Skip to main content
SpringerLink
Log in

Reflection and Transmission of Elastic Waves from the Interface of a Fluid-saturated Porous Solid and a Double Porosity Solid

  • Published:
Transport in Porous Media Aims and scope Submit manuscript

Abstract

The reflection and transmission characteristics of an incident plane P1 wave from the interface of a fluid-saturated single porous solid and a fluid-saturated double porosity solid are investigated. The fluid-saturated porous solid is modeled with the classic Biot’s theory and the double porosity medium is described by an extended Biot’s theory. In a double-porosity model with dual-permeability there exist three compressional waves and a shear wave. The effects of the incident angle and frequency on amplitude ratios of the reflected and transmitted waves to the incident wave are discussed. Two boundary conditions are discussed in detail: (a) Open-pore boundary and (b) Sealed-pore boundary. Numerical results reveal that the characteristics of the reflection and transmission coefficients to the incident angle and the frequency are quite different for the two cases of boundary conditions. Properties of the bulk waves existing in the fluid-saturated porous solid and the double porosity medium are also studied.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • G.I. Barenblatt I.P. Zheltow T.N. Kochina (1960) ArticleTitleBasic concepts in the theory of seepage homogeneous liquids in fissured rocks J. Appl. Math. Mech. 24 1286–1303 Occurrence Handle10.1016/0021-8928(60)90107-6

    Article  Google Scholar 

  • J.G. Berryman (1980) ArticleTitleConfirmation of Biot’s theory Appl. Phys. Lett. 37 IssueID4 382–384 Occurrence Handle10.1063/1.91951

    Article  Google Scholar 

  • J.G. Berryman H.F. Wang (2000) ArticleTitleElastic wave propagation and attenuation in a double-porosity dual-permeability media Int. J. Rock Mech. Mining Sci. 37 63–78 Occurrence Handle10.1016/S1365-1609(99)00092-1

    Article  Google Scholar 

  • J.G. Berryman H.F. Wang (1995) ArticleTitleThe elastic coefficients of double-porosity models for fluid transport in jointed rock J. Geo. Res. 100 24611–24627 Occurrence Handle10.1029/95JB02161

    Article  Google Scholar 

  • D.E. Beskos (1989) ArticleTitleDynamics of saturated rocks. I: Equations of Motions J. Eng. Mech. ASCE 115 983–995

    Google Scholar 

  • M.A. Biot (1956) ArticleTitleTheory of propagation of elastic waves in a fluid-saturated porous solid. I. Low frequency range. II. Higher frequency range J. Acoust. Soc. Am. 28 168–191 Occurrence Handle10.1121/1.1908239

    Article  Google Scholar 

  • M.A. Biot (1962a) ArticleTitleMechanics of deformation and acoustic propagation in porous media J. Appl. Phys. 33 1482–1498 Occurrence Handle10.1063/1.1728759

    Article  Google Scholar 

  • M.A. Biot (1962b) ArticleTitleGeneralized theory of acoustic propagation in porous dissipative media J. Acoust. Soc. Am. 34 1254–1264 Occurrence Handle10.1121/1.1918315

    Article  Google Scholar 

  • Biot M.A. and Willis D.G. (1957). The elastic coefficients of the theory of consolidation. J. Appl. Mech. 594–601

  • V. Cruz Particlede la J. Hube T.J.T. Spanos (1992) ArticleTitleReflection and transmission of seismic waves at the boundaries of porous media Wave Motion 16 323–338 Occurrence Handle10.1016/0165-2125(92)90021-S

    Article  Google Scholar 

  • Dai, Z.-J., Kuang, Z.-B. and Zhao, S.-X. (2006). Reflection and transmission of elastic waves at the interface between an elastic solid and a double porosity medium, Int. J. Rock Mech. Mining Sci. (in press).

