Permeability and Seepage Flow - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 135

On the basis of fl ow experiments conducted by Louis (1967), for laminar fl ow the fol-
lowing relationship has been found for k d as a function of the relative roughness of the
discontinuities' walls:

(6.15)

Equations (6.14) and (6.15) gave reason to defi ne a so-called “hydraulic aperture” or
“equivalent” aperture (2a fi ) h so that, in terms of (2a fi ) h , the cubic law also applies for
rough discontinuities (Brown 1987):

(6.16)

with

(6.17)

and

(6.18)

Thus, k d can be expressed as:

(6.19)

Seepage fl ow in discontinuities fi lled with soil can be described by substituting k d in
(6.10) by the permeability coeffi cient k S of the soil (Wittke 1990):

(6.20)

In (6.20) the mean velocity of fl ow corresponds to the seepage velocity {v s } of the

soil fi lling.