Engineering Rock Mechanics

Questions and answers: in situ rock stress^45

A4.3 TheJatjack method measures one normal stress; so, given that the
stress tensor has six independent components, six set-ups are required
(at different orientations).
Conventional hydraulic fracturing in a vertical borehole measures two
values, the principal stresses are assumed to be parallel and perpendicu-
lar to the borehole axis, and the vertical stress value is assumed on the
basis of gravitational stress. As a result, with two measured values and
the equivalent of four assumptions, only one set-up is required to estab-
lish the stress tensor components. For the hydraulic testing of pre-existing
fractures (HTPF), the borehole does not have to be parallel to a principal
stress and one normal stress is measured each time, similar to the flatjack
method; so six set-ups are required, but each must use a fracture at a
different orientation.
The USBM overcoring gauge provides three values in a plane; so two
set-ups are required in two boreholes at different orientations.
The CSIRO overcoring gauge provides at least six values; so one set-up
is required.

44.4 Three flatjack tests have been made close to each other in

the wall of a long, straight tunnel, the axis of which dips at 7O. The

measurement position is approximately 250 m below the ground

surface and it is assumed that the flatjacks are in the same stress

field. The slots for the flatjacks were cut normal to the wall of the

tunnel, and were oriented relative to the tunnel axis as shown.

The cancellation pressure for each of the flatjacks A, B and C

was 7.56 MPa, 6.72 MPa and 7.50 MPa, respectively. Compute the

principal stresses and their directions, and ascertain whether they

accord with worldwide trends.

A4.4 One way of solving this problem is to use the stress transformation

equations, i.e.

ai = a, cos2 e + ay sin2 8 + 2tx, sin 8 cos e

where a,, ay and txy are the global stress components, and 8 is the angle

between the global x axis and the direction of the stress in question.

Taking the x axis horizontal directed to the right, and the y axis vertical

upwards, and all orientations measured anticlockwise positive from the

positive x axis, we have the following dip angles:

= -7"; PA = -40" + Btunnel = -47";

= 0" + /?tunnel = -7"; BC = 52" + Btunnel = 45".