Analytical solutions for dynamic response in poroelastic seabed under second-order Stokes waves

WANG Zhe; ZHOU Bohao; ZHANG Zhiqing; LI Xibin

doi:10.11779/CJGE20230504

Volume 46 Issue 9

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Chinese Journal of Geotechnical Engineering > 2024 > 46(9): 1791-1799. > DOI: 10.11779/CJGE20230504

WANG Zhe, ZHOU Bohao, ZHANG Zhiqing, LI Xibin. Analytical solutions for dynamic response in poroelastic seabed under second-order Stokes waves[J]. Chinese Journal of Geotechnical Engineering, 2024, 46(9): 1791-1799. DOI: 10.11779/CJGE20230504

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Analytical solutions for dynamic response in poroelastic seabed under second-order Stokes waves

1.
Institute of Geotechnical Engineering, Zhejiang University of Technology, Hangzhou 310014, China
2.
College of Architecture and Energy Engineering, Wenzhou University of Technology, Wenzhou 325035, China
3.
School of Landscape Architecture, Zhejiang A & F University, Hangzhou 311300, China

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Received Date: June 04, 2023
Available Online: March 24, 2024

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Abstract

Abstract

Based on the theory of the second-order Stokes waves, the dynamic response of a poroelastic seabed induced by nonlinear ocean waves is investigated. The governing equations for the seabed are established in Cartesian coordinates using the Biot's general consolidation theory and the Verruijt's storage equation. The analytical solutions for the dynamic response of the seabed are obtained by extending the ocean wave function and the field quantities in the seabed to the complex domain using a rigorous mathematical derivation. The correctness and reliability of the analytical solutions are verified by comparing with the existing solutions. Finally, the effects of the characteristic parameters of the waves and seabed on the vertical effective stress, horizontal effective stress, shear stress and pore pressure distribution of the seabed are analyzed. The results show that the characteristic parameters of the waves and seabed have a significant effect on the dynamic response of the seabed. The wave period and water depth have a significant impact on the second-order term of the nonlinear waves, while the permeability and shear modulus respectively affect the rate of change and amplitude.
- second-order Stokes wave,
- seabed,
- dynamic response,
- analytical solution

