# Nonlinear Wave-Induced Uplift Force onto Pipelines Buried in Sloping Seabeds
## 4 Results and Discussions
### The Influences of Slope on Uplift Force Applied to Pipelines Buried in Sloping Seabeds  
As well known, the slope angle can affect not only the wave transformations, but also the boundary condition on the surface of the seabed model. Thus, the effect of slope angle on the uplift force applied by waves to pipelines buried in sloping seabeds is examined, and the slope angles for the present study are set at an interval of 2\({}^{\circ}\) in the range of 2\({}^{\circ}\) to 8\({}^{\circ}\). In addition, the horizontal distance of wave propagation on the slope is also taken into account, and the slope horizontal distances include 20 m, 60 m, 100 m and 140 m.  
Figure 16 shows the distributions of pore pressure next to the pipeline for various water depths under the wave trough. As noted from the distributions in Figure 16, regardless of water depth, the pore pressure grows with slope angle increase, and the growth rate above the pipeline is greater than that below. Figure 17 shows the variations of the pore pressure distribution around the pipeline with the slope horizontal distance. As noted from the distributions in Figure 17, the relationship between the pore pressure around the pipeline and the horizontal distance of the slope is not monotonic, but first increases and then decreases with the horizontal distance increasing. The reason for this phenomenon can be attributed to two aspects. The first is that as the slope distance increases, the water depth decreases, resulting in enhanced wave action on the seabed, which is drawn from Section 4.2. Secondly, the slope has a lifting effect on the wave, which increases the height of the wave crest but reduces the height of the wave trough relative to the hydrostatic surface and further reduces the pressure acting on the surface of the seabed under the wave trough. If the slope angle is large enough, the wave may even break and its effect on the seabed will be smaller. When the wave enters the slope area, the former has a greater influence on it, so it leads to an increase in the pore pressure around the pipeline, while as the water depth becomes shallower, the latter influence gradually increases, leading to a decrease in the pore pressure around the pipeline. The variations of uplift force applied by waves to a pipeline with slope angles for various water depth are illustrated in Figure 18. As noted from the curves in Figure 18, regardless of the water depth, the uplift force increases as the slope angle increases. In other words, the bigger slope angle can enhance the uplift force applied by waves to the pipeline. Moreover, the shallower the water depth is, the more likely this enhanced effect is to be weakened at large slope angles. However, this effect of slope angle on the uplift force can be ignored when the water depth is large enough. Moreover, Figure 19 shows the relationship between the uplift force and the slope horizontal distance, which shows that the nonlinear wave-induced uplift force onto the pipeline increases first and then decreases as the horizontal distance increases.  
Figure 15: Variations of uplift force onto the pipeline for various pipeline characteristics: (**a**) e, (**b**) D.  
Figure 16: Distributions of pore pressure around the pipeline for various slope angles under different water depths: (**a**) d = 27 m, (**b**) d = 30 m, (**c**) d = 33 m, (**d**) d = 36 m.  
Figure 17: Distributions of pore pressure around the pipeline for various slope horizontal distances of wave propagation.