Permeability and Seepage Flow - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 129

where V P and V S are the volume of voids (pores) and solids, respectively, in a reference
volume V. If V WP is the volume of interconnected voids then effective porosity is de-
i ned as
(6.2)
where V IP is the volume consisting of isolated pores including pores fi lled with capillary
bounded water, such as in argillaceous rocks. Equations (6.1) and (6.2) refer to fractions.
Numerical values of porosity are also frequently given as percentage rather than as frac-
tions.
6.2.2 Darcy's Law and Permeability
Since mineral grains are practically impermeable, the water must fi nd a path along the
pores, capillaries and cracks. As a consequence, considerable differences in the magni-
tude and direction of the local velocity of fl ow v arise (Fig. 6.3, left).
Figure 6.3 Darcy's law for porous intact rock
As is known from soil mechanics, the complicated processes involved in fl ow through the
irregular channels formed by voids remain unconsidered in the description of fl ow through
porous intact rock. Instead a seepage velocity v s is introduced that is defi ned as the quotient
of the amount of water per time unit Q, referred to as “discharge” or “fl ow rate”, permeat-
ing through the total cross-sectional area A normal to the direction of fl ow (Fig. 6.3, right):
(6.3)
It was found that the seepage velocity is proportional to the hydraulic gradient I
(Darcy 1856) being defi ned as the gradient of the piezometric head h. In the ex-