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Particulate flow of rock and the formation of cleavage
72 (1981) 305-321 Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
Tectonophysics,
305
PARTICULATE FLOW OF ROCK AND THE FORMATION OF CLEAVAGE
GRAHAM JOHN BORRADAILE Department
of Geology,
Lakehead
(Received June 26,1979;revised
University,
Thunder
Bay,
Ont. (Canada)
version accepted June 24,198O)
ABSTRACT Borradaile, G.J., 1981. Particulate flow of rock and the formation physics, 72: 305-321.
of cleavage. Tectono-
Sliding on grain boundaries produces particulate flow during rock deformation. Intragranular deformation and particulate flow may be uncoupled (independent particulate flow), completely coupled (dependent particulate flow) or partially coupled (controlled particulate flow). In independent particulate flow grains are not deformed. In dependent particulate flow the grain sliding is limited and dependent on the incompatible deformation of grains. In controlled particulate flow, grain sliding is encouraged by other factors (e.g. pore-fluid pressure) but the rate of grain sliding is controlled by the deformation of grains. Cataclastic flow and superplasticity are two well known types of behaviour that involve intragranular deformation mechanisms and one or more types of particulate flow. The degree of coupling between intragranular deformation and particulate flow may change during the course of natural deformation. For example, pore-fluid pressure may decrease, causing a transition from controlled to dependent particulate flow. The early part of such a history would be dominated by particulate flow and intragranular deformation would predominate later. This explains bulk strains that exceed the strains of individual grains, and it explains cleavages (formed by the deformation of grains) which transect coeval folds and show no simple relationship with the bulk strain ellipsoid. It also indicates that strain data derived from grain shapes or intragranular features may not truly reflect bulk strain.
1. INTRODUCTION
Consider a body of rock in which the location of certain material points is specified. During a deformation in which the rock remains a continuum many points will, in general, be displaced from the originally specified positions. If the magnitudes and directions of the displacement vectors vary gradually and smoothly from point to point in the body, the body will experience a continuous heterogeneous or homogeneous strain and possibly also a translation. Heterogeneous continuous strain is an approximate endresult of many natural finite strain histories and has lead to powerful tech0040-1951/81/0000-OOOO/$
02.50 @ 1981 Elsevier Scientific Publishing Company
306
niques of analysis in structural geology (Ramsay, 1967; Means, 1976). However, under some circumstances it is inappropriate to consider the rock to have remained a continuum (Ramsay, 1976; Schwerdtner, 1973) and analogue experiments have drawn attention to this (Means, 1977). The discontinuous behaviour of earth materials is particularly important in considering fabric development, in which knowledge of the total finite strain alone may be of limited value, even where the strain is considered on a scale much larger than any discontinuities. In the study of the behaviour of deforming polycrystals, understandably, emphasis is usually placed on the deformation of grains. However, permanent deformation of aggregates usually involves both intracrystalline deformation and intercrystalline deformation. An aggregate which is not recrystallising may only under very special conditions deform continuously so that the grains always fit snugly together (see Section 3). Usually grains cannot keep a good fit during deformation so that some discontinuous behaviour is to be expected. Discontinuous deformation occurs by slip across grain boundaries or across multigranular surfaces. The latter might be single or multiple grainboundary surfaces, stylolites, across which oblique shortening and thus slip occurs, microfractures and faults, bedding, or disjunctive rock-cleavage surfaces. On either side of these surfaces there are sudden changes in displacement vectors which are manifest by grains sliding along the surfaces and possibly also rotating relative to the surface and to other grains. Such differential motion has been alluded to as grain-boundary slip (Flinn, 1965), emphasising the role of the intergranular surfaces, or as “Teilbewegungen” (as used by Breddin, 1967) which emphasises the disordered componental movement. These are two different aspects of the phenomenon which is called particulate flow in this paper. The grain sliding and rotation accompanying particulate flow may take place with conservation of original gram-boundaries, that is, where atoms are neither subtracted from nor added to the grain. These would be rigid body motions. In other cases where diffusion occurs the original boundaries of the grains may not be conserved but will migrate with reference to material points located in the grain while sliding may take place along the grain boundaries. In this paper some information pertinent to particulate flow is reviewed and it is suggested that flow occurs under different categories depending on the circumstances prevailing. According to the degree of coupling between granular and intergranular deformation these categories are termed independent, dependent and controlled particulate flow. Two commonly quoted multi-mechanism, deformation processes that include particulate flow are cataclastic flow and structural superplasticity.
