## 2 Numerical Method and Its Validation
### Parameter Setup  
Considering the soil shear wave velocities (\(V_{s}\)) of most building sites are within the range of 150 to 500 m/s, the vs were respectively set as 150, 250, 350, and 500 m/s to roundly investigate the influence of the soil shear wave velocity on the SSI effect. To investigate the influence of the spectral characteristics of seismic records on the SSI effect, three ground motion records with different spectral characteristics were selected from the PEER Ground Motion Database, and the peak accelerations of the three ground motion records were adjusted as 100 gal (cm/s\({}^{2}\)). The detailed information of the three records is given in Table 1, where the R\({}_{\text{B}}\) (Joyner-Boore distance) [34] is the shortest distance to the surface projection of the fault plane. The comparison of the Fourier spectra of the three records is shown in Figure 8.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Records**} & \multicolumn{2}{c}{**Earthquake**} & \multirow{2}{*}{**Year**} & \multirow{2}{*}{**Station Name**} & \multirow{2}{*}{**Magnitude**} & \multicolumn{1}{c}{**R\({}_{\text{jb}}\)**} & \multirow{2}{*}{**Component**} \\  & **Name** & & & & & **(km)** & \\ \hline \multirow{2}{*}{RSN-445} & New & \multirow{2}{*}{1984} & Turangi & \multirow{2}{*}{5.5} & \multirow{2}{*}{3.76} & \multirow{2}{*}{TUR329.AT2} \\  & Zealand-01 & & & & & \\  & New & & & & & \\  & New & & & & & \\  & Zealand-02 & & & & & \\  & Northridge-01 & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Ground motion records.  
Figure 8: Fourier spectra of ground motion records.  
The numbers of floors for RC-frames are generally no more than 15 in reality. Therefore, 1-, 3-, 6-, 9-, 12-, and 15-story RC-frames (Frame-1, Frame-3, Frame-6, Frame-9, Frame-12, and Frame-15) were designed to roundly investigate the influence of the structure height, in which the span lengths and story heights of RC-frames were 6.0 and 3.3 m, respectively. The elevations of the fixed-base RC-frames and RC-frames considering SSI are shown in Figures 9 and 10, respectively. Regarding the RC-frames, the reinforcing bar is the HRB400 with a nominal yield strength of 400 MPa, and the concrete is C35 grade concrete with a nominal cubic compressive strength of 35 MPa [35]. The detailed parameters of the RC-frames and their pile foundations are shown in Table 2. Conducting modal analyses on fixed-base RC-frames, it can be obtained that the periods of Frame-1, Frame-3, Frame-6, Frame-9, Frame-12, and Frame-15 are 0.127, 0.384, 0.713, 1.091, 1.493, and 1.876 s, respectively. Regarding the soils in the soil-structure systems, the length of soil parallel to the seismic excitation direction should be greater than five times the width of the structural foundation to ensure the influence of the artificial boundary of the soil is slight [36]; the size of the soil element should not exceed (1/5\(\sim\)1/8)\(V_{s}\)/\(f_{max}\) to prevent the high frequency components of seismic records from being filtered out, where vs. denotes the shear wave velocity of soil and \(f_{max}\) denotes the maximum frequency of the seismic record. Accordingly, the length of soil parallel to the seismic excitation direction was determined as 60 m, and the length of soil element was set as 1.0 m. In addition, the thicknesses of soils in the soil-structure systems were set as 20 m based on the recommendation of the Chinese code [3].