  • A.I.M. Denneman G.G. Drijkoningen D.M.J. Smeulders K. Wapenaar (2002) ArticleTitleReflection and transmission of waves at a fluid/porous-medium interface Geophysics 67 282–291 Occurrence Handle10.1190/1.1451800

    Article  Google Scholar 

  • H. Deresiewicz J.T. Rice (1960) ArticleTitleThe effect of boundaries on wave propagation in a liquid-filled porous solid I. Reflection of plane waves at a true plane boundary Bull. Seism. Soc. Am. 50 599–607

    Google Scholar 

  • H. Deresiewicz J.T. Rice (1964) ArticleTitleThe effect of boundaries on wave propagation in a liquid-filled porous solid V. Transmission across a plane interface Bull. Seism. Soc. Am. 54 409–416

    Google Scholar 

  • H. Deresiewicz R. Skalak (1963) ArticleTitleOn uniqueness in dynamic poroelasticity Bull. Seism. Soc. Am. 52 595–626

    Google Scholar 

  • N.C. Dutta H. Odé (1983) ArticleTitleSeismic reflection from a gas water contact Geophysics 48 148–162 Occurrence Handle10.1190/1.1441454

    Article  Google Scholar 

  • S. Hajra A. Mukhopadhyay (1982) ArticleTitleReflection and refraction of seismic waves incident obliquely at the boundary of a liquid-saturated porous solid Bull. Seism. Soc. Am. 72 1509–1533

    Google Scholar 

  • T.J. Plona (1980) ArticleTitleObservation of a second bulk compressional wave in a porous medium at ultrasonic frequencies Appl. Phys. Lett. 36 259–261 Occurrence Handle10.1063/1.91445

    Article  Google Scholar 

  • J.E. Santos J.M. Corbero C.L. Ravazzoli J.L. Hensley (1992) ArticleTitleReflection and transmission coefficients in fluid-saturated porous media J. Acoust. Soc. Am. 91 1911–1923 Occurrence Handle10.1121/1.403702

    Article  Google Scholar 

  • A.W. Skempton (1954) ArticleTitleThe pore-pressure coefficients A and B Geotechnique 4 143–147 Occurrence Handle10.1680/geot.1954.4.4.143

    Article  Google Scholar 

  • R.D. Stoll T.-K. Kan (1981) ArticleTitleReflection of acoustic waves at a water-sendiment interface J. Acoust. Soc. Am. 70 149–156 Occurrence Handle10.1121/1.386692

    Article  Google Scholar 

  • K. Tuncay M.Y. Corapcioglu (1996a) ArticleTitleWave propagation in fractured porous media Trans. Porous Media 23 237–258

    Google Scholar 

  • K. Tuncay M.Y. Corapcioglu (1996b) ArticleTitleBody waves in fractured porous media saturated by two immiscible Newtonian fluids Trans. Porous Media 13 259–273

    Google Scholar 

  • J.E. Warren P.J. Root (1963) ArticleTitleThe behavior of naturally fractured reservoirs Soc. Petrol. Eng. J. 3 245–255

    Google Scholar 

  • R.K. Wilson E.C. Aifantis (1982) ArticleTitleOn the theory of consolidation with double porosity Int. J. Eng. Sci. 20 1009–1035 Occurrence Handle10.1016/0020-7225(82)90036-2

    Article  Google Scholar 

  • R.K. Wilson E.C. Aifantis (1984) ArticleTitleA double porosity model for acoustic wave propagation in fractured-porous rock Int. J. Eng. Sci. 22 1209–1217 Occurrence Handle10.1016/0020-7225(84)90124-1

    Article  Google Scholar 

  • K.Y. Wu Q Xue L. Adler (1990) ArticleTitleReflection and transmission of elastic waves from a fluid-saturated porous solid boundary J. Acoust. Soc. Am. 87 2349–2358 Occurrence Handle10.1121/1.399081

    Article  Google Scholar 

  • J. Yang (1999) ArticleTitleImportance of flow condition on seismic wave at a saturated porous solid boundary J. Sound Vibrat. 221 391–413 Occurrence Handle10.1006/jsvi.1998.2036

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai, 200240, P.R. China

    Zhi-Jun Dai, Zhen-Bang Kuang & She-Xu Zhao

Authors
  1. Zhi-Jun Dai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhen-Bang Kuang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. She-Xu Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhen-Bang Kuang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dai, ZJ., Kuang, ZB. & Zhao, SX. Reflection and Transmission of Elastic Waves from the Interface of a Fluid-saturated Porous Solid and a Double Porosity Solid. Transp Porous Med 65, 237–264 (2006). https://doi.org/10.1007/s11242-005-6084-5

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11242-005-6084-5

Keywords

Search

Navigation