# Intermediate Isolation System with Nonlinear Lower Structure and Isolation System
## 6 Time History Analyses on 3D Models and Comparison to IIS Design Spectrum
### Nonlinear THA: Nonlinearity in the Lower Structure and Isolation System  
Finally, both the lower structure and the isolators are modelled accounting for their hysteretic response, as reported in the previous Section 6.1.  
In Figure 9b, the relevant results of the nonlinear THA on the 3D FE models are compared to the _IIS design spectrum_. The case C and the RSA curve show similar values of displacement ratio. However, a displacement demand larger than one, and thus much larger than the value predicted from RSA, was obtained for the design solution B. The value of the displacement ratio larger than one implies an increase, rather than a reduction, of displacement compared to the reference LS model, which in turn implies that _IIS spectrum_ derived by means of RSA seems neither accurate nor safe as a design tool for maximizing the mass damping effect.  
Therefore, when the nonlinear behaviour of both the isolation devices and the lower structure are considered, the RSA provides an estimate of the expected behaviour _on the safe side_ for isolation periods falling in the transition zone or longer. Indeed, for the cases D and E, significant differences can be observed between the RSA curve and the nonlinear THA results; however, the latter are smaller than the former. Hence, the RSA-based predictions of seismic demand remain _on the safe side_, though not accurate.  
Comparing the IIS solutions to the conventional extension (point A, \(T_{1}\) = 0.43 s), in most cases the IIS counterparts exhibit lower displacement demand. However, fully nonlinear analyses, accounting for the hysteretic behaviour of both masonry structure and isolation system, have highlighted that design solutions that maximize the mass damping effect (design zone 2, case B in Figure 9b) can exhibit an amplification, rather than a reduction, of the seismic response.  
Since solution B is the only one that does not follow, more or less closely, the trend predicted through linear RSA and confirmed by linear THA, it needs further investigation. Considering that nonlinear THA response is particularly sensitive to the modelling assumptions, additional analyses are currently being developed by the authors, by modifying the values of the modal damping ratios (\(\eta_{i}\)) attributed to the masonry structure modes (i.e., to all modes, for the LS in the as-is configuration; from the fourth to the twelfth modes, for the IIS configurations). In addition to the value of 5% adopted in this paper, the value 2% has also been specified for \(\eta_{i}\). The results obtained from analyses with \(\eta_{i}\) = 2% are compared to the ones with \(\eta_{i}\) = 5% in terms of displacement ratio in Figure 10. Here, it can be observed that the results for the design solutions A (conventional extension) and E (perfect isolation) are very close varying \(\eta_{i}\). However, for the solutions B, C, and D, larger scatters can be observed, particularly for solution B. These preliminary results highlight that the modal damping value strongly influences the structural response in nonlinear THA.