The Pragmatic Wave Equations and Their Potential Equations of a Saturated Porous Micropolar Medium

Abstract

Soil is a porous medium made of rigid grains in the microscale and has an obvious grain behavior. It becomes a saturated soil when the pores between soil grains are filled with water or oil. When the porous solid skeleton is approximately taken as a micropolar medium and the fluid in the pores a point medium, the elastic pragmatic wave equations in a saturated porous micropolar medium are obtained from the results of the micropolar theory and those of Biot's pragmatic wave theory. Since the relations between the parameters of the saturated porous micropolar theory and those of the corresponding one-phase medium are obtained by means of the Greetsma theory, it has merits that the physics parameters in our dynamic equations of the saturated porous micropolar medium have a definite physics meaning and are easy to be tested in the laboratory. The dynamical equations are then simplified as the potential equations with the aid of the field theory and the dispersion equations of five elastic waves propagating in the saturated porous micropolar medium are established. Finally, the propagating characteristics of the five harmonic body waves in the saturated micropolar porous medium are investigated by the numerical methods. It is shown from the results that the dispersion curves of the velocities of P1 wave, P2 wave and shear S1 wave are similar to those in the classical saturated porous medium. When frequency is lower than the critical frequency w0, the rotation longitudinal θ wave and the rotation transverse S2 wave do not exist. When the frequency is greater than the critical frequency w0, θ wave and S2 wave both arise and their velocities decrease when frequency increases.