Wave propagation in a general anisotropic poroelastic medium: Biot’s theories and homogenisation theory |
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Authors: | M D Sharma |
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Institution: | (1) Department of Mathematics, Kurukshetra University, Kurukshetra, 136 119, India |
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Abstract: | Anisotropic wave propagation is studied in a fluid-saturated porous medium, using two different approaches. One is the dynamic
approach of Biot’s theories. The other approach known as homogenisation theory, is based on the averaging process to derive
macroscopic equations from the microscopic equations of motion. The medium considered is a general anisotropic poroelastic
(APE) solid with a viscous fluid saturating its pores of anisotropic permeability. The wave propagation phenomenon in a saturated
porous medium is explained through two relations. One defines modified Christoffel equations for the propagation of plane
harmonic waves in the medium. The other defines a matrix to relate the relative displacement of fluid particles to the displacement
of solid particles. The modified Christoffel equations are solved further to get a quartic equation whose roots represent
complex velocities of the four attenuating quasi-waves in the medium. These complex velocities define the phase velocities
of propagation and quality factors for attenuation of all the quasi-waves propagating along a given phase direction in three-dimensional
space. The derivations in the mathematical models from different theories are compared in order to work out the equivalence
between them. The variations of phase velocities and attenuation factors with the direction of phase propagation are computed,
for a realistic numerical model. Differences between the velocities and attenuations of quasi-waves from the two approaches
are exhibited numerically. |
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Keywords: | Anisotropic poroelastic (APE) solid Biot’ s theory homogenisation theory phase velocity |
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