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Experimental tests of buckling folds in relation to strain ellipsoid in simple shear deformations
Tectonophysics - Elsevier Printed in The Netherlands
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Company,
Amsterdam
EXPE~MENTAL TESTS OF BUCKLING FOLDS IN RELATION ELLIPSOID IN SIMPLE SHEAR DEFORMATIONS
TO STRAIN
SUBIR KUMAR GHOSH Institute
of Mineralogy
(Received
February
and Geology.
University
of Uppsala
(Sweden)
2. 1966)
SUMMARY A series
of experimental deformations with plastic materials, such as modelling clay, putty and wax, was carried out by simple shear in order to determine the geometrical relationships of buckling folds with the strain ellipsoid. It was found that the fold axis is not necessarily parallel to the intermediate or major axis of the strain ellipsoid. The fold axis develops parallel to the major axis of the strain ellipse (Le., a section through the strain ellipsoid) on the enveloping surface of the bed. The orientation of the fold axis is partially controlled by the viscosity of the layer and its host because in rotational strain the orientation of the strain ellipsoid is dependent on the relative viscosity of the two materials. The axial planes of folds also are not necessarily parallel to the AB plane of the strain ellipsoid. However, there is a tendency of the strain ellipsoids to be roughly symmetrical about the axial plane. There is a resistance of isolated layers of competent material embedded in an incompetent host to form asymmetrical folds by simple shear alone. Asymmetrical folds, however, readiIy form by a combination of pure shear and simple shear, and by shearing strain parallel to the enveloping surface of a series of pre-existing folds. In some of the tests a cleavage-like structure developed symmetrical about the axial plane of the folds. The structures were strictly parallel to the plane of maximum extension of the strain ellipsoid.
INTRODUCTION
A series of experiments was carried out with plastic materials to determine the geometrical relations of buckling or flexure folds with strain ellipsoid. Different types of modelling clay were used to simulate competent beds. Incompetent beds were mostly represented by painters’ putty or a mixture of painters’ putty and bouncing putty (Dow Corning silicone putty). To represent beds of intermediate viscosity different mixtures of modelling clay and putty were used. Most of the deformations were carried out by simple shear. In the following discussion the direction of shear is represented by X, the axis of shear i.e., the line at right angle to x in the plane of shear, by y, with z normal to xy plane.
Tectonophysics,
3 (3) (1966) 169-183
S.K.
tiHOSff
In a SerieS of teStS one or two sheets of modelling clay were embedded in putty at different angles and subjected to simple shear (see Plate IA). The results in these cases, were similar to those obtained by Ramberg (1959) in experiments on ptygmatic folding. In the general case, where a bed is initially oriented oblique to the principal stress axes, the structural elements of the fold do not have any simple relationships with the stress axes. Furthermore, the present series of experiments and Ramberg’s (1959) experiments on ptygmatic folds have shown that fold axis does not have strict geometric relationship with the principal axes of strain. Even in case of folds with orthorhombic symmetry the fold axis is not in general parallel to the intermediate or /j-axis of the strain ellipsoid as often believed, If a bed is initially parallel to the axis of simple shear (i.e., J) the fold axis forms parallel to the U-axis of strain ellipsoid. When the bed is initially parallel to the ss plane of simple shear, the fold axis forms in the direction of maximum extension, i.e., parallel to the &axis of the ellipsoid. In other cases, i.e., where the bed is oriented oblique to s, 1’ or J, the fold axis is oblique to the axes of the strain ellipsoid. It must be pointed out here that the orientation of the strain ellipsoid in the competent layer may be quite different from the orientation of the ellipsoid in the incompetent host. The orientation of strain ellipsoid in the host material approximates the ideal strain ellipsoid derived from the geometry of simple shear alone. Experimental tests show that the attitude of the strain ellipsoid in the embedded competent layer may be different from this ideal strain ellipsoid. In some of the tests simple shear was applied at low angle to a competent (ill) and an incompetent layer (~2) embedded in an incompetent (1~::)medium, with viscosities 1-11 > pz> illi. In some of the tests the layers were parallel to the y-axis, in others oblique to .x-, V- and z-axes of simple shear. Circles were inscribed on the .\-zsurface of the three materials and also on the free surface of the competent bed where this was inclined to the .Y-, y- and z-axes. After deformation it was found that the orientation of the strain ellipses on the .YZplane- of the model were different in the competent and incompetent layers (Fig.lA). While the major axes of the strain ellipses in the incompetent layer were tilted at strongly acute angles to the trend of the layers, the major axes of strain ellipses in the competent layer were often nearly at right angle to the trend of the bed on the .\z plane. Similarly the orientation of the major axis of the strain ellipse on the inclined surface of the competent layer (Fig.lB) was different from the attitude of the major axis of the strain ellipse derived theoretically from a section of the ideal strain ellipsoid in the enveloping material parallel to the surface of the competent bed (Fig.2). If the viscosity ratio of the competent and the incompetent materials is sufficiently high, so that buckling is possible (Biot, 1957, 1961; Ramberg, 1963a, 1964), the major axis of the strain ellipse on the competent bed is also the potential fold axis of the competent layer. There is, therefore, a relationship between the orientation of the strain ellipsoid and the orientation of the axis of buckling fold. The fold axis develops parallel to the major axis of the strain ellipse (i.e., a section through the ellipsoid in the competent bed) on the enveloping surface of the bed. The strain ellipsoid in this case refers to an early stage of deformation, when the layer-parallel shortening (Ramberg, 1964) is more dominant than buckling, because when buckling Will
EXPERIMENTAL
TESTS
OF BUCKLING
FOLDS
PLATE I
A. Essentially symmetrical folds of modelling clay formed in simple shear. Long axes of strain ellipses in putty are at angle to axial planes. B. Strain ellipses in incompetent layers converging towards fold hinge, and strain ellipses in competent layers converging towards fold core. The multilayer contains two thin white sheets of modelling clay f~,1) alternating with light gray putty ~JJZ)and bounded by dark gray sheets of modelling clay by). The viscosities ~1 > p:i > ~2. Tectonophysics.
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Fig.1. A. A competent and an incompetent layer embedded in an incompetent host on the xz plane of a model. Strain ellipses on incompetent layer are oriented at acute angle to layer boundary while the ellipses in the competent l:Lyer (in the left) are nearly at right angle to layer boundary.
