# Dynamic Lateral Response of the Partially-Embedded Single Piles in Layered Soil
## 5 Parameter Analysis  
### Effect of Scour Depth  
In this section, the effect of scour depth on the dynamic response of the partially-embedded single pile in layered soil is analyzed. Table 1 shows the physical parameters of the single pile and the layered soil required for the calculation. In the calculation, the partially-embedded single pile passes through the three-layer foundation. The geological condition from top to bottom is: the first layer is the loose sand layer (\(E_{s1}=10\) MPa); the second layer is the medium sand layer (\(E_{s2}=20\) MPa); the third layer is the tight sand layer (\(E_{s3}=50\) MPa). For sand, the Poisson's ratio is approximately 0.3. The lateral excitation amplitude of the pile top is \(P_{0}\)= 2000 N. The setting of the scouring levels is shown in Figure 3, with each scouring level separated by 1.095 m.  
Table 2 shows the variation of Vlasov foundation parameters and dynamic characteristics of partially-embedded single piles with the scour levels under the boundary conditions of free-free piles and fixed-free piles. Table 2 shows that the subgrade reaction coefficient \(k_{i}\) of each layer of soil decreases with the increase in the scour levels, while the shear coefficient \(2t_{i}\) increases with the increase in the scour levels. The frequencies of each order of the partially-embedded single pile decrease rapidly with the increase in scouring levels. The depth of the embedded soil decreases with the scour process, and the pile-soil interaction effect gradually weakens. \(l_{3}\) The effect of the degree of scouring on the dynamic response amplitudes of the partially-embedded single pile in the layered soil fields is investigated in Figure 6. As shown in Figure 6, the displacement of the pile top of the single pile increases with the increase in the scour levels. When the scour level reaches 10, that is, the length of the non-embedded section of the pile satisfies \(l_{1}\geq L/2\) (\(L\) is the pile length), the response amplitudes of the pile top of the partially-embedded single pile in the layered soil fields were greater than 0.01 m, and the single pile has presented lateral instability under dynamic load [26]. In addition, as the degree of scouring intensifies, the inverted point of the pile \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Type of Single**} & \multirow{2}{*}{**Scour Levels**} & \multirow{2}{*}{**Distribution of Soil Layers**} & \multicolumn{3}{c}{**Vlasov Foundation Parameters**} & \multirow{2}{*}{**Dynamic Characteristics of Pile**} \\  & & & & & & \\  & & & & & & \\  & & & & & & \\  & & & & & & \\ \multirow{4}{*}{Free-fixed pile} & \multirow{4}{*}{5} & \multirow{4}{*}{10} & \(l_{1}\) & 30,516,730 & 931,855 & \multirow{4}{*}{10.87} \\  & & & \(l_{2}\) & 61,033,460 & 1,863,709 & & \\  & & & \(l_{3}\) & 152,583,651 & 4,659,273 & & \\  & & & \(l_{1}\) & 24,721,884 & 1,411,277 & & \\  & & & \(l_{2}\) & 49,443,769 & 2,822,553 & & \\  & & & \(l_{3}\) & 123,609,421 & 7,056,383 & & \\  & & & \(l_{1}\) & 7 & & & \\  & & & \(l_{2}\) & 41,639,243 & 3,771,832 & 10.87 & **0.01343** \\  & & & \(l_{3}\) & 104,098,106 & 9,429,580 & & \\  & & & \(l_{1}\) & 7 & & & \\  & & & \(l_{2}\) & 40,133,534 & 3,987,401 & 7.72 & **0.02424** \\  & & & \(l_{3}\) & 100,333,835 & 9,968,503 & & \\  & & & \(l_{1}\) & 30,140,280 & 956,033 & & \\  & & & \(l_{2}\) & 60,208,561 & 1,912,067 & 24.11 & 0.00330 \\  & & & \(l_{3}\) & 150,701,402 & 4,780,167 & & \\  & & & \(l_{1}\) & 24,439,564 & 1,441,149 & & \\  & & & \(l_{2}\) & 48,879,128 & 2,882,297 & 14.63 & 0.00900 \\ Free-free pile & & & \(l_{3}\) & 122,197,820 & 7,205,743 & & \\  & & & \(l_{1}\) & 41,411,422 & 3,803,738 & 10.47 & **0.02063** \\  & & & \(l_{3}\) & 103,528,555 & 9,509,346 & & \\  & & & \(l_{1}\) & 7 & & & \\  & & & \(l_{2}\) & 40,015,209 & 4,004,815 & 7.34 & **0.04313** \\  & & & \(l_{3}\) & 100,038,023 & 10,012,037 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Effect of the scour on Vlasov foundation parameters and dynamic characteristics of the single pile.