Engineering Rock Mechanics

100 lntact rock

Frequency

Aut)

The tensile strength variation is of three main types:

Brazilian test

(a) variation with repeated testing;

(b) variation with different volume; and

(c) variation between tests.

The first type of variation occurs because each rock specimen contains a
statistical sample of flaws from the total microstructural flaw population.
The severity of the worst flaw present in each specimen taken from a set
of specimens, all obtained from the same rock block, will be highly variable.
Thus, if, say, 50 tensile strength tests are repeated, there could well be a
wide variation in the^50 values, from which we can determine the mean
and standard deviation.
The second type of variation occurs because the larger the statistical
sample, the greater the likelihood of a more severe flaw. Hence, if we were
to conduct another 50 tests on larger sized specimens, but utilizing the same
type of tensile strength test, we would also obtain a distribution of test
results, but both the mean and the standard deviation would be lower, as
illustrated in Fig. 6.14.
The third type of variation, the inter-test variation, occurs because the
critically stressed volume in each test is different. So, if a set of tensile
strength results obtained using one test is compared with those obtained
from another test, again there is a difference between the histograms of test
results, as also illustrated in Fig. 6.14.
The curves in Fig. 6.14 can be related via statistical theories. For example,
in Weibull's theory, the probability of failure is integrated over the critically
stressed volume, taking the variation in tensile stress into account.
This enables the basic probability function for a test to be specified and
hence the probability density curves in Fig. 6.14 to be characterized. The
variation in the probability density function can be established as a function
of test volume and hence the change in density curves with volume

ut - tensile strength

Figure 6.14 Tensile strength variation as a function of specimen volume and type

of test.