B. Strain ellipses on surface of competent sheet oblique to x-, y- and z-axes of simple shear. Note axes of incipient folds parallel to long axes of ellipses.
become significant the strain ellipsoid in the competent bed will be distorted. An interesting outcome of this discussion is that the attitude of the fold axis
EXPERIMENTAL
TESTS
OF BUCKLING
Plane simple
173
FOLDS
of shear
-
1
Fig.2. Difference in attitudes of major axes of strain ellipses on inclined surface of competent modelling clay and incompetent putty. The attitude of major axis of ellipse on inclined surface of modelling clay was measured directly on the model. The attitude of strain ellipse in putty on the same surface was determined graphically. The major axis of ellipse bisects the angle between the traces of circular sections of strain ellipsoid in putty on the inclined surface. will be dependent on the competency of the bed because of the fact that in rotational strain the orientation of the strain ellipsoid is dependent on the viscosity of the material.
RELATION
OF AXIAL
PLANE
TO STRAIN
ELLIPSOID
The foregoing discussion clearly shows that in cases of isolated layers occurring in an incompetent host (such as isolated layers of amphibolite in gneiss, or any competent vein in incompetent rock) the fold geometry in the competent layer does not necessarily indicate geometry of strain in the host rock. In experiments on simple shear, with single layers of modelling clay embedded in putty, the axial planes of the folds do not show systematic relations with the AB plane of the strain ellipsoid in the putty, even in those cases where the competent layers were parallel to the y-axis of simple shear. In early stages of deformation, when the fold is very open, the axial planes of the folds make an angle with the AB plane of the strain ellipsoid in putty, especially if the competent layer is at a low angle with the direction of shearing. With increasing deformation, the axial plane becomes essentially parallel to the AB plane of strain ellipsoid in the putty, if the layer was initially at Tectonophysics,
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Fig.3. Difference layers.
in attitude of strain
Fig.4. Strain ellipses in incompetent change in fold geometry.
ellipses
layers
in competent
swerving
and incompetent
in accordance
with
a high angle with X. In layers initially at low angle with the direction of shearing, the axial plane generally makes an angle with the AR plane of the strain ellipsoid even after large deformation (Plate IA). The relation of strain ellipsoid with the axial plane of folds in multilayers is more complicated because strains are different in layers of different competence. Moreover, with the initiation of buckling the attitudes of the strain ellipsoids are modified in two ways. The strain ellipsoids which had already formed in the competent layer by layer-parallel shortening (Ramberg, 1963a, 1964) are bodily rotated by buckling. In the incompetent sheets lying between the competent layers the previously formed strain ellipsoids are distorted by the buckling competent sheets. Moreover, the flexural slip rotates the strain ellipsoids in the incompetent material, so that the long axis becomes gradually less inclined to the limb of the fold. The strain ellipsoids in the incompetent layer are therefore differently oriented in the two limbs of a fold. Seen on the xz plane to fold of simple shear, with beds parallel to _V(i.e., on a plane perpendicular axis), the long axes of the ellipses on the two limbs were found to converge toward the convex side of the fold in most cases. This is in contrast to the orientation of the ellipses in the competent layer where the long axes of the ellipses on the two limbs always converge towards the core of the fold (Plate IB, Fig.3). The same orientation of strain ellipses appear also in Ramberg’s (1964, fig.8) experiments of pure shear with elastic materials. Thus, in multilayers undergoing compressional folding the axial planes are not strictly parallel to the AB plane of the strain ellipsoid. However, there is a tendency for the strain ellipsoids on the two limbs to be roughly symmetrical about the axial plane. The lack of a systematic relationship of the axial plane and the strain Tectonophysics,
3 (3) (1966) 187-207
EXPERIMENTAL
TESTS OF BUCKLING FOLDS
175
ellipsoid is not surprising. Although the concept of axial plane has considerable practical importance in structural analysis, it is after all an entirely geometrical feature dependent, in case of buckling folds, on the attitudes of the externally rotated fold limbs (or, in another definition, dependent on location of successive fold hinges), and hence needs not have any exact relationship with the geometry of strain. Since the material between the two limbs of a growing fold is being compressed by the competent limbs, a rough correspondence between the axial plane and the AB plane of the strain ellipsoid may, however, be fairly common at the cores of the folds, especially in case of tight folds. This tendency could be seen in some of the deformation tests with d&harmonic folding. When successive folds in these tests show divergent axial planes the strain ellipses in the incompetent material at the cores of the folds have changed their attitude in successive layers to maintain the rough correspondence with the axial plane (Fig.4). DEFINITION OF AXIAL PLANE
In delineating the axial plane of a fold its older definition (Billings, 1954) has been used for the present studies. In this definition the axial plane is a plane which bisects the angle made by the two limbs. The difficulty with this definition is that in some asymmetrical folds the axial plane does not pass through the successive hinges of a fold. To avoid this difficulty Turner and Weiss (1963) have redefined the axial surface as that surface which passes through the hinges of successive folds. However, this definition cannot be regarded as appropriate because it depends on the presence of more than one folded surface. The axial plane is an element of a fold in the definition of which presence of more than one surface is not a necessary condition (i.e., for instance the definition of a cylindrical fold as a curved surface formed by moving a line parallel to itself). The significance of this point can be made clear if we consider a fold shown up by the bounding surface between two
Fig.5. Fold marked by bounding surface between two massive beds.
Ng.6. Asymmetrical the hinges. Tectonophysics,
folds with separate axial planes drawn from each of
3 f3) (1966) 163-185
176
S.K. GHOSII
thick massive beds whose other two surfaces are not exposed (Fig.5). In the revised definition of Turner and Weiss (1963) the axial plane of these folds cannot be known. Hence it seems that the older definition of axial surface as the bisecting surface is more reasonable. For the particular type of asymmetric folds considered by Turner and Weiss (1963), the difficulty may be overcome if separate axial planes are drawn from each of the hinges (Fig.6).
PROBLEM
OF SYMMETRICAL
AND ASYMMETRICAL
FOLDS
Previously (Billings, 1954) a symmetrical fold was defined as a fold with a vertical axial plane, and an asymmetrical fold as one in which the axial plane is inclined. This definition does not distinguish folds of different shapes irrespective of their orientation in space. Turner and Weiss (1963) have redefined symmetrical folds as those in which the axial plane divides the fold symmetrically. There is no clear discussion in literature of structural geology about the origin of asymmetrical folds. The general idea is that such folds form by shearing strain parallel to the beds (Fig.7). Ramberg’s (1959, p. 125; 1963c) experiments with plastic and elastic materials have proved beyond doubt that buckles can never form by such a layer-parallel shearing strain. There must be a component of compression parallel to the layers. -
(a) Fig.?‘, Supposed mode of formation of asymmetrical
folds.