307 2. INDEPENDENT PARTICULATE FLOW: BY INTERGRANULAR DEFORMATION
AGGREGATE-DEFORMATION
SOLELY
Particulate flow may occur without fracturing or otherwise deforming grains under certain conditions. This then is a kind of pure intergranular deformation which allows rigid grains to slip and roll past one another without damaging grains. To do this the aggregate must be able to dilate and avoid grains from interacting. Clearly, particulate flow of this nature may be suppressed by high confining pressures. It is suggested that flow of this type takes place in soft sediments during slump folding and subaqeous inertia flow. Either a fluid or a sediment-fIuid mixture between grains is required to effect this: these are termed gr4n-flow and slurry-flow respectively by Carter (1975). This type of deformation has also been induced in rock mechanics experiments (Handin et al., 1963). Fluid pressures
and effective
stress
The existence of any fluid between the pores of grains will reduce the normal stress across any given grain from its value (uN) in the dry state. Fluid pressure, P, , acts hydrostatically reducing all normal stresses between grains, regardless of the orientation of the grain-grain contacts (Hubbert and Rubey, 1959). The value by which uN is reduced will depend on the relative compressibilities of the aggregate and the material of the grains, given by a (Robin, 1973). The effective stress across the grain contact will thus become ]% - P,(l - a)]. The normal stresses acting across grain contacts will all be reduced by the same amount. Since the sliding friction on particle contacts is directly proportional to the normal stress acting across the contact, slip will be easier where the normal stresses are reduced by Pf. This type of pure intergranular deformation has been produced in experimentally deformed Berea Sandstone with P, equal to confining pressure. The resulting deformed textures are indistinguishable from the undeformed textures because the deformation is exclusively by independent particulate flow at such low effective stresses (Handin et al., 1963, p. 733). Independent
grain boundary
sliding of porous
aggregates
Rocks often show “tectonic” folds and yet have undeformed grains. An effective stress law may be responsible for the aggregate’s deformation and the suppression of intragranular deformation. Ephemeral dilation must accompany such grain rearrangements, and a net dilation may result (e.g., Handin et al., 1963, p. 746), so that this process is less likely to occur at high confining pressures. However, in many “slate belts” (Hobbs et al., 1976) folds do occur without noticeable grain deformation and without the formation of rock cleavage (e.g., in the Rheinisches Schiefergebirge and parts of the southwest Scottish Highlands). Other features do indicate disaggregation
(Williams, 1977), at least locally, that is attributable to liquefaction in tin. genesis of slates. Examples are tectonic sand-dikelets (Powell 1972a, 1~. 1973) and some mica films (Voll, 1960). Such microstructures indicate local. secondary disruption of beds along sheets subparallel with the first cleavage in sedimentary rocks. This occurs at the interfaces between beds of contrasting permeability in rocks which may have been deeply buried; presumably the grams did not interlock sufficiently to interfere with the particulate flow of an argillaceous sand-slurry. The particulate flow may be aided by an intergranular effective pressure principle which has been postulated for the case of natural deformation (e.g., Flinn, 1965 p. 52; Williams, 1976). The application of the effective pressure principle of the preceding section to the case of more consolidated rock requires that P, is maintained through interconnected pores of the aggregate. Under experimental conditions with strain rates faster t.han 10m7 set- ’ it is known that the permeability of granite may be too low to maintain uniform Pf at suitably high levels (Brace and Martin, 1968). However, under much slower, “normal” tectonic strain rates the permeability will probably suffice to allow an effective stress law to apply and assist penetrative particulate flow in most rocks. 3. DEPENDENT PARTICULATE ON GRAIN DEFORMATION
FLOW: GRAIN-BOUNDARY
SLIDING
DEPENDENT
There are three fundamental mechanisms or groups of mechanisms involved in crystal deformation excluding conditions of dynamic recrystallisation: fracture, crystal-plasticity (related to the motion of dislocations) and diffusion processes (Paterson, 1976). These intracrystalline components of deformation are included singly or in combination by all the well-known deformation mechanisms or multi-mechanism processes: dislocation creep, dislocation glide, twinning, diffusion-accomodated grain-boundary sliding (Nabarro-Herring or Coble creep), structural superplasticity, solution- redeposition (pressure solution) and grain fracture (cataclasis). Also where an aggregate is considered, they all involve some component of grain-boundary sliding. With the exception of cataclastic flow (an extreme form of cataclasis) and structural superplasticity, the amount of strain due to particulate flow may be quite small. This might be arbitrarily set at perhaps not more than 20% of the total strain of the aggregate, while the grains themselves take up the bulk of the strain. Fracture of grams will be discussed further under cataclastic flow, which is a deformation process involving particulate flow and extensive brittle deformation of a large number of grains spread throughout an aggregate. It is selfevident that fracturing of grains requires movement on the fractures and on grain boundaries which may involve grain rotation. Where crystals deform plastically by dislocation glide, it is theoretically conceivable that an aggregate of crystals could deform continuously without any grain sliding. If dislocation glide can operate on five independent slip
