Technical Papers
Jul 29, 2024

Wave-Induced Dynamic Response of a Transversely Isotropic and Multilayered Poroelastic Seabed in Shallow Water

Publication: International Journal of Geomechanics
Volume 24, Issue 10

Abstract

In shallow water regions, ocean waves commonly propagate in the form of cnoidal waves, with the response induced in the seabed obviously being different from that involving conventional linear waves. Computational models of waves and seabeds were established based on cnoidal wave theory and Biot’s completely dynamic consolidation theory, respectively. A semianalytical solution for the dynamic response of the multilayered, transversely isotropic (TI), poroelastic seabed induced by cnoidal waves was derived via the scalar potential function and the dual variable and position method. The reliability and accuracy of the developed semianalytical solution was verified against existing solutions and experimental data. This parametric study demonstrated that cnoidal waves have a significant effect on the dynamic response of the seabed compared to linear waves. Also, the induced pore pressure/stresses and corresponding liquefaction potential were significantly affected by the anisotropy and layering of the seabed material. The newly developed solution can serve as a useful tool for estimating the liquefaction potential of a TI and multilayered poroelastic seabed in shallow water.

Get full access to this article

View all available purchase options and get full access to this article.

Data Availability Statement

Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.

Acknowledgments

The authors are grateful for the financial support provided by the Natural Science Foundation of Zhejiang Province (Grant No. LHZ21E090001) and the National Natural Science Foundation of China (Grant Nos. 52178367 and 52078467).

