# A Numerical Analysis on Lateral Resistance of Pile-Bucket Foundation for Offshore Wind Turbines
## 3 Model Test Verification  
To verify the correctness of the numerical simulations, including model size, the choice of the constitutive model, and FEM meshing, the results from the model test are compared with the results from FEM. For a super large-diameter monopile for a wind farm of offshore wind turbines, [PERSON] et al. [20], based on the rigid pile with a similar prototype and model under constant gravity, used a pilot model test with a model scale of 1:30 in the foundation, which was made of silt mining from an excavation pit in Hangzhou City.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Soil Layer**} & \multirow{2}{*}{**Effective Unit Weight**} & **Young’s Modulus** & **Friction Angle** & **Cohesive** & **Poisson’s Ratio** \\ \cline{3-6}  & & \(\gamma\)**/kN/m3** & _E_/MPa & \(\varphi\)\({}^{c}\) & _c_/kPa & \(\
u\) \\ \hline Surrounding & Muddy clay & 7.6 & 10 & 28.81 & 15 & 0.29 \\ Bottom & Silty clay & 8.2 & 20 & 35.75 & 8 & 0.32 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Physical parameters of the soil.  
Figure 3: Meshing of parts.  
For a certain group of [PERSON]'s tests, the foundation \(t\) was located in the silt soil layer. The finite element model of soil was established by the M-C model, and the parameters are shown in Table 3.  
The three-dimensional finite element software ABAQUS is used for finite element numerical analysis to model and analyze the full-scale model. The whole foundation model is a rectangular parallelepiped. The length and width of the model are 20 \(D\), and the bottom of the pile is 5 \(D\) from the bottom of the model. The parameters of the model pile are shown in Table 4.  
Figure 4 compares the load and the displacement calculated from ABAQUS to the test results by [PERSON] The loading point heights are 1 \(D\), 3 \(D\), or 6 \(D\). When the loading height is 1 \(D\), the numerical result obtained from ABAQUS is well agreed with the results from [PERSON]'s [14] test for both loading phase and unloading phase. During the loading phase, the load-displacement curve is almost identical between the numerical simulations and the model test. When the loading height is 3 \(D\), although there is a gap between the results of ABAQUS and [PERSON]'s test, the trend of load versus displacement curve is still consistent. When the loading height is 6 \(D\), the agreements of the results are also good. Figure 5 presents the pile deflection curve under the load conditions of 1068, 1214 and 1367 N (the loading point height is 6 \(D\)). Similar agreements are observed from the comparison between numerical simulations and the model test.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Diameter** & **Thickness** & **Buried Depth** & **Length** & **Density** & **Young’s Modulus** & **Poisson’s Ratio** \\ \hline \(D\)**/m** & \(\delta\)**/m** & \(h\)**/m** & \(l\)**/m** & \(\rho\)**/kg/m\({}^{3}\)** & **E**/MPa & \(\
u\) \\ \hline
0.165 & 0.003 & 0.915 & 1.905 & 7800 & \(2.1\times 10^{5}\) & 0.3 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Parameters of the model pile.  
Figure 4: Load–displacement curves at the loading point.  
Based on the above analysis, we can conclude that the results of the simulation are close to those of [PERSON]'s tests, which can verify that the model parameters in the M-C model are effective, and the M-C model is quite reliable for static analysis.