309
systems in every grain, the aggregate could accomodate a general strain and retain continuity with homogeneous strain of the grains (Von Mise’s criterion). Heterogeneous strain of grains may reduce the number of necessary slip systems to four (Ashby and Verall, 1977, p. 68). The number of necessary slip systems could also be reduced if other deformation mechanisms operate or, especially in the case of metasedimentary rocks, if pore-spaces collapsed. Special types of deformation involving coaxial prolate, oblate or plane-strain histories could also relax the constraints on the number of slip systems (Flinn, 1965). Nevertheless, most rock-forming silicates have so few slip systems that the strain is generally heterogeneous. Intragranular deformations produce voids or try to produce grain-overlap if some inter-granular sliding does not take place. This has been demonstrated by computer simulation of the deformation of a polycrystal in which the crystals have only one slip system (Etchecopar, 1974). Where diffusion is important in the deformation of grains it has also been shown that grain-boundary sliding is a requirement of granular deformation, for example accompanying diffusional creep (Raj and Ashby, 1971), and the grain-boundary sliding is dependent on the creep processes (Elliot, 1973). This appears to be the case whether the diffusion path is through the grains (Nabarro-Herring creep) or along grain boundaries (Coble creep) or via a solute (solution-redeposition). It appears that some grain sliding (particulate flow) is required by and is dependent on the deformation of crystals in an aggregate especially where they deform by fracture, or plastically, and even where diffusion processes operate. Since the crystal-deformation processes are unable to adjust grain shapes to keep them fitting neatly together, voids must be produced to allow slip. 4. CONTROLLED
PARTICULATE
FLOW
It is envisaged that this is the most general way in which particulate flow operates in rocks. Grains slide past one another at rates controlled (Flinn, 1965, p. 55) by intragranular deformation as outlined in the preceding section. However, the sliding is more than would be required by, and dependent on, the intragranular deformation. It is suggested that one factor encouraging the extra component of grain sliding is the pore fluid pressure (Pi). If all the pores in a sedimentary pile were filled with fluid (water), the value of PfIPLOAD would be given by l/p where p is the density of the dry rock. For sedimentary rocks P, would be about 43% of the lithostatic load. However, sedimentary rocks and rocks undergoing low grade and middle grade metamorphism may have elevated pore-fluid pressures approaching the lithostatic load, or mean stress. (At higher grades the presence of a melt phase between rigid particles may produce the same effect).
310
5. CATACLASTIC
FLOW AND SUPERPLASTICITY
Particulate flow plays an important role in these two types of behaviour. Each comprises at least one intragranular deformation mechanism and one of the previously discussed categories of particulate flow. Cataclastic flow Reproduced in rock mechanics experiments (Borg et al., 1960; Paterson, 1978) and inferred from natural examples (Friedman, 1969) this flow is allowed by the rolling and sliding of grams on original gram boundaries and on many new surfaces produced by rupturing grams. Between 50% and 90% of the grains were fractured after experimentally simulated cataclastic flow (Borg et al., 1960). Resistance to slip is overcome by rupture of grams, thereby progressively reducing grain size. The sliding and rolling of broken grains is more sensitive to the mean stress than is fracturing, so that progressive fracturing will dominate, and particulate flow will become less dominant at higher confining pressures (Ashby and Verrall, 1977). Cataclastic flow is not sensitive to temperature but is more important at lower temperatures since crystal plasticity is more effective than fracture at higher temperature with similar differential stress. Comparison of natural textures with those of experimentally produced cam&site suggest that cataclasis is important in fault zones where large aggregate-strains are achieved. Experimental strain rates of the order of 10W4 set-’ and natural strain rates of perhaps around 10-‘” set-’ (Price, 1975; Sibson, 1977) are associated with cataclasis. Thus in nature, cataclastic flow may be common in strain-softened zones such as fault-breccia zones and other fault rocks of the “elastic0-frictional” type (Sibson, 1977) where grain-size reduction is a brittle process and not due to recovery. Cataclastic flow involves controlled (or perhaps under some circumstances dependent) particulate flow, according to Pf , at low temperatures and at high strain rate where the dominant crystal deformation mechanism is fracture . Superplastic flow Structural superplasticity is a type of behaviour achieving very large strains of aggregates at temperatures higher than half the absolute melting temperature, The process achieves large total strains involving a very large component of intercrystalline slip at strain rates relatively insensitive to stress but sensitive to inverse grain-size. It has been suggested that slip is permitted by diffusion (Nicholas and Poirier, 1976) hence the association of superplasticity with high temperature and small, equant grams. The presence of more than one phase inhibits gram growth and may help to keep the small grain-size required by super-plastic flow.
