## 7 Conclusions  
This study investigates the seismic response of the SIS system. Physical experiments were conducted to analyze the distribution of pile bending moments, pile-soil interface interactions, and plastic hysteresis loops of the pile foundation in a detailed parameterized manner. Subsequently, numerical analysis was employed to validate the physical model, and further analysis was carried out to examine the energy variations in the sand pile and foundation within the seismic energy field. The key research findings are summarized as follows:  
The \"X-shaped\" and rectangular pile groups only exhibit heavy plastic region \(A\) with significant mass distribution and mild plastic region \(C\) with less soil compression. The absence of a moderate plastic region \(B\) is attributed to the variations in pile spacing and instability caused by the formation of quadrangular prism damping units between the piles.  
The hexagonal pile group, which forms a triangular prism damping unit with the surrounding soil, mitigates the piled foundation response. It partially counteracts the seismic wavefront, reducing the extent of injury to structures with a top-heavy mass distribution. This enhances the energy dissipation capacity of the piled foundation and stabilizes the damping characteristics.  
The greater the Energy Residual Index (ERI), the lower the structural energy dissipation, indicating poorer seismic performance. Irregular pile spacing and the instability of the quadrilateral prism damping unit formed by piles and soil increase the ERI of the piled foundation. An increased underwater pressure results in higher ERI due to the enhanced suppression of vertical seismic frequencies. The occurrence of frequency resonance-induced injury leads to additional energy.  
The relationship between the plastic region and pile arrangement was determined based on the mechanical behavior of the pile-soil interface and the energy changes. For the \"X-shaped\" pile group, the boundary between the heavy and mild plastic regions is located at a depth of \(L=2.25\)\(D\). In the hexagonal pile group, the boundaries between the heavy, moderate, and mild plastic regions are situated at depths of \(L=4\)\(D\) and \(L=8\)\(D\). The boundaries between the heavy and mild plastic regions are found in the rectangular pile group at a depth of \(L=2.08\)\(D\).  
Figure 13: Plastic regions of the pile.  
**Author Contributions:** Conceptualization, H.F. and Y.Z.; methodology, H.F.; software, J.L.; validation, H.F., Y.Z. and J.L.; formal analysis, J.L.; investigation, Z.C.; resources, Y.Z.; data curation, Z.C.; writing--original draft preparation, H.F.; writing--review and editing, H.F.; visualization, Z.C.; supervision, J.L.; project administration, Z.C.; funding acquisition, Y.Z. All authors have read and agreed to the published version of the manuscript.  
**Funding:** The financial support of the National Natural Science Foundation for General Program of China (Grant No. 52178316) and the National Science Foundation for Excellent Young Scholars of China (Grant No. 51922029) is acknowledged.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data presented in this study are available on request from the corresponding author. The data are not publicly available due to network security issues.  
**Conflicts of Interest:** The authors declare no conflict of interest.