# Dynamic Lateral Response of the Partially-Embedded Single Piles in Layered Soil
## 5 Parameter Analysis
### Effect of Soil Thickness  
In the process of parameter analysis, the steel pipe piles in Table 1 are still used. The setting of the scouring levels is shown in Figure 3. Partially-embedded single piles pass through the three-layer foundation soil, the elastic modulus is 10, 20, 50 MPa from top to bottom, and the Poisson's ratio is 0.3. In order to study the effect of the thickness of the bottom layer (third layer) of the layered soil fields on the dynamic response of a single pile, the depth of the first layer of soil is kept constant, and the thickness of the third layer is changed by changing the ratio of the thickness of the second and third layers of soil, in order: \(h_{1}=2.19\) m, \(h_{2}=3.28\) m, \(h_{3}=1.10\) m; \(h_{1}=2.19\) m, \(h_{2}=2.19\) m, \(h_{3}=2.19\) m; \(h_{1}=2.19\) m, \(h_{2}=1.10\) m, \(h_{3}=3.28\) m (\(h_{i}\) represents the thickness of the soil layer).  
In order to more clearly explore the effect of the thickness of the underlying soil in the layered soil fields on the dynamic response of the partially-embedded single pile, Table 3 shows the effect of \(h_{3}\) on the first-order natural frequencies and amplitudes of the pile top of the pile under varied scour levels. It can be seen from Table 3 that the first-order natural frequencies of the single pile under each scour level increase with the increase in \(h_{3}\). In addition, as the scour degree intensifies, the natural frequencies decrease significantly, and the response amplitudes of the pile top increase significantly. When the scour level reaches 10, the lateral instability of a single pile appears.  
The variations of the mode shapes of the partially-embedded single pile under varied scour levels with the change of the thickness of the underlying soil are investigated in Figure 7. It is shown that the response amplitudes of the pile top of the single pile and the displacement amplitudes at the inverted point of the pile body decrease with the increase in the thickness of the underlying soil, regardless of the degree of scour.  
Figure 6: Effect of the scour degree on the dynamic response of the single pile in layered foundation: (a) Free-fixed pile; (b) Free-free pile.  
Figure 7: Effect of the thickness of soil on the dynamic response of the single pile under varied scour levels: (**a**) Free-fixed pile, scour level-5; (**b**) Free-fixed pile, scour level-10; (**c**) Free-free pile, scour level-5; (**d**) Free-free pile, scour level-10.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Type of Single**} & \multirow{2}{*}{**The Thickness of**} & \multirow{2}{*}{**Scour Levels**} & \multicolumn{2}{c}{**Dynamic Characteristics of Pile**} \\ \cline{4-5}  & & **the Soil Layer \(l_{3}\)** & & **Natural** & **Amplitude of Pile** \\  & & **[m]** & & **Frequency [Hz]** & **Top [m]** \\ \hline \multirow{6}{*}{Free-fixed pile} & \multirow{3}{*}{2.19} & 0 & 24.71 & 0.002720 \\  & & 5 & 15.03 & 0.006851 \\  & & 10 & 10.85 & **0.013457** \\  & & 0 & 24.75 & 0.002701 \\  & & 5 & 15.13 & 0.006631 \\  & & 10 & 10.87 & **0.013429** \\  & & 0 & 24.83 & 0.002683 \\  & 3.29 & 5 & 15.34 & 0.006608 \\  & & 10 & 10.91 & **0.012976** \\ \hline \multirow{6}{*}{Free-free pile} & \multirow{3}{*}{1.10} & 0 & 24.07 & 0.003322 \\  & & 5 & 14.543 & 0.009181 \\  & & 10 & 10.419 & **0.020786** \\ \cline{1-1}  & & 0 & 24.11 & 0.003296 \\ \cline{1-1}  & 2.19 & 5 & 14.628 & 0.000950 \\ \cline{1-1}  & & 10 & 10.468 & **0.020628** \\ \cline{1-1}  & & 0 & 24.18 & 0.003271 \\ \cline{1-1}  & 3.29 & 5 & 14.632 & 0.008998 \\ \cline{1-1}  & & 10 & 10.503 & **0.019846** \\ \hline \hline \end{tabular}
\end{table}
Table 3: Effect of the thickness of the underlying soil on dynamic characteristics of the single pile under varied scour levels.