Engineering Rock Mechanics

68 Strain and the theory of elasticity

Force transducer signal

Displacement

transducer signals

Servo-valve

._--

I

Laboratory rock testing controlled using load or
displacement feedback (courtesy of MTS Systems
Corp.).

An underground rock pillar be-

ing stressed or strained?

If force is being controlled, then stress is the independent variable
and strain is the dependent variable. Conversely, if displacement is
being controlled, then strain is the independent variable and stress is
the dependent variable. In each case, the independent variable in the
experiment is controlled by the operator.
When in situ rock masses are compressed by tectonic forces, the situ-
ation is not so clear. Also, in rock masses hosting engineering projects,
both stress and strain can be the causative variable. For example, the
stability of a mine pillar can depend on the unloading stiffness of the
rock strata both above and below it, as illustrated in the diagram. Stress
will control failure if, for example, there is a constant loading, as in the
weight of a rock block sliding on a surface. Strain will generally control
failure if the displacement of a stiff rock is causing strain in a soft rock.
The message in this answer is that the controlled or independent vari-
able is determined by the operator in the laboratory, but the causative
variable in the in situ failure of rock masses may not be obvious, or in-
deed a single variable. However, a certain amount of energy is required
for the rock to fail and so it could be argued that the energy (a product
of stress and strain) is the cause.

5.3 Additional points

We have emphasized elasticity theory and the different types of elastic
symmetry because of the widespread use of the theory in analytical and
numerical solutions for the stresses and strains around rock excavations.
When elasticity theory is used in engineering rock mechanics, it is
important to realize the following points.