**Strain Determination in Conglomerates**

©
Copyright, 2001 by R.A.Kanen, All Rights Reserved

An
important aid to the geologist in analyzing rock deformation is the rock
particles which contain the stress history of the rock, in the form of strain.
Analysis of such particles may enable the geologist to determine the finite
strain, initial shape and orientation of the particles. The ideal strain marker
is an originally spherical body which has the same ductility as its host,
because it’s final shape is that of the strain ellipsoid itself and this will
determine the state of strain. Robin (1977) defines a strain marker as follows,
"Strain markers are geologic bodies within a rock which, during the
deformation of that rock, have retained their identity but did not differ from
their surrounding material in their mechanical behavior." Cloos (1947)
study of deformed ooids came very close to the ideal state, however, there are
departures from the ideal state and these may be of two kind: (1) there may be
ductility contrast between the strain marker and the host rock, (2) there is no
ductility contrast but the initial state of the strain markers is not
spherical. In the case of conglomerates, the shape of the constituent particles
is generally non-spherical, sub ellipsoid, but may vary. The ductility contrast
will vary between the situations where there is no ductility contrast to where
there is an extreme ductility contrast. Therefore, there can be many problems
encountered in the strain analysis of conglomerates.

**No Ductility Contrast**

Gay
(19698a) has shown that the viscosity ratio between a particle and the mean
viscosity of a particle/matrix system is dependent on the relative population
of particles and matrix present. Thus, in conglomerates, where the proportion
of pebbles to matrix is high, the ductility contrasts are probably low;
therefore, assuming the ductility contrasts are negligible it should be
possible to determine the following: (a) the initial shape of the particle; (b)
the initial axial orientation; (c) the strain intensity; and (d) the strain
orientation.

Since
the initial shapes of particles within the conglomerates are unknown simple
finite-strain analysis is not possible. Analysis of such particles requires the
following assumptions: (1) an adequate number of particles in the rock having a
variety of shapes; (2) an initially isotropic fabric so that the particles were
randomly orientated; and (3) the rock underwent no volume change. In the
treatments Ramsey and Dunnet (1969) use, a further assumption is necessary.
This is that the initial shape be ellipsoid. Robin (1977) has illustrated a
method where it is not necessary fore the particle shape to be ellipsoid.

**Dunnet's Method**

Dunnet's
(1969) method of strain analysis involves plotting an Rf (final deformed
particle axial ratio) vs f (angle from
the Rf long axis to the maximum principle strain direction or reference
direction) graph. The procedure adopted to determine the finite strain value
(Rs) is as follows.

Firstly,
the mean of both the Rf and f
axis is determined. The angular mean should coincide with the orientation of
the principle strain trace and with the maximum and minimum plotted Rf values.
The mean of the Rs values does not coincide with Rs but will be a slightly
higher value. The intersection of mean v and logarithmic mean Rf is considered
as the finite strain value (Rs). The number of points in each of the four
quadrants is counted and should be equal. If not, they define one type of
asymmetry. Lack of coincidence of f
mean with the maximum and minimum Rf values define a second type and lack of
coincidence of f mean and the
principle trace is a third type of asymmetry. If the diagram is reasonably
symmetrical, the appropriate Rf/v curves are filled to the data. A number of
such curves have been determined by Dunnet for a given Rs value. The curves are
adjusted to the visual best fit. For asymmetric diagrams, or where initial
orientation of particles in bedding is suspected, the position of the bedding
trace must be considered. Particles with their initial long axes at a high
angle to the maximum strain axis will produce Rf/f ratios less than the strain ratio (Ri). Particles
at a low angle to the maximum strain direction will produce Rf/f ratios greater than the strain
ratio. Strain ratios from the three principle planes xy, yz and xz can be
compared and, if not consistent, may be recalculated.

