Skip to main content

Determination of Material Parameters of Poroelastic Media

  • Chapter
Fundamentals of Transport Phenomena in Porous Media

Part of the book series: NATO ASI Series ((NSSE,volume 82))

Abstract

This paper addresses the interpretation and determination of the material coefficients appearing in Biot’s formulations of the equations of poroelastic media. Experimental methods suggested by Biot and Willis as well as those employed by the author and their results for a variety of material systems are discussed.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Terzaghi, K. Theoretical Soil Mechanics. John Wiley and Sons, N.Y. (1943).

    Google Scholar 

  2. Biot, M.A. General Theory of Three Dimensional Consolidation. Journal of Applied Physics 12 (1961) 155–16H.

    Article  Google Scholar 

  3. Biot, M.A. Theory of Elasticity and Consolidation for a Porous Anisotropic Solid. Journal of Applied Physics 26 (1955) 182–185.

    Article  MathSciNet  MATH  Google Scholar 

  4. b. Biot, M.A. General Solutions of the Equations of Elasticity and Consolidation for a Porous Material. Journal of Applied Mechanics (Trans ASME) 23 (1956) 91 – 96.

    MathSciNet  MATH  Google Scholar 

  5. Biot, M.A. Theory of Propagation of Elastic Waves in a Fluid- Saturated Porous Solid I. Low-Frequency Range. Journal of the Acoustical Society of America, 28 (1956) 168–178.

    Article  Google Scholar 

  6. Biot, M.A. Theory of Propagation of Elastic Waves in a Fluid Saturated Porous Solid II. Higher Frequency Range. The Journal of the Acoustical Society of America, 23 (1956) 179–191.

    Google Scholar 

  7. Biot, M.A. Mechanics of Deformation of Acoustic Propagation in Porous Media. Journal of Applied Physics, 33 (1962) 1482–1497.

    Article  MathSciNet  MATH  Google Scholar 

  8. Paria, G. Flow of Fluids Through Porous Deformable Solids. Applied Mechanics Reviews 16 (1963) 421–423.

    Google Scholar 

  9. Heinrich, G., K. Desoyer. Hydromechanische Grundlagen fur die Behandlung von Stationaren and Instationaren Grundwasser«Strömun-gen. Ingenieur Archiv 23 (1955) 73–88.

    Article  MathSciNet  MATH  Google Scholar 

  10. Heinrich, G. and K. Desoyer. Hydromechanische Grundlagen fĂ¼r die Behandlung von Stationaren and Istationaren Grundwasser-stro- mungen. II Mitteilung. Ingenieur Archiv 2 (1956) 81 - 84.

    Article  Google Scholar 

  11. Heinrich G. and K. Desoyer. Theorie Driedimensionaler, Setzungsvorgaenge in Tonschichten. Ingenieur Archiv 30 (1961) 225–253.

    Article  MATH  Google Scholar 

  12. Trusdell, C. Mechanical Basis of Diffusion. Journal of Chemical Physics. 37 (1962) 2336.

    Google Scholar 

  13. Trusdell, C. and W. Noll. The Nonlinear Field Theories of Mechanics. Encyclopedia of Physics. 111/3 Springer-Berline (1965).

    Google Scholar 

  14. ik. Adkins, J. E. Nonlinear Diffusion I Diffusion and Flow of Mixtures of Fluids. Philos. Trans, of the Royal Society Series A 255 (1963) 607–630.

    MathSciNet  MATH  Google Scholar 

  15. Adkins, J.E. Nonlinear Diffusion II. Constitutive Equations for Mixtures of Isotropic Fluids. Philo. Trans of the Royal Society Series A 255 (1963) 635–651.

    Article  Google Scholar 

  16. Green, A.E. and J.E. Adkins. A Contribution to the Theory of Nonlinear Diffusion. Arch, for Rational Mechanics and Analysis. 15 (196k) 235.

    Google Scholar 

  17. Green, A.E. and P.M. Naghdi. A Dynamical Theory of Interacting Continua. Int. Journal of Engineering Science 3 (1965) 231–248.

