Permeability and Seepage Flow - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 146

Figure 6.14 Equivalent permeability tensor of a rock mass with an orthogonal discontinuity system,
orientations not coinciding with the coordinate axes (Wittke 1990)
In certain cases the fl ow through interconnected individual discontinuities must be
taken into account when superimposing the permeability tensors of the individual sets.
A typical example is a rock mass with a joint set J oriented perpendicular to a bedding
B where the joints are terminating on bedding-parallel discontinuities (Fig. 6.15). Such
a discontinuity system is frequently encountered in nature (Fig. 2.15). If the traces of
the bedding-parallel discontinuities and the joints are oriented parallel to the x axis and
y axis, respectively, as illustrated in Fig. 6.15, the permeability of such a rock mass can
be expressed by the following equivalent permeability tensor:
(6.39)
where k xx and k yy are the permeability of the rock mass parallel and normal to the
bedding, respectively.
Assuming steady-state, laminar fl ow through the discontinuities, Doolin & Mauldon
(2001) derived an approximation for the permeability coeffi cient k yy normal to the bed-
ding. Accordingly, this is dependent on both aperture (2a i ) hBj and spacing is Bj of the
bedding-parallel discontinuities as well as aperture and spacing of the joints (2a i ) hJij
and s Jij (Fig. 6.15).