## 5 Nonlinear Time History Analyses
### Ground Motion Parameters of the Selected Records  
The H and V components of the three selected earthquake ground motions are carefully analysed by six different intensity parameters, some of which are calculated from the ground motion records and others from the response spectra. The parameters computed from the ground motion records are PGA, Peak Ground Velocity (PGV), Arias Intensity (AI) [37], and Specific Energy Density (SED). PGA corresponds to the peak of the accelerogram, while PGV corresponds to the peak of the velocigram. AI is a cumulative ground motion Intensity Measure (IM), computed based on the time integral of the squared acceleration, as shown in Equation (5), where \(a(t)\) is the ground motion acceleration at time \(t\), \(t_{\text{max}}\) is the total duration of the ground motion, and \(g\) is the acceleration of gravity.  
\[\text{AI}=\frac{\pi}{2g}{\int_{0}^{t_{\text{max}}}{[a(t)]}^{2}dt} \tag{5}\]  
Similarly, SED is computed on the time interval of the squared velocity, as shown in Equation (6), where \(v(t)\) is the ground motion velocity.  
\[\text{SED}={\int_{0}^{t_{\text{max}}}{[v(t)]}^{2}dt} \tag{6}\]  
The parameters computed from the response spectra are the following: Acceleration spectrum Intensity (ASI) [38] and Housner Intensity (HI) [39]. ASI is defined as the integral of the pseudo-spectral acceleration (\(S_{a}\)) over the period range of 0.1-0.5 s, as given by Equation (7), where \(S_{a}\) is the 5% damped spectral acceleration at vibration period T.  
\[\text{ASI}={\int_{0.1}^{0.5}{S_{a}(\xi=0.05;\text{T})}dT} \tag{7}\]  
Similarly, HI is the integral of the pseudo-spectral velocity (\(S_{v}\)) over the period range of 0.1-0.5 s.  
\[\text{HI}={\int_{0.1}^{0.5}{S_{v}(\xi=0.05;\text{T})}dT} \tag{8}\]  
Table 5 shows the values of the above-described intensity parameters calculated for the H and V components of ground motions #1, #2, and #3.  
Figure 10: Response spectra of the H component (**a**) and V component (**b**) and ratio V/H for each period of the selected ground motion records (**c**).  
In order to establish the record characterized by the maximum ground motion intensity for both seismic components, the Ground Motion Parameters (GMPs) of records #2 and #3 (GMP#i) are normalized to the corresponding GMPs of record #1 (GMP#1) (Figure 11). The ratio GMP#i/ GMP#1 shows that the GMPs of record #3 are consistently lower than those of the other two records for both seismic components. Conversely, the normalized GMPs of H components of records #1 and #2 can be greater than or less than one, depending on the GMP. In particular, the GMPs that involve acceleration terms (PGA, AI, and ASI) are greater than one, while GMPs with velocity terms (PGV, SED, and ASI) are lower than one.  
The normalized GMPs of the V components of record #2 are almost always greater than one, except for PGA, for which the ratio GMP#2/GMP#1 equals 0.879. In short, this analysis shows that: (1) the H and V intensities of record #3 are always the lowest, (2) the V intensity of record #2 is almost always the highest (except for the PGA), and (3) there is not a record characterized by the highest H intensity, because it depends on the GMP.