## 2 Rational Range of the Yield Ratio of Isolation System
### Overview of the Prototype Buildings  
The selected two real engineering practices are seismically isolated RC frame-core tube tall buildings located in a near-fault region with a seismic intensity of 8.5 degree. According to GB50011-2010 [17], the 8.5 degree means that the correspond peak ground acceleration (PGA) values of the service level earthquake (SLE) (i.e., 63% probability of exceedance in 50 years), the design basis earthquake (DBE) (i.e., 10% probability of exceedance in 50 years) and the maximum considered earthquake (MCE) (i.e., 2% probability of exceedance in 50 years) are 110 cm/s\({}^{2}\), 300 cm/s\({}^{2}\) and 510 cm/s\({}^{2}\), respectively. The total heights of these two buildings above the ground are 79.2 m with 22 stories (named as C1) and 65.8 m with 17 stories (named as C4), respectively. The height-to-width ratios are 2.3 and 1.91 for C1 and C4, respectively. The three-dimensional views and the plan views of the prototype buildings are presented in Figures 1 and 2, respectively. The site condition belongs to the Site Class III and the second group in the GB50011-2010 [17]. The characteristic period of the site is 0.55 s. The closet distance from these two buildings to the rupture plane (i.e., \(R_{\text{rupt}}\)) is 7.5 km. When \(R_{\text{rupt}}\) is lower than 10 km and higher than 5 km, a near field influence coefficient with a value not less than 1.25 is introduced to consider the near field effect according to the GB50011-2010 [17]. Because the seismic design load of these buildings is extremely large and the occupancy importance of these buildings is very high, a special advisory committee (referred to as \"the committee\" hereafter) was established to guide and monitor the seismically isolated design. The near field influence coefficient was recommended to be 1.25 through a detailed discussion by the committee, which means the PGA values of the SLE, DBE and MCE increase to 137.5 cm/s\({}^{2}\), 375 cm/s\({}^{2}\) and 637.5 cm/s\({}^{2}\), respectively. Figure 1: Three-dimensional view of prototype buildings: (**a**) C1 and (**b**) C4. It is notable that the basements of C1 and C4 are designed as 4 stories with a total height of 16.05 m and 14.15 m, respectively. The conventional base-isolated (CBI) scheme, which isolates the superstructure in the elevation of \(\pm\)0 m, cannot satisfy the architectural design requirements. Meanwhile, the base-isolated scheme, which isolates the entire structure at the bottom of the basement, leads to a total height of approximately 95 m, thus leading to a certain extent of tensile stress in the isolators. Hence, a partially basement-isolated (PBI) scheme as shown in Figure 2 is recommended by the committee and adopted for these two buildings. Specifically, the columns are isolated in the elevation of \(\pm\)0 m, while the core tubes are isolated at the bottom of the basement. Because of the limit width of the isolation gap, which is recommended to be 600 mm by the committee, 16 NFVDs are adopted to control the MBD under the MCE. Specifically, by adopting the NFVDs, the MBD under the MCE are effectively reduced from 932 to 488 mm and 656 to 488 mm for C1 and C4, respectively. It is worth mentioning here that the authors have designed 29 different RC tall buildings located in this region and 16 NFVDs with approximately identical parameters are adopted for these buildings. The damping exponent and damping coefficient of the NFVDs are approximately 0.3 and 210 kN\(\cdot\)s/mm. The maximum damping forces of the NFVDs in these buildings are all almost 2000 kN. Hence, the variation in numbers and parameters of NFVDs are herein not considered.