Quasistatic Poroelasticity - Continuum Mechanics of Anisotropic Materials - page 199

nonzero inertia terms and focuses on wave propagation. These two aspects of the
theory of poroelasticity are treated separately because both the physics and the
mathematical models are different. These differences stem from the physical
differences in the pore fluid behavior relative to the solid porous matrix material.
In the quasistatic theory the pore fluid flows through the pores, from pore to pore. In
the dynamic theory the wave passing through the porous medium travels at a speed
that does generally not permit the time for the pore fluid to flow from pore to pore.
A consequence of this difference in the pore fluid behavior leads to two theories that
have very different characteristics.
Poroelastic theory is a useful model in many geological and biological materials
because almost all of these materials have an interstitial fluid in their pores. In
biological tissues the interstitial fluid has many functions, one important function
being to transport nutrients from the vasculature to the cells in the tissue and to
transport waste products away. In some tissues the pore fluid pressure creates a
turgor or osmotic pressure that stiffens a soft tissue structure and in other tissues it is
part of the intercellular communication system. In tissues, the quasistatic deforma-
tion of the porous medium has a significant effect on the movement of pore fluid,
although the fluid pressure and fluid movement generally have only a small effect
on the deformation of the porous medium; the porous medium deformation gener-
ally pushes the fluid around, not vice-versa. The pore fluid pressure stays relatively
low in tissues because a higher pressure could collapse blood vessels and render the
tissue ischemic. However the pore fluid pressure does not have to stay low in tissues
like articular cartilage that are avascular. One could speculate that the reason
articular cartilage is avascular is to avoid the collapse of blood vessels. Many of
these effects have been, or will be, modeled using poroelasticity theory.
Quasistatic fluid movement in rocks and soils has many features of importance
to human populations. Water supply is one of the most important, removing oil
and gas from the ground is another. High water content can make soil masses
unstable; previously stable slopes may be caused to flow over human
developments. Earthquakes may cause fluid-saturated soil masses to liquefy and
the buildings situated upon them to sink into the soil mass. The theory of
poroelasticity has its origins in addressing the problem of buildings settling or
sinking into water saturated soil masses due to their own weight, not the liquefac-
tion of the soil mass.
The quasistatic poroelastic theory developed in this chapter is a combination
and modification of three of the four theories, those for elastic solids, viscous
fluids and flow through porous media, developed in Chap. 6 . The development of
the theory is strongly dependent on the microstructural modeling concepts
described in Chap. 7 . In fact much of the material that has preceded this chapter
has been laying the foundation for this chapter. Laying this foundation began with
the discussion of the Terzaghi and Darcy lumped parameter models in Chap. 1 .
Terzaghi was one of the first engineers to address the problem of buildings settling
or sinking into water saturated soil masses due to their own weight. Darcy
investigated the flow of water through sand layers as a factor in the design of
fountains in his hometown of Dijon.