# Quantification of Energy-Related Parameters for Near-Fault Pulse-Like Seismic Ground Motions
## 5 Sensitivity Analysis
### Influence of Hysteretic Model and Ductility Level  
From a qualitative standpoint, the shape of the energy-related spectra and their sensitivity with respect to the main seismological parameters (i.e., earthquake magnitude, site-to-source distance and soil  
Figure 6: Spectra of the hysteretic energy reduction factor \(R_{Ha}\) for the hysteretic model HYST1 and ductility level \(\mu\) equal to 2 considering different subsets of seismic records (filled area: envelope of the spectra; solid line: mean spectrum).  
Figure 7: Spectra of the cumulative plastic deformation ratio \(\eta\) for the hysteretic model HYST1 and ductility level \(\mu\) equal to 2 considering different subsets of seismic records (filled area: envelope of the spectra; solid line: mean spectrum).  
type) was not markedly affected by the hysteretic model and its constitutive model parameters. From a quantitative standpoint, however, significant differences could be observed for some energy-related parameters. In particular, small differences were observed when comparing mean spectra of absolute \(E_{\text{{{{{L}}}}\mu}}\) and relative \(E_{\text{{{{{L}}}}\mu}}\) input energy as well as those for input energy reduction factors \(R_{\text{{{{{E}}}}\mu}}\) and \(R_{\text{{{{E}}}}}\), and hysteretic energy dissipation demand \(E_{\text{{{{H}}}}}\). The observed differences became larger and larger for increasing values of the ductility level \(\mu\). On the other hand, the spectra of the hysteretic energy reduction factors \(R_{\text{{{{H}}}\mu}}\) and \(R_{\text{{{{H}}}\mu}}\) as well as those for the cumulative plastic deformation ratio \(\eta\) were affected to a rather larger extent by hysteretic behavior and/or the ductility level \(\mu\) (see Figures 8 and 9). Particularly, these plots emphasized that large differences can arise in the spectra of the hysteretic energy reduction factor and the cumulative plastic deformation ratio if non-degrading systems (i.e., EPP and HYST1) or degrading ones (i.e., HYST2, HYST3, HSYT4 and HYST5) are compared. These differences were also amplified for increasing values of the ductility level.  
As already pointed out in [28], structural systems experiencing stiffness and strength degradation do not necessarily require high yielding strengths for a given ductility value. The fact that the force  
Figure 8: Influence of the hysteretic model on the spectra of absolute input energy reduction factor \(R_{\text{{{{E}}}\mu}}\) for a ductility level \(\mu\) equal to 2 (filled area: envelope of the spectra; solid line: mean spectrum).  
Figure 9: Influence of the hysteretic model on the spectra of elastic limit strength \(R_{y}\) and cumulative plastic deformation ratio \(\eta\) for a ductility level \(\mu\) equal to 4 (filled area: envelope of the spectra; solid line: mean spectrum).  
imposed on systems with degrading behavior is less demanding than that imposed on elastoplastic systems can be explained by considering that the response of the former features a larger number of hysteretic cycles at smaller amplitude. Elastoplastic systems have greater chances of drifting and hence require more strength capacity than the degrading ones to limit the deformation up to the prescribed damage level.