311
Experiments by Schmid et al. (1977) showed that the strain of an aggregate may be 66% due to grain-boundary sliding and Nicholas and Poirier suggest that as much as 90% of the total strain may be due to grain-boundary sliding during superplastic flow. This contrasts with the amount of particulate flow manifest as dependent grain sliding accompanying the plastic deformation of crystals at lower temperatures and/or in coarser-grained aggregates where only 10% of the strain may be due to particulate flow (Schmid et al., 1977). Superplastic behaviour has been reproduced experimentally in limestones (Schmid, 1976, Schmid et al., 1977) and has been inferred to have occurred in some naturally deformed rocks with “mylonite” textures (Boullier and Gueguen, 1974; White, 1977; Allison et al., 1979). However, the criteria for recognising that superplastic flow has occurred in naturally deformed rock are now not clear (Schmid et al., 1977; Etheridge and Wilkie, 1979). Superplastic flow appears to involve controlled particulate flow accompanying ductile crystaldeformation at high temperatures and fast strain rates. 6. OBSERVATIONS
ON REGIONALLY
DEFORMED
ROCKS
The following observations yield circumstantial evidence for particulate flow of low-grade metamorphic rocks. Data are derived mainly from studies of sandstones accompanying slates and schists of lower greenschist facies. Original grain shapes are recognisable in the examples discussed as recrystallisation is absent. Rock-strain exceeds grain-strain Quite large total strains have been determined for some slates and schists. Phyllites and interbedded sandstones in the southwest Scottish Highlands may have bulk principal extensions of 124%, 55% and -73% and for slates and siltstones in the Rheinisches Schiefergebirge the bulk extensions may be 48%, 48% and -66% (Borradaile, 1974, 1977). Petrographic evidence often reveals little evidence of strain. Comparable observations have been made on slates from Wales, U.K. (Knipe, reported in Williams, 1976, p. 190). Similarly, tightly folded rocks in the northern Appalachians contain undeformed fossils (Borradaile, 1978, fig. 10, 15). Petrographic observations dwell on features within grains because evidence of displacements along grain boundaries is rare. (In carbonate petrography the absence of grain deformation was formerly taken to indicate absence of diagenetic compaction for similar reasons - Bathurst, 1971; Shinn et al., 1977.) In the Scottish examples the contrast between rock-strain and grain-strain has been quantified. In the Rhinns of Islay, in a Proterozoic psammitic sequence, grains have been deformed plastically and partly cataclastically. R,/@ analyses of grain shape of groups of 30 or more grains at a large number
312
In a
0 ~wtwl4rock)
1 :;f:;;I,n b
Fig. 1. Flinn diagmm (logarithmic axes) giving mean strain data for quartz and feldspar grains and mean strain data for whole rock using multigranular strain markera from the same rocks; Islay, Scotland. (a = X/Y, b = Y/Z.)
of localities (see Fig. 1) have been averaged. The results of the analysis indicate that the total strain ellipsoid for the deformation of the grains is a flatteningdeformation ellipsoid. The average strain ellipsoid for quartz clasts shows larger strain magnitudes than for feldspar clasts but the strain ellipsoid data for quartz and feldspar are different in shape and magnitudes from the average whole rock strain. The latter is determined from the shapes of In a
In a (b)
I
05
I
,,“.?I
‘0
‘5-ln b
Fig. 2. Flinn diagram (logarithmic axea) giving data for strain of oolites and of large aand dikes in adjacent rocks. Numbers deaignete localities; Inlay, Scotland. (a = X/Y, b = Y/Z.)
313
deformed multigranular pebbles and the strain of deformed sedimentary dikelets. The multigranular structures are much more deformed than individual grains. A study of Eocambrian (Dalradian) metasediments in the southwestern Highlands also yields a similar result. From reasonably close localities with similar deformation the strain of groups of individual oolites (by R,/@ analysis) and of large sand dikes has been compared. The oolites remain entire and act as integral, single grains and have strained much less than adjacent rock aggregates in which sand dikes are considerably sheared. Comparison of oolite data versus whole rock strain data are given in Fig. 2 for two groups of localities. Removal
of granular strain fails to “unfold”
rocks
The Proterozoic sandstone sequence, referred to above, is folded in contact with gneisses. Localities near the base of the sandstones have been sampled and the strain ellipsoids responsible for the grains’ shapes have been determined. Using Ramsay’s technique for removing strains and reconstructing profiles (1969) the fold plunge-profile for the area (Fig. 3a) was “unstrained” (Fig. 3b) by applying strains reciprocal to the strain determined for the grains. The reconstruction (Borradaile, 1979) fails to restore the profile to an undeformed state because much of the strain was inter-granular and left no impression on the grains themselves. Dissipation
of discrete
surfaces
in zones of particulate
flow
In phyllites bearing crenulation cleavages and in mylonite zones. discrete
Fig. 3. a. Plunge profile of major folds of a contact between Proterozoic sandstones (above) and gneisses (below). Dots indicate localities at which strain analyses of grainshape were possible. b. Profile un-strained using the data on deformation of grains and the method of Ramsay (1969).
Fig. 4. Microfolded bedding lamination in crenulated phyllite. Where the lamination is parallel to the crenulation it is red&ad in thickness. The reduction in thickness to about one grain diameter (see arrow) is largely accomplished by derogation, for the grains are reduced in number but not in size in the thinned portion of the lamination. Mull of Oa, Islay, Scotland. Width of field of view about 1 mm; crossed nicols.
Fig. 5. Mylonitic schistosity. Numerous discrete surfaces are surfaces of shear for they cut through, and displace porphyroclasts (see arrowed surface). The surfaces disappear where they merge into grain boundaries, indicating that the grain boundaries take up the motion as particulate flow, Dog Lake, northwest Ontario.
surfaces are often present along which movements have occurred. Shear-zone type displacements of silt laminae in crenulated phyllites (Fig. 4) and sheared porphyroclasts in mylonites (Fig. 5) are evidence of this. In the case of crenulated phyllites the discrete surface becomes dissipated along grain boundaries in the silt layer, and the slip is taken up in a shearzone which thins the layer, reducing it by disaggregation rather than by dissolution, to a layer a few grains thick (Fig. 4). An experimental counterpart is presented in Friedman et al. (1980). In the case of the mylonite, slip surfaces oblique to the prominent. mylonitic schistosity turn parallel to the mylonitic schistosity and “disappear” into grain boundaries which take up this displacement. Grain-boundary sliding: a mode of discontinuous strain The examples all serve to illustrate ways in which only a part of total strain has been achieved by grain deformation. A commonly undetectable component of strain of the aggregate has achieved much strain via slip along grain boundaries. There may have been penetrative grain-sliding and rotation, or the slip may have been heterogeneous, concentrating on spaced, discrete
(a)
(b)
Fig. 6. Without deforming grains an aggregate may change shape (a-c). approximately outline a strain ellipse at each stage.
