Abstract
Periodic stratified media in which either two porous Biot layer, or an elastic and a porous layers, or a fluid and a porous layer alternate are considered. The effective models of these media are constructed and investigated. In the case of alternating porous layers, the effective model is a generalized transversely isotropic Biot medium. In this medium, the density of the fluid phase and the mean density acquire tensor character. It is shown that the effective model of a porous-fluid medium is, on the one hand, a generalized transversely isotropic Biot medium of special type and, on the other hand, a generalization of the effective model of a stratified elastic-fluid medium.
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References
M. A. Biot, “Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range,”J. Acoust. Soc. Am.,28, No. 2, 168–178 (1956).
M. A. Biot, “Mechanics of deformation and acoustic propagation in porous media,”J. Appl. Phys.,33, No. 4, 1482–1498 (1962).
L. A. Molotkov, “On the equivalence of periodically stratified and transversely isotropic media,”Zap. Nauchn. Semin. LOMI,89, 219–233 (1979).
L. A. Molotkov and A. E. Khilo, “Effective media for periodic anisotropic systems,”Zap. Nauchn. Semin. LOMI,128, 130–138 (1983).
L. A. Molotkov, “Equations of the effective model of an anisotropic elastic medium with cracks filled with a fluid,”Zap. Nauchn. Semin. LOMI,210, 173–191 (1994).
L. A. Molotkov and A. E. Khilo, “Averaging of periodic nonperfectly elastic media,”Zap. Nauchn. Semin. LOMI,140, 123–131 (1984).
L. A. Molotkov and A. E. Khilo, “tOn the equations of the effective model of an elastic medium with cracks filled with a viscous fluid, in:Vopr. Dinam. Teor. Raspr. Seismich. Voln, Vol. 29, Leningrad Univ. Press (1989), pp. 14–29.
L. A. Molotkov and A. E. Khilo, “Effective models of layered media with linear contacts of general type,”Zap. Nauchn. Semin. LOMI,156, 148–157 (1986).
L. A. Molotkov, “On the effective model describing a stratified periodic elastic medium with slipping contacts on the interfaces,”Zap. Nauchn. Semin. POMI,210, 192–212 (1994).
D. E. Wait, I. G. Mikhailova, and F. M. Lyakhovitskii, “Propagation of seismic waves in layered media saturated with fluid and gas,”Izv. Akad. Nauk SSSR, Ser. Fiz. Zemli,10, 44–52 (1975).
A. Norris, “Low-frequency dispersion and attenuation in partially saturated rocks,”J. Acoust. Soc. Am.,94, No. 1, 359–370 (1993).
B. Gurevich and S. L. Lopatnikov, “Velocity and attenuation of elastic waves in finely layered porous rocks,”Geophys. J. Int.,121, 933–947 (1995).
L. A. Molotkov, “A new method for deriving the equations of the averaged effective model of periodic media,”Zap. Nauchn. Semin. LOMI,195, 82–102 (1991).
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. POMI,230, 172–195 (1995).
Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 239, 1997, pp. 140–163.
This work was supported by the Russian Foundation for Basic Research under grant Nos. 96-01-00666 and 96-05-66207.
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Molotkov, L.A., Bakulin, A.V. Effective models of stratified media containing porous biot layers. J Math Sci 96, 3371–3385 (1999). https://doi.org/10.1007/BF02172816
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DOI: https://doi.org/10.1007/BF02172816