Seminar - Frank Lu - A linear dynamic model for a saturated porous medium
Wednesday 6 September 2006, 1.10 - 1.50 pm
Civil Engineering Lecture Theatre 3
A linear isothermal dynamic model for a porous medium saturated by a Newtonian fluid is developed in the study. In contrast to the mixture theory, the assumption of phase separation is avoided by introducing a single constitutive energy function for the porous medium. The mass and momentum balance equations are obtained according to the generalized mixture theory. Constitutive relations for the stress, the pore pressure are derived from the total free energy accounting for inter-phase interaction. In order to describe the momentum interaction between the fluid and the solid, a frequency independent Biot-type drag force model is introduced. A temporal variable porosity model with relaxation accounting for additional attenuation is introduced for the first time. The details of parameter estimation are discussed in this study. The influences of the porosity relaxation coefficient on the velocities and attenuation coefficients of the three waves of the porous medium are illustrated by a numerical example.