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(a)
(b)
(c)
Rock
sample
Jacket
Confining pressure
Fig. 4.79
Sample preparation for fracture tests. Dog-bone samples
for (a) tensile and (b) compression tests. (c) Brazilian test in which
tensile failure is achieved by pressing the sample longitudinally
creating a normal tension.
Fluid pressure
by pressurized fluid. Simpler tensile experiments involve
stretching the sample from the ends under unconfined
conditions (Fig. 4.79a), creating a uniaxial extension or
tension in which
Fig. 4.80
Samples are insulated in a jacket for axial tests in which a
pressurized fluid surrounding the sample is introduced. By jacketing
the sample, the fluid pressure in the pores can be monitored
separately from the confining pressure.
3
is the tensile axial
stress). Similarly the sample can be compressed at the ends
under unconfined conditions, defining a
uniaxial compres-
sion
test in which
1
2
0
3
(
0 (Fig. 4.79b). In rock
mechanics it is of key importance to simulate the confining
pressure of the surrounding rocks (lithostatic pressure)
and fluids (hydrostatic pressure) in the natural environ-
ment and to understand the role of fluids contained in
rock pores. To achieve this,
axial
experiments (one of
the principal stresses is set and progressively increased, the
other two provide the confining pressure) or true
triaxial
tests (all stresses are different, which has been achieved only
recently) are defined and more sophisticated apparatus
needed. Although the test rigs may vary greatly in design, a
typical apparatus for an axial compression test consists of a
pressure vessel in which the sample is confined and pressed
down by pistons (Fig. 4.80) creating a load (
1
2
3
can be produced. Monitoring failure at different states of
stress (confining pressure, main load, or axial stress) it is
possible to construct
failure envelopes
and develop
fracture
criteria
(Fig. 4.81). Fracture criteria are models expressed
as mathematical equations based on empirical data; they
can be either linear or nonlinear (parabolic, as in
Fig. 4.81b). Failure envelopes represent conditions for
fracturing for a particular kind of rock and can be con-
structed joining all points of coordinates
at which
fractures are produced for different settings of confining
pressure differential stress. The failure envelope divides the
Mohr diagrams in two fields: one where the states of stress
are possible or stable and a second in which the states of
stress are not possible (Fig. 4.81). Failure envelopes mark
the rock strength at tension or compression; over this
value rock samples will break making states of stress over
this value impossible. Although there are some problems
inherent in the experimental technique due to the shapes
of the samples, observing and measuring the angle at
which fractures form is important for the construction of
models. Fracture criteria have to satisfy the stress condi-
tions to produce the fractures and predict the angle at
which the fractures form with respect to the principal stress
axes. In the Mohr diagram, the radius of the circle which
joins the tangent to the failure envelope (in both cases lin-
ear and nonlinear) defines the angle 2
n
and
1
). To pre-
pare this setting the sample is protected in a weak easily
deformable cylinder jacket, like rubber or copper
(Fig. 4.80) which insulates it from the surrounding pres-
surized fluid (
0). The sample itself can contain
some fluid in the interstitial pores (a hydrostatic pressure)
and the jacket provides a way to control both fluid
pressures separately. Temperature and both pore and
confined pressures can be adjusted independently and
monitored.
2
3
4.14.5
Fracture criterion and the fracture envelope
, which can be used
to obtain the orientation of the fractures.
is the angle of
Considering the contrasting states of stress which can be
simulated in diverse experiments, several kinds of fractures
the fracture surface with the normal to
1
(Fig. 4.81c)
which is the same angle that the normal to the fracture
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