Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-24T01:34:57.589Z Has data issue: false hasContentIssue false
  • English
  • Français

Transient wave-induced pore-water-pressure and soil responses in a shallow unsaturated poroelastic seabed

Published online by Cambridge University Press:  18 March 2022

Linlong Tong Open the ORCID record for Linlong Tong [Opens in a new window]  and
Philip L.-F. Liu Open the ORCID record for Philip L.-F. Liu [Opens in a new window]
Linlong Tong
Affiliation:
Key Laboratory of Ministry of Education for Coastal Disaster and Protection, Hohai University, Nanjing 210098, PR China Department of Civil and Environmental Engineering, National University of Singapore, 117576, Republic of Singapore College of Harbor, Coastal and Offshore Engineering, Hohai University, Nanjing 210098, PR China
Philip L.-F. Liu*
Affiliation:
Department of Civil and Environmental Engineering, National University of Singapore, 117576, Republic of Singapore Institute of Hydrological and Oceanic Sciences, National Central University, Jhongli, Taoyuan 320, Taiwan, ROC School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14850, USA Department of Hydraulic and Ocean Engineering, National Cheng Kung University, Tainan, 10701 Taiwan, ROC
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

An analytical solution is developed for studying transient water wave-induced responses inside an unsaturated poroelastic seabed of finite thickness. The soil skeleton and the pore fluid are compressible and the constitutive relationship of the soil skeleton is described by Hooke's law. Assuming that the horizontal length scale of wave motion is much larger than the seabed thickness, the leading-order analytical solutions for the seabed responses, including pore fluid pressure and soil skeleton motion, are obtained. The present solutions are suitable for general transient wave loading and for the shear modulus of the soil skeleton being of the same order of magnitude as the effective bulk modulus of elasticity of the pore fluid. The present theory is first validated by checking the solutions with the experimental data for the pore pressure induced by periodic-wave loading. The present analytical solutions are then used to investigate the seabed responses under transient waves, including linear periodic wave, a solitary wave and a bore. The effects of the wave-induced effective stresses on the bed failure potential are further analysed. The results show that the shear failure potential and its duration are highly dependent on the soil properties, such as saturation degree, shear modulus and permeability. Sensitivity analyses are presented.

