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(a)
Hydrostatic stress
(b)
Uniaxial compression
(c)
Uniaxial tension
t
t
t
s
1
=
s
2
=
s
3
s
1
s
n
s
1
=
s
2
=0
s
1
=
s
2
= 0
s
n
s
n
s
3
Axial compression
s
1
>
s
2
=
s
3
Triaxial stresses
s
1
>
s
2
>
s
3
(d)
(e)
(f )
t
t
Pure shear
t
s
2
= 0
s
1
= -
s
3
s
n
s
n
s
1
s
3
s
3
s
2
s
1
s
1
s
2
=
s
3
s
2
s
n
s
1
0 0
0
s
2
0
0 0
s
3
s
1
0 0
0 0 0
0 0 -
s
3
Fig. 3.74
Mohr circle diagrams for different states of stress.(modified from Twiss and Moors, 1992).
rocks in which all the tractions have the same value as the
vertical load, should similarly be represented by a point.
Uniaxial compression
occurs when a body of rock is
compressed in a unique direction and unconfined laterally.
This situation is not common in Nature but is used broadly
in experiments in the laboratory to test mechanical proper-
ties in rocks and other materials applied not only to struc-
tural geology but also engineering problems. The principal
stresses in uniaxial compression are
Axial stresses
, both extensional and compressive, are
those in which there is a confining pressure and an applied
stress of different value in one direction. An
axial compres-
sion
is defined by
0 is
the value of the confining pressure; whereas an axial exten-
sion or extensional stress is characterized by
1
2
3
1
2
3
0, where
2
3
0 (Fig. 3.74d). Both axial stresses are
plotted in the right-hand-side of the Mohr diagram as all
values for the normal stresses are positive.
Triaxial stresses
are those in which all three principal axes
have different values either positive or negative:
1
2
3
. Triaxial stresses are represented by three
circles, the bigger one confined between
1
2
3
0 and
are represented by a Mohr circle tangent to the
-axis and
in the right, positive side (Fig. 3.74b).
Uniaxial tension
is produced by pulling a rock body in
one direction. As for uniaxial compression, it is a favorite
experimental condition in rock mechanics. The main stress
axes have values
3
and the
other smaller ones included in the bigger circle, one con-
fined between
1
and
1
2
0
3
. The Mohr circle will
3
(Fig. 3.74e). A special example of triaxial stress is
pure
shear stress
in which all main stresses are different, but
2
1
and
2
and the other between
2
and
be tangent to the
-axis but will be located in the negative
normal stress field at the left side (Fig. 3.74c). Notice that
both the uniaxial compression and extension allows the
definition of a differential stress and so there are shear
stresses
1
3
(Fig. 3.74f); note that the surfaces
corresponding to the maximum value of shear stress are
those whose value for the normal stress is zero.
0 and
0 for different directions.
3.14
Solid strain
3.14.1
Kinematics of solid deformation
deformation. When stresses are applied to a volume of
rock the outcome depends pretty much not only on the
magnitude of the stress but also on the nature of the rock
and external circumstances such as temperature, confining
pressure by loading, fluid pressure in the pores, and so on.
If a certain threshold of inner resistance of the rock or rock
strength is attained, deformation occurs, otherwise the
rock remains unaltered. If the rock is affected by applied
stress, several alternative situations can happen. There are
Deformation kinematics is the study of the reconstruction
of movement that takes place during rock deformation at
all scales of observation. Kinematics is not concerned with
magnitude and orientation of stresses in terms of dynam-
ics, it just describes the displacements that the rock suffers
as stresses are applied to them. First of all, it is important
to distinguish between the concepts of rigid and nonrigid
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