Engineering Rock Mechanics

150 Perrneabihfy

q. =-A- ki. ap

iu 'xj

where qi is the specific discharge,
is the pressure gradient causing flow,
is the fluid viscosity and
are the components of the permeability tensor.

dP/Gkj
P
kij
These components are schematically illustrated in Fig. 9.1 to show the
analogy of permeability with stress and strain. Within the context of this
book, it is inappropriate to pursue the full mathematical development of
this subject further, because permeability is almost always regarded as a
scalar value in engineering practice: the interested reader is referred to
Raudkivi and Callander's (1976) book on groundwater flow for an
excellent treatment of the subject. Consequently, we will concentrate on
the semi-empirical approach that is utilized in engineering. As we will be
describing later, there are major problems in considering a fractured rock
mass as an effectively continuous permeable medium.
Because in practice permeability has rarely been regarded in its full
tensorial state, and because we will be considering one-dimensional flow
through discontinuities, it is convenient here to consider the reduced forms
of the above equations. Assuming permeability to be a scalar, we have

q=--. k aP

The permeability, k, is independent of the fluid under consideration having

the dimensions L2.

Very often in rock engineering the percolating fluid is water and so we

can alter the form of the above equation to

P ax

k,,, water out

Water

• kxx,
  water
  in fib out
  k,,, water out

General permeability matrix

with respect to x,y,z axes

Mohr's circle

for permeability

t

Principal permeabilities,

no cross flow

Figure 9.1 Illustration of permeability as a tensor quantity.