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References

[1]	LI X B, ZHANG Z Q, PAN E N. Wave-induced dynamic response in a transversely isotropic and multilayered poroelastic seabed[J]. Soil Dynamics and Earthquake Engineering, 2020, 139: 106365. doi: 10.1016/j.soildyn.2020.106365
[2]	JENG D S. Review of liquefaction around marine structures by B mutlu sumer[J]. Journal of Waterway, Port, Coastal, and Ocean Engineering, 2015, 141(5): 07515001. doi: 10.1061/(ASCE)WW.1943-5460.0000296
[3]	PUTNAM J A. Loss of wave energy due to percolation in a permeable sea bottom[J]. Transactions, American Geophysical Union, 1949, 30(3): 349. doi: 10.1029/TR030i003p00349
[4]	BIOT M A. Theory of propagation of elastic waves in a fluid-saturated porous solid: Ⅰ low-frequency range[J]. The Journal of the Acoustical Society of America, 1956, 28(2): 168-178. doi: 10.1121/1.1908239
[5]	SEKIGUCHI H, KITA K, OKAMOTO O. Response of poro-elastoplastic beds to standing waves[J]. Soils and Foundations, 1995, 35(3): 31-42. doi: 10.3208/sandf.35.31
[6]	BIOT M A. General theory of three-dimensional consolidation[J]. Journal of Applied Physics, 1941, 12(2): 155-164. doi: 10.1063/1.1712886
[7]	BIOT M A. Mechanics of deformation and acoustic propagation in porous media[J]. Journal of Applied Physics, 1962, 33(4): 1482-1498. doi: 10.1063/1.1728759
[8]	YAMAMOTO T, KONING H L, SELLMEIJER H, et al. On the response of a poro-elastic bed to water waves[J]. Journal of Fluid Mechanics, 1978, 87(1): 193-206. doi: 10.1017/S0022112078003006
[9]	MADSEN O S. Wave-induced pore pressures and effective stresses in a porous bed[J]. Géotechnique, 1978, 28(4): 377-393. doi: 10.1680/geot.1978.28.4.377
[10]	VERRUIJT A. Elastic storage of aquifers[M]// Flow through Porous Media. DE WIEST R J M. New York: Academic Press, 1969.
[11]	OKUSA S. Wave-induced stresses in unsaturated submarine sediments[J]. Géotechnique, 1985, 35(4): 517-532. doi: 10.1680/geot.1985.35.4.517
[12]	MEI C C, FODA M A. Wave-induced responses in a fluid-filled poro-elastic solid with a free surface: a boundary layer theory[J]. Geophysical Journal International, 1981, 66(3): 597-631. doi: 10.1111/j.1365-246X.1981.tb04892.x
[13]	HSU J R C, JENG D S. Wave-induced soil response in an unsaturated anisotropic seabed of finite thickness[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1994, 18(11): 785-807. doi: 10.1002/nag.1610181104
[14]	ZIENKIEWICZ O C, CHANG C T, BETTESS P. Drained, undrained, consolidating and dynamic behaviour assumptions in soils[J]. Géotechnique, 1980, 30(4): 385-395. doi: 10.1680/geot.1980.30.4.385
[15]	ULKER M B C, RAHMAN M S, JENG D S. Wave-induced response of seabed: various formulations and their applicability[J]. Applied Ocean Research, 2009, 31(1): 12-24. doi: 10.1016/j.apor.2009.03.003
[16]	LAUTON G, PATTIARATCHI C B, LENTINI C A D. Observations of breaking internal tides on the australian north west shelf edge[J]. Frontiers in Marine Science, 2021, 8: 629372. doi: 10.3389/fmars.2021.629372
[17]	王忠涛, 栾茂田, 刘占阁, 等. 浅水区波浪非线性效应对砂质海床动力响应的影响[J]. 海洋工程, 2005, 23(1): 41-46. doi: 10.3969/j.issn.1005-9865.2005.01.007 WANG Zhongtao, LUAN Maotian, LIU Zhange, et al. Studies on the effect of non-linear wave loading in shallow water region on dynamic response of sandy seabed[J]. The Ocean Engineering, 2005, 23(1): 41-46. (in Chinese) doi: 10.3969/j.issn.1005-9865.2005.01.007
[18]	郭秀军, 朱大伟, 孟庆生, 等. 波浪作用下黄河口多层粉质土海床动力响应特征差异性分析[J]. 岩土工程学报, 2012, 34(12): 2270-2276. http://cge.nhri.cn/article/id/14954 GUO Xiujun, ZHU Dawei, MENG Qingsheng, et al. Differences in dynamic response characteristics of multi-layer silty seabed under waves in Yellow River Estuary[J]. Chinese Journal of Geotechnical Engineering, 2012, 34(12): 2270-2276. (in Chinese) http://cge.nhri.cn/article/id/14954
[19]	ZHOU X L, XU B, WANG J H, et al. An analytical solution for wave-induced seabed response in a multi-layered poro-elastic seabed[J]. Ocean Engineering, 2011, 38(1): 119-129. doi: 10.1016/j.oceaneng.2010.10.003
[20]	ZHANG Z Q, ZHOU B H, LI X B, et al. Second-order Stokes wave-induced dynamic response and instantaneous liquefaction in a transversely isotropic and multilayered poroelastic seabed[J]. Frontiers in Marine Science, 2022, 9: 1082337. doi: 10.3389/fmars.2022.1082337
[21]	周晓智, 陈育民, 刘汉龙. 驻波作用下有限厚度海床动应力路径特性研究[J]. 岩土工程学报, 2018, 40(5): 890-899. doi: 10.11779/CJGE201805014 ZHOU Xiaozhi, CHEN Yumin, LIU Hanlong. Study on characteristics of dynamic stress path of finite-thickness seabed under standing waves[J]. Chinese Journal of Geotechnical Engineering, 2018, 40(5): 890-899. (in Chinese) doi: 10.11779/CJGE201805014
[22]	LEMÉHAUTÉ B. An Introduction to Hydrodynamics and Water Waves[M]. New York: Springer-Verlag, 1976.

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