Propagation of waves in a fluid-saturated porous elastic solid

Lévy, T.

doi:10.1016/0020-7225(79)90022-3

Cited by 125 publications

(60 citation statements)

References 6 publications

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“…The general theory of wave propagation in porous media was developed in references [8][9][10][11][12] . In these theoretical developments, it is invariably assumed that it is always possible to identify two separate spatial scales, denoted by x (the macroscopic, "slow" scale), and by y (the microscopic, "fast" scale).…”

Section: Introductionmentioning

confidence: 99%

Frequency-dependent viscous flow in channels with fractal rough surfaces

Cortis

Berryman

2010

Physics of Fluids

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The viscous dynamic permeability of some fractal-like channels is studied. For our particular class of geometries, the ratio of the pore surface area-to-volume tends to ∞ (but has a finite cutoff), and the universal scaling of the dynamic permeability, k(ω), needs modification. We performed accurate numerical computations of k(ω) for channels characterized by deterministic fractal wall surfaces, for a broad range

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Section: Introductionmentioning

confidence: 99%

Frequency-dependent viscous flow in channels with fractal rough surfaces

Cortis

Berryman

2010

Physics of Fluids

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“…Instead, the "closed-off" pores would induce an apparent viscoelastic effect. Levy (1979) observed the effect of unconnected fluid in a similar way. We must point out that this can be avoided by using the "effective porosity" concept and modifying the stress-strain relations for any possible viscoelastic be havior due to dead-end pores.…”

Section: Applicability Of Biofs Theorymentioning

confidence: 54%

“…It was first developed and studied by SanchezPalancia (1980) and Keller (1977). It was applied to wave propagation by Burridge and Keller (1981), Levy (1979), and Auriault (1980Auriault ( , 1985. In principle both local volume averaging and two-space method yield the same results.…”

Section: Application Of Mixture Theorymentioning

confidence: 99%

Chapter 5 Propagation of waves in porous media

Çorapçıoplu

Tuncay

1996

Advances in Porous Media

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Wave propagation in porous media is of interest in various diversified areas of science and engineer ing. The theory of the phenomenon has been studied extensively in soil mechanics, seismology, acoustics, earthquake engineering, ocean engineering, geophysics, and many other disciplines. This review presents a general survey of the Hterature within the context of porous media mechanics. Following a review of the Biot's theory of wave propagation in Unear, elastic, fluid saturated porous media which has been the basis of many analyses, we present various analytical and numerical solutions obtained by several researchers. Biot found that there are two dilatational waves and one rotational wave in a saturated porous medium. It has been noted that the second kind of dilatational wave is highly attenuated and is associated with a diffusion type process. The influence of couphng between two phases has a decreasing effect on the first kind wave and an increasing effect on the second wave. Procedures to predict the hquefaction of soils due to earthquakes have been reviewed in detail. Extension of Biot's theory to unsaturated soils has been discussed, and it was noted that, in general, equations developed for saturated media were employed for unsaturated media by replacing the density and compressibility terms with modified values for a water-air mixture. Various approaches to determine the permeabihty of porous media from attenuation of dilatational waves have been described in detail. Since the prediction of acoustic wave speeds and attenuations in marine sediments has been extensively studied in geophysics, these studies have been reviewed along with the studies on dissipation of water waves at ocean bottoms. The mixture theory which has been employed by various researchers in continuum mechanics is also discussed within the context of this review. Then, we present an alternative approach to obtain governing equations of wave propagation in porous media from macro scopic balance equations. Finally, we present an analysis of wave propagation in fractured porous media saturated by two immiscible fluids.

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“…In Clopeau et al (2001) and Gilbert and Mikelić (2000) the rigorous derivation of a dynamic Biot-model corresponding to different choices of scalings of the microstructure is undertaken, and in Ferrin and Mikelić (2003) the case of an inviscid fluid filling the pore space is treated. In Lévy (1979) elastic wave propagation is considered. Additional cases and results can also be found in the references of these works.…”

Section: Introductionmentioning

confidence: 99%

Upscaling of the Coupling of Hydromechanical and Thermal Processes in a Quasi-static Poroelastic Medium

et al. 2018

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We undertake a formal derivation of a linear poro-thermo-elastic system within the framework of quasi-static deformation. This work is based upon the well-known derivation of the quasi-static poroelastic equations (also known as the Biot consolidation model) by homogenization of the fluid-structure interaction at the microscale. We now include energy, which is coupled to the fluid-structure model by using linear thermoelasticity, with the full system transformed to a Lagrangian coordinate system. The resulting upscaled system is similar to the linear poroelastic equations, but with an added conservation of energy equation, fully coupled to the momentum and mass conservation equations. In the end, we obtain a system of equations on the macroscale accounting for the effects of mechanical deformation, heat transfer, and fluid flow within a fully saturated porous material, wherein the coefficients can be explicitly defined in terms of the microstructure of the material. For the heat transfer we consider two different scaling regimes, one where the Péclet number is small, and another where it is unity. We also establish the symmetry and positivity for the homogenized coefficients.

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Propagation of waves in a fluid-saturated porous elastic solid

Cited by 125 publications

References 6 publications

Frequency-dependent viscous flow in channels with fractal rough surfaces

Frequency-dependent viscous flow in channels with fractal rough surfaces

Chapter 5 Propagation of waves in porous media

Upscaling of the Coupling of Hydromechanical and Thermal Processes in a Quasi-static Poroelastic Medium

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