# A Numerical Analysis on Lateral Resistance of Pile-Bucket Foundation for Offshore Wind Turbines
## 4 Results of Numerical Analysis
### Lateral Bearing Capacity of P-BF  
In this paper, for comparison beside the P-BF model, a PF model is also established. Finally, the lateral displacement, shear force and moment of the foundation can be read from ABAQUS naturally.  
Under the lateral load, the soil of around 4\(D\) depth provides the main stiffness of the foundation. In order to study the influence of the diameter (\(D\)) and height (\(h\)) of the bucket on the reinforcement, the height of the bucket is 1 \(D\), 2 \(D\) and 3 \(D\), respectively. The bucket with a diameter of 3 \(D\), 4 \(D\) and 5 \(D\) is adopted. The specific parameters are shown in Table 5.  
Under the working conditions allowed by the specification, the soil around the foundation is still in the elastic domain. The bucket has a significant reinforcement effect on the foundation, and there are subtle differences in the different diameters and heights of the bucket for its reinforcement effect. After adding the bucket onto the PF, the lateral bearing capacity of the foundation is improved. Table 6 shows the improvement of lateral load capacity under different diameters and heights for the bucket. It can be obtained from Table 6 that the lateral bearing capacity can be increased by about 33.21% for each increase in the diameter of the bucket, and the lateral bearing capacity can be increased by about 21.43% for each increase in the height of the bucket. After comparative analysis, the effect of increasing the diameter of the bucket is 10% to 13% higher than that of increasing the height of the bucket.  
Figure 8 shows the plastic zone under the normal working limit state of the monopile foundation and pile-bucket foundation (taking \(D\) = 18 m, \(h\) = 12 m foundation as an example). As shown in Figure 8a, the plastic zone of the monopile foundation is mainly distributed around the soil-facing surface of the pile side, and the depth of the plastic zone is within the range of one pile diameter. As shown in Figure 8b, the plastic zone of the pile-bucket foundation is also observed at the soil-facing surface of the foundation, but it is different from the monopile foundation case. The depth of the plastic zone on the soil-facing surface on the side of the bucket is about one pile diameter, while the depth of the plastic zone on the side of the pile is about the same as the bucket height (\(h\)).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Foundation** & **Bearing Capacity/kN** & **Improvement/\%** \\ \hline PF (\(D\) = 6 m) & 5409 & - \\ P–BF (\(D/h\) = 18 m/12 m) & 8657 & 60.05 \\ P–BF (\(D/h\) = 24 m/6 m) & 9212 & 70.31 \\ P–BF (\(D/h\) = 24 m/12 m) & 10,460 & 93.38 \\ P–BF (\(D/h\) = 24 m/18 m) & 11,530 & 113.16 \\ P–BF (\(D/h\) = 30 m/12 m) & 12,250 & 126.47 \\ \hline \hline \end{tabular}
\end{table}
Table 6: The increment of bearing capacity.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Model 1** & **Model 2** & **Model 3** & **Model 4** & **Model 5** \\ \hline Diameter & & & & & \\ \(D\)/m & 18 & 24 & 24 & 24 & 30 \\ Height & 12 & 6 & 12 & 18 & 12 \\ \(h\)/m & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 5: Parameters of model bucket.