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The propagation of interface waves at the interface between a fluid-saturated porous medium and a fluid has been extensively investigated in the last three decades due to its various and wide applications in several fields including earthquake engineering and materials testing. Although the sea floor is usually covered with porous marine sediment, the previous interface wave theories are rarely used for submarine acoustic problems for the following reasons. 1) In addition to hard porous media, unconsolidated soft porous media exist widely in the seabed, which are seldom considered in previous studies. 2) The depth of seawater is limited, and in many cases it cannot be regarded as a half-space. 3) The fluid-saturated porous medium model cannot describe the effect of a small number of bubbles caused by decomposition of organic matter in the sediment. Hence, the present paper focuses on the low-frequency pseudo-Scholte waves at the interface between an overlying fluid layer of finite thickness and a quasi-saturated porous half-space. The overlying fluid is assumed to be ideal compressible water and the quasi-saturated porous media are assumed to be sandstone and unconsolidated sediment and modeled by Biot theory. A fluid equivalent model is used to analyze the effects of the bubbles in the pores. Based on the boundary conditions, the closed-form dispersion equations of far-field interface waves are derived by using classical potential function method. The velocity and attenuation of pseudo-Scholte wave are determined by Newton iteration in a reasonable rooting interval. The analytical expressions of the displacement field and fluid pressure distribution caused by pseudo-Scholte waves are also derived. Then, based on the derived theoretical formulation, the numerical examples of calculations are presented. Our calculation results show that the stiffness of porous medium significantly affects the mode, phase velocity, displacement and fluid pressure distribution of interface waves; the phase velocity of the pseudo-Scholte wave in the finite-thickness fluid/fluid-saturated porous half-space is related to the ratio of the wavelength to the thickness of the fluid layer; the phase velocity of the shear wave is insensitive to a small number of bubbles dissolved in the pores, but the existence of bubbles has a significant influence on the phase velocity of the compressional wave and the pseudo-Scholte wave. Furthermore, the existence of bubbles can significantly affect the distribution of the pore pressure.
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Keywords:
- porous media /
- interface wave /
- wave velocity ratio /
- displacement distribution /
- propagation characteristics
[1] Han Q B, Qian M L, Zhu C P 2007 Acta Phys. Sin. 56 313 (in Chinese)[韩庆邦, 钱梦騄, 朱昌平 2007 物理学报 56 313]
[2] Xia T D, Wu S M 1999 J. Hydraul. Eng. 6 26 (in Chinese) [夏唐代, 吴世明 1999 水利学报 6 26]
[3] Xia T D, Chen H L, Wu S M 1999 J. Vib. Eng. 3 348 (in Chinese) [夏唐代, 陈汉良, 吴世明 1999 振动工程学报 3 348]
