Coupling of Stress-Strain Behavior and Seepage Flow - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 174

To describe the equivalent permeability of jointed rock according to the homogeneous
model, the nonlinear relations between normal displacement, normal stress and shear
displacement on discontinuities can be idealized by linear relationships (Section 3.4.2,
Fig. 3.27).
The equivalent permeability of jointed rock can be expressed in terms of averaged
strains. The averaged elastic strain of the rock mass normal to a set D is the superpo-
sition of the averaged elastic normal strain

ε n,IR el of the intact rock and the averaged

ε n,D el of the discontinuities of set D (cf. Equation (3.84)):

elastic normal strain

(7.13)

in which E IR,n and E n are Young's moduli of the intact rock and the rock mass, respec-
tively, normal to the discontinuities of set D. This leads to

(7.14)

The mean viscoplastic normal strain of the discontinuities of set D is given by (Section
3.4.2):

ε n,D vp = - tan γ res,D vp . ψ D ⋅ (3.108)

Superposition of (3.108) and (7.14) yields:

(7.15)

ε n el and γ res vp then is obtained

The permeability k D in terms of the strain components

by inserting (7.15) into (7.12):

(7.16)