References

An, R., L. W. Kong, X. W. Zhang, and C. S. Li. 2022. “Effects of dry-wet cycles on three-dimensional pore structure and permeability characteristics of granite residual soil using X-ray micro computed tomography.” J. Rock Mech. Geotech. Eng. 14: 851–860. https://doi.org/10.1016/j.jrmge.2021.10.004.
An, R., Y. X. Wang, X. W. Zhang, C. Chen, X. Y. Liu, and S. T. Cai. 2023. “Quantitative characterization of drying-induced cracks and permeability of granite residual soil using micron-sized X-ray computed tomography.” Sci. Total Environ. 876: 163213. https://doi.org/10.1016/j.scitotenv.2023.163213.
Biot, M. A. 1941. “General theory of three-dimensional consolidation.” J. Appl. Phys. 122: 155–164. https://doi.org/10.1063/1.1712886.
Biot, M. A. 1956. “Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range.” J. Acoust. Soc. Am. 282: 168–178. https://doi.org/10.1121/1.1908239.
Biot, M. A. 1962. “Mechanics of deformation and acoustic propagation in porous media.” J. Appl. Phys. 334: 1482–1498. https://doi.org/10.1063/1.1728759.
Chen, W. Y., G. X. Chen, W. Chen, C. C. Liao, and H. M. Gao. 2019. “Numerical simulation of the nonlinear wave-induced dynamic response of anisotropic poro-elastoplastic seabed.” Mar. Georesour. Geotechnol. 378: 924–935. https://doi.org/10.1080/1064119X.2018.1507064.
Chen, X., Q. Zhang, X. Y. Zheng, and Y. Lei. 2022. “Dynamic responses of a multilayered transversely isotropic poroelastic seabed subjected to ocean waves and currents.” J. Mar. Sci. Eng. 101: 73. https://doi.org/10.3390/jmse10010073.
Cheng, A. H. D. 1997. “Material coefficients of anisotropic poroelasticity.” Int. J. Rock Mech. Min. Sci. 34: 199–205. https://doi.org/10.1016/S0148-9062(96)00055-1.
Cui, C., Z. Liang, C. Xu, Y. Xin, and B. Wang. 2023. “Analytical solution for horizontal vibration of end-bearing single pile in radially heterogeneous saturated soil.” Appl. Math. Modell. 116: 65–83. https://doi.org/10.1016/j.apm.2022.11.027.
Damgaard, J. S., B. M. Sumer, T. C. Teh, A. C. Palmer, P. Foray, and D. Osorio. 2006. “Guidelines for pipeline on-bottom stability on liquefied noncohesive seabeds.” J. Waterw. Port Coastal Ocean Eng. 1324: 300–309. https://doi.org/10.1061/(ASCE)0733-950X(2006)132:4(300).
Gatmiri, B. 1992. “Response of cross-anisotropic seabed to ocean waves.” J. Geotech. Eng. 1189: 1295–1314. https://doi.org/10.1061/(ASCE)0733-9410(1992)118:9(1295).
He, R., A. M. Kaynia, J. Zheng, and J. Zhang. 2022. “Effect of gap and scour on dynamic behavior of monopiles and offshore wind structures.” Ocean Eng. 243: 110336. https://doi.org/10.1016/j.oceaneng.2021.110336.
Hsu, C. J., Y. Y. Chen, and C. C. Tsai. 2019. “Wave-induced seabed response in shallow water.” Appl. Ocean Res. 89: 211–223. https://doi.org/10.1016/j.apor.2019.05.016.
Hsu, C. J., C. C. Tsai, and Y. Y. Chen. 2021. “Wave-induced seabed momentary liquefaction in shallow water.” Appl. Ocean Res. 115: 102819. https://doi.org/10.1016/j.apor.2021.102819.
Hsu, J. R. C., D. S. Jeng, and C. P. Lee. 1995. “Oscillatory soil response and liquefaction in an unsaturated layered seabed.” Int. J. Numer. Anal. Methods Geomech. 1912: 825–849. https://doi.org/10.1002/nag.1610191202.
Hsu, J. R. C., D. S. Jeng, and C. P. Tsai. 1993. “Short-crested wave-induced soil response in a porous seabed of infinite thickness.” Int. J. Numer. Anal. Methods Geomech. 178: 553–576. https://doi.org/10.1002/nag.1610170803.
Jeng, D. S. 1996. “Wave-induced liquefaction potential in a cross-anisotropic seabed.” J. Chin. Inst. Eng. 191: 59–70. https://doi.org/10.1080/02533839.1996.9677765.
Jeng, D. S. 2015. “Review of liquefaction around marine structures by B. Mutlu Sumer.” J. Waterw. Port Coastal Ocean Eng. 1415: 07515001. https://doi.org/10.1061/(ASCE)WW.1943-5460.0000296.
Jeng, D. S., and D. H. Cha. 2003. “Effects of dynamic soil behavior and wave non-linearity on the wave-induced pore pressure and effective stresses in porous seabed.” Ocean Eng. 3016: 2065–2089. https://doi.org/10.1016/S0029-8018(03)00070-2.
Jeng, D. S., and M. S. Rahman. 2000. “Effective stresses in a porous seabed of finite thickness: Inertia effects.” Can. Geotech. J. 376: 1383–1392. https://doi.org/10.1139/t00-063.
