Engineering Rock Mechanics

32 Stress

43.5 What is a principal stress plane? What is a principal stress?

A3.5 A principal stress5 plane is a plane on which there are no shear
stresses. A principal stress is the normal stress acting on a principal
stress plane. In 3-D, the three principal stresses are written as 01, 02,
and a3, in order of the largest value, intermediate value, smallest value,
respectively. For any given stress state, the maximal and minimal normal
stresses occur on the principal stress planes: see where 01 and 02 are
plotted on the Mohr circle above for the 2-D case.
In Chapter 16 of ERM 1, we explained that all unsupported rock
excavation surfaces are principal stress planes, because there are no
shear stresses acting on them. Thus, one of the effects of excavation is
to define locally the orientations of the principal stresses, i.e. they will
be parallel and perpendicular to the excavation surfaces. Moreover, the
principal stress component acting normal to unsupported excavation
surfaces is also zero.
When the principal stresses at an excavation surface are shown in the
stress matrix (with the z-axis perpendicular to the excavation surface),
most of the terms have zero value.

Principal stresses parallel to excavation

[::f- 0 0, 0 surface

Principal stress

excavation surf

=O

This is for the case where there are no tensile stresses in the rock, i.e.

the a3 value of zero is the lowest of the three principal stresses.

43.6 What are the following stress states: uniaxial stress, biaxial
stress, triaxial stress, polyaxial stress, pure shear stress, hydrostatic
stress?

A3.6 These terms are commonly used to describe the stress states
applied to laboratory test specimens.

Do not use 'principle stress'! The correct term is 'prinapal stress'.