The black grains
surfaces such as some crenulation cleavage surfaces or some discrete schistosity planes in mylonites. On a suitably large scale, many times larger than individual grains, there may occur an approximately homogeneous strain arising from penetrative grain-sliding with little or no deformation of the grains (Fig. 6). 7. RELATIVE ROLES OF PARTICULATE DURING NATURAL DEFORMATION
FLOW AND I~TRAGRANULAR
STRAIN
Under the circumstances that conspire to produce dependent particulate flow, intergranular sliding is a consequence of grain deformation. ‘I’be two are then contemporary. However, grain sliding may be encouraged by factors other than grain deformation and occurs with different intensities under different circumstances, For this reason it is useful to draw attention to the degree of coupling between grain deformation and particulate flow using the terms dependent, independent and controlled. In the particular case of controlled particulate flow, the importance of grain sliding may vary with the ratio of Pr to mean normal stress. This may change; for example, decrease during tectonic dewatering, so that the controlled grain-boundary sliding may also decrease in importance. During a deformation history in which dewatering occurs the early strain will be due mostly to controlled flow and, perhaps locally, independent particulate flow may occur (tectonic sand intrusions). Subsequently, controlled grain-sliding will be less important and then strain will be due mostly to grain defo~ation with smaller component of strain due to dependent grain sliding. This sequence of events may be recognised in the deformation of many sedimentary and metasedimentary rocks. Some special features and observations which might be explained in this way are discussed below.
317
Formation
of cleavage and particulate
flow
Unambiguous examples of cleavage oblique to the axial surfaces of coeval folds (“transected folds”) are relatively rare (Hamilton, 1961; Ramsay, 1963; Plessmann, 1965; Tobisch and Glover, 1971; Powell, 1974; Cook, 1975; Davies and Cave, 1976; Borradaile, 1978). Similarly, first phase tectonic cleavages oblique to XY of the total strain ellipsoid are not commonly recorded (Borradaile, 1977, 1979). Nevertheless, their occurrence draws attention to processes that must accompany cleavage formation in less exotic examples. Especially in early stages of deformation of sedimentary rocks, considerable deformal;ion may be achieved by grain sliding, enhanced by high P,. In some instances deformation may proceed no further: folds and deformed sedimentary structures occur frequently without any rock cleavage or schistosity and consequently with little evidence of grain deformation. However, some grain deformation usually does occur. In some of the examples cited in Section 6, this was by pressure solution which produced stylolitic cleavage or by plastic deformation processes producing a penetrative cleavage defined as a weak alignment of grain shapes. Because initially high P, promoted controlled particulate flow and at the same time inhibits grain deformation by producing low effective intragranular stresses, a dichotomy in rock behaviour may be expected. As the rock de-waters, effective stresses will build up to the value expected in a dry aggregate and eventually grain deformation processes (with dependent particulate flow) will replace controlled particulate flow as the deformation progresses. Strains usually accumulate non-coaxially in deforming rock so that structures produced in the early part of the strain history, largely by grain sliding, may be asymmetrically disposed with respect to the cleavage or schistosity largely formed by grain deformation in response to later strain increments. In Fig. 7 a sequence of events is indicated that explains “non-principal plane” cleavage and transected folds. Consider the case of cleavage which forms relatively late in a deformation episode. It may be a “principal plane cleavage” in as much that it formed parallel to the principal plane of the later incremental strain ellipsoids (Fig. 7D). But, because the rock started deforming before cleavage was generated, the principal plane of the total strain ellipsoid (as determined by the “sanddike test”: Fig. 7B) will be oblique to cleavage (cf. Fig. 7B with Fig. 7D). Similarly, folds may begin to form before cleavage (cf. Fig. 7C with Fig. 7D). When controlled particulate flow ceases to be the dominant mode of straining the aggregate, grain deformation takes over. Grain deformation constitutes the main cleavage-forming process and is accompanied by a small component of dependent particulate flow. Because the cleavage only forms in response to later increments of strain, it transects the fold (cf. Fig. 7D and Fig. 7C). It is believed that partition of strain between intergranular deformation and intragranular deformation is similar for the formation of both transected
k -fs:YYElTEF:L%2 rI-
-
-
CONTlWLWF’&RTKULATE
-
-CEPEN~ENT&RTICULATE
- -
cumuhltiw stroln
E
Fig. 7. A strain history in which particulate flow dominates the earlier stages and where grain deformation dominates at later stages. Cleavage formed by deformation of grains may thus cause cleavage to develop oblique to the fl plane of the total strain ellipsoid and transect folds formed in the same strain history. A. Successive finite strain ellipses in a noncoaxial strain history. B. Deformation of sanddikes and bedding: the XY plane lies in the acute dihedral angle between deformed dikes and bedding. C. Formation of fold. D. Grain deformation partly suppressed until later stages of strain history. Grain deformation responds to later incremental strain ellipses and produced cleavage oblique to XY of the total strain ellipsoid-and transecting the fold. E. Partition of cumulative total strain between grain strain and particulate flow.
