## 2 Materials and Methods
### Phase Three: Determination of Site Coefficients and Design Horizontal Response Spectra  
Phase three was designed to achieve the third objective of this study. In this phase, the response spectra, which were obtained from the ground response analysis, were analyzed to determine the designed horizontal response spectral acceleration. The curves and spikes in the horizontal response spectra were smoothed by proposing a single line known as designed horizontal response spectral acceleration (DHRSa). For response spectra, only results of the 1000-year return periods were used, and the damping was assumed to be 5%. The spectral acceleration (Sa) values of the 1000-year return period for 0.2 s and 1.0 s were extracted from a previous study [34]. Details of the site coefficients and designed horizontal response spectra in acceleration are presented herein. The process of proposing DHRSa started with analyzing horizontal spectral acceleration output from GRa conducted using NERA, a one-dimensional nonlinear ground response analysis. Horizontal response spectra for each site were analyzed according to seismic events and sites, then the results were plotted for spectral acceleration versus the period. Comparisons of the horizontal spectral accelerations were made to determine the effects of far-field and near-field and a combination of far-field and near-field seismic events. Then, plotting of horizontal response spectra for the average as well as the envelope was made based on soil type. After that, comparisons were made between horizontal response spectral accelerations obtained with the proposed horizontal response spectra by ISO19901-2 [26]. A sample of the horizontal response spectra for site D4 is presented in Figure 6 for far-field seismic events. The same analysis was conducted for all sites. The average of each site was used to obtain the average and envelope for soil types D and E. From the plotting, the constant acceleration value was selected and used in the process of proposing the site coefficient for acceleration (Ca) and site coefficient for velocity (Cv). The Ca and Cv values are important in the construction of horizontal response spectra in acceleration. The values of the proposed Ca and Cv in this study were calculated by implementing back-calculations of the equation suggested in ISO19901-2. The equations used in the construction of DHRSa can be seen in Equation (3) to Equation (6). Equation (3) is used when T (natural period) is less or equal to 0.2 s while Equation (4) is for T greater than 0.2 s but less than 4 s if only the Sa for that site follows the condition in Equation (5). Equation (6) is used when the period is greater than 4 s but less than 10 s. To calculate the site coefficients, the values of Sa at 0.2 s and 1.0 s periods must be known. In this study, the values were extracted from a previous study [34] where a probabilistic seismic hazard assessment was conducted to predict the value. The Sa values and values of Ca and Cv proposed by ISO19901-2 were used in this study. The Sa map for 0.2 s was 0.05 and the Sa map for 1 s was 0.02. For soil type D, Ca was 1.6 and Cv was 2.4, while in soil type E, Ca was 2.5 and Cv was 3.5. \[S_{a,\,site}(T)=(3T+0.4)C_{a}\times S_{a,map}(0.2) \tag{3}\]  
\[S_{a,\,site}(T)=C_{v}\times S_{a,map}(1.0)\,/T \tag{4}\]  
\[S_{a,\,site}(T)\leq C_{a}\times S_{a,map}(0.2) \tag{5}\]  
\[S_{a,\,site}(T)=4C_{v}\times S_{a,map}(1.0)\,/T^{2} \tag{6}\]  
where;  
\(T\) is the natural period;  
\(C_{a},C_{v}\) are the site coefficients;  
\(S_{a,\,site}(T)\) is the site spectral acceleration corresponding to period \(T\);  
\(S_{a,map}(0.2)\) is the site spectral acceleration corresponding to period 0.2 s;  
\(S_{a,map}(1.0)\) is the site spectral acceleration corresponding to period 1.0 s.  
Site coefficients and Ca-Cv values proposed in this study were calculated by setting the maximum Sa value at 0.2 s based on the plotted HRSa. The Ca value was calculated using Equation (5).