3.1 Understanding stress
To become at all proficient in engineering rock mechanics, it is essential
to understand the concept of stress. Stress is not the same type of
quantity as pressure or force because stress is not a scalar or vector:
it is a tensor quantity. Since a tensor is a mathematical entity that
obeys a certain set of rules, it is not difficult to develop a superficial
understanding of stress. However, it is also important to have a deeper
understanding of why these rules apply, and we have prepared this
chapter to provide that understanding.
Pressure in a fluid is a scalar quantity: this means that it has a certain
magnitude, which is independent of direction, e.g. the pressure in a car
tyre' is 25 lbf/in2 in all directions. Force is a vector quantity: it has
magnitude and direction and must be specified by three components
in the three-dimensional case, usually the three components in three
mutually orthogonal (perpendicular) directions. However, the stress at
a point inside a rock has three components acting perpendicular to the
faces of a cube, and six stress components acting along the faces. The way
in which these components vary as the cube is rotated means that stress
is a tensor quantity and it must be specified in the three-dimensional case
by six independent components. The normal and shear stresses acting on
planes at different orientations inside the rock mass are required for rock
engineering design studies and can be calculated using transformation
equations, as we will illustrate.
The problem with perceiving stress is that humans deal with scalar
and vector quantities during daily life, but not tensors. For example,
temperature is a scalar quantity and wind velocity is a vector quantity,
and so we have no difficulty relating to these concepts. However, stress,
strain, permeability and moments of inertia, which are tensor quantities,
We emphasize that it is the engineering rock mechanics principles that are important.
Once you understand the principles, you can work with any units (such as the Imperial,
or 'British', units used here) and with any symbols. Most of the time we will use SI
(System International) units.