The
main factors which affect the interpreted value of Rs are the effects of: (1)
initial orientation of particles; (2) superimposed deformation; (3) rotational
strain; (4) ductility contrasts; and (5) inhomogeneous strain over the
specimens analyzed. Initial preferred orientation and superimposed deformation
produce artificially similar results. Ramsay (1967) has illustrated that an
initial planar oriented fabric produces an Ri/f distribution to Rf/f curves. Thus, modification of an initially
preferred oriented fabric is similar to the modification of a fabric produced
by earlier deformation. In the case of an initial oriented fabric which has
undergone deformation the final fabric is generally asymmetric. However, if the
initial fabric is perfectly planar the Rs value, as in the case of a
superimposed fabric, is the finite product of the initial and secondary fabric.

In
an example, Dunnet cites that it is impossible to determine whether two strains
have produced a fabric unless additional evidence, such as cleavage oblique to
the total finite strain orientation is present. He also cites that perfect
initially planar fabrics are extremely uncommon; therefore, the finite strain
orientation of an initially oriented fabric will almost always be asymmetric.

Rotational
strain similarly produces a finite strain oblique to the axes and it will also
be less than the product of the strain increments. Therefore, finite strain can
be derived for both irrotational and rotational strain.

The
presence of inhomogeneous strain on the scale of a single thin section is
uncommon. If present, the sample should be avoided. Inhomogeneous strain can be
recognized by visual inspection since a gradational variation in the strain
intensity necessitates a variation in the strain orientation. Therefore,
divergence of cleavage may indicate inhomogeneous strain.

In
summary, comparison of the deformed fabrics of initially non-spherical
sub-ellipsoid particles with a theoretical analysis of ellipses deformed by
homogenous strain allows determination of the finite strain and initial axial
ratio. Samples of several particle lithologies should be avoided or measurement
restricted to particles of a single lithology. Similarly, specimens showing
initial preferred orientation in bedding should be avoided or treated with
caution. Furthermore, samples collected from areas of rotational strain or
superimposed deformation should be analyzed with care.

**Robin's Method**

Ramsay
(1967, Dunnet (1969) and Shimamoto and Ikeda (1976) have all developed methods
to obtain strain when the strain markers are assumed randomly oriented and are
ellipsoids of unknown initial axial ratio. Robin (1977) has removed one of
these restrictions in order to calculate strain; that is, the strain markers
are not necessarily ellipsoid but may be of any shape. Of course, ellipsoid
particles may also be used. Robin's method requires the following assumptions:
(1) an adequate number of particles within the rock having varied shape; (2) no
ductility contrast between the particles and host rock; (3) an initially
isotropic fabric so that the particles are randomly oriented; and (4) the rock
underwent no volume change. These assumptions are less restrictive than those
of Ramsay and Dunnet.

Robin's
treatment is restricted to two dimensions, however, results obtained from
several planar directions may be combined into a single three dimensional
model. Robin designates the maximum and minimum strain directions as l 1 and l 3 respectively. Through the
centre of gravity, c, of each unstrained marker, two diameters, parallel to the
1 and 3 directions, can be drawn. Therefore, in each marker, j, a diameter aj,
parallel to the 1 direction, and a diameter cj, parallel to the 3 direction are
present. In the strained state, these diameters are defined as aj' and cj'.
Robin mathematically proves the following:

(sum
from j=1 to n) log (aj'/cj') n log (sqr(l
1/l 3))

Therefore,
the diameter aj' and cj' are measured on n strain markers, the ratios aj'/cj'
calculated, and the axial strain ratio is given by their logarithmic average.
The method requires that the strain directions of 1 and 3 be known. They could
be found by evaluating the equation for many directions and choosing the
direction for which its value is the maximum. However, it is simpler and
probably sufficient to estimate the direction of maximum principle strain from
the trace on a planar section of a foliation, or from a histogram of directions
of the longest diameter of each deformed marker.

Robin
says, " A difficulty arises from the fact that the center, c, for each
marker must be determined in the strained state rather than in the undeformed
one. He goes on to say, " However, the center of gravity is not easy to
determine, except for centrosymmetric markers, such as ellipsoids. Other rules
to choose a center, such as the midpoint between two points that are the
farthest apart on the contour of the marker are much easier to use. However,
because this determination must be made in the strained state rather than in
the unstrained state, and because two markers which were initially identical
except for a rotation, are no longer identical in the strained state, the
centers determined by such rule would not coincide in the two
"destrained" markers", and, " For most markers it is
unlikely that choosing centers with such a simple rule would lead to
significant errors in practice, as a/c is generally not very sensitive to the
exact location of c."

