Engineering Rock Mechanics

41 0 Questions 4.1-4.70: in situ rock stress

jacks 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.

44.5 Two further flatjack measurements have been made in the wall of

the tunnel considered in Q4.4. These dip at 20" and 90" relative to the

tunnel axis, and produced cancellation pressures of 7.38 MPa and 7.86

MPa, respectively. Compute the best estimate of the principal stresses.

44.6 The stress in a granitic rock mass has been measured by the

hydraulic fracturing technique. Two tests were conducted in a vertical

borehole: one test at a depth of 500 m, and the other test at a depth of

1000 m. The results were as follows:

Depth Breakdown pressure, PB Shut-in pressure, Ps

(4 (ma) (MW

500 14.0 8.0

1000 24.5 16.0

Given that the tensile strength, a,, of the rock is 10 MPa, estimate and list

the values of al, az and a3 at the two depths.

State all of the assumptions you have to make in order to produce

these estimates. Are any of them doubtful? State whether the two sets

of results are consistent with each other, and justify your reasons for the

statement. Are the results in agreement with trends exhibited by collated

worldwide data?

44.7 How are three-dimensional tensors transformed so that the stress

components on any plane can be calculated?

44.8 Suppose that we have measured the pre-existing stress state in the

ground by some means and that the results are as follows:

01, magnitude 15 MPa, plunges 35" towards 085";

az, magnitude 10 MPa, plunges 43" towards 217";

a3, magnitude 8 MPa, plunges 27" towards 335".

Find the 3-D stress tensor in the right-handed xyz

co-ordinate system with Right-

handed

co-ordinate

system

x, horizontal to the east,

y, horizontal to the north,

z, vertically upwards.

44.9 A fault is present in the same rock (continuing from 44.8) with

an orientation of 295"/50". Determine the stress components in a local

co-ordinate system aligned with the fault. Assume for this question that

the presence of the fault does not affect the stress field.