    Article  MathSciNet  Google Scholar 

  18. Bowen, R.M. Toward a Thermodynamics and Mechanics of Mixtures. Archive for Rational Mechanics and Analysis 2 (1967) 370.

    MathSciNet  Google Scholar 

  19. Bowen, R.M. Theory of Mixtures Continuum Physics Vol. Ill Mixtures and EM Field Theories edited by A. Cemal Erigen. Academic Press New York (1976) 560–569.

    Google Scholar 

  20. Rice, J.R. and M.P. Clearly. Some Basic Stress Diffusion Solutions for Fluid-Saturated Elastic Porous Media with Compressible Constitutents. Reviews of Geophysics and Space Physics. 1b (1976) 227–231.

    Article  Google Scholar 

  21. Kingsbury, H.B. Applications of the Theory of Poroelasticity in Biomechanics. Proceedings of the Mechanical Engineering Congress, Pahlavi University edited by M.A. Satter. Pahlavi University, Shiraz, Iran (1975) 990–1006.

    Google Scholar 

  22. Biot, M.A. and D.G. Willis. The Elastic Coefficients of The Theory of Consolidation. Journal of Applied Mechanics (1957) 594 - 601.

    Google Scholar 

  23. Bear, Jacob. Dynamics of Fluids in Porous. Media. American Elsevier, New York, 1972.

    Google Scholar 

  24. Hubbert, M. King. The Theory of Ground-Water Motion. The Journal of Geology ILVIII Pt. 1 (1990). 785–900.

    Google Scholar 

  25. Verruijt, A. Elastic Storage of Aquiers Flow Through Porous Media. Edited by Roger J. M. DeWiest. Academic Press N.Y. (1969) 331–375.

    Google Scholar 

  26. Yew, C. H. and P.N. Jogi. The Determination of Biot’s Parameters for Sandstones - Part 1: Static Tests. Experimental Mechanics (1978) 167–172.

    Google Scholar 

  27. Fatt, I. The Biot-Willis Elastic Coefficients for a Sand-stone. Journal Applied Mechanics, 26 (1959) 296–297.

    Google Scholar 

  28. Dziecielak, R. On the Determination of the Constants of Consolidating Medium. Acta Technica Academiae Scientiarum Hungaricae, 73 (1972) 123–129.

    Google Scholar 

  29. Chae, Y.S. The Material Constants of Soils as Determined from Dynamic Testing. Proc. Int. Symp. on Wave Propagation and Dynamic Properties of Earth Materials (1968) 759–770.

    Google Scholar 

  30. Ishihara, K. Propagation of Compressional Waves in a Saturated Soil. Proceedings Inter. Symposium on Wave Propagation and Dynamic Properties of Earth Materials. University of New Mexico Press, Albuquerque (1967).

    Google Scholar 

  31. Brown, K.M. A Quadratically Convergent Newton-like Method Based upon Gaussian Elimination, SIAM Journal of Numerical Analysis 6 (k) (1969) 560–569.

    Article  MATH  Google Scholar 

  32. Lambe T.W. and R.V. Whitman. Soil Mechanics, John Wiley and Sons, Inc. N.Y. (1965).

    Google Scholar 

  33. Handbook of Chemistry and Physics. 55th Edition CRC Press Cleveland, Ohio (1974).

    Google Scholar 

  34. Wijesinghe, A.M. and H. B. Kingsbury. On the Dynamic Behavior of Poroelastic Materials. Journal Acoustical Society of America 65 (1979) 90–95.

    Article  Google Scholar 

  35. Kim, Y.K. and H. B. Kingsbury. Dynamic Characterization of Poroelastic Materials. Experimental Mechanics 19 (1979) 252–258.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Martinus Nijhoff Publishers, Dordrecht

About this chapter

Cite this chapter

Kingsbury, H.B. (1984). Determination of Material Parameters of Poroelastic Media. In: Bear, J., Corapcioglu, M.Y. (eds) Fundamentals of Transport Phenomena in Porous Media. NATO ASI Series, vol 82. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6175-3_12

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-6175-3_12

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-6177-7

  • Online ISBN: 978-94-009-6175-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics