Engineering Rock Mechanics

84 lnfad rock: deformabi/i% strength and failure

Hoek-Brown criterion
We can either simply take appropriate values for the parameters in the
criterion from a table or attempt to statistically fit the criterion to the
data. Using the former method, we have s = 1 and m = 15, and with
O, = 200 MPa we obtain:

03 -13.3 0 5 10 20 50 100

-3.3 200.0 239.5 274.6 336.2 485.9 683.1

Using the latter method, we rearrange the criterion to

(2 - z)’ = m, a3 +s

which corresponds to the linear form y = mx + c, and obtain values for

m and s by linear regression. In this case, we know that s = 1, and so we

perform a linear regression on

while constraining the solution to pass through the origin. The result is a

parameter value of m = 20.5, with corresponding stress values of

03 -13.3 0 5 10 20 50 100

01 -10.4 200.0 251.0 294.6 369.3 545.1 770.9

-20

-100

20 40 60 80 100

Assessment

As the plot above shows, the statistical fit of the Hoek-Brown criterion is

the best of the three criteria. The curvilinear nature of the results means

that the Mohr-Coulomb criterion will never be a good fit over the entire

stress range, and the fundamental behaviour of rock over large stress

ranges means that this is a general conclusion.