[4] Xia T D, Sun M Y, Chen H L 2000 J. Zhejiang Univ. (Eng. Sci.) 34 355 (in Chinese)[夏唐代, 孙鸣宇, 陈汉良 2000 浙江大学学报(工学版) 34 355]
[5] Padilla F, Billy M D, Quentin G 1999 J. Acoust. Soc. Am. 106 666
[6] Zhang H G, Pu S C, Yang S E 2010 J. Harbin Eng. Univ. 31 879 (in Chinese)[张海刚, 朴胜春, 杨士莪 2010 哈尔滨工程大学学报 31 879]
[7] Zhu H H, Zheng H, Lin J M, Tang Y F, Kong L M 2016 J. Shanghai Jiaotong Univ. 50 257 (in Chinese)[祝捍皓, 郑红, 林建民, 汤云峰, 孔令明 2016 上海交通大学学报 50 257]
[8] Markov M G 2009 Geophys. J. Int. 177 603
[9] Biot M A 1956 J. Acoust. Soc. Am. 28 168
[10] Biot M A 1956 J. Acoust. Soc. Am. 28 179
[11] Plona T J 1980 Appl. Phys. Lett. 36 259
[12] Han Q B, Xu S, Xie Z F, Ge R, Wang Q, Zhao S Y 2013 Acta Phys. Sin. 62 194301 (in Chinese)[韩庆邦, 徐杉, 谢祖峰, 葛蕤, 王茜, 赵胜永 2013 物理学报 62 194301]
[13] Feng S, Johnson D L 1983 J. Acoust. Soc. Am. 74 906
[14] Allard, J F, Henry M, Glorieux C, Petillon S, Lauriks W 2003 J. Appl. Phys. 93 1298
[15] Allard J F, Henry M, Glorieux C, Lauriks W, Petillon S 2004 J. Appl. Phys. 95 528
[16] van Dalen K N, Drijkoningen G G, Smeulders D M 2011 J. Acoust. Soc. Am. 129 2912
[17] Wang F, Huang Y W, Sun Q H 2017 Acta Phys. Sin. 66 194302 (in Chinese)[王飞, 黄益旺, 孙启航 2017 物理学报 66 194302]
[18] Wang J T, Jin F, Zhang C H 2013 Ocean Eng. 63 8
[19] Yang J 2005 Acta Geotech. 55 409
[20] Verruijt A 1969 Flow Through Porous Media (New York: Academic Press) pp331-376
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[1] Han Q B, Qian M L, Zhu C P 2007 Acta Phys. Sin. 56 313 (in Chinese)[韩庆邦, 钱梦騄, 朱昌平 2007 物理学报 56 313]
[2] Xia T D, Wu S M 1999 J. Hydraul. Eng. 6 26 (in Chinese) [夏唐代, 吴世明 1999 水利学报 6 26]
[3] Xia T D, Chen H L, Wu S M 1999 J. Vib. Eng. 3 348 (in Chinese) [夏唐代, 陈汉良, 吴世明 1999 振动工程学报 3 348]
[4] Xia T D, Sun M Y, Chen H L 2000 J. Zhejiang Univ. (Eng. Sci.) 34 355 (in Chinese)[夏唐代, 孙鸣宇, 陈汉良 2000 浙江大学学报(工学版) 34 355]
[5] Padilla F, Billy M D, Quentin G 1999 J. Acoust. Soc. Am. 106 666
[6] Zhang H G, Pu S C, Yang S E 2010 J. Harbin Eng. Univ. 31 879 (in Chinese)[张海刚, 朴胜春, 杨士莪 2010 哈尔滨工程大学学报 31 879]
[7] Zhu H H, Zheng H, Lin J M, Tang Y F, Kong L M 2016 J. Shanghai Jiaotong Univ. 50 257 (in Chinese)[祝捍皓, 郑红, 林建民, 汤云峰, 孔令明 2016 上海交通大学学报 50 257]
[8] Markov M G 2009 Geophys. J. Int. 177 603
[9] Biot M A 1956 J. Acoust. Soc. Am. 28 168
[10] Biot M A 1956 J. Acoust. Soc. Am. 28 179
[11] Plona T J 1980 Appl. Phys. Lett. 36 259
[12] Han Q B, Xu S, Xie Z F, Ge R, Wang Q, Zhao S Y 2013 Acta Phys. Sin. 62 194301 (in Chinese)[韩庆邦, 徐杉, 谢祖峰, 葛蕤, 王茜, 赵胜永 2013 物理学报 62 194301]
[13] Feng S, Johnson D L 1983 J. Acoust. Soc. Am. 74 906
[14] Allard, J F, Henry M, Glorieux C, Petillon S, Lauriks W 2003 J. Appl. Phys. 93 1298
[15] Allard J F, Henry M, Glorieux C, Lauriks W, Petillon S 2004 J. Appl. Phys. 95 528
[16] van Dalen K N, Drijkoningen G G, Smeulders D M 2011 J. Acoust. Soc. Am. 129 2912
[17] Wang F, Huang Y W, Sun Q H 2017 Acta Phys. Sin. 66 194302 (in Chinese)[王飞, 黄益旺, 孙启航 2017 物理学报 66 194302]
[18] Wang J T, Jin F, Zhang C H 2013 Ocean Eng. 63 8
[19] Yang J 2005 Acta Geotech. 55 409
[20] Verruijt A 1969 Flow Through Porous Media (New York: Academic Press) pp331-376
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