Quasistatic Poroelasticity - Continuum Mechanics of Anisotropic Materials - page 198

Chapter 8
Quasistatic Poroelasticity
The theme for this chapter is contained in a quote from the 1941 paper of M. A. Biot
that clearly describes an RVE: “Consider a small cubic element of soil, its sides
being parallel with the coordinate axes. This element is taken to be large enough
compared to the size of the pores so that it may be treated as homogeneous, and at
the same time small enough, compared to the scale of the macroscopic phenomena
in which we are interested, so that it may be considered as infinitesimal in the
mathematical treatment.”
8.1 Poroelastic Materials
Thinking about, or experimenting with, a fluid-saturated sponge can develop an
intuitive sense of the response of a saturated elastic porous medium to mechanical
loading. If a fluid-saturated sponge is compressed, fluid will flow from the sponge.
If the sponge is in a fluid reservoir and compressive pressure is subsequently
removed, the sponge will reimbibe the fluid and expand. The volume of the sponge
will also increase if its exterior openings are sealed and the external pore fluid
pressure is increased. However, the volume of the sponge will also decrease if its
exterior openings are sealed and the external pore fluid pressure is decreased. The
basic ideas underlying the theory of poroelastic materials are that the pore fluid
pressure contributes to the total stress in the porous matrix medium and that the pore
fluid pressure alone can strain the porous matrix medium. There is fluid movement
in a porous medium due to differences in pore fluid pressure created by different
pore volume strains associated with the mechanical loading of the porous medium.
This chapter contains a presentation of the quasistatic theory of poroelasticity.
Quasistatic means that inertia terms, that is to say mass times acceleration terms, are
neglected. Thus quasistatic means that processes are either static or moving so
slowly that the inertia terms are much smaller than other terms in the balance
equations for linear and angular momentum. The following chapter contains a
presentation of the dynamic theory of poroelasticity, the theory that deals with