Engineering Rock Mechanics

38 Stress

body subjected to given loading will depend on the orientation of the cube
in the body itself. We should consider, therefore, the directions in which
the normal stress components take on maximum and minimum values. It
is found that in these directions the shear components on all the faces of
the cube become zero.
The principal stresses are defined as those normal components of stress
that act on planes that have shear stress components with zero magnitude.
It is convenient to specify the stress state using these principal stresses
because they provide direct information on the maximum and minimum
values of the normal stress components-but the orientation of these
stresses must also be specified (remembering that six independent values
are required to specify a stress state).
The values q, o2 and o3 in the matrix in Fig. 3.7 are the principal stresses.
The Arabic subscript notation is used in this book, but it should be noted
that other notations can be used, e.g. oI, oII and oIIr. In our notation, we
make the convention that q > o2 > 03.
The dramatic significance of this principal stress concept for rock
engineering is explained in Section 3.9.

3.9 All unsupported excavation surfaces are

principal stress planes

Not only are the principal stresses and their directions of fundamental

significance in stress analysis, the concept of a principal stress also has

particular significance for rock engineering. This is because all unsupported

excavation suvfaces, whether at the ground surface or underground, have no

Figure 3.7 The stress components on the reference cube and the principal stress

components.