Fig.8. Symmetrical fold in competent sheet formed by simple shear. The strain ellipses are not parallel to axial planes. -
( bf (0) Fig.9. Formation of asymmetrical surface of pre-existing fold. Tectonophysics,
3 (3) (1966) 169-185
-
-
(cl fold by simple
(d)
shear parallel to enveloping
EXPERIMENTAL
TESTS
OF BUCKLING
FOLDS
177
In a series of tests stiff layers of modelling clay were embedded in soft putty and subjected to simple shear. The competent layers in the different models were put in different angles to the shear plane (i.e. xy plane of simple shear). The initial angles varied from 15“ to 45O in the different models. It was found that in all cases there was a strong tendency for the competent sheets to form symmetrical folds only (Plate IA). Where the initial angle of the layers with xy plane was low, the axial planes of the folds showed strong departures from the AB plane of the strain ellipsoid (Fig.8). In layers at initially low angles to the xy plane most of the folds are symmetrical, although asymmetrical folds have developed locally with axial planes tilted in either direction. The overall symmetry of the folded layers were always orthorhombic. The present series of tests with isolated layers of modelling clay embedded in putty, failed to form asymmetrical folds by simple shear alone. It is not yet clear whether the particular choice of model materials in these tests has any significance in this respect. The tests, however, suggest that the stiffer the competent material in relation to its environment the greater is the resistance for formation, of asymmetrical folds. It has been shown previously that in competent layers embedded in incompetent hosts, the orientation of the strain ellipsoid may be different from the ideal strain ellipsoid derived from the geometry of simple shear alone. In the tests described previously it has been mentioned that the major axes of the strain ellipses on xy plane of simple shear, in the competent layer, were often nearly at right angle to the trend of the bed on the xz plane (Fig. 1A). This is apparently the reason why a stiff layer tends to form mainly orthorhombic folds. Asymmetric folds, however, readily form in other types of strain as shown by the following three series of tests. (1) In the first series the deformation was carried out in two stages. If a folded layer of modelling clay in an envelope of putty is cut into a slab parallel to the enveloping surface and then subjected to simple shear parallel to this surface, the earlier folds are tilted in one direction to a monoclinic symmetry (Fig.9). In these and other experiments, when earlier symmetrical folds are sheared to asymmetric shapes the length of arc (see Ramberg, 1963a) of the folds remains the same. The unequal lengths of the limbs are brought about by shifting of positions of hinges. Evidently, the two-stage deformation in the first series of tests is not geologically realistic except in very special cases. (2) Asymmetrical folds have readily formed in the experiments by a combination of simple shear and pure shear (Plate IIA). The combination of simple shear and pure shear brings the resultant strain ellipsoid in such a position that a plane of maximum shearing strain becomes nearly parallel to the enveloping surface. The strain in this case is triaxial (since the area abed is reduced to a lb % %’ in Fig. lo), and there is a considerable amount of longitudinal or axial flowage. This is undoubtably a geologically realistic process. However, it is not at all certain whether this is very frequent in nature. (3) Finally, strongly asymmetric “drag folds” can form within multilayers under proper conditions of thickness and viscosity. In some of the tests a single thin layer of modelling clay (pl) was embedded between two thick layers of painters’ putty or bouncing putty (p2) and the whole slab was sandwiched between two thick layers of a mixture of Tectonophysics,
3 (3) (1966)
169-185
PLATE II
A. Asymmetrical folds in modelling clay embedded in putty, formed by combination of pure shear and simple shear. B. Multilayer with thin white sheet of modelling clay (1-11)with layers of silicone (~~1 on the sides which are bounded by two layers of modelling clay mixed with putty (p:$. The whole multilayer is embedded in putty (~4). Viscosities p1 > pLI> p4 > w2. Undeformed model. l’ectonophysics,
:J (3) (1966)
169-183
EXPERIMENTAL
TESTS
a
b >
d
c
OF BUCKLING
d’
Fig.10. Formation of asymmetrical simple shear.
FOLDS
179
c’ fold by a combination of pure shear and
modelling clay and putty (~3). The multilayer was embedded in a somewhat dried putty (~4). The viscosities PI> (~3> ~4 > ~2, The viscosities and the thicknesses chosen fulfil the conditions (Ramberg, 1963a, 1964) in which only the thin stiff layer of modelling clay would buckle and the other Iayers would show mainly layer-parallel shortening. When such multilayers were subjected to simple shear at an angle to them the stiff central layer initially formed a series of symmetrical folds which were later tilted in one direction to asymmetrical shapes (Plate IIB, III). The reason for this is that when the whole multilayer rotates by simple shear a layer-parallel shearing strain is generated in the multilayer (Fig.11). When the layer-parallel shearing strain becomes sufficiently large it deforms the incompetent layer. The shearing strain parallel to the enveloping surface tilts the folds of the thin stiff layer lying within the incompetent material. Asymmetric “drag folds” of this type can form merely by the rotation of the whole series of beds, without accompanying buckling of the whole multilayer. In another series of tests the viscosity of the thick layers (pLg)was increased so that it could give rise to folds of the whole multilayer. In the particular situations described by Ramberg (1964) in case of models of elastic material showing two orders of folds, the shearing strain generated during buckling at the limbs of the larger folds have tilted the earlier formed small folds to asymmetrical shapes. The same pattern of folds has been obtained in the present studies with models of plastic materials (Plate IV, VA). The layer-parallel shearing strain tilts the strain ellipsoids toward the plane of the layer itself. In the asymmetrical “drag folds” produced in some of the tests, one of the limbs also is gradually tilted toward the layer itself. Therefore, with continued strain this limb of the “drag fold” becomes oriented in the extension quadrant of the strain ellipsoid. On the limbs of the large fold the smaller folds then tend to flatten out (Plate VA) and ultimately to form tension fracture and boudinage. The smaller folds at the cores or hinge regions of the large folds, however, can still get compressed and grow in amplitude because of their favourable orientation in relation to the strain ellipsoid. This may be one of the reasons why in many areas the tightly oppressed small folds are mostly found near the hinge regions of large folds while they are much less frequent at the flanks. An interesting outcome of the above discussion about the origin of asymmetric “drag folds” is that theoretically two different arrangements of these folds are possible on the limbs of large folds if the deformation takes place by simple shear. This depends on whether the thickness and viscosity ratios of the layers are such that buckling of the multilayer can start early or not. Tectonophysics,
3 (3) (1966)
169-185
180 PLATE III
l‘ectonophysics,
3 (3) (1966)
169-185
EXPERIMENTAL
TESTS
OF BUCKLING
181
FOLDS
.
-
-
icf
fb)
(0)
Fig.11. Formation of asymmetrical fold by layer parallel shearing strain generated during wholesale rotation of a multilayer. The black central layer is a thin competent sheet. The white layers are incompetent. The stippled layers have intermediate competence. They deform only by layer-parallel sho~ening because they have a viscosity below the critical value for buckling. The relationship between the rates of buckle shortening and layer shortening is given by Ramberg’s (1964, p.310) equations relating these two processes. If the buckling of the multilayer starts at an early stage of formation of the second order (i.e., smaller) folds, the common “drag folds” will result, with their axial planes symmetrically oriented in the different limbs (Fig. 12). However, if a gentle buckling of the multilayer takes place at a late stage, when the smaller folds have already been strongly tilted by layer-parallel shearing due to wholesale rotation of the multilayer, the asymmetry of the “drag folds” will be in the same sense in both limbs of the large fold (F&.13). Incidentally, there is hardly any justification to use the term “drag fold” to designate any special type. Experimental tests (Ramberg, 1963c) on drag folds have shown that the so-called “drag” does not initiate folding but merely tilts the already formed folds. Such secondary tilting can take place in small as well as in large folds. The modes of formation of the so-called drag folds are the same in any kind of principal and subsidiary folds. In case of buckling they depend entirely on critical relations of thickness and viscosity of the layers (Ramberg, 1963a, 1964).
RELATION
OF TRANSVERSE
“CLEAVAGE”
TO STRAIN
ELLIPSOID
AND AXIAL
PLANE
In some of the experimental deformations with multilayers, a transverse structure developed in the incompetent layers. The transverse structures are well developed if a very soft material is used to represent the incompetent beds. In the present study these structures have developed in stitching wax (Plate VB) and in a mixture of bouncing putty and painters’ putty (Fig.14, Plate VA). These structures appear as very fine and closely spaced wrinkles on the surface of the model and resemble very much in their relations with folds the naturally occurring.axial plane cleavage in transverse sections Plate III A. Same model as in Plate IIB, after initial deformation by simple shear. Note essentially symmetrical folds. B. Final stage of deformation of model in ‘A. Earlier symmetrical folds have been made asymmetrical by layer-parallel shearing. Tectonophysics,
3 (3) (1966)
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182 PLATE IV
A. Multilayer with two white sheets of modelling clay (~1) alternating with silicone-putty mixture (pz) and bounded by two dark layers of modelli ng clay (b~:j). The whole multilayer is embedded in putty (~4). Undeformed moidel. Viscosities i_ll> ~3 > 1-14 > ~2. B. Model after initial deformation. Tcctonophysics, 3 (3) (1966) 169-185
EXPERIMEKTAL
PLATE
TESTS
OF
BUCKLING
FOLDS
183
V
A. Model after final deformation. The cleavage-like structures in the siliconeputty mixture are strictly parallel to local attitudes of strain ellipsoids in them. Note the undulating attitudes of the cleavage-like structures. B. Cleavage-like structures produced in stitching wax by simple shear. The folded layers are very viscous sheets of stitching wax. T&ctonophysics,
3 (3) (1966)
161t183
.::. D .
‘.:..
‘::..
. . . ... ‘._.
‘.:’
::
‘..‘:. .f.‘
.f...
2.
.. .,:
$1.;
..’ . :.
.. . * .. ::
.,i.’
::
.:: .::-:
,:::” ...> .a..
:.: 5’
.
Fig.12. Formation of “drag folds” tilted on either directions. The black is competent and the white layers are incompetent. The stippled layers intermediate competence above the critical viscosity ratio for buckling. buckling of the stippled layer started early before the folds in the black could be tilted by layer-parallel shearing strain. .
\
-Gi
-0
sheet have The layer .
-xi
Fig.13. Formation of “drag folds” tilted in the same direction. The stippled layer started buckling at a late stage when the thin layer (black) had already formed asymmetric folds by layer-parallel shearing strain. of folds. This cleavage-like structure shows a rough relationship to the axial plane of folds. In most cases they show a fan-shaped pattern converging toward the convex side of a fold. Although in detail there are local deviations from the attitude of the axial plane, there is no doubt an overall tendency for a roughly symmetrical arrangement about the axial plane of the folds. Such relations are also common in naturally occurring axial-plane cleavage. It is also interesting to note that the cleavage-like structures in the models faithfully simulate the slightly undulating attitude of many natural cleavages. This undulation in the models is because of the fact that previously formed strain eIIipses in the incompetent layer are gradually distorted by the buckling of the competent beds. The most significant point in these tests is that the cleavage-like structures are always strictly parallel to the r-1B plane of the strain ellipsoid. This is also in accord with Ramberg’s experimental deformations with elastic materials, where the strain distribution in the different parts of a fold suggests that cleavages in rocks would tend to form parallel to the plane of maximum extension of the strain ellipsoid (Ramberg, 1963b, pp.l?-19).
Tectonophysics.
3 (3) (1966)
16S-f-185
EXPERIMENTAL TESTS OF BUCKLING FOLDS
185
Fig.14. “Axial plane cleavage” in incompetent material. The multilayer, embedded in putty b4), contains white central layer of modelling clay 011) occurring between two layers of silicone-putty mixture bp) in which the “cleav.ages” have developed, and two bounding layers of dark coloured modelling clay (~3 ). Viscosities ~1 > ~-13> y4 > &.Note undulating shape of the cleavage.
ACKNOWLEDGEMENT
The author is indebted to Hans Ramberg for many helpful discussions the investigations and for critically reading the manuscript.
during
REFERENCES Billings, M.P., 1954. Structural Geology, 2nd ed. Prentice-Hall, Englewood Cliffs, N.J,, 514 pp. Biot, M.A., 1957. Folding instability of Iayered viscoelastic medium under compression, Proc. Roy, Sot. (London), Ser. A., 242: 444-454. Biot, M.A., 1961. Theory of folding of stratified viscoelastic medium. J. Franklin Inst., 267: 211-228. Ramberg, H., 1959. Evolution of ptygmatic folding. Norsk Geol. Tidsskr., 39: 99-152. Ramberg, H., 1963a. Fluid dynamics of viscous buckling applicable to folding of layered rocks. Bull. Am. Assoc. Petrol. Geologists, 47: 484-505. Ramberg, H., 1963b. Strain distribution and geometry of folds. Bull. Geol. Inst. Univ. Uppsala, 42: l-20. Ramberg, H., 1963~. Evolution of drag folds. Geol. Mag., 100: 97-106. Ramberg, H., 1964. Selective buckling of composite layers with contrasted rheological properties, a theory for formation of several orders of folds. Tectonophysics, 1 (4): 307-341. Turner, F.J. and Weiss, L.E., 1963. Structural Analysis of Metamorphic Tectonites. McGraw-Hill, New York, N.Y., 545 pp.
