## 3 Analysis of Experimental Results
### Piled Foundation Energy Absorption and Dissipation  
The seismic performance of a structure fundamentally represents its capacity to dissipate seismic energy. This dissipation of seismic energy within a structure occurs primarily in two main forms: firstly, through internal damage transforming into thermal energy dissipated into space, and secondly, through external dissipation associated with the pile-soil interface interaction. These correspond primarily to the internal strain energy (ALLSE) and the external kinetic energy (ALLKE). Therefore, analyzing these two energy variations determines the position and size of the plastic region of the pile [49].  
Figure 7a-c represent the plastic hysteresis loops from the piled foundation seismic loads tests. The area under the loading-displacement curve in the hysteresis loop reflects the magnitude of energy absorbed by the structure, while the area under the unloading-displacement curve represents the dissipated energy. It can be observed that the area under the loading curve is consistently greater than the area under the unloading curve.  
Figure 7: _Cont._  
Figure 7: Plastic hysteresis curves for different \(\theta\) values of the piled foundation: (**a**) \(H=23\) m; (**b**) \(H=32.12\) m; (**c**) \(H=44.78\) m; (**d**) Area different of hysteresis curves.  
The Energy Residue Index (ERI) of the piles is shown in Figure 7d. ERI is calculated as the difference between energy absorption and dissipation in the piles, divided by the total work done by seismic loads on the piled foundation. When \(\theta=90^{\circ}\), the ERI at \(H=32.12\) m under water pressure is 2.67 times higher than that at \(H=23\) m. Additionally, at \(H=44.78\) m, the ERI is two times higher than that at \(H=23\) m. At this point, the pile group forms a rectangular spatial volume. The piles experience irregular lateral displacement due to insufficient stability. The surrounding soil experiences relatively minor deformation, resulting in low energy dissipation. Most of the energy is transformed into the internal energy of the soil, leading to an increase in ERI. When \(\theta=45^{\circ}\), the maximum ERI value occurs at an \(H=44.78\) m water pressure. This is due to the inhibitory effect of water pressure on the vertical frequency of the structure [50; 51]. The foundation acts as a transmission medium between these two factors. The piled foundation experiences frequency resonance. Resonance results in additional energy being absorbed by the foundation. This leads to the peak in the ERI. When \(\theta=60^{\circ}\), the ERI values under three different water pressures are relatively close. This reflects the stability of the hexagonal pile arrangement.  
The ratio \(\gamma\) of the damping coefficient is between the piled foundation and the non-piled foundation. This ratio \(\gamma\) reflects the energy dissipation capacity when the foundation exhibits elastic-plastic behavior. From the relationship shown in Figure 8, the change in the \(\gamma\) over the course of the earthquake can be seen. At \(\theta=60^{\circ}\), as a result of the seismic-induced plastic deformation of the foundation increasing, \(\gamma\) gradually decreases. However, the decrease in value \(\Delta\gamma\) is consistently 2.5. At \(\theta=4\)\(5^{\circ}\) and \(\theta=90^{\circ}\), \(\gamma\) values exhibit significant fluctuations. These fluctuations may pose a safety risk due to the instability of the damping ratio in seismic design.