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Transport in Porous Media

, Volume 86, Issue 2, pp 537–557 | Cite as

Linear Elastic Wave Propagation in Unsaturated Sands, Silts, Loams and Clays

  • Bettina Albers
Article

Abstract

Due to its propitious material properties sandstone is the most studied porous medium for the investigation of linear wave propagation. However, in practical applications the behavior of other soil types, i.e., especially the three main soil types sand, silt, and clay, are much more important. Therefore, the model for partially saturated soils introduced by Albers (Habilitation Thesis, 2010a) is applied to 11 soil types classified in the German standard DIN 4220 to obtain information on the phase velocities and attenuations of the three longitudinal waves and the shear wave appearing in such media.

Keywords

Unsaturated soils Wave propagation Porous media Main soil types 

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References

  1. Albers B.: Analysis of the propagation of sound waves in partially saturated soils by means of a macroscopic linear poroelastic model. Transp. Porous Mater. 80(1), 173–192 (2009)CrossRefGoogle Scholar
  2. Albers, B.: Modeling and Numerical Analysis of Wave Propagation in Saturated and Partially Saturated Porous Media. Veröffentlichungen des Grundbauinstitutes der Technischen, Universität Berlin, vol. 48. Habilitation thesis, Shaker Verlag, Aachen (2010)Google Scholar
  3. Albers, B.: On a micro–macro transition for a poroelastic three-component model. ZAMM (2010). Early View. doi: 10.1002/zamm.201000061.
  4. Albers B., Wilmanski K.: On modeling acoustic waves in saturated poroelastic media. J. Eng. Mech. 131(9), 974–985 (2005)CrossRefGoogle Scholar
  5. Anderson A.L., Hampton L.D.: Acoustics of gas-bearing sediments., I. Background, II. Measurements and models. J. Acoust. Soc. Am. 67(6), 1865–1898 (1980) 1890–1903CrossRefGoogle Scholar
  6. Berryman J.G., Thigpen L., Chin R.C.Y.: Bulk elastic wave propagation in partially saturated porous solids. J. Acoust. Soc. Am. 84(1), 360–373 (1988)CrossRefGoogle Scholar
  7. Biot M.A.: Theory of propagation of elastic waves in a fluid saturated porous solid, I. low frequency range, II. higher frequency range. J. Acoust. Soc. Am. 28(2), 168–178 (1956) 179–191CrossRefGoogle Scholar
  8. Carcione J.M., Gurevich B., Cavallini F.: A generalized Biot-Gassmann model for the acoustic properties of shaley sandstones. Geophys. Prospect. 48, 539–557 (2000)CrossRefGoogle Scholar
  9. de la Cruz V., Sahay P.N., Spanos T.J.T.: Thermodynamics of porous media. Proc. Royal Soc. A 443(1917), 247–255 (1993)CrossRefGoogle Scholar
  10. DIN 18196: Earthworks and foundations—soil classification for civil engineering processes. DIN Deutsches Institut für Normung e.V., Beuth Verlag GmbH (2006) (in German), German title: Erd- und Grundbau—Bodenklassifikation für bautechnische ZweckeGoogle Scholar
  11. DIN 4220: Pedologic site assessment—Designation, classification and deduction of soil parameters (normative and nominal scaling). DIN Deutsches Institut für Normung e.V., Beuth Verlag GmbH (2005) (draft, in German), German title: Bodenkundliche Standortbeurteilung—Kennzeichnung, Klassifizierung und Ableitung von Bodenkennwerten (normative und nominale Skalierungen)Google Scholar
  12. Drew D., Passman S.L.: Theory of Multicomponent Fluids. Springer, New York (1999)Google Scholar
  13. Gebrande, H., Kern, H., Rummel, F.: Elasticity and inelasticity. In: Hellwege K.-H. (ed.) Landolt-Brnstein. Numerical Data and Functional Relationships in Science and Technology, New Series; Group V. Geophysics and Space Research. Vol. 1b: Physical Properties of Rocks. Springer, Berlin, pp. 1–233 (1982)Google Scholar
  14. Geertsma J.: The effect of fluid pressure decline on volumetric changes of porous rocks. Trans. AIME 210, 331–340 (1957)Google Scholar
  15. Girsang, C.H.: A numerical investigation of the seismic response of the aggregate pier foundation system. Master’s thesis, Virginia Polytechnic Institute and State University (2001)Google Scholar
  16. Gray W.: General conservation equations for multi-phase systems: 4. constitutive theory including phase change. Adv. Water Resour. 6(3), 130–140 (1983)CrossRefGoogle Scholar
  17. Gudehus G., Gudehus G., Gudehus G.: Einfluss von Ionen und Gasblasen auf die Kollapsneigung feinstkrniger Bden. Geotechnik 25(1), 12–20 (2002) (in German)Google Scholar
  18. Hartge, K.H., Horn, R.: Einführung in die Bodenphysik. Schweizerbart, Stuttgart (1999) (in German)Google Scholar
  19. Klein, G.: Bodendynamik und Erdbeben. In Smoltczyk, U. (ed.) Grundbau-Taschenbuch Teil 1—Geotechnische Grundlagen, vol. 1, Chap. 1.8. Ernst & Sohn (2001) (in German); also available in English: Geotechnical Engineering Handbook, volume 1Google Scholar
  20. Klimentos T., McCann C.: Why is the Biot slow compressional wave not observed in real rocks? Geophysics 53(12), 1605–1609 (1988)CrossRefGoogle Scholar
  21. Liu I.-S.: Continuum Mechanics. Springer, Berlin (2002)Google Scholar
  22. Lo W.-C., Sposito G., Majer E.: Immiscible two-phase flows in deformable porous media. Adv. Water Resour. 25, 1105–1117 (2002)CrossRefGoogle Scholar
  23. Lo, W.-C., Sposito, G., Majer, E.: Wave propagation through elastic porous media containing two immiscible fluids. Water Resour. Res. 41, W02025 (20 pp) (2005)Google Scholar
  24. Lo W.-C., Yeh C.-L., Tsai C.-T.: Effect of soil texture on the propagation and attenuation of acoustic wave at unsaturated conditions. J. Hydrol. 338, 273–284 (2007)CrossRefGoogle Scholar
  25. Pavlovic V.D., Velickovic Z.S.: Measurement of the seismic waves propagation velocity in the real medium. Facta Universitatis: Phys. Chem. Technol. 1(5), 63–73 (1998)Google Scholar
  26. Pham N., Carcione J., Helle H., Ursin B.: Wave velocities and attenuation of shaley sandstones as a function of pore pressure and partial saturation. Geophys. Prospect. 50, 615–627 (2002)CrossRefGoogle Scholar
  27. Schmidt, H.-H.: Grundlagen der Geotechnik. Teubner, Stuttgart (1996) (in German)Google Scholar
  28. Schultze, E., Muhs, H.: Bodenuntersuchungen für Ingenieurbauten. Springer, Berlin, Göttingen, Heidelberg (1950) (in German)Google Scholar
  29. Studer, J.A., Koller M.G.: Bodendynamik. Springer, Berlin, Heidelberg, New York (1997) (in German)Google Scholar
  30. Truesdell C.A.: A First Course in Rational Continuum Mechanics. The Johns Hopkins University, Baltimore, Maryland (1972)Google Scholar
  31. Truesdell C.A.: Rational Thermodynamics. 2nd edn. Springer, Berlin (1984)Google Scholar
  32. US. Soil Taxonomy, A Basic System of Soil Classification for Making and Interpreting Soil Surveys. Download via http://soils.usda.gov/technical/classification/taxonomy/
  33. van Genuchten M.T.: A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44, 892–898 (1980)CrossRefGoogle Scholar
  34. van Genuchten M.T., Nielsen D.R.: On describing and predicting the hydraulic properties of unsaturated soils. Annales Geophysicae 3(5), 615–628 (1985)Google Scholar
  35. van Genuchten M.T., Leij F.J., Yates S.R.: The RETC code for quantifying the hydraulic functions of unsaturated soils. Tech. rep., U.S. Salinity Laboratory, Riverside, CA (1991)Google Scholar
  36. Vanorio T., Prasad M., Nur A.: Elastic properties of dry clay mineral aggregates, suspensions and sandstones. Geophys. J. Int. 155(1), 319–326 (2003)CrossRefGoogle Scholar
  37. von Soos, P.: Eigenschaften von Boden und Fels—ihre Ermittlung im Labor. In: Smoltczyk, U. (ed.) Grundbau-Taschenbuch Teil 1—Geotechnische Grundlagen, vol. 1, chap. 1.4. Ernst & Sohn (2001) (in German); also available in English: Geotechnical Engineering Handbook, volume 1Google Scholar
  38. White J.E.: Underground sound: application of seismic waves, Methods in Geochemistry and Geophysics, vol. 18. Elsevier, Amsterdam, New York (1983)Google Scholar
  39. Wilmanski K.: Tortuosity and objective relative accelerations in the theory of porous materials. Proc. R. Soc. A 461, 1533–1561 (2005)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Institute for Geotechnical Engineering and Soil MechanicsTechnical University of BerlinBerlinGermany

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