Engineering Rock Mechanics

78 lntacf rock: deformabiliv, strength and failure

From this, we see that (rc - rt)/(rc + r,) = sin +, and upon rearrangement
we obtain rc/rt = (1 + sin#)/(l - sin#).
Finally, as each of rc and r, is one half of the corresponding compress-
ive and tensile strengths, we find that aC/q = (1 + sin #)/(1 - sin+).
Clearly, the commonly held belief that the compressive strength of
rock is about ten times the tensile strength will only be true for a
particular value of the friction angle. Indeed, we can graph the equation
above, as shown below.

12.0 14'01

0.0 4

0 10 20 30 40 50 60

Friction angle, degrees

This shows that aC/q = 1 for + = o", and aC/q + 00 for + = 90".

Furthermore, we can see that aC/q = 10 for the specific case of # = So,

and that for the more frequent case of # = 35" we have q/at = 3.7.

The difficulty with the relation arises because rock failure modes in

compression, tension and shear are different 3.

Q6.5 A firm whose judgement has been questioned on a previous

occasion has been entrusted with the strength testing of rock in

a site investigation project. During their first uniaxial compression

test, the equipment failed to measure the peak axial load, but the

technician did record that the specimen failed by the formation of a

single fracture inclined at ZOO to the loading axis. In a subsequent

triaxial test, as the confining pressure was being increased before

application of the axial stress, the specimen failed prematurely

when the confining pressure in the Hoek cell was 85 MPa. On

the basis of these results, propose a failure criterion of the form

cr1 = au3 + b for the rock.

A6.5 The two tests, although incorrectly performed, do give us informa-

tion about the strength of the rock in terms of the linear Mohr-Coulomb

Cohesion is the resistance to failure in shear; adhesion is the resistance to failure in

tension. Under uniaxial loading, rocks break perpendicular to the least principal stress -

perpendicular to the loading in tension and parallel to the loading in compression. Thus,

we see that both cohesion and adhesion play a part in determining the strength of the

rock.