Decoupling of the coupled poroelastic equations for quasistatic flow in deformable porous media containing two immiscible fluids

Lo, Wei Cheng

doi:10.1016/j.advwatres.2006.01.002

Cited by 4 publications

(2 citation statements)

References 27 publications

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“…For many practical applications, a linear theory of poroelasticity can be safely exploited for stress analyses of porous media. To date, such a theory has been widely applied to a large body of problems pertinent to biomechanics and medical engineering [8][9][10], geomechanics [11][12][13], hydrology [14,15], materials science [16][17][18], physics and geophysics [19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

An exact solution to the problems of flexo-poro-elastic structures rested on elastic beds acted upon by moving loads

2019

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This paper aims to examine flexural vibrations of fully saturated poroelastic structures on an elastic bed subjected to moving point loads via an analytical solution. Using a flexural beam model in conjunction with the Biot's poro-elasticity theory, the equations of motion of the porous structure are derived. Using assumed mode method and Laplace transform, the explicit expressions of displacement and pore pressure are obtained carefully.For a particular case, the predicted results are also compared with those of another work and a reasonably good agreement is achieved. The influences of the moving load velocity, permeability ratio, transverse stiffness of the foundation, viscosity of the pore fluid, and porosity on the maximum elasto-dynamic fields and pore pressure are conclusively discussed.The velocity pertinent to the maximum possible dynamic response is graphically determined and the roles of influential parameters on this crucial factor are displayed. The present model could be easily extended to multi-layered poroelastic structures under moving loads.

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Section: Introductionmentioning

confidence: 99%

An exact solution to the problems of flexo-poro-elastic structures rested on elastic beds acted upon by moving loads

2019

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“…[ 32] Not available One-fluid system Two-fluid system Models without inertial coupling Time Chandler and Johnson [28] L o [ 31] domain, yielding a propagating-wave equation for the Biot fast wave and a dissipative wave equation for the Biot slow wave [30]. Decoupling of the Lo et al [13] poroelasticity equations for dilatational waves in a porous medium containing two immiscible fluids also can be accomplished in the time domain if inertial coupling terms are dropped [31]. Berryman et al [24] decoupled their model equations, which neglect capillary pressure changes but retain inertial coupling terms, following the frequency-domain method used by Berryman [27] for the single-fluid case ( Table 1).…”

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confidence: 99%

Analytical decoupling of poroelasticity equations for acoustic-wave propagation and attenuation in a porous medium containing two immiscible fluids

Sposito

Majer

2008

J Eng Math

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Poroelasticity theory has become an effective and accurate approach to analyzing the intricate mechanical behavior of a porous medium containing two immiscible fluids, a system encountered in many subsurface engineering applications. However, the resulting partial differential equations in the theory intrinsically take on a coupled form in the terms pertinent to inertial drag, viscous damping, and applied stress, making it difficult to obtain closed-form, steady-state analytical solutions to boundary-value problems except in special cases. In the present paper, we demonstrate that, for dilatational wave excitations, these partial differential equations can be decoupled analytically into three Helmholtz equations featuring complex-valued, frequency-dependent normal coordinates that correspond physically to three independent modes of dilatational wave motion. The normal coordinates in turn can be expressed in the frequency domain as three different linear combinations of the solid dilatation and the linearized increment of fluid content for each pore fluid, or equivalently, as three different linear combinations of total dilatational stress and two pore fluid pressures. These representations are applicable to strain-controlled and stress-prescribed boundary conditions, respectively. Numerical calculations confirm that the phase speed and attenuation coefficient of the three dilatational waves represented by the Helmholtz equations are exactly identical to those obtained previously by numerical solution of the dispersion relations for dilatational wave excitation of a porous medium containing two immiscible fluids. Thus, dilatational wave motions in unsaturated porous media subject to suitable boundary conditions can now be accurately modeled analytically.

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The Analysis of Unsaturated Ground Vibration Induced by Train Loading by 2.5D FEM

2017

Environmental Vibrations and Transportation Geodynamics

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Decoupling of the coupled poroelastic equations for quasistatic flow in deformable porous media containing two immiscible fluids

Cited by 4 publications

References 27 publications

An exact solution to the problems of flexo-poro-elastic structures rested on elastic beds acted upon by moving loads

An exact solution to the problems of flexo-poro-elastic structures rested on elastic beds acted upon by moving loads

Analytical decoupling of poroelasticity equations for acoustic-wave propagation and attenuation in a porous medium containing two immiscible fluids

The Analysis of Unsaturated Ground Vibration Induced by Train Loading by 2.5D FEM

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