319
folds and cleavage cated schematically
oblique to XY of the total strain ellipsoid. This is indiin a graph of cumulative strain versus time (Fig. 7E).
9. REMARKS
Emphasis has been given to the discontinuous aspects of rock behaviour. This does not imply that continuum mechanics concepts are inapplicable to natural rock deformation. Applied carefully, studies considering rock as a continuum on a suitable scale can provide useful data on finite, though not necessarily total, strains. Indeed, the very application of finite-strain concepts can allow the component of grain sliding to be identified in naturally deformed rock. The most useful strain study should use grain-scale and multigranular strain markers since these both contribute to the magnitude and to the orientation of the total strain ellipsoid. In porous aggregates the contributions of the granular and intergranular components of strain differ in emphasis with time, producing special features such as transected folds and graindeformation fabrics (e.g. cleavage) not simply related to the total strain ellipsoid. ACKNOWLEDGEMENTS
The paper benefited from reviews by Win Means and Mel Friedman and from constructive discussions with Howard Poulsen. Wendy Bons and Sam Spivak are thanked for technical assistance. The research was supported by the Natural Sciences and Engineering Research Council of Canada (grant A6861). REFERENCES Allison, I., Barnett, R.L. and Kerrich, R., 1979. Superplastic flow and changes in crystal chemistry of feldspars. Tectonophysics, 53’ T41--T45. Ashby, M.F. and Verrall, R.A., 1977. Micromechanisms of flow and fracture, and their relevance to the rheology of the Upper Mantle. Philos. Trans. R. Sot. London, Ser. A., 288: 59-95. Bathurst, R.G.C., 1971. Carbonate Sediments and Their Diagenesis. Develop. Sedimentol., 12. Elsevier, Amsterdam, 658 pp. Borradaile, G.J., 1974. Bulk finite tectonic strain estimates from the deformation of neptunian dykes. Tectonophysics, 22: 127-139. Borradaile, G.J., 1977. On cleavage and strain: results of a study in West Germany using tectonically deformed sand dykes. J. Geol. Sot. London, 133 : 146-l 64. Borradaile, G. J., 1978. Transected folds - a study illustrated with examples from Canada and Scotland. Geol. Sot. Am. Bull., 89: 481-493. Borradaile, G.J., 1979. Strain study of the Caledonides in the Islay region, S.W. Scotland. implications for strain histories and deformation mechanisms in greenschist. J. Geol. Sot. London, 136: 77-88. Origin of some mylonites by superBoullier, A.M. and Gueguen, Y., 1974. SP-mylonites: plastic flow. Contrib. Mineral. Petrol., 50: 93-104. Experimental deformation of Borg, I., Friedman, M., Handin, J. and Higgs, D.V., 1960.
St. Peter Sand: a study of catacfastic flow. In: 13. Griggs and J. Handin (Editors), Rock Deformation. Geol. Sot. Am., Mem., 79: 133-192. Brace, W.F. and Martin, R.J., III, 1968. A test of the law of effective stress for crystatlinc rocks of BOW porosity. Int. J. Rock Mech. Min. Sci., 5: 415-426. Breddin, H., 1967. Quantitative Tektonik. Qeol. Mitt. Aachen, 7: 205-238. Carter, KM., 1975. A discussion and classification of subaqueous mass-transport with Particular reference to grain-flow, slurry-flow and fluxoturbidites. Earth-&i. Rev,, 1 1. 145-177. Cook, D.G., 1975. Structural style influenced by lithofacies: Rocky Mountain Ranges, Alberta - British Columbia. Geol. Surv. Can. Bull., 233: 77 pp. Davies, W. and Cave., R., 1976. Folding and cleavage determined during sedimentation. Sediment. Geol., 15: 89-133. Elliot, D., 1973. Diffusion flow laws in metamorphic rocks. Geol. Sot. Am. Buli., 84: 2645-2664, Etchecopar, A., 1974. Etude de Developpement de Structures orientees par Ecrasement et Cisaillement. These, Universite de Names, 135 pp. Etheridge, M.A. and Wilkie, J.C., 1979. Grain-size reduction, grain-boundary sliding and the flow strength of mylonites. Tectonophysies, 58 : 159-l 78. Flinn, D., 1965. Deformation in metamorphism. In: W.S. Pitcher and G.W. Flinn (Editors), Controls of Metamorphism. Oliver and Boyd, London, pp. 73-102. Friedman, M., 1969. Structural analysis of