## 4 Conclusions  
Via model tests, the acceleration inside and on the surface of the sand around the pile during the hammering process was monitored and analyzed, and the dynamic response of the pile under hammering conditions was investigated. However, the soil material used in this study remains homogenous. The following research should focus on the dynamic response of piles in different types of soil across different strata, aligning more closely with practical engineering and offering more direct references for construction. The following major conclusions can be drawn:  
* During the hammering process, the peak accelerations measured at different distances increased progressively with increasing penetration depth. Under the constant striking energy, the soil became denser, resulting in more contact between the pile and surrounding soil particles. Consequently, the increased pile-soil contacts facilitated a more efficient transmission of vibrations. Furthermore, it could be observed that the soil plug was about totally plugged, which led to a greater dissipation of energy by the transmission of vibrations into the adjacent soil rather than the formation of soil plug and pile penetration. That is why the later phases of hammering have the most significant effect on the pile response to fluctuations. Except for a distinction at a sensor depth of 375 mm, where only one acceleration peak was synchronized with the earth's pressure. * There was a correlation between the peak acceleration and the peak lateral earth pressure during the hammering procedure. In the tests of open-ended pipe piles, the sensors located at the front 62.5% of the pile length detected two crests of the lateral earth pressure and acceleration. The first crest was detected before the pile tip reached the sensors, and the acceleration was synchronized with the earth pressure. Subsequently, the acceleration reached a second crest, while the earth pressure remained relatively constant. The first crest was caused by the close oblique distance between the measuring point and the pile tip, which resulted in a pronounced effect from the strike-induced vibration. Subsequently, as the penetration depth increased, the majority of hammering energy was converted into propagating vibrations. Combined with the effect of soil compaction and the soil plug plugged, the second crest appeared at a depth of approximately 400 mm. Sensors with a burial depth exceeding 62.5% of the length of the pile detected a single simultaneous crest of earth pressure and acceleration at a relatively large depth. The fixed-length soil plug test exhibited comparable fluctuation trends in both earth pressure and acceleration as observed in the open-ended pipe pile test. However, owing to the greater soil compaction and a higher degree of soil plug closure, the fixed-length soil plug group showed higher peak values. Furthermore, it was observed that piles with a greater length of soil plug had denser acceleration crests. Figure 12: Variations of maximum amplitude along horizontal distance. * The influence range of the principal frequency expanded as the increase of penetration depth and the length of the soil plug. Meanwhile, the vibration frequency corresponding to the maximum amplitude gradually increased as well, because the sand became denser as the pile descended, resulting in a higher principal frequency. As the horizontal distance from the pile increased, the fluctuation in the maximal amplitude decreased. The strike-induced vibration decayed rapidly with the increase in distance between the measuring point and the pile tip. In general, the maximum amplitudes were measured when the penetration depth was equal to half the length of the pile. Conceptualization, C.Z. and Y.L. ; methodology, C.Z. ; data curation, S.L. ; writing-original draft preparation, C.Z. and S.L. ; writing-review and editing, S.L. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable.