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Body forces equivalent to jumps of stresses and displacements in the Biot model of an anisotropic porous medium

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Abstract

Formulas for the body forces equivalent to given jumps of stresses and displacements in the anisotropic Biot model are obtained. Similarly to the case of elastic media, Betti's identity, the reciprocity relations, and the representation integrals for a porous media are derived first. The equivalent body forces are obtained by applying the representation integrals to a volume with surfaces of discontinuity. Some physical consequences are indicated, and examples of equivalent body forces for the isotropic Biot model are provided.

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References

  1. G. I. Petrashen, L. A. Molotkov, and P. V. Krauklis,Waves in Layered Isotropic Elastic Media [in Russian], Leningrad (1982).

  2. K. Aki and P. Richards,Quantitative Seismology: Theory and Methods, W. H. Freeman (1980).

  3. G. Bonnet, “Basic singular solutions for a poroelastic medium in the dynamic range,”J. Acoust. Soc. Am.,82, 1758–1762 (1987).

    Google Scholar 

  4. L. A. Molotkov and A. V. Bakulin, “Sources of the center of dilatation and center of compression types in the Biot model,”Zap. Nauchn. Semin. POMI,230, 196–213 (1995).

    Google Scholar 

  5. M. A. Biot, “Mechanics of deformation and acoustic propagation in porous media,”J. Appl. Phys.,33, 1482–1498 (1962).

    Google Scholar 

  6. L. A. Molotkov and A. V. Bakulin, “The effective model of a stratified solid-fluid medium as a special case of the Biot model,”Zap. Nauchn. Semin. P0MI,230, 172–195 (1995).

    Google Scholar 

  7. G. I. Petrashen,Foundations of the Mathematical Theory of Propagation of Elastic Waves [in Russian], Vol. 17, Leningrad Univ. Press (1978).

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Authors
  1. A. V. Bakulin
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Additional information

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 239, 1997, pp. 33–44.

The author wishes to express his sincere gratitude to V. M. Babich and L. A. Molotkov for helpful discussions. This work was supported in part by the Soros Foundation under grant A96-378 and the Russian Foundation for Basic Research under grant 96-05-65904.

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Bakulin, A.V. Body forces equivalent to jumps of stresses and displacements in the Biot model of an anisotropic porous medium. J Math Sci 96, 3305–3311 (1999). https://doi.org/10.1007/BF02172805

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  • DOI: https://doi.org/10.1007/BF02172805

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