## 3 Test Results
### Spectrum Analysis of Surface Wave  
There was a certain frequency of vibration waves generated by the striking method of pile driving. The vibration waves caused the ground surrounding the pile to vibrate forcibly. Resonance will occur when the forced vibration frequency of the ground is similar to the natural frequency of surrounding structures. This will cause the structure surrounding the pile to generate a significant vibration amplitude, resulting in fractures or even structural damage. In open-ended pipe pile tests, when the pile tip reached the depths of H = 100 mm, 300 mm, and 575 mm (the length of the soil plug was measured as 90 mm, 194 mm, and 280 mm), the vibration waves on the ground surface around the pile were measured within a distance range of 40 mm to 200 mm (from X = 1D-5D) to investigate the frequency spectrum pattern of vibration waves at various distances from the pile and penetration depths.  
As shown in Figure 11 and Table 4, the vibration waves measured at various distances from the pile and penetration depths exhibited distinct patterns. As the penetration depth increased, the range of the principal frequency increased. When the penetration depth was 100 mm, the frequency range of the maximum amplitude ranged from 74 Hz to 121 Hz, depending on the sensor distances from the pile. Similarly, when the penetration depth was 300 mm and 575 mm, the maximal amplitude frequency range was 117 Hz to 136 Hz and 123 Hz to 159 Hz, respectively. As penetration depth and the formation of soil plugs increased, the principal frequency range of the surface wave expanded, and the frequency corresponding to the maximal amplitude increased.  
Figure 11: _Cont._  
The spectrum analysis revealed that, with the same penetration depth, the maximal amplitudes were all measured at a horizontal distance of 40 mm (X = 1D) from the pile, i.e., the closest measure point to the pile. Moreover, as the horizontal distance increased, the maximal amplitude fluctuated downward. At a penetration depth of 575 mm, as shown in Figure 12, the maximal amplitude at X = 1D was 0.53 and decreased to 0.17 at a distance of 200 mm from the pile. As the penetration depth increased, the maximal amplitude measured at each horizontal distance from the pile reached its maximum value at a penetration depth of 300 mm. At a distance of 40 mm from the pile, for instance, the maximal amplitudes measured at a penetration depth of 100 mm, 300 mm, and 575 mm were 0.1, 0.62, and 0.53, respectively. There were two reasons why the maximum amplitude appeared at a penetration depth of 300 mm as opposed to 575 mm: on the one hand, as the penetration depth increased, the sand became denser, and less penetration depth was produced by a single hammering, resulting in greater vibration during the subsequent striking process. On the other hand, the high-frequency vibration wave always attenuates abruptly during transmission, and the distance between the pile tip and the surface of the ground increases as the pile is driven. At a penetration depth of 300 mm, the oblique distance between the pile tip and the measuring point at X = 1D was only 52.5% of the distance at the same horizontal distance for a penetration depth of 575 mm. During the striking process, the peak frequency fluctuation amplitude reached its maximum when the penetration depth was equal to half the length of the pile. Therefore, when driving piles that may lead to soil plugging, it is essential to monitor the length of the soil plug and implement anti-vibration measures prior to the soil plug height reaching half the pile length to prevent the pile from impacting adjacent buildings and previously installed piles.  
Figure 11: Spectrum analysis of ground vibration.