## 5 Conclusions  
To date, it has been assumed in most seismic designs that the structures are fixed-supported on the foundation, or that the underlying soil is completely rigid. In fact, the mechanism of the soil-structure interaction introduces considerable differences to the seismic performance of a structure. This study investigated the possibility of SSI amplifying the dynamic responses of a structure, or SSI having detrimental effects on the seismic performance of a structure, by comparing the dynamic responses of the SSI system and a fixed-base structure. The SSI model consists of an oscillator, a 3D rectangular foundation, and a multi-layered half-space. The foundation impedance functions are obtained by the high-precision indirect boundary element method from our previous studies.  
The soil behaves like a cushion under the structure and adds additional flexibility, so from the viewpoint of the spectrum in the frequency domain, the system frequency of SSI is lower than the resonant frequency of the fixed-base structure, the system damping of SSI is larger than the structure damping, and the system amplitude of SSI is smaller than the peak amplitude of fixed-base structure. However, a smaller peak amplitude of the SSI system in the frequency domain does not necessarily mean that the dynamic responses of SSI in the time domain are always smaller than the fixed-base structure. Case studies on four buildings to 42 earthquakes in the time domain show a 15-20% possibility that SSI would have detrimental effects on the seismic performances of structure, or SSI amplifying the dynamic responses of structure.  
This is because there is a shift in peak frequency between the SSI system and the fixed-base structure. When the predominant frequency of the incident wave matches the peak frequency of the SSI system, the dynamic responses of the SSI system are probably larger than the fixed-base oscillator, which probably has detrimental SSI effects on the seismic performance of a structure. The influence of SSI on the seismic performance of a structure depends on the dynamic properties of both the structure itself and the soil.  
It should be noted that the possibility of SSI having detrimental effects is based on the four selected buildings as well as the earthquake records obtained from the buildings, so the database is not very plentiful, and the result is not very generalized. More cases are needed in the future to enrich the topic and the conclusion. It should also be noted that both the soil and the structure are likely to experience some degree of nonlinearity during strong earthquake events, and the detrimental effects of SSI under nonlinear conditions are the focus of our future work.  
Conceptualization, J.F.; Methodology, J.F.; Software, J.F.; Formal analysis, J.F.; Investigation, J.F. and Y.L.; Writing--original draft, W.T.; Writing--review & editing, W.T.; Funding acquisition, W.T., J.F. and Y.L. All authors have read and agreed to the published version of the manuscript.  
This study was supported by the Provincial Natural Science Foundation of Shaanxi (2022 JMR-226, 2022 JQ-513), National Natural Science Foundation of China (52278218), Fundamental Research Funds for Central Universities (G2021 KY05103).  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
The authors are grateful to one of the anonymous reviewers for his/her constructive comments, which lead to improvements in the manuscript.  
The authors declare no conflict of interest.