96 Intact rock
It is well known that many materials exhibit a size effect in terms of
strength, with smaller specimens indicating a higher strength than larger
specimens. This was probably first recognized by Leonard0 da Vinci, who
found that longer wires were not as strong as shorter wires of the same
diameter. In more recent times, Griffith (1921) showed that thin filaments
of glass displayed much higher tensile strengths than thick filaments.
Similarly, there are ductility effects as the temperature of a material is
increased.
Thus, it is prudent to consider the effects of specimen geometry, loading
conditions and environment on the complete stress-strain curve. This is
because we need to understand the effects of these variables in order to
be able to predict the mechanical behaviour of rock under conditions
which may differ from those under which a specimen of the same rock
was tested in the laboratory. The discussion below on these effects
describes the general trends that have been observed in laboratory tests
over the years.
6.4. I The size effect
In Fig. 6.11, we illustrate how the complete stress-strain curve varies with
specimen size, as the ratio of length to diameter is kept constant. The main
effects are that both the compressive strength and the brittleness are
reduced for larger specimens. The specimen contains microcracks (which
are a statistical sample from the rock microcrack population): the larger the
specimen, the greater the number of microcracks and hence the greater the
likelihood of a more severe flaw. With respect to the tensile testing
described earlier, it has been said (Pierce, 1926) that "It is a truism, of which
the ramifications are of no little interest, that a chain is only as strong as its
weakest link".
The elastic modulus does not vary significantly with specimen size
because the relation between overall stress and overall strain is an average
response for many individual aspects of the microstructure. However, the
compressive strength, being the peak stress that the specimen can sustain,
is more sensitive to exfremes in the distribution of microstructural flaws in
the sample. A larger sample will have a different flaw distribution and, in
general, a more 'extreme' flaw. Also, this statistical effect will influence the
form of the post-peak curve.
There have been many attempts to characterize the variation in
strength with specimen size using extreme value statistics and, in partic-
ular, Weibull's theory, but it should be remembered that this theory is based
on fracture initiation being synonymous with fracture propagation, which
is not the case in compression. Thus, if extreme value statistics are to be
applied to the analysis of compressive strength, then some form of parallel
break-down model is required, rather than the weakest-link Weibull
approach.
Naturally, a relation needs to be developed between strength and sample
size when extrapolating laboratory determined values of strength to site
scales.