Mechanics of Deformation and Acoustic Propagation in Porous Media

Abstract

A unified treatment of the mechanics of deformation and acoustic propagation in porous media is presented, and some new results and generalizations are derived. The writer's earlier theory of deformation of porous media derived from general principles of nonequilibrium thermodynamics is applied. The fluid-solid medium is treated as a complex physical-chemical system with resultant relaxation and viscoelastic properties of a very general nature. Specific relaxation models are discussed, and the general applicability of a correspondence principle is further emphasized. The theory of acoustic propagation is extended to include anisotropic media, solid dissipation, and other relaxation effects. Some typical examples of sources of dissipation other than fluid viscosity are considered.

Constitutive equation for concrete creep and shrinkage based on thermodynamics of multiphase systems

“…Obviously, the described mechanisms for both the chemically bound and capillary water are phenomenologically similar to our mechanism for adsorbed water, so that formally same equations as (17), (25), (26), (32d), (38), (39) would be obtained. We can thus conclude that the resulting macroscopic constitutive equation is the same as ·for microscopic diffusion of any form of load-bearing water, whether it is adsorbed, or chemically bound, or capillary.…”

“…2) a small change of water content produces a small change of humidity. This fact has an important mathematical consequence-the macroscopic water flow problem is uncoupled with the stress and strain problem and may be solved independently (unlike in the vibration of the saturated sand [39]). …”

“…Then we can write simply ~ = According to our assumptions, aa is independent of deformation (unlike in a medium with pores saturated by liquid, at high flow rates [39]). The provenance and significance of the terms aa and aad is differ.ent.…”

“…We shall treat the cement paste and concrete as a multi-phase medium, the theory of which has been developed until now only in soil mechanics [39]. Besides the conditions of static equilibrium between phases we shall have to introduce the conditions for thermodynamic equilibrium of various phases of water and investigate the microscopic local diffusion of water.…”

Two-Dimensional Fractional Order Generalized Thermoelastic Porous Material

“…A short list of papers pertinent to the present study includes Biot(1941Biot( , 1956, Gassmann (1951), Biot and Willis (1957), Biot (1962), Deresiewicz and Skalak (1963), Mandl (1964), Nur and Byerlee (1971), Brown and Korringa (1975), Rice and Cleary (1976), Burridge and Keller (1981), Zimmerman et al (1986Zimmerman et al ( ,1994, Berryman and Milton (1991), Thompson and Willis (1991)], Pride et al (1992), Berryman and Wang (1995), Tuncay and Corapcioglu (1995), Alexander and Cheng (1991), Charlez, P. A., and Heugas, O. (1992), Abousleiman et al (1998), Ghassemi and Diek (2002), Tod (2003).…”