fractures in cores from Saticoy Field, Ventura County, California. Am. Assoc. Pet. Geoi. Bull, 53: 367-389. Friedman, M., Hugman HI, R.H.H. and Handin, ,J., 1980. Experimental folding of rocks under confining pressure, Part VIXI - Forced folding of unconsolidated sand and of lubricated layers of limestone and sandstone. Geol. Sot. Am. Bull,, 91: 307-312. Handin, J., Hager, R.V., Friedman, M. and Feather, J.N., 1963. Experimental deformation of sedimentary rocks under confining pressure: pore pressure effects. Am. Assoc. Pet. Geol. Bull., 47: 717-755. Hamilton, W., 1961. Geology of the Richardson Cove and Jones Cove Quadrangles, Tennessee. U.S. Geol. Surv., Prof. Pap., 349-A, 55 pp. Hobbs, B.E., Means, W.D. and Williams, P.F., 1976. An outline of structural geology. Wiley, New York, N.Y., 571 pp. Hubbert, M.K. and Rubey, W.W., 1959. Role of fluid pressure in mechanics of overthrust fautting. Geol. Sot. Am. Bull., 70: 115-205. Means, W.D., 1976. Stress and Strain. Springer, New York, N.Y., 339 pp. Means, W.D., 3977. A deformation experiment in transmitted light. Earth Planet. Sci. Lett., 35: 169-179. Nicolas, A. and Poirier, J.P., 1976. Crystalline plasticity and solid state flow in metamorphic rocks. Wiley, New York, N.Y., 444 pp. Paterson, M.S., 1976. Some current aspects of experimental rock deformation. Philos. Trans. R. Sot. London, Ser. A, 283: 163-172. Rock Deformation -the Brittle Field. Springer, Paterson, M.S., 1978. Experimental Berlin, 254 pp. Plessmann, W., 1965. Laterale Gesteinsverformung vor Faltungsbeginn in Unterkarbondes Edersees (Rheinisches Schiefergebirge). Geol. Mitt. Aachen, 5: 271-284. Powell, C!. McA., 1972a. Tectonically dewatered slates in the Ludlovian of the Lake District, England. Geol. J., 8: 95-l 10. Powell, C. McA., 1972b. Tectonic dewatering and strain in the Michigamme Slate, Michigan. Geol. Sot. Am. Bull., 83: 2149-2158. Powell, C.McA., 1973. Clastic dikes in the Bull Formation of Cambrian age, Taconic allochthon, Vermont. Geol. Sot. Am. Bull., 84: 3045-3050. Powell, C. McA., 1974. Timing of slaty cleavage during folding of Precambrian rocks, northwest Tasmania. Geol. Sot. Am. Bull,, 85: 1043-1060.
321 Price, N.J., 1975. Rates of deformation. J. Geol. Sot. London, 131: 553-575. Ray, R. and Ashby, M.F., 1971. On grain boundary sliding and diffusional creep. Metall. Trans., 2: 1113-1127. Ramsay, J.G., 1963. Structural investigations in the Barberton Mountain Land, eastern Transvaal. Geol. Sot. South Africa Trans. and Proc., 66: 353-401. Ramsay, J.G., 1967.Folding and Fracturing of Rocks. McGraw-Hill, New York, N.Y., 568 PP. Ramsay, J.G., 1969. The measurement of strain and displacement in erogenic belts. In: P.E. Kent, G.E. Satterthwaite and A.M. Spencer (Editors), Time and Place in Orogeny. London Geol. Sot. Spec. Publ., 3: 43-79. Ramsay, J.G., 1976. Displacement and strain. Philos. Trans. R. Sot. London, Ser. A., 283: 3-25. Robin, P-Y. R., 1973. Note on effective pressure. J. Geophys. Res., 78: 2434-2437. Schmid, S.M., 1976. Rheological evidence for changes in the deformation mechanism of Solenhofen limestone towards low stresses. Tectonophysics, 43: T21-T28. Schmid, S.M., Boland, J.N. and Paterson, M.S., 1977. Superplastic flow in fine-grained limestone. Tectonophysics, 43: 257-291. Schwerdtner, W.M., 1973. A scale problem in paleo-strain analysis. Tectonophysics, 16: 47-54. Shinn, E.A., Halley, R.B., Hudson, J.H. and Lidz, B.H., 1977. Limestone compaction: an enigma. Geology, 5: 21-24. Sibson, R.H., 1977. Fault rocks and fault mechanisms. J. Geol. Sot. London, 133: 191213. Tobisch, P.T. and Gover, O., 1971. Nappe formation in part of the Southern Appalachian Piedmont. Geol. Sot. Am. Bull., 82: 2209-2230. Voll, G., 1960. New work on petrofabrics. Liverpool Manchester Geol. J., 2: 503-567. White, S., 1977. Geological significance of recovery and recrystallisation processes in quartz. Tectonophysics, 39: 143-170. Williams, P.F., 1976. Relationships between axial-plane foliations and strain. Tectonophysics, 30: 181-196. Williams, P.F., 1977. Foliation: a review and discussion. Tectonophysics, 39: 305-328.
