PROPERTIES OF ROCKS UNDER STRESS
Objectives:- Evaluate the behavior of various rock types when placed under stress and determine specific physical values or modulii characterizing their responses.
DISCUSSION-
Rocks, be they igneous, metamorphic or sedimentary, do not behave in the same
manner when placed in different environments when they are deformed. Deeply
buried rocks exposed to large confining pressures become more ductile than when
they are deformed at shallow depths in low confining pressures. Regardless of
the environment some rocks are inherently weak and others very strong. The
nature and direction of the applied forces also affects the way various rocks
behave. For example, a metamorphic schist will be much stronger when compressed
at ninety degrees- normal- to its foliation than if it was pulled apart - placed
in tension-in the same direction.
Mechanical characteristics of rocks are usually determined in the laboratory
using hydraulic devices which can compress or extend (place in tension) the rock
samples. Because it is difficult to attach testing devices to rock samples for
extension most of this type of work compresses samples. The associated animation
(this is a large file- don't download it unless you have a very fast connection)
provides some idea about what the apparatus looks like and what happens as a
typical sample is compressed. The example shows simple uniaxial compression.
Some laboratories utilize triaxial devices where it is possible not only to
compress the sample parallel to its long axis but also perpendicular to the axis
thus imitating conditions where the sample might lie at great depth within the
earth. This is carried out by changing the configuration of the sample chamber
by placing the sample, now in a soft, copper jacket, between the pistons, as
usual, but closing chamber so the sample can be confined laterally by the
introduction of high-pressure hydraulic fluid around it. Note that in the
animation as the sample is compressed it not only shortens but also increases in
width or bulges. The small diagram - a stress-strain diagram- which appears
after the sample begins to undergo strain (deformation is usually designated
with the shorthand lower case Greek symbol e
-
epsilon
and stress is designated with lower case s
-sigma) plots the amount of stress applied
to the sample (this can be in pounds per square inch (psi), tons/square inch,
kilobars, where one bar is about one atmosphere or in mega Pascals ( MPa) where
one bar = 100,000 Pascals (100 KPa) and 1bar is 100 KPa- one might put 700 KPa in a
high-pressure bike tire) versus the amount of shortening in percent. The stress
applied can be read directly off the instrument and the strain is measured by a
precise caliper-like device attached, but not shown, to the main instrument.
Each rock type, when deformed, displays a different response to stress. These
difference can be represented by variously defined modulii. Each modulus
describes various types of physical responses of the sample. As the sample
deforms it passes through three different types of behaviors: elastic-
recoverable strain- , ductile/plastic- non-recoverable- strain and finally
failure where cohesion is lost between the components of the rock.
To show these responses graphically stress-strain curves ( see below) are plotted from data derived from the compression tests. The horizontal axis is commonly reserved for strain and the vertical axis for stress values.
The avi demonstrates how a sample is deformed. It is suggested that the avi be downloaded and saved on your local computer. Then play it so it runs more smoothly. You may stop it at any time by clicking on the small black square and then dragging the slider with your mouse. Examine the stress/strain curve which appears after the deformation starts. Compare the animation's curve with the one shown just above. Click the small speaker-shaped icon in the extreme lower right-hand side of your computer screen to mute the sound if it's annoying.
The elastic (Hookean) portion of the curve is approximately linear where strain is proportional to stress The ductile part is broadly curved. Here strain is not directly proportional to stress. The loss of cohesion is shown where the sample fails and stress falls to zero.
As mentioned above, the
response of a particular type of rock to applied stress can be described by
various quantitative values or modulii. Among the most widely used are Young's
modulus, Poisson's ratio, rigidity modulus and bulk modulus.
Young's modulus 'E' is applied to so-called Hookean solids where
strain is proportional to applied stress. This
value can be extracted from the first portion of the stress-strain curve where
the relationship is linear. One simply divides stress in whatever units is
desired by the amount of strain (0.1% = .001). Thus if on the linear part of the
curve the sample shortened 0.1% when 0.5 kbar stress was applied E = 0.5 kbar/
.001 = 500 kbar.
Poisson’s ratio 'n ' is a measure of how much the sample increases in its lateral dimension as it is compressed axially. This is determined by measuring the lateral shortening and dividing it by the axial shortening. Only axial strain can be extracted from our stress-strain curves so a little extra data must be provided to derive Poisson’s ratio. If a sample were an ideal incompressible sample where no volume change occurs under strain the Poisson’s ratio is 0.5. In reality the Poisson’s ratio of rocks is less than 0.5.
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