Specimen geometry, loading conditions and environmental effects 1 0 1may be predicted. Indeed, the probability density function for any
test condition can be established and hence the inter-test variation can
be predicted. One of the most useful formulae to arise from this approach
is
where otl and ot2 are the mean tensile strengths obtained for two sets of
samples with different volumes (for any test configuration), Vl and V, are
the associated specimen volumes, and m is one of the three material
constants used in Weibull's theory. This provides a direct relation between
the mean tensile strength and the specimen volume.
At this stage, we should like to caution the reader. Weibull's theory is
solely statistical and does not include any specific mechanism of fracture or
failure. Moreover, the formula above is represented by the ubiquitous
straight line in log-log space. There have been several published 'verifica-
tions' of the theory, based on straight lines in log-log space, but these
results alone do not isolate Weibull's theory. Indeed, any such confirmation
for the validity of the formula in compression tests is highly unlikely to be
valid because of the distinction between failure initiation and failure
propagation in the compression test.
This cautionary note related to the avoidance of blind acceptance
of any particular theory based on power laws (and material constants
which can be determined by curve fitting) applies to all rock testing, and
particularly to failure criteria (which we will be discussing later in this
chapter).
Another factor altering the shape of the complete stress-strain curve in
compression is the effect of the confining pressure applied during a
test, which can be quite pronounced. The general trend is shown in
Fig. 6.15.
The most brittle behaviour is experienced at zero confining pressure:
the curve demonstrates less brittle behaviour (or increasing ductility)
as the confining pressure is gradually increased. At one stage in this
trend, the post-peak curve is essentially a horizontal line, representing
continuing strain at a constant stress level; or, in the interpretation
of a strain controlled test, the strength is not affected by increasing
strain. Below this line, the material strain softens: above this line strain
hardening occurs. The horizontal line is termed the brittle-ductile
transition.
Although it may be thought that this transition would only be of interest
to geologists considering rocks subjected to the high pressures and temper-
atures that exist at great depths, there can be engineering circumstances
where the transition is of importance. This is because the confining pressure
associated with the brittle-ductile transition varies with rock type and is
low in some cases. Coupling this with the increasing depth at which some
projects are undertaken can mean that the transition is important. Note that
the transition also represents the boundary between instability with
increasing strain (brittle behaviour) and stability with increasing strain
(ductile behaviour).