Modification of Biot’s theory of porous materials

1997 ◽  
Vol 101 (5) ◽  
pp. 3145-3145
Author(s):  
H. Tavossi ◽  
B. R. Tittmann
Keyword(s):  
Porous Materials ◽  
Biot’S Theory ◽  
Biot's Theory

The Modified Mixture Theory for Fluid-Filled Porous Materials: Theory

1987 ◽  
Vol 54 (1) ◽  
pp. 35-40 ◽  
Author(s):  
N. Katsube ◽  
M. M. Carroll
Keyword(s):  
Porous Materials ◽  
Velocity Gradient ◽  
Mechanical Response ◽  
Fluid Velocity ◽  
Mixture Theory ◽  
Biot’S Theory ◽  
Homogeneous Fluid ◽  
Biot's Theory ◽  
Flow Mechanisms ◽  
Flow Through

The mixture theory by Green and Naghdi is modified and applied to the problems of flow-through porous materials. By introducing porosity, we make clear that two constituents occupying the same point in the original mixture theory are an equivalent homogeneous solid and an equivalent homogeneous fluid which, respectively, represent a porous solid and a porous fluid in the actual sample. The micro-mechanical response studied by Carroll and Katsube is introduced and detailed deformation and flow mechanisms are provided at each point of the mixture. The resulting theory is compared with Biot’s theory and in fact reduces to Biot’s theory when the fluid velocity gradient terms are ignored.

The Modified Mixture Theory for Fluid-Filled Porous Materials: Applications

1987 ◽  
Vol 54 (1) ◽  
pp. 41-46 ◽  
Author(s):  
N. Katsube ◽  
M. M. Carroll
Keyword(s):  
Steady State ◽  
Porous Materials ◽  
Boundary Value Problems ◽  
Characteristic Length ◽  
Boundary Value ◽  
Fluid Velocity ◽  
Mixture Theory ◽  
Biot’S Theory ◽  
Biot's Theory ◽  
State Boundary

The recently established modified mixture theory for fluid-filled porous materials is applied to two steady state boundary value problems; also, how the newly developed theory provides more general solution than Biot’s theory is examined. The velocity profiles in steady state boundary value problems are found to depend on the ratio of a characteristic length of the microstructure to a characteristic length defined by the boundary conditions. As opposed to Biot’s theory, the zero fluid velocity condition on the boundary are satisfied and the existence of a non-Darcy flow closer to the boundary are shown.

Biot’s theory and granular media

Poromechanics ◽  
2020 ◽  
pp. 191-196
Author(s):  
Nicholas P. Chotiros
Keyword(s):  
Granular Media ◽  
Biot’S Theory ◽  
Biot's Theory

scholarly journals Axially Symmetric Vibrations of Composite Poroelastic Spherical Shell

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Rajitha Gurijala ◽  
Malla Reddy Perati
Keyword(s):  
Wave Propagation ◽  
Phase Velocity ◽  
Spherical Shell ◽  
Wave Number ◽  
Biot’S Theory ◽  
Impervious Surfaces ◽  
Axially Symmetric ◽  
Spherical Shells ◽  
Biot's Theory

This paper deals with axially symmetric vibrations of composite poroelastic spherical shell consisting of two spherical shells (inner one and outer one), each of which retains its own distinctive properties. The frequency equations for pervious and impervious surfaces are obtained within the framework of Biot’s theory of wave propagation in poroelastic solids. Nondimensional frequency against the ratio of outer and inner radii is computed for two types of sandstone spherical shells and the results are presented graphically. From the graphs, nondimensional frequency values are periodic in nature, but in the case of ring modes, frequency values increase with the increase of the ratio. The nondimensional phase velocity as a function of wave number is also computed for two types of sandstone spherical shells and for the spherical bone implanted with titanium. In the case of sandstone shells, the trend is periodic and distinct from the case of bone. In the case of bone, when the wave number lies between 2 and 3, the phase velocity values are periodic, and when the wave number lies between 0.1 and 1, the phase velocity values decrease.

Wave propagation in cancellous bone in terms of Biot's theory

2008 ◽  
Vol 123 (5) ◽  
pp. 3513-3513
Author(s):  
Michal Pakula ◽  
Frederic Padilla ◽  
Mariusz Kaczmarek ◽  
Pascal Laugier
Keyword(s):  
Wave Propagation ◽  
Cancellous Bone ◽  
Biot’S Theory ◽  
Biot's Theory

A theory of compressional wave attenuation in noncohesive sediments

Geophysics ◽  
1985 ◽  
Vol 50 (8) ◽  
pp. 1311-1317 ◽  
Author(s):  
C. McCann ◽  
D. M. McCann
Keyword(s):  
Wave Attenuation ◽  
Compressional Wave ◽  
Solid Particles ◽  
Biot’S Theory ◽  
Attenuation Coefficients ◽  
Low Frequencies ◽  
Biot's Theory ◽  
Compressional Waves ◽  
High Frequencies ◽  
Water Saturated

Published reviews indicate that attenuation coefficients of compressional waves in noncohesive, water‐saturated sediments vary linearly with frequency. Biot’s theory, which accounts for attenuation in terms of the viscous interaction between the solid particles and pore fluid, predicts in its presently published form variation proportional to [Formula: see text] at low frequencies and [Formula: see text] at high frequencies. A modification of Biot’s theory which incorporates a distribution of pore sizes is presented and shown to give excellent agreement with new and published attenuation data in the frequency range 10 kHz to 2.25 MHz. In particular, a linear variation of attenuation with frequency is predicted in that range.

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