JFM classification

Geophysical and Geological Flows: Coastal engineering Waves/Free-surface Flows: Solitary waves Waves/Free-surface Flows: Hydraulics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 938 , 10 May 2022 , A36
Check for updates
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Abdolali, A., Kadri, U. & Kirby, J. 2019 Effect of water compressibility, sea-floor elasticity, and field gravitational potential on tsunami phase speed. Sci. Rep. 9 (1), 16874.CrossRefGoogle ScholarPubMed
Anderson, D., Cox, D., Mieras, R., Puleo, J.A. & Hsu, T.-J. 2017 Observations of wave-induced pore pressure gradients and bed level response on a surf zone sandbar. J. Geophys. Res. 122, 5169–5193.CrossRefGoogle Scholar
Baumgarten, A.S. & Kamrin, K. 2019 A general fluid–sediment mixture model and constitutive theory validated in many flow regimes. J. Fluid Mech. 861, 721–764.CrossRefGoogle Scholar
Bear, J. 1972 Dynamics of Fluids in Porous Media. Dover.Google Scholar
Biot, M.A. 1941 General theory of three-dimensional consolidation. J. Appl. Phys. 26, 155–164.CrossRefGoogle Scholar
Body, G.L. & Ehrenmark, U.T. 1998 Reflection of gravity waves by a steep beach with a porous bed. J. Fluid Mech. 359, 265–280.CrossRefGoogle Scholar
Chan, I.C. & Liu, P.L.-F. 2012 On the runup of long waves on a plane beach. J. Geophys. Res. 117, 1–17.Google Scholar
Chanson, H. 2009 Current knowledge in hydraulic jumps and related phenomena. A survey of experimental results. Eur. J. Mech. B/Fluids 28, 191–210.CrossRefGoogle Scholar
Dean, R.G. & Dalrymple, R.A. 1991 Water wave mechanics for engineers and scientists. In Advanced Series on Ocean Engineering (ed. P.L.-F. Liu). World Scientific.CrossRefGoogle Scholar
Hsu, C.J., Chen, Y.Y. & Tsai, C.C. 2019 Wave-induced seabed response in shallow water. Appl. Ocean Res. 89, 211–223.CrossRefGoogle Scholar
Hsu, J.R.C. & Jeng, D.S. 1994 Wave-induced soil response in an unsaturated anisotropic seabed of finite thickness. Intl J. Numer. Anal. Meth. Geomech. 18, 785–807.CrossRefGoogle Scholar
Jeng, D.S. 1997 Wave-induced seabed instability in front of a breakwater. Ocean Engng 24, 887–917.CrossRefGoogle Scholar
Jeng, D.S. 2003 Wave-induced sea floor dynamics. Appl. Mech. Rev. 56, 407–429.CrossRefGoogle Scholar
Jeng, D.S. & Rahman, M. 2000 Effective stresses in a porous seabed of finite thickness: inertia effects. Can. Geotech. J. 37, 1383–1392.CrossRefGoogle Scholar
Jeng, D.S., Ye, J.H., Zhang, J.S. & Liu, P.L.-F. 2013 An integrated model for the wave-induced seabed response around marine structures: model verifications and applications. Coastal Engng 72, 1–19.CrossRefGoogle Scholar
Jia, Y.G, Tian, Z., Shi, X., Liu, J.P., Chen, J., Liu, X., Ye, R., Ren, Z. & Tian, J. 2019 Deep-sea sediment resuspension by internal solitary waves in the northern South China Sea. Sci. Rep. 9, 12137.CrossRefGoogle ScholarPubMed
Kim, Y., Mieras, R.S., Cheng, Z., Anderson, D., Hsu, T.-J., Puleo, J.A. & Cox, D. 2019 A numerical study of sheet flow driven by velocity and acceleration skewed near-breaking waves on a sandbar using SedWaveFoam. Coastal Engng 152, 103526.CrossRefGoogle Scholar
Knowles, J. & Yeh, H. 2018 On shoaling of solitary waves. J. Fluid Mech. 848, 1073–1097.CrossRefGoogle Scholar
Lin, M. & Li, J.C. 2001 Effects of surface waves and marine soil parameters on seabed instability. Appl. Math. Mech. 22, 904–916.CrossRefGoogle Scholar
Liu, B. & Jeng, D.S. 2013 Laboratory study for pore pressure in sandy bed under wave loading. In Proceedings of the 23th International Offshore and Polar Engineering Conference, pp. 1432–1437. International Society of Offshore and Polar Engineers.Google Scholar
Liu, B., Jeng, D.S., Ye, G.L. & Yang, B. 2015 Laboratory study for pore pressures in sandy deposit under wave loading. Ocean Engng 106, 207–219.CrossRefGoogle Scholar
Liu, P.L.-F. 1973 Damping of water waves over porous bed. J. Hydraul. Div. ASCE 99, 2263–2271.CrossRefGoogle Scholar
Liu, P.L.-F., Davis, M.H. & Downing, S. 1996 Wave-induced boundary layer flows above and in a permeable bed. J. Fluid Mech. 325, 195–218.CrossRefGoogle Scholar
Liu, P.L.-F., Park, Y.S. & Lara, J.L. 2007 Long-wave-induced flows in an unsaturated permeable seabed. J. Fluid Mech. 586, 323–345.CrossRefGoogle Scholar
Madsen, O.S. 1978 Wave-induced pore pressures and effective stresses in a porous bed. Géotecnique 28, 377–393.CrossRefGoogle Scholar
Mei, C.C. & Foda, M.A. 1981 Wave-induced responses in a fluid-filled poro-elastic solid with a free surface – a boundary layer theory. Geophys. J. R. Astron. Soc. 66, 597–631.CrossRefGoogle Scholar
Merxhani, A. & Liang, D.F. 2012 Investigation of the poro-elastic response of seabed to solitary waves. In Proceedings of the 22nd International Offshore and Polar Engineering Conference, pp. 101–108. International Society of Offshore and Polar Engineers.Google Scholar
Meyer, V., Langford, T. & White, D.J. 2016 Physical modelling of pipe embedment and equalisation in clay. Géotecnique 66, 602–609.CrossRefGoogle Scholar
Mieras, R.S., Puleo, J.A., Anderson, D., Cox, D.T. & Hsu, T.J. 2017 Large-scale experimental observations of sheet flow on a sandbar under skewed-asymmetric waves. J. Geophys. Res. 122, 5022–5045.CrossRefGoogle Scholar
