Geoscience Reference
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cylindrical rock samples. Both tensional (the sample is gen-
erally pulled along the long axis) and compressive (sample
is pushed down the long axis) stresses can be applied, both
in laterally confined (axial or triaxial tests) or unconfined
conditions (uniaxial texts). Experiments involving the
application of a constant load to a rock sample and observ-
ing changes in strain with time are called
creep tests
.
Experimental results are analyzed graphically by plotting
stress, (
3.15.2
Elastic model
Elastic deformation
is characterized by a linear relationship
in stress-strain space. This means that the relation between
the applied stress and the strain produced is proportional
(Fig. 3.91a). An instantaneous applied stress is followed
instantly by a certain level of strain. The larger the stress
the larger the strain, up to a point at which the rock can be
distorted no further and it breaks. This limit is called the
elastic boundary and represents the maximum stress that
the rock can suffer before fracturing. If the stress is
released before reaching the elastic limit such that no frac-
tures are produced, elastic deformation disappears. In
other words, elastic strained bodies recover their original
shape when forces are no longer applied. The classical ana-
log model is a spring (Fig. 3.92a). The spring at repose
represents the nondeformed elastic object. When a load is
/d
t
), the
latter obtained by dividing the strain by time (Fig. 3.91).
Simple mathematical models can be developed for different
regimes of rheological behavior. Stress is usually repre-
sented as the differential stress (
), against strain, (
), or strain rate (d
1
3
). Other important
variables are lithology, temperature, confining pressure,
and the presence of fluids in the interstitial pores
causing
pore fluid pressures
. There are three different pure
rheological behavioral regimes:
elastic, plastic
, and
viscous
(Fig. 3.91). Elastic and plastic are characteristic of solids
whereas viscous behavior is characteristic of fluids. Solids
under certain conditions, for example, under the effect of
permanent stresses, can behave in a viscous way. Elastic,
plastic, and viscous are end members of a more complex
suite of behaviors. Several combinations are possible, such
as
visco-elastic, elastic-plastic
, and so on.
(a)
(a)
Elastic
(b)
Viscous
(b)
h
t
d
e
/d
t
=
E=
s
/
e
Strain rate d
e
/d
t
Strain (
e
)
Object is static
(c)
Plastic
(c)
s
<
s
y
s
y
s
>
s
y
Object moves
Strain (
e
)
Fig. 3.91
Strain/stress diagrams for different rheological behaviors.
(a) Elastic solids show linear relations. The slope of the straight line
is the Young's modulus; (b) viscous behavior is characteristic of flu-
ids. Fluids deform continuously at a constant rate for a certain stress
value. The slope of the line is the viscosity (
Fig. 3.92
Classical analogical models for (a) elastic behavior, is
compared to a spring; (b) viscous behavior is compared to a
hydraulic piston or dashpots; and (c) plastic behavior, like moving
a load by a flat surface with an initial resistance to slide.
); (c) plastics will not
deform under a critical stress value or yield stress (
y
).
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