columns and RC beams, a discretization approach based on fiber cross-section has been adopted with the aim of defining the non-linear behavior of the plastic hinges according to the concentrated plasticity philosophy (SAP2000 [25]). Specifically, for each type of cross-section, the constitutive laws of the fibers have been distinguished between steel longitudinal reinforcement, core (i.e., confined by stirrups), and cover concrete. The plastic hinges based on fiber discretization allow for taking into account the axial load and bending (biaxial) inter-relationship [25]. The non-linear response of the hinges takes place within a predetermined length \(L_{p}\) that denotes the plastic hinge length. The plastic hinge length \(L_{p}\) has been determined in line with the equation proposed by [41]. The constitutive law of [42; 43] has been adopted to simulate non-linear responses in compressions of fibers representing the core and the cover concrete. The related tensile behavior has been modeled by means of LTS (i.e., linear tension softening). All the needed mechanical characteristics of concrete have been obtained as a function of the mean value of the experimental results for cylinder strength in compression \(f_{cm}\) and modulus of elasticity \(E_{cm}\) in line with the specifications of EN1992 [44]. With the aim of taking into account the degradation of the mechanical properties due to the accumulation of damage during the seismic event, the model of [45] has been adopted. With reference to the constitutive law for bar reinforcement, an elastic with perfect plasticity model has been used, taking care to limit the ultimate strain at a value of 7.5% [44]. According to the experimental tests, the mean value \(f_{gm}\) has been adopted as the yield strength concerning both the compressive and tensile behavior. The modulus of elasticity has been set to 200,000 MPa. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(E_{m1}\) & \(E_{m2}\) & \(f_{cm}\) & \(f_{m1}\) & \(f_{m2}\) \\
**[MPa]** & **[MPa]** & **[MPa]** & **[MPa]** & **[MPa]** \\ \hline
4325 & 4804 & 0.75 & 3.9 & 7.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mechanical properties of masonry panels. As anticipated in Section 2, the masonry infills have been modeled adopting a macro-modeling approach. The partially infilled panels have been modelled using \"frame elements\" in SAP2000 [25] that are active in compression only with elastic behavior. The geometric average elastic modulus of masonry between \(E_{m1}\) and \(E_{m2}\) has been adopted. The fully infilled frames have been modeled adopting the link element \"Multilinear plastic\" [25] active in compression only.