## 3 Case Study
### Characteristics of the Seed IGMs  
The target spectra for selecting and scaling the seed IGMs are conditional mean spectra (CMSs) and the ASCE 7 design spectra (DSs). Two DSs were constructed using two suites of parameters to consider different intensity levels. Table 2 summarizes the design parameters for the construction of the DSs. For wall structure \(\mathrm{Wn}\) (\(n=1\), \(2\), \(3\)), two CMSs, namely \(\mathrm{Wn}\) CMS 1 and \(\mathrm{Wn}\) CMS 2, was constructed adopting the fundamental mode of the structure \(\mathrm{T}1\) of \(\mathrm{Wn}\) as the conditional period. Thus, overall six CMSs have been built. The Abrahamson-Silva-Kamai model, Boore-Stewart-Seyhan-Atkinson, Campbell-Bozorgnia, and Chiou-Youngs models were adopted to construct CMSs. Each target CMS is the average spectrum of CMSs built with the four ground motion models mentioned above using the same construction conditions. The moment magnitude was 8.5 and 9.0 for \(\mathrm{Wn}\) CMS 1 and \(\mathrm{Wn}\) CMS 2, respectively. The fault type is a strike-slip fault, and the distance from the site to the rupture plane is not less than 12 km. The \(\mathrm{Vs}_{30}\) of site soil is the average shear velocity of top 30 m site soil and is assumed to be 400 m/s. Therefore, the site is classified as Class C of NEHRP. Detailed information for constructing the CMS are summarizes in Table 3, and the target CMSs and DSs are shown in Figure 2. It is seen from Figure 2 that CMSs built with the exact moment magnitude, but different conditioning periods are identical. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**NO.**} & \multirow{2}{*}{**1**} & \multicolumn{6}{c}{**Mode**} & \multirow{2}{*}{**4**} & \multirow{2}{*}{**5**} \\  & & & & & & & & & & \\  & **T (s)** & \(\alpha\) & **T (s)** & \(\alpha\) & **T (s)** & \(\alpha\) & **T (s)** & \(\alpha\) \\ \hline W1 & 0.625 & 0.680 & 0.127 & 0.200 & 0.061 & 0.045 & 0.047 & 0.009 & 0.041 & 0.016 \\ W2 & 1.830 & 0.642 & 0.341 & 0.205 & 0.145 & 0.060 & 0.090 & 0.027 & 0.066 & 0.015 \\ W3 & 2.392 & 0.630 & 0.436 & 0.200 & 0.182 & 0.064 & 0.110 & 0.031 & 0.079 & 0.020 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Modal properties of shear wall structures. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Spectrum No.** & \(S_{\text{ds}}\) **(g)** & \(S_{\text{d1}}\) **(g)** & \(T_{\text{L}}\) **(s)** \\ \hline DS 1 & 1.00 & 0.75 & 12 \\ DS 2 & 1.20 & 0.85 & 10 \\ \hline \hline \end{tabular} Note: \(S_{\text{ds}}\) and \(S_{\text{d1}}\) are spectral accelerations at 0.2 s and 1 s, respectively. \(T_{\text{L}}\) is the transition period of the long-period.  
\end{table} 
Table 2: Design parameters of the ASCE design spectra. A set of twenty seed IGMs were selected and scaled from the strong ground motion database of the Pacific Earthquake Engineering Research Centre (PEER) [40], concerning each target spectrum. Therefore, eight sets of seed IGMs were selected. The criteria for the IGMs selection were: (1) the soil type of the site is class C of NEHRP for all the IGMs; (2) the distance from the recording stations to the epicentre should be not less than 12 km; (3) the range of moment magnitudes of earthquake events for all the IGMs is 6.5 to 9.0. To ensure the response spectra of selected IGMs fit well with the target spectra, the average computed weighted mean squared error (MSE) between the response spectrum of each IGMs and target spectrum was minimized. When selecting and scaling seed IGMs for motion sets 1 and 2 with respect to the DSs, the scale factor has a value range of 1.0 to 5.0, and the weight value of 1.0 is set for periods ranging from 0.1 s to 5.0 s in the computation of MSE. The scale factor value ranges from 3.0 to 5.0 for motion sets 3-8, whose IGMs were selected and scaled with respect to CMS [41]. When minimizing the MSE for motion sets 3-8, the weight value is set to be 1.0 for from 0.2 TI to 2 TI, where TI is the conditioning period for the target CMS.