Tectonophysics,
3 (3) (1966) 169-185
Publishing
Company,
Amsterdam
EXPE~MENTAL TESTS OF BUCKLING FOLDS IN RELATION ELLIPSOID IN SIMPLE SHEAR DEFORMATIONS
TO STRAIN
SUBIR KUMAR GHOSH Institute
of Mineralogy
(Received
February
and Geology.
University
of Uppsala
(Sweden)
2. 1966)
SUMMARY A series
of experimental deformations with plastic materials, such as modelling clay, putty and wax, was carried out by simple shear in order to determine the geometrical relationships of buckling folds with the strain ellipsoid. It was found that the fold axis is not necessarily parallel to the intermediate or major axis of the strain ellipsoid. The fold axis develops parallel to the major axis of the strain ellipse (Le., a section through the strain ellipsoid) on the enveloping surface of the bed. The orientation of the fold axis is partially controlled by the viscosity of the layer and its host because in rotational strain the orientation of the strain ellipsoid is dependent on the relative viscosity of the two materials. The axial planes of folds also are not necessarily parallel to the AB plane of the strain ellipsoid. However, there is a tendency of the strain ellipsoids to be roughly symmetrical about the axial plane. There is a resistance of isolated layers of competent material embedded in an incompetent host to form asymmetrical folds by simple shear alone. Asymmetrical folds, however, readiIy form by a combination of pure shear and simple shear, and by shearing strain parallel to the enveloping surface of a series of pre-existing folds. In some of the tests a cleavage-like structure developed symmetrical about the axial plane of the folds. The structures were strictly parallel to the plane of maximum extension of the strain ellipsoid.
INTRODUCTION
A series of experiments was carried out with plastic materials to determine the geometrical relations of buckling or flexure folds with strain ellipsoid. Different types of modelling clay were used to simulate competent beds. Incompetent beds were mostly represented by painters’ putty or a mixture of painters’ putty and bouncing putty (Dow Corning silicone putty). To represent beds of intermediate viscosity different mixtures of modelling clay and putty were used. Most of the deformations were carried out by simple shear. In the following discussion the direction of shear is represented by X, the axis of shear i.e., the line at right angle to x in the plane of shear, by y, with z normal to xy plane.
Tectonophysics,
3 (3) (1966) 169-183
S.K.
tiHOSff
In a SerieS of teStS one or two sheets of modelling clay were embedded in putty at different angles and subjected to simple shear (see Plate IA). The results in these cases, were similar to those obtained by Ramberg (1959) in experiments on ptygmatic folding. In the general case, where a bed is initially oriented oblique to the principal stress axes, the structural elements of the fold do not have any simple relationships with the stress axes. Furthermore, the present series of experiments and Ramberg’s (1959) experiments on ptygmatic folds have shown that fold axis does not have strict geometric relationship with the principal axes of strain. Even in case of folds with orthorhombic symmetry the fold axis is not in general parallel to the intermediate or /j-axis of the strain ellipsoid as often believed, If a bed is initially parallel to the axis of simple shear (i.e., J) the fold axis forms parallel to the U-axis of strain ellipsoid. When the bed is initially parallel to the ss plane of simple shear, the fold axis forms in the direction of maximum extension, i.e., parallel to the &axis of the ellipsoid. In other cases, i.e., where the bed is oriented oblique to s, 1’ or J, the fold axis is oblique to the axes of the strain ellipsoid. It must be pointed out here that the orientation of the strain ellipsoid in the competent layer may be quite different from the orientation of the ellipsoid in the incompetent host. The orientation of strain ellipsoid in the host material approximates the ideal strain ellipsoid derived from the geometry of simple shear alone. Experimental tests show that the attitude of the strain ellipsoid in the embedded competent layer may be different from this ideal strain ellipsoid. In some of the tests simple shear was applied at low angle to a competent (ill) and an incompetent layer (~2) embedded in an incompetent (1~::)medium, with viscosities 1-11 > pz> illi. In some of the tests the layers were parallel to the y-axis, in others oblique to .x-, V- and z-axes of simple shear. Circles were inscribed on the .\-zsurface of the three materials and also on the free surface of the competent bed where this was inclined to the .Y-, y- and z-axes. After deformation it was found that the orientation of the strain ellipses on the .YZplane- of the model were different in the competent and incompetent layers (Fig.lA). While the major axes of the strain ellipses in the incompetent layer were tilted at strongly acute angles to the trend of the layers, the major axes of strain ellipses in the competent layer were often nearly at right angle to the trend of the bed on the .\z plane. Similarly the orientation of the major axis of the strain ellipse on the inclined surface of the competent layer (Fig.lB) was different from the attitude of the major axis of the strain ellipse derived theoretically from a section of the ideal strain ellipsoid in the enveloping material parallel to the surface of the competent bed (Fig.2). If the viscosity ratio of the competent and the incompetent materials is sufficiently high, so that buckling is possible (Biot, 1957, 1961; Ramberg, 1963a, 1964), the major axis of the strain ellipse on the competent bed is also the potential fold axis of the competent layer. There is, therefore, a relationship between the orientation of the strain ellipsoid and the orientation of the axis of buckling fold. The fold axis develops parallel to the major axis of the strain ellipse (i.e., a section through the ellipsoid in the competent bed) on the enveloping surface of the bed. The strain ellipsoid in this case refers to an early stage of deformation, when the layer-parallel shortening (Ramberg, 1964) is more dominant than buckling, because when buckling Will
EXPERIMENTAL
TESTS
OF BUCKLING
FOLDS
PLATE I
A. Essentially symmetrical folds of modelling clay formed in simple shear. Long axes of strain ellipses in putty are at angle to axial planes. B. Strain ellipses in incompetent layers converging towards fold hinge, and strain ellipses in competent layers converging towards fold core. The multilayer contains two thin white sheets of modelling clay f~,1) alternating with light gray putty ~JJZ)and bounded by dark gray sheets of modelling clay by). The viscosities ~1 > p:i > ~2. Tectonophysics.
3 (3) (1966)
169-183
Fig.1. A. A competent and an incompetent layer embedded in an incompetent host on the xz plane of a model. Strain ellipses on incompetent layer are oriented at acute angle to layer boundary while the ellipses in the competent l:Lyer (in the left) are nearly at right angle to layer boundary.
