# Quantification of Energy-Related Parameters for Near-Fault Pulse-Like Seismic Ground Motions
## 5 Sensitivity Analysis
### Influence of Seismological Parameters
It was also convenient to investigate the input energy reduction factors \(R_{Ea}\) and \(R_{Er}\) for a given ductility demand \(\mu\). To this end, the spectra related to \(R_{Ea}\) only are shown in Figure 4 because they have similar results as those carried out for \(R_{Er}\). It can be noted from Figure 4 that the mean spectra of the absolute input energy reduction factor \(R_{Ea}\) in terms of earthquake magnitude and site-to-source distance were not too far each other for period values less than 4 s. On the other hand, mean spectra of the absolute input energy reduction factor in terms of soil type were closer to each other for almost the whole range of period values. The analysis of the hysteretic energy dissipation demand spectra \(E_{H}\) provided no enlightening new evidence about the role of seismological parameters on the energy demand with respect to the conclusions already drawn from the analysis of absolute \(E_{\mathrm{I}\mu}\) and relative \(E_{\mathrm{I}\mu}\) input energy spectra, as can be concluded by comparing Figures 3 and 5. It was also opportune to investigate the hysteretic energy reduction factors \(R_{H\mathrm{a}}\) and \(R_{Hr}\) for a given ductility demand \(\mu\). Assuming the hysteretic energy reduction factor \(R_{H\mathrm{a}}\) as a reference parameter, Figure 6 shows that it was strongly affected by the earthquake magnitude and to a lesser extent by soil type, whereas the site-to-source distance did not produce very large effects. Specifically, the increment of the earthquake magnitude caused a shifting on the right of the period at which the peak of the hysteretic energy reduction factor was attained. In addition, the larger the earthquake magnitude  
Figure 4: Spectra of the absolute input energy reduction factor \(R_{Ea}\) 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 5: Spectra of the hysteretic energy dissipation demand \(E_{H}\) 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). was, the lower was the slope of the post-peak branch of the hysteretic energy reduction factor \(R_{Ha}\) spectrum. Note, however, that the peak value of the hysteretic energy reduction factor \(R_{Ha}\) spectrum did not seem much affected by the earthquake magnitude, and its variability decreased when the earthquake magnitude increased. Regarding the influence of the soil type, it appeared evident for rather low values of \(V_{S30}\) only, but it might be possible that this evidence could have been corrupted by the low number of seismic records available for \(V_{S30}\) less than 180 m/s. Finally, the spectra for the cumulative plastic deformation ratio \(\eta\) are reported in Figure 7. The analysis of this energy-related parameter was especially important because the hysteretic energy demand \(E_{H}\) alone cannot provide a proper assessment of the structural behavior, particularly for reinforced concrete structures. In fact, the hysteretic energy associated with structural systems having small strength and undergoing a large cyclic response can be similar to that experienced by structural systems having large strength but undergoing a small cyclic response. It is evident that the cumulative plastic deformation ratio \(\eta\) was less affected by seismological parameters with respect to the hysteretic energy demand \(E_{H}\). As a matter of fact, the mean spectra of the cumulative plastic deformation ratio \(\eta\) differed significantly only for very large earthquake magnitude values and period values less than 4 s.