Engineering Rock Mechanics

Questions and answers: intact rock 79

envelope. Firstly, if a fracture forms at 20" to the loading axis, then the
angle between the major principal stress (i.e. the axial stress) and the
normal to this plane is 70". The point on a Mohr circle associated with
the stress state on the fracture surface will then make an angle of 140" to
the major principal stress. The geometry of the failure envelope shows
that the friction angle is then 50".

/

perpendicular to

fl failure envelope

z

0,

In the second test, the axial stress is zero and the confining pressure
is the stress at failure, i.e. the compressive strength. The compressive
strength is simply 85 MPa. Knowing that the friction angle is 50" and the
compressive strength is 85 MPa, we can find the failure criterion in the
required form. The Mohr-Coulomb failure criterion when written in its
principal stress form is 01 = aa3 + b, and so we find that

1 + sin4

1 - sin4

u1 = 1+sin'03+acwitha = = 7.55 and b = uc = 85 MPa.

1 - sin4

46.6 A servo-controlled compression test has been conducted on
a weak soapstone such that the specimen length remained un-
changed throughout: as the axial stress, ua, was increased, so the
confining pressure, p, was increased so that no net axial strain
resulted. A plot of axial stress (vertical axis) against confining pres-
sure (horizontal axis) gave an initial straight line passing through
the origin. At a critical confining pressure of p = 85 MPa (when
ua c 39.1 MPa), the slope of the ua - p plot suddenly changed to 29O
and remained constant for the remainder of the test. This change in
slope may be taken to represent the onset of yield.

(i) Determine an elastic constant from the slope of the initial portion
of the ua - p curve.
(ii) Assuming that the Mohr-Coulomb criterion is applicable, de-
termine uc, c and + for the rock.

A6.6 In this question we are given information regarding two different
types of behaviour: elastic behaviour up to yield, and strength behaviour
after yield (it is a strain-controlled test, and so post-peak behaviour can
be obtained). We are told that before yield - when the specimen is
behaving elastically - the a, - p plot passes through the origin, and
the point (p = 85, a, = 39.1). After yield (i.e. when the specimen has, in
some sense, failed) the slope of the a, - p plot is 29".