Permeability and Seepage Flow - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 141

If the aperture and spacing of the discontinuities are not constant, the corresponding valu-
es in (6.27) need to be replaced by the hydraulic aperture and the mean spacing

(6.28)

To obtain the hydraulic aperture, strictly speaking, the mean apertures and friction
factors of all discontinuities must be subjected to an averaging procedure. Since, as
already mentioned, apertures cannot be directly determined in practice (2a i ) h can only
be roughly estimated.
To illustrate the huge infl uence of aperture on the magnitude of the permeability of
jointed rock, in Fig. 6.11 the permeability coeffi cients k D parallel to a discontinuity set
with constant spacing of s = 1 m and with differing mean apertures and relative rough-
nesses k/D h are compared with the permeability coeffi cients of soil (Wittke 1990). k D was
calculated according to Equation (6.28) in consideration of (6.17) and (6.18), setting
ν = 1.3 · 10 -6 m2/s corresponding to a water temperature of 10°C (Fig. 6.6). According-

ly, the permeability of a rock mass with a mean aperture of per meter
corresponds to that of fi ne sand, while permeability coeffi cients corresponding to gravel
are obtained for of around 1 mm. This result refl ects the fact that a rock mass of
only 0.1% porosity has the same permeability as gravel with a porosity of some 20% to
40%. Thus, the storage capacity of a rock mass is considerably smaller than that of a
soil with the same permeability. This will be demonstrated later in this section by means
of an example (Fig. 6.20).

Figure 6.11 Comparison of coeffi cients of permeability of a rock mass containing one set
of persistent, open discontinuities with those of a soil