B. Strain ellipses on surface of competent sheet oblique to x-, y- and z-axes of simple shear. Note axes of incipient folds parallel to long axes of ellipses.
become significant the strain ellipsoid in the competent bed will be distorted. An interesting outcome of this discussion is that the attitude of the fold axis
EXPERIMENTAL
TESTS
OF BUCKLING
Plane simple
173
FOLDS
of shear
-
1
Fig.2. Difference in attitudes of major axes of strain ellipses on inclined surface of competent modelling clay and incompetent putty. The attitude of major axis of ellipse on inclined surface of modelling clay was measured directly on the model. The attitude of strain ellipse in putty on the same surface was determined graphically. The major axis of ellipse bisects the angle between the traces of circular sections of strain ellipsoid in putty on the inclined surface. will be dependent on the competency of the bed because of the fact that in rotational strain the orientation of the strain ellipsoid is dependent on the viscosity of the material.
RELATION
OF AXIAL
PLANE
TO STRAIN
ELLIPSOID
The foregoing discussion clearly shows that in cases of isolated layers occurring in an incompetent host (such as isolated layers of amphibolite in gneiss, or any competent vein in incompetent rock) the fold geometry in the competent layer does not necessarily indicate geometry of strain in the host rock. In experiments on simple shear, with single layers of modelling clay embedded in putty, the axial planes of the folds do not show systematic relations with the AB plane of the strain ellipsoid in the putty, even in those cases where the competent layers were parallel to the y-axis of simple shear. In early stages of deformation, when the fold is very open, the axial planes of the folds make an angle with the AB plane of the strain ellipsoid in putty, especially if the competent layer is at a low angle with the direction of shearing. With increasing deformation, the axial plane becomes essentially parallel to the AB plane of strain ellipsoid in the putty, if the layer was initially at Tectonophysics,
3 (3) (1966)
169-185
Fig.3. Difference layers.
in attitude of strain
Fig.4. Strain ellipses in incompetent change in fold geometry.
ellipses
layers
in competent
swerving
and incompetent
in accordance
with
a high angle with X. In layers initially at low angle with the direction of shearing, the axial plane generally makes an angle with the AR plane of the strain ellipsoid even after large deformation (Plate IA). The relation of strain ellipsoid with the axial plane of folds in multilayers is more complicated because strains are different in layers of different competence. Moreover, with the initiation of buckling the attitudes of the strain ellipsoids are modified in two ways. The strain ellipsoids which had already formed in the competent layer by layer-parallel shortening (Ramberg, 1963a, 1964) are bodily rotated by buckling. In the incompetent sheets lying between the competent layers the previously formed strain ellipsoids are distorted by the buckling competent sheets. Moreover, the flexural slip rotates the strain ellipsoids in the incompetent material, so that the long axis becomes gradually less inclined to the limb of the fold. The strain ellipsoids in the incompetent layer are therefore differently oriented in the two limbs of a fold. Seen on the xz plane to fold of simple shear, with beds parallel to _V(i.e., on a plane perpendicular axis), the long axes of the ellipses on the two limbs were found to converge toward the convex side of the fold in most cases. This is in contrast to the orientation of the ellipses in the competent layer where the long axes of the ellipses on the two limbs always converge towards the core of the fold (Plate IB, Fig.3). The same orientation of strain ellipses appear also in Ramberg’s (1964, fig.8) experiments of pure shear with elastic materials. Thus, in multilayers undergoing compressional folding the axial planes are not strictly parallel to the AB plane of the strain ellipsoid. However, there is a tendency for the strain ellipsoids on the two limbs to be roughly symmetrical about the axial plane. The lack of a systematic relationship of the axial plane and the strain Tectonophysics,
3 (3) (1966) 187-207
EXPERIMENTAL
TESTS OF BUCKLING FOLDS
175
ellipsoid is not surprising. Although the concept of axial plane has considerable practical importance in structural analysis, it is after all an entirely geometrical feature dependent, in case of buckling folds, on the attitudes of the externally rotated fold limbs (or, in another definition, dependent on location of successive fold hinges), and hence needs not have any exact relationship with the geometry of strain. Since the material between the two limbs of a growing fold is being compressed by the competent limbs, a rough correspondence between the axial plane and the AB plane of the strain ellipsoid may, however, be fairly common at the cores of the folds, especially in case of tight folds. This tendency could be seen in some of the deformation tests with d&harmonic folding. When successive folds in these tests show divergent axial planes the strain ellipses in the incompetent material at the cores of the folds have changed their attitude in successive layers to maintain the rough correspondence with the axial plane (Fig.4). DEFINITION OF AXIAL PLANE
In delineating the axial plane of a fold its older definition (Billings, 1954) has been used for the present studies. In this definition the axial plane is a plane which bisects the angle made by the two limbs. The difficulty with this definition is that in some asymmetrical folds the axial plane does not pass through the successive hinges of a fold. To avoid this difficulty Turner and Weiss (1963) have redefined the axial surface as that surface which passes through the hinges of successive folds. However, this definition cannot be regarded as appropriate because it depends on the presence of more than one folded surface. The axial plane is an element of a fold in the definition of which presence of more than one surface is not a necessary condition (i.e., for instance the definition of a cylindrical fold as a curved surface formed by moving a line parallel to itself). The significance of this point can be made clear if we consider a fold shown up by the bounding surface between two
Fig.5. Fold marked by bounding surface between two massive beds.
Ng.6. Asymmetrical the hinges. Tectonophysics,
folds with separate axial planes drawn from each of
3 f3) (1966) 163-185
176
S.K. GHOSII
thick massive beds whose other two surfaces are not exposed (Fig.5). In the revised definition of Turner and Weiss (1963) the axial plane of these folds cannot be known. Hence it seems that the older definition of axial surface as the bisecting surface is more reasonable. For the particular type of asymmetric folds considered by Turner and Weiss (1963), the difficulty may be overcome if separate axial planes are drawn from each of the hinges (Fig.6).
PROBLEM
OF SYMMETRICAL
AND ASYMMETRICAL
FOLDS
Previously (Billings, 1954) a symmetrical fold was defined as a fold with a vertical axial plane, and an asymmetrical fold as one in which the axial plane is inclined. This definition does not distinguish folds of different shapes irrespective of their orientation in space. Turner and Weiss (1963) have redefined symmetrical folds as those in which the axial plane divides the fold symmetrically. There is no clear discussion in literature of structural geology about the origin of asymmetrical folds. The general idea is that such folds form by shearing strain parallel to the beds (Fig.7). Ramberg’s (1959, p. 125; 1963c) experiments with plastic and elastic materials have proved beyond doubt that buckles can never form by such a layer-parallel shearing strain. There must be a component of compression parallel to the layers. -
(a) Fig.?‘, Supposed mode of formation of asymmetrical
folds.
