Compressional waves in fluid-saturated elastic porous media

Garg, S.K.; Nayfeh, Adnan H.; Good, A. J.

doi:10.1063/1.1663532

Cited by 103 publications

(45 citation statements)

References 8 publications

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“…If constitutive parameters do not depend from the pre-stress, 3 then conditions (5.4) 2 and (5.6) are halfplanes and condition (5.7) defines a region bounded by an hyperbola. If we use the numerical example of Garg et al (1974), then the conservative interaction parameter γ sf is deduced, γ sf = 4.37 m 8 /Kg 2 s 2 .…”

Section: A Numerical Examplementioning

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: A Numerical Examplementioning

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

View full text Add to dashboard Cite

show abstract

“…We should note that for in all figures the numerical solutions cause the wave front(s) to smear. Yew and Jogi (1976) also obtained a solution by Laplace transformation similar to Garg et al's. (1974).…”

Section: Analytical Solutions Of Biofs Formulationmentioning

confidence: 76%

“…Furthermore, it is determined that transient permeabihty is approximately one-third of the stationary value. The contribution of added mass which is neglected by most researchers (e.g., Garg et al, 1974;Mei and Foda, 1981) was found to be signifi cant. Later, van der Grinten et al, (1987a) provided new experimental evidence by measuring pore pressures and strain simultaneously.…”

Section: 3 Solutions By the Methods Of Characteristicsmentioning

confidence: 99%

“…However, we must note that in general, neither of these waves propagate as a wave in the fluid or in the solid matrix alone, both travel jointly in the matrix and the fluid. If coupling is weak (see the solution of Garg et al (1974) in section 3.1) waves propagate in a form which closely resemble a wave in the soUd matrix alone, and a wave in the fluid alone. Biot (1956a) demonstrated the possible existence of an elastic wave, in which no relative motion between the fluid and solid phases occurs (e = e) and the dissipation due to fluid friction disappears.…”

Section: P11p22-p12mentioning

confidence: 99%

“…Among various solutions obtained within last two decades, (e.g., Kingsbury's (1979, 1980) solution with no coupling, i.e., b = 0, for a harmonic loading of saturated porous layer or Cleary's (1977) solution without inertia, or Verruijt's (1982) solution for cydic sea wave generated pore pressures), Garg and his coworkers' analytical solution (Garg et al, 1974) is an important one. Garg et al solved Biot's equations for dilatational waves in terms of displacements u^ and U^ [equations (2.25) and (2.28)] for a one-dimensional column.…”

Section: Analytical Solutions Of Biofs Formulationmentioning

confidence: 99%

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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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Silent Boundary Conditions for Wave Propagation in Saturated Porous Media

Gajo

Saetta

Vitaliani

1996

Int. J. Numer. Anal. Methods Geomech.

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Wave propagation both in one‐ and in two‐dimensional saturated elastic porous media is analysed by means of a two‐field finite element model with silent boundaries. An extension of the elastic ‘multidirectional’ transmitting boundary to two‐phase media is developed to simulate the silent boundary condition. The theoretical assessment and the numerical formulation of the first‐order silent boundary technique is presented in detail. Some examples are used to demonstrate the reliability of the first‐order method, especially for problems with plane and axisymmetric waves having various angles of incidence. Finally, the wave propagation along a pile shaft is presented, to simulate a common non‐destructive dynamic pile test.

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Compressional waves in fluid-saturated elastic porous media

Cited by 103 publications

References 8 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

Chapter 5 Propagation of waves in porous media

Silent Boundary Conditions for Wave Propagation in Saturated Porous Media

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