Engineering Rock Mechanics

82 lnfad rock: deformabili% strength and failure

A Shearstress,r Effect of intermediate principal stress magnitude is

in the Hoek-Brown criterion

Normal stress,

unconfined compressive strength, and so it is worthwhile investigating

the triaxial compression case.

Thus, for 02 = 03 = 20 MPa we find that

u1 = 20 + J7.88 x 20 x 80 + 1 x SO2 = 157.8 MPa

and for 02 = a3 = 40 MPa we find that

a1 = 40 + J7.88 x 40 x 80 + 1 x 802 = 217.8 MPa

However, it is likely that these will both be over-estimates of the major

principal stress at failure.

Griflth criterion

There are two expressions for the Griffith criterion in compression:

(a1 - 03)~ = 8To(al + u3)

a3 = -To

when a1 + 3a3 > 0

when a1 + 3a3 < 0

and in both of these compression is positive and To = -at is also

positive.

As with the Hoek-Brown criterion, the Griffith criterion ignores the

effect of the intermediate principal stress, and so neither of these criteria

is valid for biaxial compression. Again, we will need to make the

assumption that the biaxial conditions in the tests may be represented

by triaxial conditions in the Griffith criterion. Rearranging the first of the

Griffith criterion equations gives us

from which, on substitution of To = 10 MPa and the appropriate value of

a3, we can determine the major principal stress at failure.

Thus, for 9 = a3 = 20 MPa we find that

61 = 20 + 4 x 10 zk 4J10 x 20 + lo2 = 129.3 MPa

and for a2 = a3 = 40 MPa we find that

01 = 40 + 4 x 10 f 4J10 x 40 + 1@ = 169.4 MPa.

Assessment

Determining which of these criteria is the best predictor of peak strength

is difficult. Strictly, neither of the criteria are valid for biaxial conditions,