# Quantification of Energy-Related Parameters for Near-Fault Pulse-Like Seismic Ground Motions
## 5 Sensitivity Analysis
### Influence of Seismological Parameters  
Henceforth, for the sake of conciseness, the spectra calculated for the hysteretic model HYST1 and a ductility level \(\mu\) equal to 2 only were given in order to assess the influence of most common seismological parameters employed for hazard quantification in design codes, namely earthquake \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Moment Magnitude \(M_{w}\)**} & **Closest Site-to-Source Distance** & **Soil Type** \\  & \(D_{f}\) **(km)** & \(V_{S30}\) **(m/s)** \\ \hline
5–6 (14) & 0–5 (31) & \(<\)180 (10) \\
6–7 (64) & 5–15 (63) & 180–360 (66) \\ \(>\)7 (49) & 15–30 (24) & 360–800 (51) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Definition of the subsets of seismic records for the sensitivity analysis (the number of records is indicated within brackets). Figure 2: Variability of moment magnitude \(M_{w}\), closest site-to-source distance \(D_{f}\) and soil preferred shear-velocities \(V_{S30}\) as function of the pulse period \(T_{p}\) within the considered dataset. magnitude, site-to-source distance and soil type. It was found, however, that the main findings of this evaluation also hold true for other hysteretic models and ductility level. In this perspective, absolute \(E_{I\mu\mu}\) and relative \(E_{I\mu\mu}\) input energy are shown in Figure 3.  
It can be inferred from Figure 3 that the differences between absolute and relative input energy spectra were basically negligible. In this regard, it was pointed out in [30] that relative and absolute input energies usually exhibit similar spectra in cases of forward directivity without distinctive acceleration pulses. It was also noted in [30] that the presence of a distinct acceleration pulse generates smaller or larger amplitudes in the short- and long-period ranges of the relative energy spectra, respectively, than those observed in the absolute energy spectra (i.e., the difference between relative and absolute energy becomes largest during sudden energy spikes). As seen in Figure 3, therefore, it is understood that distinctive acceleration pulses are not very common (at least within the considered database), since a large enough set of seismic records basically hides the possible differences between absolute and relative input energy. As expected, the larger the magnitude was, the larger was the period at which the peak value of the relative or absolute energy spectrum was attained. This is attributable to the fact that the peak value of the relative or absolute energy spectrum is commonly attained in the vicinity of the pulse period which, in turn, scales up when the earthquake magnitude increases [14]. Moreover, the larger is the earthquake magnitude, the longer is the period range for which relative or absolute energy spectral values are close to the peak. Figure 3 also confirms that higher energy demands are expected as the site-to-source distance becomes shorter and shorter, whereas it highlights that input energy spectra also become significantly flatter when the distance increases. Furthermore, Figure 3 suggests that absolute and relative input energy spectra are influenced by the soil type for rather low values of \(V_{530}\) only, namely less than 180 m/s. Otherwise, no significant effects are produced, since the mean spectra for \(V_{530}\) larger than 180 m/s are very close to each other and almost overlap for period values larger than 4 s. This evidence, however, is not conclusive and might be affected by  
Figure 3: Spectra of the absolute \(E_{I\mu\mu}\) and relative \(E_{I\mu\mu}\) input energy 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). statistical distortion, since the number of seismic records with \(V_{S30}\) less than 180 m/s is low and much less than the number of those available for \(V_{S30}\) between 180 m/s and 360 m/s or between 360 m/s and 800 m/s.