Jeng, D. S., M. S. Rahman, and T. L. Lee. 1999. “Effects of inertia forces on wave-induced seabed response.” Int. J. Offshore Polar Eng. 9: 307–313.
Jeng, D. S., and B. R. Seymour. 1997. “Wave-induced pore pressure and effective stresses in a porous seabed with variable permeability.” J. Offshore Mech. Arct. Eng. 1194: 226–233. https://doi.org/10.1115/1.2829100.
Jeng, D. S., and H. Zhang. 2005. “An integrated three-dimensional model of wave-induced pore pressure and effective stresses in a porous seabed: II. Breaking waves.” Ocean Eng. 3216: 1950–1967. https://doi.org/10.1016/j.oceaneng.2005.01.005.
Kitano, T., and H. Mase. 2001. “Wave-induced porewater pressure in a seabed with inhomogeneous permeability.” Ocean Eng. 283: 279–296. https://doi.org/10.1016/S0029-8018(00)00010-X.
Li, X. B., Z. Q. Zhang, and E. Pan. 2020. “Wave-induced dynamic response in a transversely isotropic and multilayered poroelastic seabed.” Soil Dyn. Earthquake Eng. 139: 106365. https://doi.org/10.1016/j.soildyn.2020.106365.
Liu, K. F., Z. Q. Zhang, and E. Pan. 2022. “Dynamic response of a transversely isotropic and multilayered poroelastic medium subjected to a moving load.” Soil Dyn. Earthquake Eng. 155: 107154. https://doi.org/10.1016/j.soildyn.2022.107154.
Lu, H. B. 2005. “The research on pore water pressure response to waves in sandy seabed.” Master’s thesis, Changsha University of Science and Technology.
Madsen, O. S. 1978. “Wave-induced pore pressures and effective stresses in a porous bed.” Géotechnique 284: 377–393. https://doi.org/10.1680/geot.1978.28.4.377.
Mei, C. C., and M. A. Foda. 1981. “Wave-induced responses in a fluid-filled poro-elastic solid with a free surface – A boundary layer theory.” Geophys. J. Int. 663: 597–631. https://doi.org/10.1111/j.1365-246X.1981.tb04892.x.
Okusa, S. 1985. “Wave-induced stresses in unsaturated submarine sediments.” Géotechnique 354: 517–532. https://doi.org/10.1680/geot.1985.35.4.517.
Padgett, J., R. DesRoches, B. Nielson, M. Yashinsky, O. S. Kwon, N. Burdette, and E. Tavera. 2008. “Bridge damage and repair costs from Hurricane Katrina.” J. Bridge Eng. 131: 6–14. https://doi.org/10.1061/(ASCE)1084-0702(2008)13:1(6).
Pan, E. 2019. “Green’s functions for geophysics: A review.” Rep. Prog. Phys. 8210: 106801. https://doi.org/10.1088/1361-6633/ab1877.
Quiuqui, J. P. C., J. P. Tamayo, and S. Maghous. 2022. “Closed-form solutions for wave-induced poroelastic response in seabed under dynamic and quasi-static regimes.” J. Braz. Soc. Mech. Sci. Eng. 441: 16. https://doi.org/10.1007/s40430-021-03300-1.
Sakai, T., H. Mase, and A. Matsumoto. 1988. “Effects of inertia and gravity on seabed response to ocean waves.” In Modeling soil-water-structure interactions, edited by P. A. Kolkman, J. Linderberg, and K. Pilarczyk, 61–66. Rotterdam: A. A. Balkema.
Seymour, B. R., D. S. Jeng, and J. R. C. Hsu. 1996. “Transient soil response in a porous seabed with variable permeability.” Ocean Eng. 231: 27–46. https://doi.org/10.1016/0029-8018(95)00018-G.
Shan, Z., Y. Dou, M. Sun, K. Wang, L. Qu, J. He, and J. Zhu. 2022. “Experimental investigation the characteristics of three-dimensional wave field and its effect on sandy sloping seabed.” Mar. Georesour. Geotechnol. 41: 791–805. https://doi.org/10.1080/1064119X.2022.2101963.
Terzaghi, K. 1925. Erdbaumechanik auf bodenphysikalischer grundlage. Leipzig und Wien: Franz Deuticke.
Tsai, C. P., and T. L. Lee. 1995. “Standing wave induced pore pressures in a porous seabed.” Ocean Eng. 226: 505–517. https://doi.org/10.1016/0029-8018(95)00003-4.
Ulker, M. B. C. 2012a. “Pore pressure, stress distributions, and instantaneous liquefaction of two-layer soil under waves.” J. Waterw. Port Coastal Ocean Eng. 1386: 435–450. https://doi.org/10.1061/(ASCE)WW.1943-5460.0000155.
Ulker, M. B. C. 2012b. “Dynamic pore pressure response of two-layer seabed under nonlinear waves.” AIP Conf. Proc. 1479: 1480–1483. https://doi.org/10.1063/1.4756443.
Ulker, M. B. C., M. S. Rahman, and D. S. Jeng. 2009. “Wave-induced response of seabed: Various formulations and their applicability.” Appl. Ocean Res. 311: 12–24. https://doi.org/10.1016/j.apor.2009.03.003.