Moshagen, H. & Tørum, A. 1975 Wave induced pressures in permeable seabeds. J. Waterways Harbors Coast. Engng. Div. ASCE 101, 49–57.CrossRefGoogle Scholar
Packwood, A.R. & Peregrine, D.H. 1980 Loss of water wave energy due to percolation in a permeable sea bottom. Coastal Engng 3, 221–242.CrossRefGoogle Scholar
Pujara, N., Liu, P.L.-F. & Yeh, H. 2015 The swash of solitary waves on a plane beach: flow evolution, bed shear stress and run-up. J. Fluid Mech. 779, 556–597.CrossRefGoogle Scholar
Putnam, J.A. 1949 Loss of wave energy due to percolation in a permeable bottom. Trans. Am. Geophys. Union 30, 349–355.CrossRefGoogle Scholar
Qi, W.G., Li, C.F., Jeng, D.S., Gao, F.P. & Liang, Z.D. 2019 Combined wave–current induced excess pore-pressure in a sandy seabed: flume observations and comparisons with theoretical models. Coastal Engng 147, 89–98.CrossRefGoogle Scholar
Ragione, L.L., Laurent, K., Jenkins, J.T. & Bewley, G.P. 2019 Bedforms produced on a particle bed by vertical oscillations of a plate. Phys. Rev. Lett. 123, 058501.CrossRefGoogle ScholarPubMed
Rahman, M.M., Lo, S.-C.R. & Dafalias, Y.F. 2014 Modelling the static liquefaction of sand with low-plasticity fines. Géotecnique 64, 881–894.CrossRefGoogle Scholar
Ren, Y.P., Xu, G.H., Xu, X.B., Zhao, T.L. & Wang, X.Z. 2020 The initial wave induced failure of silty seabed: liquefaction or shear failure. Ocean Engng 200, 106990.CrossRefGoogle Scholar
Rivera-Rosario, G.A., Diamessis, P.J. & Jenkins, J.T. 2017 Bed failure induced by internal solitary waves. J. Geophys. Res. 122, 5468–5485.CrossRefGoogle Scholar
Rivera-Rosario, G.A., Diamessis, P.J., Lien, R.C., Lamb, K.G. & Thomsen, G.N. 2020 Formation of recirculating cores in convectively breaking internal solitary waves of depression shoaling over gentle slopes in the South China Sea. J. Phys. Oceanogr. 50, 1137–1157.CrossRefGoogle Scholar
Sumer, B.M. 2014 Liquefaction around marine structures. In Advanced Series on Ocean Engineering (ed. P.L.-F. Liu). World Scientific.Google Scholar
Sumer, B.M. & Fredsøe, J. 2002 The mechanics of scour in the marine environment. In Advanced Series on Ocean Engineering (ed. P.L.-F. Liu). World Scientific.CrossRefGoogle Scholar
Sumer, B.M., Sen, M.B., Karagali, I., Ceren, B., Fredsøe, J., Sottile, M., Zilioli, L. & Fuhrman, D.R. 2011 Flow and sediment transport induced by a plunging solitary wave. J. Geophys. Res. 116, C01008.Google Scholar
Tehranirad, B., Kirby, J.T. & Shi, F. 2020 A numerical model for tsunami-induced morphology change. Pure Appl. Geophys. 178, 5031–5059.CrossRefGoogle Scholar
Terzaghi, K. 1943 Theoretical Soil Mechanics. John Wiley & Sons.CrossRefGoogle Scholar
Tong, L.L., Zhang, J.S., Zhao, J.L., Zheng, J.H. & Guo, Y.K. 2020 Modelling study of wave damping over a sandy and a silty bed. Coastal Engng 161, 103756.CrossRefGoogle Scholar
Tørum, A. 2007 Wave-induced pore pressures-air/gas content. ASCE J. Waterway Port Coastal Ocean Engng 133, 83–86.CrossRefGoogle Scholar
Ulker, M.B.C. & Rahman, M.S. 2009 Response of saturated and nearly saturated porous media: different formulations and their applicability. Intl J. Numer. Anal. Meth. Geomech. 33, 633–664.CrossRefGoogle Scholar
Verruit, A. 1969 Elastic storage of aquifers. In Flow through Porous Media (ed. J.M. DeWiest). Academic Press.Google Scholar
Wang, Y.N. & Yang, D. 2019 Load-bearing analysis of the rock-socketed monopile in the shallow covering batholith seabed by finite element method. Wind Power 2, 26–31.Google Scholar
Wen, J.G. & Liu, P.L.-F. 1995 Mass transport in water waves over an elastic bed. Proc. R. Soc. A 450, 371–390.Google Scholar
Yamamoto, T. 1977 Wave-induced instability in sea beds. In Proceedings of the ASCE Symposium on Coastal Sediments, vol. 77, pp. 898–913. ASCE.Google Scholar
Yamamoto, T. 1978 Sea bed instability from waves. In Proceedings of the Annual Offshore Technology Conference, vol. 1, pp. 1819–1828. Offshore Technology Conference.CrossRefGoogle Scholar
Yamamoto, T., Koning, H.K., Sellmeijer, H. & Hijum, E.V. 1978 On the response of a poro-elastic bed to water waves. J. Fluid Mech. 87, 193–206.CrossRefGoogle Scholar
Young, Y.L., White, J.A., Xiao, H. & Borja, R.I. 2009 Liquefaction potential of coastal slopes induced by solitary waves. Acta Geotech. 4, 17–34.CrossRefGoogle Scholar
Young, Y.L., Xiao, H. & Maddux, T. 2010 Hydro- and morpho-dynamic modeling of breaking solitary waves over a fine sand beach. Part 1. Experimental study. Mar. Geol. 269, 107–118.CrossRefGoogle Scholar
Zen, K. & Yamazaki, H. 1991 Field observation and analysis of wave-induced liquefaction in seabed. Soils Found. 31, 161–179.CrossRefGoogle Scholar
Zhai, Y.Y., He, R., Zhao, J.L., Zhang, J.S., Jeng, D.S. & Li, L. 2018 Physical model of wave-induced seabed response around trenched pipeline in sandy seabed. Appl. Ocean Res. 75, 37–52.CrossRefGoogle Scholar
Zhao, H.Y., Zhu, J.F., Zheng, J.H. & Zhang, J.S. 2020 Numerical modelling of the fluid-seabed-structure interactions considering the impact of principal stress axes rotations. Soil Dyn. Earthq. Engng 136, 106242.CrossRefGoogle Scholar