Coupling of Stress-Strain Behavior and Seepage Flow - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 171

Figure 7.5 Mean aperture of a discontinuity as a function of normal stress and shear displacement
(Erichsen 1987)

Using (6.19) and (7.8) the permeability of a discontinuity as a function of σ n and δ s,D

can be expressed as

(7.9)

Erichsen (1987) used the approach of Erban (1986) to calculate δ n,D ( δ s,D ) in the pre-peak

zone I ( δ s,D ≤ δ p,D ) and in the post-peak zone II ( δ s,D > δ p,D ), respectively, where δ p,D

is the shear displacement at failure (Fig. 3.21). In the pre-peak zone I ( δ s,D ≤ δ p,D ) the

δ n,D - δ s,D relationship (Fig. 3.21) is:

if δ s,D ≤ δ p,D

(7.10)

where is a parameter describing dilatancy and i is the sliding-up angle. In the post-

peak zone II (

ψ

δ s,D > δ p,D ) the relationship between δ n,D and δ s,D is:

if δ s,D > δ p,D , (7.11)

where is the so-called “softening parameter” describing strength reduction in the post-

peak zone II (Fig. 3.21). The negative sign of

χ

δ n,D indicates dilatant displacements dur-
ing shearing leading to an increase in aperture (Figs. 3.21 and 7.5).

Alternative formulations for the stress-dependent permeability of discontinuities can be
found, for example, in Olsson & Barton (2001).