DING Bo-yang, CHEN Zhang-long, XU Ting. Degeneration and Tranfer of the Displacement-Stress Functions From Poroelastic Layered Media to Elastic Layered Media[J]. Applied Mathematics and Mechanics, 2014, 35(2): 162-180. doi: 10.3879/j.issn.1000-0887.2014.02.005
Citation: DING Bo-yang, CHEN Zhang-long, XU Ting. Degeneration and Tranfer of the Displacement-Stress Functions From Poroelastic Layered Media to Elastic Layered Media[J]. Applied Mathematics and Mechanics, 2014, 35(2): 162-180. doi: 10.3879/j.issn.1000-0887.2014.02.005

Degeneration and Tranfer of the Displacement-Stress Functions From Poroelastic Layered Media to Elastic Layered Media

doi: 10.3879/j.issn.1000-0887.2014.02.005
Funds:  The National Natural Science Foundation of China(11172268)
  • Received Date: 2013-07-15
  • Rev Recd Date: 2013-10-30
  • Publish Date: 2014-02-15
  • Based on Biot’s dynamic governing equations, through decoupling of the fast and slow dilational waves, the first-order differential simultaneous equations for the displacement-stress propagation were obtained, which satisfy the kinetics of wave propagation in the multilayer poroelastic saturated media. Both the simultaneous equations and the transfer funtions could be degenerated to those for the multilayer single-phase media. With the displacement-stress continuity conditions at the interface between the poroelastic and single-phase media, the interfacial transitional transfer matrix was established by analysis of the propagation of displacement-stress from the poroelastic medium to the single-phase medium. The 4×6 transfer matrix was derived from the 6×6 transitional transfer matrix of the multilayer poroelastic medium and could be combined with the 4×4 transfer matrix of the single-phase medium. Finally, the degenerated results from the presented method were compared with those from the previous classical wave-propagation models to get good consistency between them. The presented method has merits of simpler calculation and clearer physical sense compared with the classical ones.
  • loading
  • [1]
    Aki K, Richards P G. Quantitative Seismology: Theory and Methods [M]. San Francisco: W H Freeman, 1980.
    [2]
    Paillet F L, Cheng C H. Acoustic Waves in Boreholes [M]. CRC Press, 1991.
    [3]
    Ewing W M, Jardetzky W S, Press F. Elastic Waves in Layered Media [M]. McGraw-Hill, 1957.
    [4]
    Brekhovskikh L M. Waves in Layered Media [M]. New York: Academic Press, 1960.
    [5]
    Thomson W T. Transmission of elastic waves through a stratified solid medium[J]. Journal of Applied Physics,1950,21(2): 89-93.
    [6]
    Haskell N A. The dispersion of surface waves in multilayered media[J]. Bulletin of the Seismological Society of America,1953,43(1): 17-34.
    [7]
    Haskell N A. Radiation pattern of surface waves from point sources in multilayered medium[J]. Bulletin of the Seismological Society of America,1964,54(1): 377-393.
    [8]
    Harkrider D G. Surface waves in multilayered elastic medium I: rayleigh and love waves from buried sources in a multilayered elastic half-space[J]. Bulletin of the Seismological Society of America,1964,54(2): 627-679.
    [9]
    Ben-Menahem A, Singh S J. Multipolar elastic fields in a layered half-space[J]. Bulletin of the Seismological Society of America,1968,58(5): 1519-1572.
    [10]
    Hansen W W. A new type of expansion in radiation problems[J]. Phys Rev,1935,47(2): 139-143.
    [11]
    陈运泰. 多层弹性半空间中的地震波(一)[J]. 地球物理学报, 1974,17(1): 20-43.(CHEN Yun-tai. Seismic waves in multilayered elastic half-space(I)[J]. Acta Geophysica Sinica,1974,17(1): 20-43.(in Chinese))
    [12]
    Gilbert F, Backus G E. Propagator matrices in elastic wave and vibration problems[J]. Geophysics,1966,31(2): 326-332.
    [13]
    Kennett B L N, Kerry N J. Seismic waves in a stratified half space[J]. Geophysical Journal of the Royal Astronomical Society,1979,57(3): 557-583.
