Structural strain can be
observed in a number of ways:
looking at changes in ellipticity,
objects in rock of known
shape, and in folds and
foliations. Strain can be
analyzed through the Rf-, Fry,
and Wellman Methods.
is important to note that, in reality, these
“circular objects” are not perfectly
circular and strain is never perfectly
homogeneous. So, in the field several
measurements must be taken and used to
compute the average ellipticity.
15.1 Measuring Strain in Rocks
Ellipticity R describes the shape and
strain of an ellipse by determining the
ratio of the principal axes:
R= s1/s3 = (e1+1)/(e3+1) = (l1/L)/(l3/L) =
l1/l3
Note: Volumetric Strain can only be
determined
for
very
specific
circumstances.
Only three independent measurements are
needed in the principle plane to define the
shape, size, and orientation of the strain
ellipse: the lengths l1 and l3 and the
orientation angle alpha. (See fig 15.1) The
area of the undeformed circle will also be
the same as the area of the deformed
ellipse:
L= (l1l3), where L is the radius of the
circle. The ratio of the deformed to the
undeformed lengths determine s1 and s3,
the principle stretches.
The simplest and easiest way to determine
strain is to look at initially circular objects
in a rock such as ooids, spherulites, and
radiolaria, and measuring how much they
have deformed. You can use a similar
method with linear objects like acicular
crystals, fossils, and veins, by measured
the amount of deformation compared to
their original shape. Shear strain can be
determined in many fossils with
perpendicular features by measuring the
change in angles of those deformed
features, however this method cannot
determine complete volumetric strain. It
15.3 Measurement of Strain in Folds
The folding process is more complex than
is shown in kinematic models! Studying
ooids alone can lead to underestimation of
total strain from folding.
Foliation patterns in folded layers reflects
diverse strain distribution and there exists
a parallelism between foliation and the
flattening plane in finite strain.
Orthogonal flexure: (see fig. 15.5) These
models show strain distribution around a
fold hinge zone. Model E most accurately
represents the orientation and magnitude
of strains. The orthogonal model best
represents the model for the limbs of a
fold.
In folds, the orientation of foliation and
variations in foliation patterns can the
strain distribution that the fold
experienced while it was being deformed.
15.2 Relationship of Strain to Foliations
and Lineations
Slate is most commonly used to
study the relationship between strain and
foliation/lineations. They preserve fossils
and other strain markers. There is a
parallelism between the plane of
flattening on the strain ellipse and the
slaty foliation.
15.4 Strain in Shear Zones
The bulk principle instantaneous stretch
axes are the sum of the individually
accumulated instantaneous strains on the
shear zones. Equal conjugate sets on each
fault means that averaging over the
volume of the shear zone rock indicates
the principle axes of bulk instantaneous
stretch intersecting the angle between
conjugate shear zones, no matter the
angle. Unequal fault slips indicate that the
principle instantaneous stretch relies on
the relative shear accumulating on the
1
individual fractures. The bulk finite strain
for a rock cut by many shear zones equals
the sum of the average strain for each
shear zone.
Tangent Lineation Diagrams: Show
patterns of shear-plane/slip-direction data
for three instantaneous strain ellipsoids.
In massive crystalline rocks with low to
medium metamorphism, deformation
tends to accumulate along the defined
shear zones. Schistosity tend to form
aligned with these well-defined shear
zones, becoming increasingly foliated
over time. Thee Schistosity is more
developed towards the center of these
shear zones.
In an inhomogeneous progressive simple
shear in the shear zone, the magnitude is
zero at the shear boundaries and goes to
its maximum value at the center of the
zone. If the schistosity is parallel to the
flattening plane, it should exhibit the
characteristic sigmoidal trajectory of the
s1 axis of the resultant strain ellipse of the
deformation.
Models using progressive simple shear are
useful for ductile shear, but can yield
inaccurate results. More complex
deformation models include shortening or
lengthening normal to the shear zone
boundary (often heterogeneous volume
loss or gain). One can often use an
assumption of constant volume, where
lengthening or shortening parallel to the
shear zone boundary compensates the
shortening or lengthening perpendicular
to the boundary.
15.5 Deformation History
In order to determine the deformation
path, one must know information about
the
rock’s
deformation
history.
Determining the finite strain ellipsoid is
not sufficient, as this is the result of the
rock’s deformation history and does not
define a certain deformation path. The
knowledge of this history is necessary to
determine
many
properties,
or
distinguishing between coaxial and
noncoaxial deformation. Features, such as
veins, dikes, metamorphic segregation, or
fibers growing in deformed areas, can be
Brooke Rumley &Michelle Myers, 2011
Edited by Weihan Liu and Billy
incredibly useful in determining the
history of deformation in the rock.
15-A.1
The Rf- Method: Uses objects not
initially spherical (like
deformed
conglomerates) to measure deformation
by looking at original ellipticity and
deformed ellipticity.
Rf(max)= RiRs
Rf(min)=Ri/Rs if Rs Ri
= Rs/Ri if Rs Ri
15-A.2
The Fry Method: Uses the distances
between the centers of objects (ie ooids)
that were initially constantly and
isotropically distributed to provide a
measure of deformation and strain (see
Lab 9).
15-A.3
The Wellman Method: a graphical
construction method for determining
strain. (see fig 15-A.5)
References & Resources
Robert J. Twiss, Eldridge M. Moores,
Structural Geology 2nd edition, (W. H.
Freeman), p. 423-455, 2006
Brooke Rumley &Michelle Myers, 2011
Edited by Weihan Liu and Billy
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