# Intermediate Isolation System with Nonlinear Lower Structure and Isolation System
## 4 Parametric Response Spectrum Analysis and IIS Design Spectra
It is worth observing that the range of period ratios \(T_{ISO}/T_{LS}=\) 1-3 identifies zone 2, conventionally defined for \(\overline{d}\leq\) 0.9; then, in the range \(T_{ISO}/T_{LS}=\) 3-5, the displacement ratio \(\overline{d}\) increases from 0.9 to 1.0. Hence, in brief, the results provided in Figure 3b lead to the following remarks:  
* The seismic demand on the LS of the IIS building can be almost the same as the existing construction if the isolation system (ISO) is designed to disconnect the upper and lower structures; or, even better, the seismic demand can be reduced if the isolation system is designed to connect appropriately the two portions, thus converting the isolated extension into a mass damper with a large mass ratio. * For ratios of \(T_{ISO}/T_{LS}\) not much larger than 1 (zone 2), the _mass damping effect_ arises, and the isolated upper structure (US + ISO) works as a nonconventional (tuned or  
Figure 3: (**a**) Code Response Spectrum for the selected site (Pozzuoli) [52]; (**b**) graph of displacement ratio \(\overline{d}=d_{1,IIS}/d_{LS}\) as a function of the period ratio \(T_{ISO}/T_{LS}\), considered as _IIS design spectrum_. KEYS: \(T_{B}\) and \(T_{C}\) are the lower and upper limit of the period of the constant acceleration branch; \(T_{D}\) is the value defining the beginning of the constant displacement range; \(T_{ISO,B}\), \(T_{ISO,C}\), \(T_{ISO,D}\), \(T_{ISO,E}\) are the periods of the isolation system in the B, C, D, E design solutions. un-tuned) mass damper (TMD) for the lower structure (LS), leading to a reduced top displacement in the masonry lower structure as compared to the original building;
* For ratios \(T_{ISO}/T_{LS}\) much larger than 1 (zone 3), the _isolation effect_ is emphasized, with almost no variation in the top displacement of the existing lower structure with respect to value registered in the as-is configuration. Other examples of _IIS design spectra_, derived for buildings characterized by different values of the fundamental period (i.e., \(T_{LS}\) = 0.18, 0.55, 0.72, 0.81 s), are given in Figure 4[33], where the base shear ratio (\(\overline{v}=V_{b,IIS}/V_{b,LS}\)) is chosen as response parameter and depicted as a function of the period of the isolation system \(T_{ISO}\). The displacement ratio, adopted for plotting the results in Figure 3b, could be chosen also in this case, with only a change in the \(y\)-axis scale but not in the results trend, due the linearity of the analysis. In each chart, by varying the value of the mass ratio \(\alpha\), the results are provided as fitting curves [33]. Each fitting curve is obtained by post-processing the results, representing the effect of stiffness ratio \(K\) (\(K=\overline{k}_{US}/\overline{k}_{LS}\) = 0.1, 0.5, 1, 2), through low-pass and mean filters [58]. In general, the beneficial effect of mass ratio \(\alpha\) on the mass damping zone can be clearly observed: by adopting larger values of the mass ratio, the shear response is reduced for a wider range of periods of the isolation system. It is also worth observing that not all the cases corresponding to \(\overline{v}\) < 1 can be considered as feasible design solutions; the minimum values of the shear ratio, in fact, often correspond to excessively flexible upper structures (\(K<1\)). Moreover, although \(\overline{v}\) < 1, an unfavourable resonance response, can arise in the upper structure, this occurrence, due to the coupling of higher modes of US and LS, does not depend on \(T_{ISO}\) and leads to an amplified response of the vertical addition [32; 59]. Nevertheless, since mode coupling arises when the periods of the two higher modes in the 3 DOF IIS model are comparable (maximum scatter of 15%), this detrimental effect can be predicted and avoided by design [59]. By varying the period of the lower structure, \(T_{LS}\), the same trend observed in Figure 3b is obtained, with the fixed-base, mass damping and isolation behaviour zones clearly recognizable.