## 2 Rational Range of the Yield Ratio of Isolation System
### Design of the Study Cases  
Through the introduction of the prototype buildings, it can be seen that two different heights and one seismically isolated scheme (i.e., PBI scheme) have been taken into consideration. As mentioned above, different schemes of the isolation system, which are usually determined by the real architectural design requirements, may be adopted in the design of seismically isolated RC frame-core tube tall buildings. Hence, in addition to the PBI scheme, the conventional base-isolated scheme should also be taken into account. The cases using the CBI scheme are herein designed based on the structures of C1 and C4 above the ground. Subsequently, different yield ratios are considered. 28 study cases with different yield ratios and seismically isolated schemes were redesigned based on the prototype buildings. The upper and lower limits of the yield ratios are approximately 1.5% and 3.5%, respectively. Different yield ratios are achieved through the adjustment of the type and quantity of the isolators. Detailed information (consisting of the height, seismically isolated scheme and yield ratio) and the corresponding \(T_{\text{is}}\) of these cases are presented in Table 3. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Indexes** & **C1** & **C4** \\ \hline \(T_{\text{f}}\) (s) & 1.59 & 1.52 \\ \(T_{\text{is}}\) (s) & 4.44 & 4.08 \\ \(Q_{\text{y}}/W\) (\%) & 2.7 & 3.2 \\ \(\beta\) & 0.36 & 0.36 \\ MBD (mm) & 488 & 488 \\ \(\sigma_{\text{max}}^{\text{g}}\) (MPa) & 12.38 & 13.17 \\ \(\sigma_{\text{max}}^{\text{r}}\) (MPa) & 29.07 & 26.43 \\ \(\sigma_{\text{max}}^{\text{r}}\) (MPa) & 0.00 & 0.09 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Critical design parameters and indexes of prototype structures. The single-degree-of-freedom (SDOF) model and multi-degree-of-freedom (MDOF) shear model are widely used to guide the preliminary design and conceptual research of seismically base-isolated structures exhibiting significant shear deformation mode [9; 22; 24; 27; 28; 29]. However, the RC frame-core tube buildings exhibit a flexural-shear deformation mode [30]. A reliable numerical model that can consider such deformation characteristic is required. The refined finite element (FE) model, which is widely acknowledged to be capable of reflecting such deformation characteristic [31; 32; 33; 34], is adopted here. The general-purpose commercial software ETABS [35] is used to establish the refined FE model and conduct the seismically isolated design as well as the seismic performance assessment of the abovementioned 28 cases. It is notable that the superstructure of the isolated buildings usually experiences minor damage as expected; therefore, an elastic model for the superstructure is usually adopted [36; 37]. Because of this, the beams and columns of the superstructure are modeled with elastic frame elements. The shear walls are simulated using the elastic shell element. In contrast, as the plastic response of the seismically isolated structures is mostly concentrated in the isolation system, a plastic model is usually adopted for the isolation system. Hence, the Rubber Isolator element and the Gap element are herein adopted for the isolators, while the Damper-Exponential element is used for the NFVDs. The abovementioned modeling methods are widely adopted and have been proved to be reliable [20; 38]. For the ground motions, two natural ground motion records and one artificial ground motion are used to design the study cases and investigate the rational yield ratio according to GB50011-2010 [17]. The response spectrum of each ground motion is compared with the design response spectrum as shown in Figure 3. The ranges of interest for the period are 1.31-1.59 s for the fixed-base structures and 3.90-4.95 s for the seismically isolated structures. It can be found that the mean response spectrum agrees well with the design response spectrum at these period ranges. The ground motions are scaled to 375 cm/s\({}^{2}\) and 637.5 cm/s\({}^{2}\) to conduct time history analyses (THAs) under DBE and MCE,