Permeability and Seepage Flow - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 156

The effective porosity of jointed rock corresponds to the volume of open interconnect-
ed discontinuities V D related to the reference volume V referred to as the relative joint
volume:

(6.61)

For a rock mass with m orthogonal discontinuity sets (n = 1, 2, 3) with mean aperture
and mean spacing , n D may be calculated by way of approximation as

(6.62)

Thus, for this particular case the following relationship is obtained:

(6.63)

In a homogeneous unconfi ned aquifer in unjointed porous rock the specifi c storage
coeffi cient is

(6.64)

From (6.63) and (6.64) the specifi c storage coeffi cients of a homogeneous unconfi ned
double porous aquifer, such as the jointed porous sandstone illustrated in Fig. 6.19, can
be expressed as

(6.65)

(6.66)

The specifi c storage coeffi cient of a joint aquifer is normally considerably smaller than
that of a pore aquifer. As a consequence, the time required for a lowering of the water
table in a joint aquifer is much smaller than that in a pore aquifer of the same perme-
ability. This will be shown in the following by means of an example.
For this purpose, a joint aquifer and a pore aquifer with the same isotropic permeability
of k = 1 · 10 -6 m/s are considered. The joint aquifer consists of an orthogonally jointed
rock with two vertical joint sets and one horizontal bedding-parallel set. For simplicity,
equal and constant spacing and an aperture of s = 1 m and 2a i = 0.12 mm is assumed
for all three discontinuity sets (Fig. 6.20, left). According to (6.62), the relative joint
volume can then be calculated as