# A Site-Specific Response Analysis: A Case Study in Hanoi, Vietnam
## 4 Spectral Shapes  
The soil nonlinearity can be characterized either through the equivalent linear or the fully nonlinear approach. In this section, the normalized spectral shapes from both the NL and EQL approaches are compared with the normalized design spectrum from TCVN 9386: 2012 to evaluate the applicability of the design code. Figures 7 and 8 compare the spectral shapes from the NL and EQL analyses with the design spectrum for the profiles of both site classes C and D. Districts 1 and 3 consist of site class C profiles. The mean normalized spectrum calculated in this study is higher than the normalized design spectrum for the period range from 0.6 to 2 s in the case of both the NL and EQL approaches. District 2 and District 3 consist of site class D profiles. The normalized spectral shape is lower than the design spectrum across the whole period range in the case of the NL method, whereas it matches the design spectrum well in the case of the EQL method. The underestimation of calculated spectral shape in the case of the NL approach can be attributed to the high levels of nonlinearity induced because of the  
Figure 6: Comparison of selected input ground motions with the target spectrum. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**No** & **Earthquake Name** & **Year** & **Station** & \begin{tabular}{c} **Mag.** \\ **(M\({}_{W}\))** \\ \end{tabular} & **Mechanism** & \
\begin{tabular}{c} **R\({}_{\text{rop}}\)** \\ **(Km)** \\ \end{tabular} &
\begin{tabular}{c} **V\({}_{\text{Sao}}\)** \\ **(m/s)** \\ \end{tabular} \\ \hline
1 & San Fernando & 1971 &
\begin{tabular}{c} Pasadena—Old \\ Seismo Lab \\ Pasadena–CIT \\ Kresge Lab \\ \end{tabular} & 6.61 & Reverse & 21.5 & 969.07 \\
2 & Whititer Narrows-01 & 1987 &
\begin{tabular}{c} Pasadena—Old \\ Pasadena–CIT \\ Kresge Lab \\ \end{tabular} & 5.99 & Reverse & 18.12 & 969.07 \\
3 & Loma Prieta & 1989 & \
\begin{tabular}{c} Piedmont Jr High \\ School Grounds \\ \end{tabular} & 6.93 &
\begin{tabular}{c} Reverse \\ Oblique \\ Reverse \\ \end{tabular} & 73 & 895.36 \\
4 & Loma Prieta & 1989 & Point Bonita & 6.93 &
\begin{tabular}{c} Reverse \\ Oblique \\ \end{tabular} & 83.45 & 1315.92 \\
5 & Loma Prieta & 1989 & \
\begin{tabular}{c} SF—Pacific Heights \\ So. San \\ \end{tabular} & 6.93 &
\begin{tabular}{c} Reverse \\ Oblique \\ \end{tabular} & 75.96 & 1249.86 \\
6 & Loma Prieta & 1989 &
\begin{tabular}{c} So. San \\ Francisco, Sierra Pt. \\ LAA—Wondeland Ave \\ \end{tabular} & 6.93 & Reverse & 63.15 & 1020.62 \\
7 & Northridge-01 & 1994 & LA—Wondeland Ave & 6.99 & Reverse & 20.29 & 1222.52 \\
8 & Northridge-01 & 1994 & Vasquez Rocks Park & 6.99 & Reverse & 23.64 & 996.43 \\
9 & Chi-Chi, Taiwan-05 & 1999 & TTN042 & 6.20 & Reverse & 85.17 & 845.34 \\
10 & Umbria-03, Italy & 1984 & Gubbio & 5.60 & Normal & 15.72 & 922 \\
11 & Kobe, Japan & 1995 & Kobe University & 6.90 & Strike slip & 0.92 & 1043 \\
12 & Chi-Chi, Taiwan-05 & 1999 & HWA002 & 6.20 & Reverse & 45.03 & 789.18 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Selected earthquake events. softness of site class D profiles, which could lead to a certain amount of deamplification. It should be noted that most building periods are greater than 0.3 s [29]. Figure 9 shows a comparison of the NL and EQL analysis response spectra and the design spectrum. As can be seen from the figure, the mean normalized response spectrum in the case of the EQL analysis is higher than that of the NL analysis in both the site classes, especially near the natural site periods. The NL analysis predicts smaller spectral accelerations from 0.2 s to 1.6 s in case of profiles of site class C, whereas the period range extends up to 2.4 s in case of site class D profiles. This difference is attributed to the persistent softening of properties used in the nonlinear analysis which is not the case in the EQL analysis, where constant and strain compatible properties are used. These results are in line with the study of [PERSON] and [PERSON] [30].