Skip to main content
SpringerLink
Log in

The effect of fluid streams in porous media on acoustic compression wave propagation, transmission, and reflection

  • Original Article
  • Published:
Continuum Mechanics and Thermodynamics Aims and scope Submit manuscript

Abstract

In geomechanics, a relevant role is played by coupling phenomena between compressible fluid seepage flow and deformation of the solid matrix. The behavior of complex porous materials can be greatly influenced by such coupling phenomena. A satisfactorily theoretical framework for their description is not yet completely attained. In this paper, we discuss how the model developed in dell’Isola et al. (Int J Solids Struct 46:3150–3164, 2009) can describe how underground flows or, more generally, confined streams of fluid in deformable porous matrices affect compression wave propagation and their reflection and transmission at a solid-material discontinuity surface. Further work will investigate the effect of stream flow in porous media on shear waves, generalizing what done in Djeran Maigre and Kuznetsov (Comptes Rendus Mécanique 336(1–2):102–107, 2008) for shear waves in one-constituent orthotropic two-layered plates. The presented treatment shows that the presence of fluid streams considerably affect reflection and transmission phenomena in porous media.

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

  1. Aknine, A., Castagnède, B., Depollier, C.: Réflexion/réfraction d’ondes acoustiques à à une interface fluide/matériau poreux anisotrope. C. R. Acad. Sci. Paris, t. 324, Série II b, 501–511 (1997)

  2. Andreaus, U., dell’Isola, F., Porfiri, M.: Piezoelectric passive distributed controllers for beam flexural vibrations. J Vib. Control, 10:5, 625–659 (2004).Piezoelectric passive distributed controllers for beam flexural vibrations

    Google Scholar 

  3. Biot M.A.: Theory of propagation of elastic waves in a fluid-saturated porous solid, I. Low frequency range. J. Acoust. Soc. Am. 28, 168–178 (1956)

    Article  MathSciNet  ADS  Google Scholar 

  4. Biot M.A.: Theory of propagation of elastic waves in a fluid-saturated porous solid, II. Higer frequency range. J. Acoust. Soc. Am. 28, 179–191 (1956)

    Article  MathSciNet  ADS  Google Scholar 

  5. Biot M.A., Willis D G.: The elastic coefficients of the theory of consolidation. J. Appl. Mech. 24, 594–601 (1957)

    MathSciNet  Google Scholar 

  6. Biot M.A.: Theory of finite deformation of porous solids. Indiana Univ. Math. J. 21(7), 597–620 (1972)

    Article  MathSciNet  Google Scholar 

  7. Biot M.A.: Nonlinear and semilinear rheology of porous solids. J. Geophys. Res. 78(23), 4924–4937 (1973)

    Article  ADS  Google Scholar 

  8. Carcaterra A., Ciappi E., Iafrati A., Campana E.F.: Shock spectral analysis of elastic systems impacting on the water surface. J. Sound Vib. 229(3), 579–605 (2000)

    Article  ADS  Google Scholar 

  9. Carcaterra A., Ciappi E.: Prediction of the compressible stage slamming force on rigid and elastic system impacting over the water surface. Nonlinear Dyn. 21(2), 193–220 (2000)

    Article  MATH  Google Scholar 

  10. Chandesris M., Jamet D.: Boundary conditions at a planar fluidporous interface for a Poiseuille flow. Int. J. Heat Mass Transf. 49, 2137–2150 (2006)

    Article  MATH  Google Scholar 

  11. Coussy O., Bourbie T.: Propagation des ondes acoustiques dans les milieux poreux saturés. Rev. Inst. Fr. Pétrole 39(1), 47–66 (1984)

    Google Scholar 

  12. Coussy O.: Poromechanics. Wiley, Chichester (2004)

    Google Scholar 

  13. Denneman A.I.M., Drijkoningen G.G., Smeulders D.M.J., Wapenaar K.: Reflection and transmission of waves at a fluid/porous-medium interface. Geophysics 67(1), 282–291 (2002)

    ADS  Google Scholar 

  14. Djeran Maigre I., Kuznetsov S.: Solitary SH waves in two-layered traction-free plates. Comptes Rendus Mécanique 336(1–2), 102–107 (2008)

    Article  ADS  MATH  Google Scholar 

  15. dell’Isola F., Seppecher P.: The relationship between edge contact forces, double forces and interstitial working allowed by the principle of virtual power. CRAS Mécanique 321(8), 303–308 (1995)

