# Nonlinear Wave-Induced Uplift Force onto Pipelines Buried in Sloping Seabeds
## 4 Results and Discussions
### The Influences of Soil Properties on Uplift Force onto Pipelines Buried in Sloping Seabeds  
For the purpose of investigating the influences of seabed properties on the uplift force applied by waves to pipelines buried in sloping seabeds; in present section, the permeability varies from \(10^{-6}\) m/s to \(10^{-2}\) m/s, the Young's modulus ranges from 10 MPa to 50 MPa and the Poisson's ratio ranges from 0.2 to 0.35.  
Considering that the uplift force applied to the buried structure may be affected by the pore pressure response inside the soil, the pore pressure distribution around the pipeline with various soil properties is illustrated in Figure 12. Figure 12a shows that the pore pressure increases as the permeability grows both above and below the pipeline, but the increase rate is decreasing. Moreover, the increase rate is greater above the pipeline than that below the pipeline within \(10^{-4}\) m/s. As shown in Figure 12b, when the Young's modulus is less than 40 MPa, the pore pressure next to the pipeline increases as the Young's modulus grows, and the increase rate below the pipeline is greater than that above the pipeline. However, when the Young's modulus exceeds 40 MPa, the pore pressure reduces as the Young's modulus grows, and its decrease rate above the pipeline is slightly greater than that below the pipeline. As noted from the distribution in Figure 12c, the influence of Poisson's ratio on the pore pressure response around the pipeline is very small, thus it can be ignored.  
Figure 11: Variations of the uplift force onto the pipeline for variable wave parameters: (**a**) H, (**b**) T, (**c**) d.  
To analyze the influences of the soil properties on the uplift force applied by waves to pipelines buried in sloping seabeds, Figure 13 illustrates some variations of the uplift force applied to the pipeline with the soil properties. Figure 13a shows that the wave-caused uplift force increases with soil permeability increasing until it reaches \(10^{-4}\) m/s, and the change trend is opposite after exceeding this value. From Figure 13b,c, it can be observed that both Young's modulus and Poisson's ratio have weakening effects on the uplift force onto the pipeline.  
Figure 12: Distribution of pore pressure around the pipeline for various soil properties under the wave trough: (**a**) ks, (**b**) E, (**c**) \(v\).  
Figure 13: _Cont._  
The Influences of Pipeline Characteristics on the Uplift Force onto Pipelines Buried in Sloping Seabeds  
The pipeline burial depth and diameter may affect the boundary condition of the seabed next to the pipeline, which is able to further influence the wave-caused pore pressure around it. In order to explore how the pipeline characteristic affects the uplift force applied to the pipeline, for present study, the burial depth is set at an interval of 0.5 m in the range of 0.5 m to 2.0 m, and the pipeline diameter is set at an interval of 0.2 m in the range of 0.8 m to 1.4 m.  
Figure 14 illustrates the pore pressure distributions next to the pipeline with different pipeline characteristics under the wave trough. As noted from the distribution in Figure 14a, as the burial depth grows, the pore pressure next to the pipeline reduces, and its decrease rate above the pipeline is always greater than that below. As noted from the distribution in Figure 14b, the pore pressure above the pipeline tends to gradually grow as the pipeline diameter increases, while an opposite phenomenon occurs below the pipeline. Figure 15 shows the variations of the uplift force applied to the pipeline with various pipeline characteristics. As noted from the curves in Figure 15, the uplift force applied by wave to the pipeline reduces as the buried depth grows, while it grows with the pipeline diameter increasing.  
Figure 14: Distribution of pore pressure around the pipeline for various pipeline characteristics under the wave trough: (**a**) **e**, (**b**) D.  
Figure 13: Variations of the uplift force onto the pipeline for various soil properties: (**a**) k\({}_{\text{s}}\), (**b**) E, (**c**) \(v\).