# Nonlinear Wave-Induced Uplift Force onto Pipelines Buried in Sloping Seabeds
## 4 Results and Discussions
### The Oscillatory Soil Response around the Pipeline Buried in Sloping Seabed  
As mentioned previously, the key innovation for present research is examining the wave-caused oscillatory seabed responses next to the pipeline buried in the sloping seabed. Therefore, Figure 7 shows the comparison of wave trough-caused pore pressure response inside the sloping seabed with and without pipeline. As noted from Figure 7, the pipeline has a considerable impact on the pore pressure distribution within the seabed, especially in the area around the pipeline. In order to gain a more intuitive understanding of this difference, Figure 8 illustrates the wave trough and crest-caused pore pressure varying as the soil depth, and Figure 9 illustrates that around the pipeline. As shown in Figure 8, under the wave trough, compared to the condition without pipeline, the pipeline will cause lower pore pressure at the corresponding area above the pipeline and higher pore pressure below it, while the opposite phenomenon occurs in Figure 8. This phenomenon may be related to the \"shielding effect\" of pipelines. In addition, neither the surface soil nor the slightly deeper soil below the pipeline are affected by the pipeline under the wave trough or the wave crest. Based on Figure 9, the pore pressure above the pipeline is less than that below the wave trough, while it displays an opposite phenomenon under the wave crest. This phenomenon may be related to the \"shielding effect\" of pipelines and the pore pressure gradient in the seabed. In addition, affected by the slope, the distribution of pore pressure next to the pipeline also shows an inclined state.  
In fact, the uplift force applied by a wave to a pipeline correlates closely with the oscillating seabed response. As noted from the curve in Figure 8, the pore pressure inside the seabed grows with the seabed depth growing under the wave trough. That is to say, below the pipeline, the pore pressure under the wave trough is always greater than that above. However, this phenomenon is opposite under the wave crest, which can be seen in Figure 8. And the \"shielding effect\" of a pipeline exacerbates this difference between the pore pressure above and below the pipeline. Figure 8 also shows that the pore pressure gradient gradually decreases with the soil depth, especially when the depth exceeds 6 m, it decreases more rapidly. In other words, the deeper the pipeline is buried, the smaller the pore pressure difference between the upper and lower part of the pipeline.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Saturation (S\({}_{\tau}\)) & 1 \\ Slope angle (\(\alpha\)), \({}^{\circ}\) & 6 \\ Horizontal distance on the slope (S), m & 100 \\ Pipeline diameter (D), m & 1.0 \\ Bural depth (e), m & 0.5 \\ \hline \hline \end{tabular}
\end{table}
Table 4: _Cont._  
Figure 7: Comparison of wave-induced pore pressure response within the sloping seabed between cases without and with a pipeline: (**a**) without a pipeline, (**b**) with a pipeline.  
The above pore pressure difference under the wave trough should be the reason for the uplift force applied by wave to the pipeline. To further quantify the influencing factors of this uplift force, this study obtained the uplift force onto the pipeline by integrating the pore pressure next to the pipeline. The following chapters will analyze the influencing factors of uplift force onto the pipeline in detail.