    [14]
    Kennett B L N. Seismic Wave Propagation in Stratified Media [M]. Cambridge University Press, 1983.
    [15]
    Pride S, Tromeur E, Berryman J. Biot slow-wave effects in stratified rock[J]. Geophysics,2002,67(1): 452-467.
    [16]
    Biot M. Theory of propagation of elastic waves in a fluid-saturated porous solid[J]. Journal of the Acoustical Society of America,1956,28(2): 168-191.
    [17]
    Biot M, Willis D. The elastic coefficients of the theory of consolidation[J]. Journal of Applied Mechanics,1957,24(4): 594-601.
    [18]
    Deresiewicz H. The effect of boundaries on wave propagation in a liquid-filled porous solid—I: reflection of plane waves at a free plane boundary (non-dissipative case)[J]. Bulletin of the Seismological Society of America,1960,50(4): 599-607.
    [19]
    Deresiewicz H, Rice J T. The effect of boundaries on wave propagation in a liquid filled porous-solid—III: reflection of plane waves at a free plane boundary (general case)[J]. Bulletin of the Seismological Society of America,1962,52(3): 505-625.
    [20]
    Deresiewicz H, Levy A. The effect of boundaries on wave propagation in a liquid-filled porous solid—X: transmission through a stratified medium[J]. Bulletin of the Seismological Society of America,1967,57(3): 381-392.
    [21]
    Gilbert K E. Reflection of sound from a randomly layered ocean bottom[J]. J Acoust Soc Am,1980,68(5): 1454-1458.
    [22]
    Yamamoto T, Badiey M. Propagator matrix for acoustic wave propagation through anisotropic porous media[C]//Akal, Berkson eds. Ocean Seismo-Acoustic Symp.Plenum Press, 1985: 463-472.
    [23]
    QIAO Wen-xiao. Reflection and transmission of acoustic waves on multilayered porous media[J]. Chinese Journal of Acoustics,1993,12(1): 25-37.
    [24]
    王耀俊. 多层固体媒质对声波的反射和透射[J]. 南京大学学报(自然科学版), 1993,29(1): 49-62.(WANG Yao-jun. Acoustic wave reflection and transmission on multilayered media[J].Journal of Nanjing University(Natural Sciences Edition),1993,29(1): 49-62.(in Chinese))
    [25]
    Badiey M, Jaya L, Cheng A H-D. Propagator matrix for plane wave reflection from inhomogeneous anisotropic poroelastic seafloor[J]. Journal of Computational Acoustics,1994,2(1): 11-27.
    [26]
    Dominguez J. Boundary element approach for dynamic poroelastic problems[J]. International Journal for Numerical Methods in Engineering,1992,35(2): 307-324.
    [27]
    Jocker J, Smeulders D, Drijkoningen G, Van der Lee C, Kalfsbeek A. Matrix propagator method for layered porous media: analytical expressions and stability criteria[J]. Geophysics,2004,69(4): 1071-1081.
    [28]
    Ding B Y, Chen J. Solutions of Green’s function for Lamb’s problem of a two-phase saturated medium[J]. Theoretical & Applied Mechanics Letters,2011,1: 052003.
    [29]
    丁伯阳, 党改红, 袁金华. 伴有排水的两相饱和介质动力问题的LAMB积分公式[J]. 应用数学和力学, 2010,31(9): 1066-1074.(DING Bo-yang, DANG Gai-hong, YUAN Jin-hua. Lamb’s integral formulas of two-phase saturated medium for soil dynamic problems with drainage[J]. Applied Mathematics and Mechanics,2010,31(9): 1066-1074.(in Chinese))
    [30]
    DING Bo-yang, YUAN Jin-hua, PAN Xiao-dong. The abstracted and saturated integrated Green functions and OOP of BEM in soil dynamics[J]. Science in China Series G: Physics, Mechanics and Astronomy,2008,51(12): 1926-1937.
    [31]
    DING Bo-yang, YUAN Jin-hua. Dynamic Green’s functions of a two-phase saturated medium subjected to concentrated force[J]. International Journal of Solid Structures,2011,48(16/17): 2288-2303.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (1083) PDF downloads(1047) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return