## 2 Numerical Analysis
### Design of Structural Model for Simulation  
This study simulates one of the horizontal frames in the middle position of the above prototype structure. The dynamic characteristics and response of the longitudinal direction (X-direction) of the model under earthquake excitations are investigated. The model has a geometric similarity ratio of 1:5. The detailed similarity ratios of model parameters are shown in Table 2. The model has two spans in the X direction and one span in the Y direction; its total height is 4.92 m. The first story and its above story height are 0.96 m and 0.66 m, respectively. The isolation system is inserted on the top of columns at the position of 0.23 m below the first floor. There are no infilled walls in the model frames. A non-isolated model without an isolation layer and the coupled beams was also simulated as a reference model for comparison. Figure 3 shows the top view and the front view of the isolation model and non-isolated model.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Design Parameters** & **Values** & **Design Parameters** & **Values** \\ \hline \hline Fortification intensity & 8 degrees & Peak acceleration (PGA) & 0.20 g \\ Characteristic period & 0.40 s & & \\ Column section in the first story & 750 mm \(\times\) 750 mm \(\times\)1 & Column section of the 2 nd to 7 th & 550 mm \(\times\) 550 mm \(\times\)3 \\ Section of the coupled beam and the isolation layer frame beam & 400 mm \(\times\) 700 mm \(\times\)2 & Section of beams in other layers & 300 mm \(\times\) 550 mm \(\times\)4 \\ Isolation layer thickness & 170 mm & Other story thicknesses & 120 mm \\ Steel type and its strength & HRB400 with yield strength = 400 MPa & Concrete strength grade & C30 \\ \hline \hline \end{tabular} Note: *1 Section reinforcement ratio of 2%; *2 the reinforcement ratios of upper and lower section are both 1.2%; *3 (section reinforcement ratio of 1.5%); *4 the reinforcement ratios of upper and lower section are both 1.5%).  
\end{table}
Table 1: Main design parameters for the prototype structure.  
Figure 3: Top view and front view of the isolation model and non-isolated model (unit: mm): (**a**) Top view of the simulated model; (**b**) isolation model (front view); (**c**) non-isolated model (front view).  
The first story of the prototype is composed of six columns that connect to beams, the section of which was then scaled to be 150 mm \(\times\) 150 mm (Figure 4a). The column height of the first-story isolated model reduces to 730 mm from 960 mm. The column slenderness ratio is calculated as 4.87 after the isolation layer with the slab thickness of 35 mm was inserted on the top of the column. While in the non-isolated model, the section of the column is 125 mm \(\times\) 125 mm with a column height of 960 mm and slenderness ratio of 7.68; the slab thickness is 25 mm. Figure 4 presents the frame beam, the column section size, and the reinforcement distribution of the structural model.  
The concrete cubic (strength grade C30) used in the prototype structure has the compressive strength of 38.4 MPa and the elastic modulus of 3.81 \(\times\) 10\({}^{4}\) MPa. Table 3 shows the coupon test data of the steel bar. The high-strength steel wires are used as steel slab bars and stirrup bars.