Verruijt, A. 1969. “Elastic storage of aquifers.” In Flow through porous media, edited by R. J. M. De Weist, and J. Bear, 331–376. New York: Academic Press.
Wang, G., S. Chen, C. Liu, K. Shao, and Q. Liu. 2020. “Wave-induced dynamic response and liquefaction of transversely isotropic seabed.” Int. J. Geomech. 20: 04019192. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001570.
Wiegel, R. L. 1960. “A presentation of cnoidal wave theory for practical application.” J. Fluid Mech. 7: 273–286. https://doi.org/10.1017/S0022112060001481.
Yamamoto, T. 1981. “Wave-induced pore pressures and effective stresses in inhomogeneous seabed foundations.” Ocean Eng. 81: 1–16. https://doi.org/10.1016/0029-8018(81)90002-0.
Yamamoto, T., H. L. Koning, H. Sellmeijer, and E. V. Hijum. 1978. “On the response of a poro-elastic bed to water waves.” J. Fluid Mech. 871: 193–206. https://doi.org/10.1017/S0022112078003006.
Yang, Q., and H. Liu. 2018. “Dynamic response of multilayered silty seabeds under wave-current action in the Yellow River Estuary.” Int. J. Geomech. 19: 04018031. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001109.
Ye, J. H., and D. S. Jeng. 2012. “Response of porous seabed to nature loadings: Waves and currents.” J. Eng. Mech. 1386: 601–613. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000356.
Yuhi, M., and H. Ishida. 1998. “Analytical solution for wave-induced seabed response in a soil-water two-phase mixture.” Coastal Eng. J. 404: 367–381. https://doi.org/10.1142/S0578563498000212.
Zhang, Y., M. H. El Naggar, W. Wu, Z. Wang, X. Yang, and G. Jiang. 2022a. “Dynamic torsional impedance of large-diameter pipe pile for offshore engineering: 3D analytical solution.” Appl. Math. Modell. 111: 664–680. https://doi.org/10.1016/j.apm.2022.07.017.
Zhang, Z. Q., S. B. Liu, E. Pan, and Q. Wang. 2023. “Dynamic loading in a transversely isotropic and layered elastic half-space.” Int. J. Mech. Sci. 260: 108626. https://doi.org/10.1016/j.ijmecsci.2023.108626.
Zhang, Z. Q., and E. Pan. 2020. “Time-harmonic response of transversely isotropic and layered poroelastic half-spaces under general buried loads.” Appl. Math. Modell. 80: 426–453. https://doi.org/10.1016/j.apm.2019.11.035.
Zhang, Z. Q., and E. Pan. 2023. “Coupled horizontal and rocking vibrations of a rigid circular disc on the surface of a transversely isotropic and layered poroelastic half-space.” Appl. Math. Modell. 114: 270–290. https://doi.org/10.1016/j.apm.2022.10.005.
Zhang, Z. Q., B. H. Zhou, X. B. Li, and Z. Wang. 2022b. “Second-order Stokes wave-induced dynamic response and instantaneous liquefaction in a transversely isotropic and multilayered poroelastic seabed.” Front. Mar. Sci. 9: 1082337. https://doi.org/10.3389/fmars.2022.1082337.
Zhou, X. L., J. Zhang, J. J. Guo, J. H. Wang, and D. S. Jeng. 2015. “Cnoidal wave induced seabed response around a buried pipeline.” Ocean Eng. 101: 118–130. https://doi.org/10.1016/J.OCEANENG.2015.04.032.
Zienkiewicz, O. C., C. T. Chang, and P. Bettess. 1980. “Drained, undrained, consolidating and dynamic behaviour assumptions in soils.” Géotechnique 304: 385–395. https://doi.org/10.1680/geot.1980.30.4.385.

Information & Authors

Information

Published In

Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 24Issue 10October 2024

History

Received: Jun 28, 2023
Accepted: Apr 15, 2024
Published online: Jul 29, 2024
Published in print: Oct 1, 2024
Discussion open until: Dec 29, 2024

Permissions

Request permissions for this article.

ASCE Technical Topics:

Authors

Affiliations

Professor, School of Landscape Architecture, Zhejiang A & F Univ., Hangzhou, Zhejiang 311300, China. ORCID: https://orcid.org/0000-0002-4455-908X. Email: [email protected]
Master’s Student, Institute of Geotechnical Engineering, Zhejiang Univ. of Technology, Hangzhou, Zhejiang 310014, China. Email: [email protected]
Professor, College of Architecture and Energy Engineering, Wenzhou Univ. of Technology, Wenzhou, Zhejiang 325035, China. ORCID: https://orcid.org/0000-0002-9331-4302. Email: [email protected]
Professor, Institute of Geotechnical Engineering, Zhejiang Univ. of Technology, Hangzhou, Zhejiang 310014, China (corresponding author). Email: [email protected]

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share