Fig.8. Symmetrical fold in competent sheet formed by simple shear. The strain ellipses are not parallel to axial planes. -
( bf (0) Fig.9. Formation of asymmetrical surface of pre-existing fold. Tectonophysics,
3 (3) (1966) 169-185
-
-
(cl fold by simple
(d)
shear parallel to enveloping
EXPERIMENTAL
TESTS
OF BUCKLING
FOLDS
177
In a series of tests stiff layers of modelling clay were embedded in soft putty and subjected to simple shear. The competent layers in the different models were put in different angles to the shear plane (i.e. xy plane of simple shear). The initial angles varied from 15“ to 45O in the different models. It was found that in all cases there was a strong tendency for the competent sheets to form symmetrical folds only (Plate IA). Where the initial angle of the layers with xy plane was low, the axial planes of the folds showed strong departures from the AB plane of the strain ellipsoid (Fig.8). In layers at initially low angles to the xy plane most of the folds are symmetrical, although asymmetrical folds have developed locally with axial planes tilted in either direction. The overall symmetry of the folded layers were always orthorhombic. The present series of tests with isolated layers of modelling clay embedded in putty, failed to form asymmetrical folds by simple shear alone. It is not yet clear whether the particular choice of model materials in these tests has any significance in this respect. The tests, however, suggest that the stiffer the competent material in relation to its environment the greater is the resistance for formation, of asymmetrical folds. It has been shown previously that in competent layers embedded in incompetent hosts, the orientation of the strain ellipsoid may be different from the ideal strain ellipsoid derived from the geometry of simple shear alone. In the tests described previously it has been mentioned that the major axes of the strain ellipses on xy plane of simple shear, in the competent layer, were often nearly at right angle to the trend of the bed on the xz plane (Fig. 1A). This is apparently the reason why a stiff layer tends to form mainly orthorhombic folds. Asymmetric folds, however, readily form in other types of strain as shown by the following three series of tests. (1) In the first series the deformation was carried out in two stages. If a folded layer of modelling clay in an envelope of putty is cut into a slab parallel to the enveloping surface and then subjected to simple shear parallel to this surface, the earlier folds are tilted in one direction to a monoclinic symmetry (Fig.9). In these and other experiments, when earlier symmetrical folds are sheared to asymmetric shapes the length of arc (see Ramberg, 1963a) of the folds remains the same. The unequal lengths of the limbs are brought about by shifting of positions of hinges. Evidently, the two-stage deformation in the first series of tests is not geologically realistic except in very special cases. (2) Asymmetrical folds have readily formed in the experiments by a combination of simple shear and pure shear (Plate IIA). The combination of simple shear and pure shear brings the resultant strain ellipsoid in such a position that a plane of maximum shearing strain becomes nearly parallel to the enveloping surface. The strain in this case is triaxial (since the area abed is reduced to a lb % %’ in Fig. lo), and there is a considerable amount of longitudinal or axial flowage. This is undoubtably a geologically realistic process. However, it is not at all certain whether this is very frequent in nature. (3) Finally, strongly asymmetric “drag folds” can form within multilayers under proper conditions of thickness and viscosity. In some of the tests a single thin layer of modelling clay (pl) was embedded between two thick layers of painters’ putty or bouncing putty (p2) and the whole slab was sandwiched between two thick layers of a mixture of Tectonophysics,
3 (3) (1966)
169-185
PLATE II
A. Asymmetrical folds in modelling clay embedded in putty, formed by combination of pure shear and simple shear. B. Multilayer with thin white sheet of modelling clay (1-11)with layers of silicone (~~1 on the sides which are bounded by two layers of modelling clay mixed with putty (p:$. The whole multilayer is embedded in putty (~4). Viscosities p1 > pLI> p4 > w2. Undeformed model. l’ectonophysics,
:J (3) (1966)
169-183
EXPERIMENTAL
TESTS
a
b >
d
c
OF BUCKLING
d’
Fig.10. Formation of asymmetrical simple shear.
FOLDS
179
c’ fold by a combination of pure shear and
modelling clay and putty (~3). The multilayer was embedded in a somewhat dried putty (~4). The viscosities PI> (~3> ~4 > ~2, The viscosities and the thicknesses chosen fulfil the conditions (Ramberg, 1963a, 1964) in which only the thin stiff layer of modelling clay would buckle and the other Iayers would show mainly layer-parallel shortening. When such multilayers were subjected to simple shear at an angle to them the stiff central layer initially formed a series of symmetrical folds which were later tilted in one direction to asymmetrical shapes (Plate IIB, III). The reason for this is that when the whole multilayer rotates by simple shear a layer-parallel shearing strain is generated in the multilayer (Fig.11). When the layer-parallel shearing strain becomes sufficiently large it deforms the incompetent layer. The shearing strain parallel to the enveloping surface tilts the folds of the thin stiff layer lying within the incompetent material. Asymmetric “drag folds” of this type can form merely by the rotation of the whole series of beds, without accompanying buckling of the whole multilayer. In another series of tests the viscosity of the thick layers (pLg)was increased so that it could give rise to folds of the whole multilayer. In the particular situations described by Ramberg (1964) in case of models of elastic material showing two orders of folds, the shearing strain generated during buckling at the limbs of the larger folds have tilted the earlier formed small folds to asymmetrical shapes. The same pattern of folds has been obtained in the present studies with models of plastic materials (Plate IV, VA). The layer-parallel shearing strain tilts the strain ellipsoids toward the plane of the layer itself. In the asymmetrical “drag folds” produced in some of the tests, one of the limbs also is gradually tilted toward the layer itself. Therefore, with continued strain this limb of the “drag fold” becomes oriented in the extension quadrant of the strain ellipsoid. On the limbs of the large fold the smaller folds then tend to flatten out (Plate VA) and ultimately to form tension fracture and boudinage. The smaller folds at the cores or hinge regions of the large folds, however, can still get compressed and grow in amplitude because of their favourable orientation in relation to the strain ellipsoid. This may be one of the reasons why in many areas the tightly oppressed small folds are mostly found near the hinge regions of large folds while they are much less frequent at the flanks. An interesting outcome of the above discussion about the origin of asymmetric “drag folds” is that theoretically two different arrangements of these folds are possible on the limbs of large folds if the deformation takes place by simple shear. This depends on whether the thickness and viscosity ratios of the layers are such that buckling of the multilayer can start early or not. Tectonophysics,
3 (3) (1966)
169-185
180 PLATE III
l‘ectonophysics,
3 (3) (1966)
169-185
EXPERIMENTAL
TESTS
OF BUCKLING
181
FOLDS
.
