Permeability and Seepage Flow - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 144

(6.34)

The angles are defi ned according to Fig. 3.4. Equation (6.33) represents the

generalized Darcy's law for a rock mass with one discontinuity set with arbitrary orien-
tation. The permeability coeffi cient k D here is replaced by a permeability tensor [K D ]
which was fi rst introduced into rock mechanics by Snow (1965).
In case of several discontinuity sets D 1 to D m the permeability tensor [K] of a rock mass
can be approximately computed by superimposing the permeability tensors [K Di ] of the
individual sets (Snow 1969, Wittke 1990):

α and β

(6.35)

where steady state fl ow is presumed. Furthermore, the energy losses arising at disconti-
nuity intersections when fl ows from individual discontinuities meet and when the direc-
tion of fl ow or the cross-section is changed are neglected. The vector of seepage velocity
is then obtained as

(6.36)

with

(6.37)

Equation (6.36) represents the generalized Darcy's law of a rock mass which exhibits
anisotropic permeability. [K] is also referred to as the “equivalent permeability tensor”
of the rock mass.
If the principal axes of permeability coincide with the coordinate axes x, y and z [K]
takes on the form of a diagonal matrix:

(6.38)

The permeability tensor of a rock mass can be established on the basis of the cor-
responding structural model (Section 2.7.3). Figs. 6.13 and 6.14 show the equivalent
permeability tensors of rock masses containing an orthogonal discontinuity system