Engineering Rock Mechanics

Questions and answers: intact rock 83

but the Hoek-Brown criterion is for strength (i.e. a structure breakdown

criterion), whereas the Griffith criterion relates to the onset of fracturing.

As the onset of fracturing occurs before peak strength and usually well

before complete failure, perhaps the Hoek-Brown criterion is the better

of the two. However, it is more likely that the peak strength will lie

somewhere between the two sets of results.

46.8 Comment on the applicability of each of the Griffith, Mohr-

Coulomb, and Hoek-Brown criteria for the following triaxial test

results on quartzite:

(a1 +a3)/2 -6.65 100 135 160 200 298 435 MPa

(a1 -a3)/2 6.65 100 130 150 180 248 335 MPa

A6.8 The first step is to convert the given data into principal stress
values:

(al +a3)/2 -6.65 100 135 160 200 298 435

(ar -a3)/2 6.65 100 130 150 180 248 335

a1 0 200 265 310 380 546 770

a3 -13.3 0 5 10 20 50 100

From the final two rows of the table we can see that ot = -13.3 MPa

and a, = 200 MPa. The values of 01 and a3 are plotted at the end of this

answer.

Grifji’th criterion

The relevant expression for the Griffith criterion in compression is

(a1 - ad2 = STo(a1 + a3)

where compression is positive and To is also positive. For given values

of a3 we need to compute values of 01, using a value of To = 13.3 MPa.

The result is

a3 -13.3 0 5 10 20 50 100

01 39.9 106.4 120.6 133.6 157.4 219.3 308.5

Mohr-Coulomb criterion

The data are clearly curvilinear, whereas the Mohr-Coulomb criterion is

linear. As a result, the Mohr-Coulomb criterion will not be a good fit to

the data, at least not over their entire range. However, if we wish to fit a

straight line to the data, the results are

a3 -13.3 0 5 10 20 50 100

(TI 118.6 201.0 232.0 263.0 324.9 510.9 820.7