48 In situ rock stress
The expected stresses, a,, are given by
OA = 7.56 MPa, aB = 6.94 ma, ac = 7.37 MPa, UD = 7.19 MPa, and
UE = 7.96 MPa.
These are not the same as the measured values and so a least-squares
solution should always involve computation of the errors involved, as
described in statistical textbooks.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, Ps Shut-in pressure, PS
(m) (MPal (MPal
500 14.0
1000 24.58.0
16.0Given that the tensile strength, ut, of the rock is 10 MPa, estimate
and list the values of ul, u2 and 63 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 iustify your reasons for
the statement. Are the results in agreement with trends exhibited by
collated worldwide data?HydraulicA4.6 Using the hydraulic fracturing
stress measurement technique, a por-
tion of a borehole, say a 1 m length, is
sealed off. Water in this borehole portion
is pressurized until the rock fractures,
giving the breakdown pressure. Then,
the pressure required to just keep the
fracture open is measured, giving the
shut-in pressure (see sketch to the right
of a cross-section through a borehole).
The assumptions required for hydrau-
lic fracturing are:
(a) one principal stress is vertical, which is usually acceptable unless in
hilly terrain;
(b) the vertical stress is due to the weight of the overburden, which is
usually a reasonable approximation unless in local problem areasqrre Borehole
t