    MATH  Google Scholar 

  16. dell’Isola F., Gouin H., Seppecher P.: Radius and surface-tension of microscopic bubbles by second gradient theory. CRAS Mécanique 320, 211–216 (1995)

    MATH  Google Scholar 

  17. dell’Isola F., Seppecher P.: Edge contact forces and quasi-balanced power. Meccanica 32, 33–52 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  18. dell’Isola F., Rosa L., Wozniak CZ.: Dynamics of solids with micro periodic nonconnected fluid inclusions. Arch. Appl. Mech. 67(4), 215–228 (1997)

    MATH  Google Scholar 

  19. dell’Isola F., Hutter K.: A qualitative analysis of the dynamics of a sheared and pressurized layer of saturated soil. Proc. Royal Soc. A 454, 3105–3120 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  20. dell’Isola F., Hutter K.: What are the dominant thermomechanical processes in the basal sediment layer of large ice sheets?. Proc. Royal Soc. A Math. Phys. Eng. Sci. 454, 1169–1195 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  21. dell’Isola F., Vidoli S.: Damping of bending waves in truss beams by electrical transmission lines with PZT actuators. Arch. Appl. Mech. 68(9), 626–636 (1998)

    Article  ADS  MATH  Google Scholar 

  22. dell’Isola F., Hutter K.: Variations of porosity in a sheared pressurized layer of saturated soil induced by vertical drainage of water. Proc. Royal Soc. Lond. A 455, 2841–2860 (1999)

    Article  MATH  Google Scholar 

  23. dell’isola F., Guarascio M., Hutter K.: A variational approach for the deformation of a saturated porous solid. A second-gradient theory extending Terzaghi’s effective stress principle. Arch. Appl. Mech. 70, 323–337 (2000)

    Article  ADS  MATH  Google Scholar 

  24. dell’Isola F., Madeo A., Seppecher P.: Boundary conditions at fluid permeable interfaces in porous media: a variational approach. Int. J. Solids Struct. 46, 3150–3164 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  25. Friedrichs K.O., Lax P.D.: Systems of conservation equations with a convex extension. Proc. Nat. Acad. Sci. USA 68(8), 1686–1688 (1971)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  26. Gavrilyuk, S.L., Gouin, H., Perepechko, Yu.V.: A variational principle for two-fluid models. C.R. Acad. Sci. Paris, 324, Série IIb, 483–490 (1997)

    Google Scholar 

  27. Gavrilyuk S.L., Gouin H., Perepechko Yu.V.: Hyperbolic models of homogeneous two-fluid mixtures. Meccanica 33, 161–175 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  28. Godunov S.K., Romenskii E.I.: Elements of Continuum Mechanics and Conservation Laws. Kluwer Academic Plenum Publishers, New York (2003)

    Book  MATH  Google Scholar 

  29. Gurevich B., Schoenberg M.: Interface conditions for Biot’s equations of poroelasticity. J. Acoust. Soc. Am. 105(5), 2585–2589 (1999)

    Article  ADS  Google Scholar 

  30. Gurevich B., Ciz R., Denneman A.I.M.: Simple expressions for normal-incidence reflection coefficients from an interface between fluid-saturated porous materials. Geophysics 69(6), 1372–1377 (2004)

    Article  ADS  Google Scholar 

  31. Jeffrey A.: Quasilinear Hyperbolic Systems and Waves. Pitman Publishing, London (1976)

    MATH  Google Scholar 

  32. Lion M., Skoczylas F., Ledésert B.: Determination of the main hydraulic and poro-elastic properties of a limestone from Bourgogne, France. Int. J. Rock Mech. Min. Sci. 41, 915–925 (2004)

    Article  Google Scholar 

  33. Lion M., Skoczylas F., Ledésert B.: Effects of heating on the hydraulic and poroelastic properties of Bourgogne limestone. Int. J. Rock Mech. Min. Sci. 42, 508–520 (2005)

    Article  Google Scholar 

  34. Madeo A., Gavrilyuk S.: Propagation of acoustic waves in porous media and their reflection and transmission at a pure fluid/porous medium permeable interface. Eur. J. Mech. 29(5), 897–910 (2010)

    Article  MathSciNet  Google Scholar 

  35. Madeo A., dell’Isola F., Ianiro N., Sciarra G.: A variational deduction of second gradient poroelasticity II: an application to the consolidation problem. J. Mech. Mater. Struct. 3(4), 607–625 (2008)