-
-
icf
fb)
(0)
Fig.11. Formation of asymmetrical fold by layer parallel shearing strain generated during wholesale rotation of a multilayer. The black central layer is a thin competent sheet. The white layers are incompetent. The stippled layers have intermediate competence. They deform only by layer-parallel sho~ening because they have a viscosity below the critical value for buckling. The relationship between the rates of buckle shortening and layer shortening is given by Ramberg’s (1964, p.310) equations relating these two processes. If the buckling of the multilayer starts at an early stage of formation of the second order (i.e., smaller) folds, the common “drag folds” will result, with their axial planes symmetrically oriented in the different limbs (Fig. 12). However, if a gentle buckling of the multilayer takes place at a late stage, when the smaller folds have already been strongly tilted by layer-parallel shearing due to wholesale rotation of the multilayer, the asymmetry of the “drag folds” will be in the same sense in both limbs of the large fold (F&.13). Incidentally, there is hardly any justification to use the term “drag fold” to designate any special type. Experimental tests (Ramberg, 1963c) on drag folds have shown that the so-called “drag” does not initiate folding but merely tilts the already formed folds. Such secondary tilting can take place in small as well as in large folds. The modes of formation of the so-called drag folds are the same in any kind of principal and subsidiary folds. In case of buckling they depend entirely on critical relations of thickness and viscosity of the layers (Ramberg, 1963a, 1964).
RELATION
OF TRANSVERSE
“CLEAVAGE”
TO STRAIN
ELLIPSOID
AND AXIAL
PLANE
In some of the experimental deformations with multilayers, a transverse structure developed in the incompetent layers. The transverse structures are well developed if a very soft material is used to represent the incompetent beds. In the present study these structures have developed in stitching wax (Plate VB) and in a mixture of bouncing putty and painters’ putty (Fig.14, Plate VA). These structures appear as very fine and closely spaced wrinkles on the surface of the model and resemble very much in their relations with folds the naturally occurring.axial plane cleavage in transverse sections Plate III A. Same model as in Plate IIB, after initial deformation by simple shear. Note essentially symmetrical folds. B. Final stage of deformation of model in ‘A. Earlier symmetrical folds have been made asymmetrical by layer-parallel shearing. Tectonophysics,
3 (3) (1966)
169-185
182 PLATE IV
A. Multilayer with two white sheets of modelling clay (~1) alternating with silicone-putty mixture (pz) and bounded by two dark layers of modelli ng clay (b~:j). The whole multilayer is embedded in putty (~4). Undeformed moidel. Viscosities i_ll> ~3 > 1-14 > ~2. B. Model after initial deformation. Tcctonophysics, 3 (3) (1966) 169-185
EXPERIMEKTAL
PLATE
TESTS
OF
BUCKLING
FOLDS
183
V
A. Model after final deformation. The cleavage-like structures in the siliconeputty mixture are strictly parallel to local attitudes of strain ellipsoids in them. Note the undulating attitudes of the cleavage-like structures. B. Cleavage-like structures produced in stitching wax by simple shear. The folded layers are very viscous sheets of stitching wax. T&ctonophysics,
3 (3) (1966)
161t183
.::. D .
‘.:..
‘::..
. . . ... ‘._.
‘.:’
::
‘..‘:. .f.‘
.f...
2.
.. .,:
$1.;
..’ . :.
.. . * .. ::
.,i.’
::
.:: .::-:
,:::” ...> .a..
:.: 5’
.
Fig.12. Formation of “drag folds” tilted on either directions. The black is competent and the white layers are incompetent. The stippled layers intermediate competence above the critical viscosity ratio for buckling. buckling of the stippled layer started early before the folds in the black could be tilted by layer-parallel shearing strain. .
\
-Gi
-0
sheet have The layer .
-xi
Fig.13. Formation of “drag folds” tilted in the same direction. The stippled layer started buckling at a late stage when the thin layer (black) had already formed asymmetric folds by layer-parallel shearing strain. of folds. This cleavage-like structure shows a rough relationship to the axial plane of folds. In most cases they show a fan-shaped pattern converging toward the convex side of a fold. Although in detail there are local deviations from the attitude of the axial plane, there is no doubt an overall tendency for a roughly symmetrical arrangement about the axial plane of the folds. Such relations are also common in naturally occurring axial-plane cleavage. It is also interesting to note that the cleavage-like structures in the models faithfully simulate the slightly undulating attitude of many natural cleavages. This undulation in the models is because of the fact that previously formed strain eIIipses in the incompetent layer are gradually distorted by the buckling of the competent beds. The most significant point in these tests is that the cleavage-like structures are always strictly parallel to the r-1B plane of the strain ellipsoid. This is also in accord with Ramberg’s experimental deformations with elastic materials, where the strain distribution in the different parts of a fold suggests that cleavages in rocks would tend to form parallel to the plane of maximum extension of the strain ellipsoid (Ramberg, 1963b, pp.l?-19).
Tectonophysics.
3 (3) (1966)
16S-f-185
EXPERIMENTAL TESTS OF BUCKLING FOLDS
185
Fig.14. “Axial plane cleavage” in incompetent material. The multilayer, embedded in putty b4), contains white central layer of modelling clay 011) occurring between two layers of silicone-putty mixture bp) in which the “cleav.ages” have developed, and two bounding layers of dark coloured modelling clay (~3 ). Viscosities ~1 > ~-13> y4 > &.Note undulating shape of the cleavage.
ACKNOWLEDGEMENT
The author is indebted to Hans Ramberg for many helpful discussions the investigations and for critically reading the manuscript.
during
REFERENCES Billings, M.P., 1954. Structural Geology, 2nd ed. Prentice-Hall, Englewood Cliffs, N.J,, 514 pp. Biot, M.A., 1957. Folding instability of Iayered viscoelastic medium under compression, Proc. Roy, Sot. (London), Ser. A., 242: 444-454. Biot, M.A., 1961. Theory of folding of stratified viscoelastic medium. J. Franklin Inst., 267: 211-228. Ramberg, H., 1959. Evolution of ptygmatic folding. Norsk Geol. Tidsskr., 39: 99-152. Ramberg, H., 1963a. Fluid dynamics of viscous buckling applicable to folding of layered rocks. Bull. Am. Assoc. Petrol. Geologists, 47: 484-505. Ramberg, H., 1963b. Strain distribution and geometry of folds. Bull. Geol. Inst. Univ. Uppsala, 42: l-20. Ramberg, H., 1963~. Evolution of drag folds. Geol. Mag., 100: 97-106. Ramberg, H., 1964. Selective buckling of composite layers with contrasted rheological properties, a theory for formation of several orders of folds. Tectonophysics, 1 (4): 307-341. Turner, F.J. and Weiss, L.E., 1963. Structural Analysis of Metamorphic Tectonites. McGraw-Hill, New York, N.Y., 545 pp.
Tectonophysics,
3 (3) (1966) 169-185