Cnoidal Water Wave Induced Pore Pressure Accumulation in the Seabed

ZHU Jieran


The pore water pressure accumulation in the seabed soil under cnoidal water waves is examined in detail. The cnoidal water wave theory is employed to calculating the water pressure on the double-layer seabed in shallow water region. The modified Terzaghi consolidation equation is the governing equation. A general analytical solution for the consolidation equation is given in an integral form. And a comparative study is carried out to verify the two previous pore pressure generation models: the linear relation and the hyperbola model. Accordingly, a joint model is presented to analysis the pore pressure accumulation in seabed and the soil liquefaction in a practical accident happened in China Shengli Oil Field.
Key words: Cnoidal water wave; Pore pressure accumulation; Hyperbola model; Modified Terzaghi consolidation equation


Cnoidal water wave; Pore pressure accumulation; Hyperbola model; Modified Terzaghi consolidation equation

Full Text:



[1] Chappelear, J. E. (1962). Shallow Water Waves. Journal of Geophysics Research, 67, 4693-4704.

[2] Cheng, L., Sumer, B. M., & Fredsøe, J. (2001). Solutions of Pore Pressure Build up Due to Progressive Waves. International Journal for Numerical and Analytical Methods in Geomechanics, 25, 885-907.

[3] Dormieux, L., & Delage, P. (1988). Effective Stress Response of a Plane Sea-Bed Under Wave Loading. Geotechnique, 38, 445-450.

[4] Fenton, J. D. (1979). A High-Order Cnoidal Wave Theory. Journal of Fluid Mechanics, 94, 129-161.

[5] Isobe, M. (1985). Calculation and Alication of First-Order Cnoidal Wave Theory. Coastal Engineering, 9, 309-325.

[6] Jeng, D. S., & Hsu, J. R. C. (1996). Wave Induced Soil Response in a Nearly Saturated Sea-Bed of Finite Thickness. Geotechnique, 46, 427-440.

[7] Jeng, D. S., Seymour B., & Li J. (2007). A New Aroximation for Pore Pressure Accumulation in Marine Sediment Due to Water Waves. International Journal for Numerical and Analytical Methods in Geomechanics, 31, 53-69.

[8] Keulegan, G. H., & Patterson, G. W. (1940). Mathematical Theory of Irrotational Translation Waves. Journal of Research of the National Bureau of Standards, 24, 47-101.

[9] Korteweg, D. J., & De Vries, G. (1895). On the Change of Form of Long Waves Advancing in a Rectangular Canal, and on a New Type of Long Stationary Waves. Philosophical Magazine, 39, 422-443.

[10] Laitone, E. V. (1960). The Second Aroximation to Cnoidal and Solitary Waves. Journal of Fluid Mechanics, 9, 430-444.

[11] Madsen, O. S. (1978). Wave-Induced Pore Pressures and Effective Stresses in a Porous Bed. Geotechnique, 28, 377-393.

[12] Mcdougal, W. G., Tsai, Y. T., & Liu, P. L. F. (1989). Wave-Induced Pore Water Pressure Accumulation in Marine Soils. Journal of Offshore Mechanics and Arctic Engineering, 111, 1-11.

[13] Mei, C. C., Stiassnie, M., & Yue, D. K. P. (2005). Theory and Alications of Ocean Surface Waves Part 2: Nonlinear Aspects. World Scientific.

[14] Sassa, S., & Sekiguchi, H. (2001). Analysis of Wave-Induced Liquefaction of Sand Beds. Geotechnique, 51, 115-126.

[15] Seed, H. B., & Rahman, M. S. (1978). Wave-Induced Pore Pressure in Relation to Ocean Floor Stability of Cohesionless Soils. Marine Geotechnology, 3, 123-150.

[16] Sumer, B. M., & Fredsøe, J. (2002). The Mechanics of Scour in the Marine Environment. World Scientific.

[17] Sumer, B. M., Kirca, V. S. O., & Fredsøe, J. (2011). Experimental Validation of a Mathematical Model for Seabed Liquefaction in Waves. Proceedings of the 21st International Offshore and Polar Engineering Conference, Maui, Hawai, USA.

[18] Wiegel, R. (1960). A Presentation of Cnoidal Wave Theory for Practical Alication. Journal of Fluid Mechanics, 7, 273-286.

[19] Wu, M. X., & Lou, Z. G. (2002). Stability and Liquefaction Analysis of Seabed to Wave Loading. Engineering Mechanics, 19, 97-102.

[20] Yamamoto, T. (1978). Wave-Induced Pore Pressures and Effective Stresses in Inhomogeneous Seabed Foundations. Ocean Engineering, 8, 1-16.

[21] Zen, K., & Yamazaki, H. (1990). Mechanism of Wave-Induced Liquefaction and Densification in Seabed. Soil and Foundation, 30, 90-104.



  • There are currently no refbacks.

Copyright (c)

Share us to:   


  • How to do online submission to another Journal?
  • If you have already registered in Journal A, then how can you submit another article to Journal B? It takes two steps to make it happen:

1. Register yourself in Journal B as an Author

  • Find the journal you want to submit to in CATEGORIES, click on “VIEW JOURNAL”, “Online Submissions”, “GO TO LOGIN” and “Edit My Profile”. Check “Author” on the “Edit Profile” page, then “Save”.

2. Submission

  • Go to “User Home”, and click on “Author” under the name of Journal B. You may start a New Submission by clicking on “CLICK HERE”.

We only use three mailboxes as follows to deal with issues about paper acceptance, payment and submission of electronic versions of our journals to databases:;;

 Articles published in Advances in Petroleum Exploration and Development are licensed under Creative Commons Attribution 4.0 (CC-BY)


Address:1020 Bouvier Street, Suite 400, Quebec City, Quebec, G2K 0K9, Canada.

Telephone: 1-514-558 6138
Website: Http://

Copyright © 2010 Canadian Research & Development Centre of Sciences and Cultures