Engineering Rock Mechanics

Questions and answers: intact rock 81

14.5 MPa

I

axial stress

The principal stress form of the Mohr-Coulomb criterion tells us that

1 +sin$ tan61 - 1

tan61" = or sin4 =

1 - sin4 tan61 + 1 '

giving 4 = 16.7'.

c = a,( 1 - sin 4)/(2cos I$), with the result that c = 5.4 MPa.

And finally we have a, = (2ccos4)/(1- sin#), from which we obtain

Q6.7 laboratory tests on specimens of a limestone have produced
unconfined compressive and tensile strengths of 80 MPa and 10 MPa,
respectively. Using the Hoek-Brown and plane Griffith criteria, es-
timate the maximum principal stress at failure for two biaxial tests
in which u2 = 20 MPa and u2 = 40 MPa. Which of these two criteria
would best predict peak strength under these conditions?

A6.7 We are told that a, = 80 MPa and at = -10 MPa (noting that our
sign convention is compression-positive).

Hoek-Brown criterion
If we substitute 03 = a, and a1 = 0 into the Hoek-Brown criterion,
a1 = a3 + (ma,a3 + SU,~)O.~, and rearrange the resulting equation, we find

a: - a,"

m = -.

atac

Here, we are dealing with intact rock, and so s = 1. Consequently we
find that m = 7.88.
For the biaxial tests, we have been given values for a2 and asked to find
values for (TI. As the tests are biaxial, we can presume a3 = 0. However,
the Hoek-Brown criterion ignores the effect of the intermediate principal
stress.
We could estimate the magnitude of the major principal stress at
failure either assuming a2 = a3 = 0 or 02 = a3 = p. The first of
these represents uniaxial compression, the second represents triaxial
compression. The case of uniaxial compression will simply give the