Engineering Rock Mechanics

144 Permeability

ture network, rather than equally through all fractures. The idea of the
Representative Elemental Volume (REV) (Bear, 1979 ') was developed
because of this type of local influence of the fractures. The REV is the
sample size above which a measured rock property becomes essentially
constant; any significant property variation caused by the idiosyncrasies
in small samples becomes less and less as the sample volume is in-
creased, until a reproducible value is obtained.
Currently, the problem we face is to obtain sufficient information
about the fractures to make rock mass simulations realistic. It is only
after obtaining good fracture data and using a fracture flow program
that one can consider whether the continuum tensor approximation at a
given REV level is likely to be useful. This logic is similar to that for the
elasticity of fractured rocks: one can only decide whether an isotropic
assumption is appropriate once one understands the anisotropic nature
of the rock mass.

9.2 Question and answers: permeability

Q9.1 How long does it takes for water, subiected to a 10 m head

difference, to pass horizontally through

(a) a 5 m length of intact granite which has an isotropic hydraulic

conductivity, K, of 1 x 1 0-l2 m/s and

(b) through a 5 m length of fractured limestone with an isotropic

hydraulic conductivity of 1 x~O-~ m/s?

A9. I We use Darcy's law, Q = KAi, where Q is the flow rate in m3/s, K

is the hydraulic conductivity in m/s, A is the cross-sectional rock area in

m2, and i is the dimensionless hydraulic gradient, m/m.

(a) The volume of water flowing, V, is Qf, where t is the time.

Therefore, f = V/Q = V/KAi. For a length of 5 m and a cross-sectional

area A, V = 5A and so t = SA/KAi or t = 5/Ki. Substituting K =

1 x and i = 10/5 = 2, we obtain, t = 2.5 x 10l2 s % 790,000 years.

This rate of water penetration is not significant during engineering

works, but it is significant for water flowing through granite masses

over geological time: in a hundred million years, the water will have

penetrated more than half a kilometre.

(b) For the fractured limestone, K = 1 x IO4 m/s, and we have

t = 2.5/K = 2.5 x lo4 s rs 7 h. This result is significant for engineering.

It means that for the conditions assumed and with the introduction of

water with a 10 m head difference, water would penetrate into the rock

mass for 17 m in all directions in a day.

49.2 The hydraulic conductivity of an array of parallel fractures

(Hoek and Bray, 1977') in the direction parallel to the plane of

The Representative Elemental Volume concept was originally developed for permeab-

'Hoek E. and Bray J. W. (1977) Rock Slope Engineering. Institution of Mining and

ility by Bear J. (e.g.) (1979) Hydraulics of Groundwater. McGraw-Hill, New York.

Metallurgy, London, 402pp.