Engineering Rock Mechanics

Questions and answers: intact rock 85

46.9 In 1926, in a paper on tensile tests for cotton yarns (Pierce,

19264), Pierce stated, "it is a truism, of which the mathematical

implications are of no little interest, that the strength of a chain is

that of its weakest link". What is the relevance of this statement to

the tensile strength of intact rock?

A6.9 The statement is relevant because intact rock failure is initiated by
flaws in the rock microstructure. There is a distribution of such flaws
(microcracks and grain boundaries) and so a larger specimen contains a
larger sample of flaws than a smaller specimen, meaning that there is a
greater probability that the large sample will contain the largest flaw.

Chain strength

Predicted 27"

Observed 1 length

120

100

; '. 1

, :t 1; '

(^0) C ; : ,:I I' '
2 80
0- !\, ,'h Observed
$ 60
2.1 p
0- A ..:.
120. 200. 280 ' 360
Breaking load (grams)
In terms of the chain strength, two of Pierce's diagrams are shown
above. The left-hand one indicates how the chain strengths will vary
as a function of the number of links, and the right-hand one presents
tensile strength results for two different lengths of cotton yarn. The same
phenomenon applies to the tensile strength testing of different sized
specimens of intact rock.
(a) when testing many rock specimens under the same conditions, there
will be a distribution of tensile strengths, i.e. a within-test statistical
variation,
@) on average, larger specimens will exhibit lower tensile strengths, i.e.
a within-test scale effect, and
(c) different methods of testing the tensile strength (see diagram on the
next page) will give different results, because there will be different
critically stressed volumes in each test specimen, i.e. a between-test
variation. In the direct tension test, the whole specimen is subjected
to the same tensile stress, and so the whole volume is critically
stressed. In the ring test, only the zones directly above and below the
hole are subjected to the tensile stress.
We note that
Pierce E T. (1926) Tensile tests for cotton yams, V. The weakest link, theorems on the
strength of long and composite specimens. I. Ta. Inst., 17,355-368.