## 5 Parametric Analysis
### Parametric Analysis and Discussion  
#### 5.2.1 Coupling Effect of Sediment Thickness and Pile Parameters  
The coupling effect of the sediment thickness and pile parameters (i.e., the pile Poisson's ratio, radius, and longitudinal wave velocity)is investigated here. The corresponding results are portrayed in Figures 4-9. Figure 4 presents the coupling effect of the sediment thickness and the pile Poisson's ratio on the pile complex impedance. Compared to the strictly end-bearing pile (i.e., \(H_{\text{s}}\) = 0 mm), the presence of sediment significantly reduces the support stiffness at the pile tip. As a result, the oscillation amplitude and resonant frequency of \(K_{\text{p}}\) and \(C_{\text{p}}\) become lower, especially at higher frequencies. As the sediment thickness increases, the oscillation amplitude and resonant frequency of the pile complex impedance decrease with the decreasing rate, which decreases with frequency. When the pile's transverse inertia is taken into account, the oscillation amplitude and resonant frequency of \(K_{\text{p}}\) and \(C_{\text{p}}\) within the high-frequency range decrease, especially at higher frequencies. In addition, the decrease in the oscillation amplitude of the complex impedance due to the sediment becomes less pronounced to some degree when the pile's transverse inertia is considered while that in the resonant frequency of the complex impedance remains unchanged. Figure 3: Comparison with [PERSON] et al. [56]. Figure 4: Coupling effect of the sediment thickness and pile Poisson’s ratio on the pile complex impedance. Figure 5: Coupling effect of the sediment thickness and pile Poisson’s ratio on the velocity response. Figure 6: Coupling effect of the sediment thickness and pile radius on the pile complex impedance. Figure 7: Coupling effect of the sediment thickness and pile radius on the velocity response. Figure 8: Coupling effect of the sediment thickness and pile’s longitudinal wave velocity on the pile complex impedance. Figure 9: Coupling effect of the sediment thickness and the pile’s longitudinal wave velocity on the velocity response. The coupling effect of the sediment thickness and pile Poisson's ratio on the velocity response is illustrated in Figure 5. When there exists a certain thickness of sediment, the signal reflected by the pile tip weakens because of the greater dissipation of the elastic wave in the sediment compared to the rigid bedrock. In addition, the time lag of the reflected signal increases notably, leading to the overestimation of the pile length calculated using the low-strain reflected wave method. It is also noted that a synthetic reflected signal can be observed before the reverse reflected signal, which may interfere with the detection of the support condition at the pile tip. The aforementioned phenomena are found to become more pronounced with a larger sediment thickness. Furthermore, when considering the pile's transverse inertia (\(\mu_{\text{p}}=0.2\)), it takes longer to receive the signal reflected by the pile tip, and the signal is less weakened by the sediment, indicating the decreased influence of the sediment. Given the notable influence of the sediment presented in Figures 4 and 5, the pile hole should be cleared as thoroughly as possible in engineering. Figure 6 presents the coupling effect of the sediment thickness and pile radius on the pile complex impedance. The oscillation amplitudes of \(K_{\text{p}}\) and \(C_{\text{p}}\) are higher for the pile with a radius of 0.5 m compared to one with a radius of 0.4 m. In addition, the resonant frequency is found to be lower for the pile with a larger radius, which demonstrates that the pile's transverse inertia plays a more apparent role in its dynamic response. It should also be noted that the oscillation amplitude of the complex impedance is more notably decreased by the increase in the sediment thickness when the pile radius is larger, indicating the greater influence of sediment.