Engineering Rock Mechanics

Primary and secondary permeability 1 5 1

KdP

4=--.

The term, K, is the coefficient of permeability (or hydraulic conductivity)
with dimensions LIT, and the term yf is the fluid specific weight. The
relation between k and K is therefore

YrdX

permeability, k = pWyf (L’) or

hydraulic conductivity, K = yfk/p (LIT).

In its most basic form, and for the case of laminar flow, Darcy’s law links
the water flow rate to the pressure gradient, i.e.

Q=KAi

where Q is the flow rate (dimensions of L3T-l),
A
i

is the cross-sectional area of the flow, and

is the hydraulic gradient, AhIAl.

9.2 Primary and secondary permeability

Because of the presence of discontinuities in a rock mass, we have the
concepts of primary permeability and secondary permeability. Primary
permeability refers to the rock matrix permeability, whereas, the secondary
permeability refers to the rock mass permeability. In some circumstances,
e.g. petroleum engmeering, we will be specifically interested in the primary
permeability, but in most rock engineering it is the secondary permeability
which dominates the design and construction procedures. It has already
been mentioned that there are interrelations between most of the rock
properties: the flow of fluid through a fractured rock mass is no exception,
as it will depend on:

(a) the aperture of the fractures, which in turn will depend on
(b) the normal stress acting across the fractures, which in turn will depend

(c) the depth below the ground surface.

In the extreme case, at great depth, all the fractures may be effectively
closed, so that the primary and secondary permeabilities are similar.
Figure 9.2 illustrates the variabilities of primary and secondary hydraulic
conductivity for different rock types. A key aspect of the primary hydraulic
conductivity diagram is the extreme range-through at least 8 orders of
magnitude. Similarly, for the secondary hydraulic conductivity, there is an
even greater range-of 11 orders of magnitude-with limestones,
dolomites and basalts covering the entire range.

on

9.3 Flow through discontinuities

The development of the theory for considering fluid flow through a
discontinuity is described by Hoek and Bray (1977) and is based on the flow
between a parallel pair of smooth plates. Darcy’s law can be rewritten as