Compressional wave propagation in liquid and/or gas saturated elastic porous media

Garg, S.K.; Nayfeh, Adnan H.

doi:10.1063/1.337760

Cited by 73 publications

(70 citation statements)

References 23 publications

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“…It is therefore a crucial issue the characterisation of the restriction to be imposed to such pre-stress in order to have assured well-posedness and stability. In the present paper some stability conditions are captured with a simple analysis of the dispersion relation following the methods developed in Foch and Ford (1970) in a general case and in Bowen and Chen (1975), Borrelli and Patria (1984), Garg and Neyfeh (1986), Batra and Bedford (1988), Nigmatulin and Gubaidullin (1992), Smeulders and Van Dongen (1997), Abellan and de Borst (2006) for wave propagation in porous media. Preliminaries and notations ends the first section of this paper.…”

Section: Historical Backgroundmentioning

confidence: 99%

Variational formulation of pre-stressed solid–fluid mixture theory, with an application to wave phenomena

Placidi

Dell’Isola

Ianiro

et al. 2008

European Journal of Mechanics - A/Solids

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Fluid saturated porous media are modelled by the theory of mixtures and the placement maps of the solid and of the fluid are considered. The momentum balance equations are derived in the framework of a variational approach: We take an action functional and two families of variations and assume that the sum of the virtual work of the external forces and the variation of such an action along each variation are zero. Constitutive equations for the two Cauchy stress tensors and for the interaction force are derived taking into account a general state of pre-stress for the solid and for the fluid species. Governing equations are therefore formulated, however, for the sake of simplicity, only the case of pure initial pressure is further investigated. The propagation of bulk (transversal and longitudinal) waves and the influence of pre-stress are studied: In particular, stability analyses are carried out starting from dispersion relations and the role of pre-stress is investigated. Finally, a numerical example is established for a given state of pre-stress, deriving the phase velocities and the attenuation coefficients of transversal and longitudinal waves.

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Section: Historical Backgroundmentioning

confidence: 99%

Variational formulation of pre-stressed solid–fluid mixture theory, with an application to wave phenomena

Placidi

Dell’Isola

Ianiro

et al. 2008

European Journal of Mechanics - A/Solids

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“…In this study, barium titanate is chosen as the anisotropic porous material with 20 per cent pore-space of tortuosity (a ∞ ) 6 occupied by a fluid of density 50 kg m −3 . This symbolic fluid-density is chosen to lie between 1.2 kg m −3 , the density of air, and 103 kg m −3 , the partial density of CO 2 (Garg & Nayfeh 1986). Numerical values of various constants and parameters involved in the derivations of previous sections are chosen as follows.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

Piezoelectric effect on the velocities of waves in an anisotropic piezo-poroelastic medium

Sharma

2010

Proc. R. Soc. A.

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A mathematical model for mechanical and electrical dynamics in an anisotropic piezoporoelastic (hereafter referred to as APP) medium is solved for three-dimensional propagation of harmonic plane waves. A system of modified Christoffel equations is derived to explain the existence and propagation of four waves in the medium of arbitrary anisotropy. This system is solved to calculate the phase velocities of four waves in an unbounded APP medium. Directional derivatives of phase velocity are derived analytically and are used to calculate the components of the ray velocity vector. A hypothetical numerical model is considered to compute the phase velocity for given (arbitrary) phase direction and then the ray velocity vector. Surfaces are plotted for the phase velocity and ray velocity of each wave in a saturated poroelastic medium in the absence/presence of piezoelectricity. The contributions of the piezoelectric activeness of the solid frame and pore-fluid to the phase and ray velocities are identified and analysed for each of the four waves in the medium.

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“…Their kinetic energy expression included terms for microstructural kinetic energy due to the dynamics of local expansion and contraction of individual phases and virtual mass due to relative flow of each phase in addition to usual kinetic energy terms given by equation (5.2). Drag coefficients were identical to that of Garg and Nayfeh (1986) (see equations (5.6) through (5.8)). However, Berryman et al included the virtual mass effect in their formulation.…”

Section: Wave Propagation In Unsaturated Porous Mediamentioning

confidence: 99%

“…Three fronts merge into one with strong viscous coupling. Kansa (1987Kansa ( , 1988Kansa ( , 1989 and Kansa et al (1987) solved governing equations similar to that of Garg and Nayfeh (1986) by using an explicit Lagrangian code. They concluded that due to its small inertia, the gas phase response is basically uncoupled from solid and liquid phases.…”

Section: Wave Propagation In Unsaturated Porous Mediamentioning

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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Compressional wave propagation in liquid and/or gas saturated elastic porous media

Cited by 73 publications

References 23 publications

Variational formulation of pre-stressed solid–fluid mixture theory, with an application to wave phenomena

Variational formulation of pre-stressed solid–fluid mixture theory, with an application to wave phenomena

Piezoelectric effect on the velocities of waves in an anisotropic piezo-poroelastic medium

Chapter 5 Propagation of waves in porous media

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