## 6 Conclusion  
(1) When the SSI effect is considered in the resonance of isolation structures, the natural vibration characteristics of the interlayer isolation system change obviously. According to the modal analysis of the rigid interlayer isolation system and the soft soil interval isolation system, the natural vibration period of the interlayer isolation structure when considering the SSI effect is approximately 1.20 times that of the rigid foundation, and the damping ratio is approximately 1.40 times that of the rigid foundation.  
(2) The acceleration response of the upper structure is reduced after considering the impact of the SSI effect; however, as the PGA increases, the acceleration response of the long-periodic seismic action is less than that in the case of a normal earthquake. The maximum PGA at the top of the rigid foundation is 1.32, and the soft land base is 0.74. The PGA was used in the case of 0.2 g long-period seismic action, and the maximum acceleration amplification coefficient of the upper structure on the rigid foundation is 2.06, with the soft land base of 1.74. However, when considering the SSI effect, the acceleration amplification factor of the top of the substructure is obviously greater than that of the top of the superstructure; therefore, in the designing of a seismic structure, the safety of the lower structure under the action of earthquakes must be focused on.  
(3) After considering the impact of the SSI effect, the displacement response of the interlayer isolation structure is enlarged. The PGA was calculated under normal seismic action of 0.2 g. In addition, the displacement response of the upper layer of the upper structure was 1.52 times that of the rigid foundation, and that of the lower structure was 2.01 times. The PGA was calculated for the long-periodic seismic action of 0.2 g, and the upper layer of the upper structure is 1.88 times the rigid foundation, and that of the lower structure was 2.39 times that of the rigid foundation.  
(4) After considering the impact of the SSI effect, the shear force of the average seismic movement was significantly reduced, and the long-periodic seismic movements for the PGA of 0.1 g were significantly increased in the lower layer; however, the PGA was close to that of the rigid foundation at 0.2 g. In the case of the normal seismic action, PGA = 0.2 g; the shear force of the base of the interlayer isolation structure of the rigid foundation is 1.21 times that of the soft land. The PGA is used for the long-periodic seismic action of 0.1 g, with the base shear force of the soft land base as 1.38 times that of the rigid foundation. The PGA is used for the long-periodic seismic action of 0.2g, with almost similar base shear forces of the two ground conditions.  
Conceptualization, L.X., J.S. and Y.W.; methodology, L.X., Y.L. and Y.W.; validation, L.X. and Y.W.; investigation, L.X., Y.W. and Y.L.; resources, J.S. and Y.W.; data curation, Y.W. and L.X.; writing--original draft preparation, L.X. and Y.W.; writing--review and editing, Y.W., Y.L. and J.S.; visualization, L.X.; supervision, Y.W., J.S. and Y.L.; project administration, Y.W. and J.S. All authors have read and agreed to the published version of the manuscript.  
This work was supported by Scientific Research Fund of Institute of Engineering Mechanics, China Earthquake Administration (Grant No. 2021D03) and the Sichuan Provincial Natural Science Foundation Project (Grant No:2022 NSFSC1174).  
Not applicable.  
The authors declare no conflict of interest.