    Article  Google Scholar 

  36. Maurini C., dell’Isola F., Del Vescovo D.: Comparison of piezoelectronic networks acting as distributed vibration absorbers. Mech. Syst. Signal Process. 18(5), 1243–1271 (2004)

    Article  ADS  Google Scholar 

  37. Maurini, C., Pouget, J., dell’Isola, F.: On a model of layered piezoelectric beams including transverse stress effect. Int. J. Solids Struct. 41(16–17), 4473–4502 (2004)

    Google Scholar 

  38. Placidi L., Dell’Isola F., Ianiro N., Sciarra G.: Variational formulation of pre-stressed solid-fluid mixture theory, with an application to wave phenomena. Eur. J. Mech. A/Solids 27(4), 582–606 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  39. Plona T.J.: Observation of a second bulk compressional wave in a porous medium at ultrasonic frequencies. Appl. Phys. Lett. 36, 259–261 (1980)

    Article  ADS  Google Scholar 

  40. Quiligotti S., Maugin G.A., dell’isola F.: Wave motions in unbounded poroelastic solids infused with compressible fluids. ZAMP 53(6), 1110–1138 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  41. Quiligotti S., Maugin G.A., dell’Isola F.: An Eshelbian approach to the nonlinear mechanics of constrained solid-fluid mixtures. Acta Mech. 160(1–2), 45–60 (2003)

    Article  MATH  Google Scholar 

  42. Rasolofosaon N.J.P., Coussy O.: Propagation des ondes acoustiques dans les milieux poreux saturés. Eff d’interface. Rev. Inst. Fr. Pétrole 40, 581–594 (1985)

    Google Scholar 

  43. Rasolofosaon N.J.P., Coussy O.: Propagation des ondes acoustiques dans les milieux poreux saturs: effets dinterface II. Rev. Inst. Fr. Pet. 40, 785–802 (1985)

    Google Scholar 

  44. Rasolofosaon N.J.P., Coussy O.: Propagation des ondes acoustiques dans les milieux poreux saturs: effets dinterface III. Rev. Inst. Fr. Pet. 41, 91–103 (1986)

    Google Scholar 

  45. Rubino J.G., Ravazzoli C.L., Santos J.E.: Reflection and transmission of waves in composite porous media: a quantification of energy conversions involving slow waves. J. Acoust. Soc. Am. 120(5), 2425–2436 (2006)

    Article  ADS  Google Scholar 

  46. Sciarra G., dell’Isola F., Hutter K.: A solid-fluid mixture model allowing for solid dilatation under external pressure. Cont Mech. Thermodyn. 13, 287–306 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  47. Sciarra G., dell’Isola F., Ianiro N., Madeo A.: A variational deduction of second gradient poroelasticity I: general theory. J. Mech. Mater. Struct. 3(3), 507–526 (2008)

    Article  Google Scholar 

  48. Sharma M.D.: 3D wave propagation in a general anisotropic poroelastic medium: reflection and refraction at an interface with fluid. Geophys. J. Int. 157, 947–958 (2004)

    Article  ADS  Google Scholar 

  49. Sharma M.D.: Wave Propagation across the boundary between two dissimilar poroelastic solids. J. Sound Vib. 314, 657–671 (2008)

    Article  ADS  Google Scholar 

  50. DOE Geophysical MonitoringWorking Group: Advanced noninvasive geophysical monitoring techniques. Annu. Rev. Earth Planet. Sci. 35, 653–683 (2007)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Université de Lyon-INSA, Laboratoire de Génie Civil et Ingénierie Environnementale (LGCIE), 69621, Villeurbanne Cedex, France

    A. Madeo, I. Djeran-Maigre & C. Silvani

  2. International Research Center M&MoCS, via S. Pasquale snc, Cisterna di Latina, Italy

    A. Madeo, I. Djeran-Maigre & G. Rosi

  3. Institut de Mathématiques (IMath), Université du Sud-Toulon-Var, Avenue de l’Université, BP 132, 83957, La Garde Cedex, Toulon, France

    G. Rosi

Authors
  1. A. Madeo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. Djeran-Maigre
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. Rosi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. C. Silvani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Madeo.

Additional information

Communicated by Francesco Dell’Isola and Samuel Forest.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Madeo, A., Djeran-Maigre, I., Rosi, G. et al. The effect of fluid streams in porous media on acoustic compression wave propagation, transmission, and reflection. Continuum Mech. Thermodyn. 25, 173–196 (2013). https://doi.org/10.1007/s00161-012-0236-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00161-012-0236-y

Keywords

Search

Navigation