9 Permeability
The subject of permeability is concerned with fluid flow through a material,
or rocks and rock masses in our current context, and is one of the most
difficult topics facing the practising rock engineer. There are formal
definitions of permeability and the associated characteristics for continuous
materials but, as is emphasized throughout this book, a rock mass contains
discontinuities, and discontinuities are preferential flow paths. In this
chapter, therefore, we will initially present the definitions of permeability
and hydraulic conductivity and discuss the tensorial nature of permeability.
We will then consider fluid flow in discontinuities and the associated ideas
of primary and secondary permeability. The subject of the permeability of
the rock mass can be studied in terms of the effective permeability of
discontinuity networks: there is then the corollary of a natural scale effect
and the representative elemental volume. Finally, we will discuss the
difficulty of dealing with effective stresses in rock mechanics and the
permeability-related applications of grouting and blasting.
We should note in passing that the phenomenon of water flowing
through rock has been observed since antiquity. In Creechs (1683) English
translation of Lucretius’ six books of Epicurean philosophy on the nature
of things, in Book I are the lines,
Tho free from Pores, and Solid Things appear,
Yet many Reasons prove them to be Rare:
For drops distill, and subtle moisture creeps
Thro hardest Rocks, and every Marble weeps ...9.1 Fundamental definitions
Permeability, kij, is a mathematical quantity directly analagous to stress and
strain which we have already described. It is a second-order tensor,
meaning that it is a quantity with magnitude, direction and a reference
plane. Permeability has six independent components and follows mathe-
matical transformation equations when the orientation of the reference
plane is changed. Permeability is formally defined as