Coupling of Stress-Strain Behavior and Seepage Flow - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 169

In consideration of (6.19) the permeability of a discontinuity as a function of σ n can

be expressed as

(7.3)

where

(7.4)

To describe the stress-dependent permeability of a discontinuity under normal stress
Erichsen (1987) used the following

δ n,D - σ n relationship (cf. Section 3.3.2):

(3.45)

Inserting (3.45) into (7.3) yields

(7.5)

From the asymptotic behavior of (7.5) it follows that at high stress levels a residual
permeability k d,res will remain:

(7.6)

where

is a residual aperture that is responsible for k d,res . This is in agreement with experimen-
tal data (Witherspoon et al. 1980). Thus, can also be expressed in terms of δ m

and (Fig. 7.4):

(7.7)