Two-Dimensional Numerical Study of Seabed Response around a Buried Pipeline under Wave and Current Loading
Abstract
:1. Introduction
2. Methods
2.1. Wave–Current Model
2.2. Seabed Model
2.2.1. Oscillatory Soil Response
2.2.2. Residual Soil Response
2.3. Boundary Condition
2.4. Numerical Scheme
3. Results and Discussion
3.1. Wave Characteristics
Influence of Current Velocities
3.2. Seabed Characteristics
3.2.1. Effects of Soil Permeability
3.2.2. Effects of Shear Modulus
3.2.3. Effects of Relative Density
3.3. Around the Vicinity of the Pipeline
4. Conclusions
- (1)
- In the analysis of wave-seabed-structure interaction, the current should be taken into consideration—an increase in the current flow results in an increase in wave pressure. When wave pressure increases, the oscillatory pore pressure tends to increase with increasing current velocity.
- (2)
- Soil permeability governs the seepage of fluid passing through or flowing out of the seabed. Low permeability, i.e., pore fluids cannot dissipate efficiently, resulted in higher residual pore pressure due to the increase in the buildup of excess pore pressure.
- (3)
- Shear modulus has a relationship with Young’s modulus and Poisson’s ratio, which describe the rigidity of the seabed. Keeping the Poisson’s ratio as a constant value, a higher value of shear modulus generates a higher value of Young’s modulus, which represents a denser soil. As presented above, loose sand tends to produce a higher value of residual pore pressure.
- (4)
- Relative density controls the empirical coefficients αr and βr in source term, which affects the generation of residual pore pressure. It concludes that a smaller value of relative density results in a higher value of residual pore pressure. However, there is no visible difference in the oscillatory pore pressure.
Author Contributions
Acknowledgments
Conflicts of Interest
References
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Module | Parameter | Notation | Magnitude | Unit |
---|---|---|---|---|
Wave | Water Depth | d | 12 | m |
Wave Height | H | 4 | m | |
Wave Period | T | 10 | s | |
Current | Velocity | vc | 0, 0.25, 0.5 | m/s |
Seabed | Permeability | ks | 1.0 × 10−2, 1.0 × 10−3, 1.0 × 10−4 | m/s |
Degree of Saturation | Sr | 1 | - | |
Shear Modulus | G | 5.0 × 106, 1.5 × 107 | N/m2 | |
Poisson’s Ratio | ν | 0.35 | - | |
Relative Density | 0.2, 0.3, 0.5 | - | ||
Porosity | ns | 0.4 | - | |
Pipeline | Pipe Diameter | D | 2.0 | m |
Burial Depth | e | 3.0 | m | |
Young Modulus | EP | 2.09 × 1011 | N/m2 | |
Shear Modulus | 6.8 × 1010 | N/m2 |
Type of Soil | Young’s Modulus, E (MPa) | Poisson’s Ratio, v |
---|---|---|
Loose sand | 10.5–24.0 | 0.20–0.40 |
Medium dense sand | 17.25–27.60 | 0.25–0.40 |
Dense sand | 34.50–55.20 | 0.30–0.45 |
Silty sand | 10.35–17.25 | 0.20–0.40 |
Sand and gravel | 69.00–172.50 | 0.15–0.35 |
Soft clay | 4.1–20.7 | - |
Medium clay | 20.7–41.4 | 0.20–0.50 |
Stiff clay | 41.4–96.6 | - |
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Foo, C.S.X.; Liao, C.; Chen, J. Two-Dimensional Numerical Study of Seabed Response around a Buried Pipeline under Wave and Current Loading. J. Mar. Sci. Eng. 2019, 7, 66. https://doi.org/10.3390/jmse7030066
Foo CSX, Liao C, Chen J. Two-Dimensional Numerical Study of Seabed Response around a Buried Pipeline under Wave and Current Loading. Journal of Marine Science and Engineering. 2019; 7(3):66. https://doi.org/10.3390/jmse7030066
Chicago/Turabian StyleFoo, Cynthia Su Xin, Chencong Liao, and Jinjian Chen. 2019. "Two-Dimensional Numerical Study of Seabed Response around a Buried Pipeline under Wave and Current Loading" Journal of Marine Science and Engineering 7, no. 3: 66. https://doi.org/10.3390/jmse7030066
APA StyleFoo, C. S. X., Liao, C., & Chen, J. (2019). Two-Dimensional Numerical Study of Seabed Response around a Buried Pipeline under Wave and Current Loading. Journal of Marine Science and Engineering, 7(3), 66. https://doi.org/10.3390/jmse7030066