If
the assumptions made earlier are upheld then only one major problem in the
strain analysis of conglomerates becomes apparent. That is, like most methods
of strain analysis, only the total strain will be determined in situations
where an initial preferred orientation of particles in bedding or deformation
is present. In the case of ellipsoid strain markers, a randomness test (See
Robin, 1977) may be used to detect an initial fabric. For non-ellipsoid
particles, it is impossible to determine an initial fabric; therefore,
restricting the use of the method.

**Ductility Contrast**

Gay
(1968a) has shown that the viscosity ratio between a particle and the mean
viscosity of a particle/matrix system is dependent on the concentration of the
particles. Therefore, where the proportion of pebbles to matrix is low there
will be a high ductility contrast. He has illustrated that an increase in the
viscosity of an initial ellipsoid particle will greatly reduce the change in
shape of the particle and the rate at which the long axis will move towards the
maximum principle strain direction. The final Rf/f ratio will produce curves similar to those
presented by Dunnet, but with the maximum fluctuation reduced and an Rs value
which is much less than the deformation the matrix has undergone. A high
particle to matrix ratio will have the effect of reducing the ductility
contrast.

Gay
(1968b) illustrates a method to determine finite strain in deformed
conglomerates. This method requires an estimation of the "viscosity
ratio" between pebbles and matrix , and the initial shape of the pebbles.
When Dunnet's technique is used to calculate Rs values in particles of
different lithology, the viscosity ratio can be determined without estimation
of the initial particle shape by substituting the relative strain ratios,
determined by Dunnet's method, into equations of Gay.

The
major problem associated with Gay's method is that the initial pebble shape and
orientation must be known to calculate viscosity ratios. In the calculations,
Gay assumes the original shape to be spherical and orientation to be parallel
to the axes of the strain ellipse. This results in a very approximate viscosity
ratio and it is necessary to make as many pebble measurements as possible to
refine the calculation.

**Conclusion**

The
problems associated with strain analysis in conglomerates are not unique. They
are also encountered in the study of other rocktypes, such as oolites and
pisolites. In general, the major problems affecting the determined value of
finite strain are: (1) initial preferred orientation of fabrics; (2)
superimposed deformation; (3) rotational strain; (4) ductility contrasts; and
(5) inhomogeneous strain. Numerous techniques , discussed above, have been
developed to overcome these problems. The end product of all these techniques
is to determine the strain intensity and orientation. This permits us to
interpret the fabrics of deformed rocks, the significance of cleavage and
lineation, and to correlate strain magnitudes and fabric patterns.

**References**

Cloos.
E., 1947, "Oolite Deformation In South Mountain Fold, Maryland".
Geol. Soc Amer., Bull. 58, pp.843-918.

Dunnet,
D., 1969, " A Technique of Finite Strain Analysis Using Elliptical
Particles". Tectonophysics, V.7, pp. 117-136.

Dunnet,
D. and Siddans, A.W.B., 1971, " Non Random Sedimentary Fabrics and Their
Modification By Strain", Tectonophysics, V12, pp.307-325.

Elliot,
D, 1970, "Determination of Finite Strain and Initial Shape from Deformed
Elliptical Objects", Geol. Soc. Amer., Bull. 81, pp.2221-2236.

Gay,
N.C., 1968, "Pure Shear and Simple Shear Deformation of Inhomogeneous
Viscous Fluids", Tectonophysics, V.5, pp.211-234, pp.295-302.

Ramsay,
J.G., 1967, "Folding and Fracturing of Rocks", MacGraw-Hill, NY,
568p.

Robin,
P.F., 1977, "Determination of Geologic Strain Using Randomly Oriented
Strain Markers of Any Shape", Tectonophysics, V.42, ppT7-T16.

Shimamoto
and Ikeda, 1976, "A Simple Algebraic Method for Strain Estimation From
Deformed Ellipsoid Objects", Tectonophysics, V.36, pp.315-337.