The state OF stress at a point has six independent camponents 37If we consider the stress matrix again, we find that it is symmetrical about
the leading diagonal, i.e. the diagonal from top left to bottom right. The
matrix below shows this symmetry after the equality of the respective shear
components has been taken into account:
It should be noted that we have considered only the stress components
that exist at a point, their equilibrium, and the method of listing them in
the matrix. We have not yet considered how the actual values of these
components would change as the reference cube is rotated. We emphasize
this because the discussion here is completely general and applies to the
stress state at any point anywhere in any rock mass, or for that matter, in
any material that can sustain shear stresses.
3.7 The state of stress at a point has six
independent components
From our final listing of the stress components in the matrix at the end of
Section 3.6, it is clear that the state of stress at a point is defined completely
by six independent components. These are the three normal stress
components and three shear stress components, i.e. o,,, oyy, ozz, qy,
:vz and qZ.
The fact that the state of stress is completely specified by six independent
components is important and has direct ramifications for the stress
measurement methods discussed in Chapter 4. Note that a scalar quantity
can be completely specified by one value, and that a vector quantity can
be completely specified by three values. However, the stress state at a point,
which is a tensor quantity, requires six values.
Furthermore, it should be noted that stress is not the same as pressure.
The word 'pressure' should be reserved for a specific stress state in which
there are no shear components and all the normal components are equal-
as exists in a static fluid, which can sustain no shear stress. Pressure is a
scalar quantity because it can be completely specified by one value; the
stress state, on the other hand, requires six independent components.
The stress state can be specified with reference to a given set of x-, y- and
z-axes via the components we have expfained, or via the magnitudes and
directions of the principal stresses which are explained in Section 3.8.
Whatever method is used to specify the stress state, there must be six
independent pieces of information.
3.8 The principal stresses
The stress components in the stress matrix are the three normal stresses and
the three shear stresses. The actual values of these components in a given