Tectonophysics,
305
PARTICULATE FLOW OF ROCK AND THE FORMATION OF CLEAVAGE
GRAHAM JOHN BORRADAILE Department
of Geology,
Lakehead
(Received June 26,1979;revised
University,
Thunder
Bay,
Ont. (Canada)
version accepted June 24,198O)
ABSTRACT Borradaile, G.J., 1981. Particulate flow of rock and the formation physics, 72: 305-321.
of cleavage. Tectono-
Sliding on grain boundaries produces particulate flow during rock deformation. Intragranular deformation and particulate flow may be uncoupled (independent particulate flow), completely coupled (dependent particulate flow) or partially coupled (controlled particulate flow). In independent particulate flow grains are not deformed. In dependent particulate flow the grain sliding is limited and dependent on the incompatible deformation of grains. In controlled particulate flow, grain sliding is encouraged by other factors (e.g. pore-fluid pressure) but the rate of grain sliding is controlled by the deformation of grains. Cataclastic flow and superplasticity are two well known types of behaviour that involve intragranular deformation mechanisms and one or more types of particulate flow. The degree of coupling between intragranular deformation and particulate flow may change during the course of natural deformation. For example, pore-fluid pressure may decrease, causing a transition from controlled to dependent particulate flow. The early part of such a history would be dominated by particulate flow and intragranular deformation would predominate later. This explains bulk strains that exceed the strains of individual grains, and it explains cleavages (formed by the deformation of grains) which transect coeval folds and show no simple relationship with the bulk strain ellipsoid. It also indicates that strain data derived from grain shapes or intragranular features may not truly reflect bulk strain.
1. INTRODUCTION
Consider a body of rock in which the location of certain material points is specified. During a deformation in which the rock remains a continuum many points will, in general, be displaced from the originally specified positions. If the magnitudes and directions of the displacement vectors vary gradually and smoothly from point to point in the body, the body will experience a continuous heterogeneous or homogeneous strain and possibly also a translation. Heterogeneous continuous strain is an approximate endresult of many natural finite strain histories and has lead to powerful tech0040-1951/81/0000-OOOO/$
02.50 @ 1981 Elsevier Scientific Publishing Company
306
niques of analysis in structural geology (Ramsay, 1967; Means, 1976). However, under some circumstances it is inappropriate to consider the rock to have remained a continuum (Ramsay, 1976; Schwerdtner, 1973) and analogue experiments have drawn attention to this (Means, 1977). The discontinuous behaviour of earth materials is particularly important in considering fabric development, in which knowledge of the total finite strain alone may be of limited value, even where the strain is considered on a scale much larger than any discontinuities. In the study of the behaviour of deforming polycrystals, understandably, emphasis is usually placed on the deformation of grains. However, permanent deformation of aggregates usually involves both intracrystalline deformation and intercrystalline deformation. An aggregate which is not recrystallising may only under very special conditions deform continuously so that the grains always fit snugly together (see Section 3). Usually grains cannot keep a good fit during deformation so that some discontinuous behaviour is to be expected. Discontinuous deformation occurs by slip across grain boundaries or across multigranular surfaces. The latter might be single or multiple grainboundary surfaces, stylolites, across which oblique shortening and thus slip occurs, microfractures and faults, bedding, or disjunctive rock-cleavage surfaces. On either side of these surfaces there are sudden changes in displacement vectors which are manifest by grains sliding along the surfaces and possibly also rotating relative to the surface and to other grains. Such differential motion has been alluded to as grain-boundary slip (Flinn, 1965), emphasising the role of the intergranular surfaces, or as “Teilbewegungen” (as used by Breddin, 1967) which emphasises the disordered componental movement. These are two different aspects of the phenomenon which is called particulate flow in this paper. The grain sliding and rotation accompanying particulate flow may take place with conservation of original gram-boundaries, that is, where atoms are neither subtracted from nor added to the grain. These would be rigid body motions. In other cases where diffusion occurs the original boundaries of the grains may not be conserved but will migrate with reference to material points located in the grain while sliding may take place along the grain boundaries. In this paper some information pertinent to particulate flow is reviewed and it is suggested that flow occurs under different categories depending on the circumstances prevailing. According to the degree of coupling between granular and intergranular deformation these categories are termed independent, dependent and controlled particulate flow. Two commonly quoted multi-mechanism, deformation processes that include particulate flow are cataclastic flow and structural superplasticity.
307 2. INDEPENDENT PARTICULATE FLOW: BY INTERGRANULAR DEFORMATION
AGGREGATE-DEFORMATION
SOLELY
Particulate flow may occur without fracturing or otherwise deforming grains under certain conditions. This then is a kind of pure intergranular deformation which allows rigid grains to slip and roll past one another without damaging grains. To do this the aggregate must be able to dilate and avoid grains from interacting. Clearly, particulate flow of this nature may be suppressed by high confining pressures. It is suggested that flow of this type takes place in soft sediments during slump folding and subaqeous inertia flow. Either a fluid or a sediment-fIuid mixture between grains is required to effect this: these are termed gr4n-flow and slurry-flow respectively by Carter (1975). This type of deformation has also been induced in rock mechanics experiments (Handin et al., 1963). Fluid pressures
and effective
stress
The existence of any fluid between the pores of grains will reduce the normal stress across any given grain from its value (uN) in the dry state. Fluid pressure, P, , acts hydrostatically reducing all normal stresses between grains, regardless of the orientation of the grain-grain contacts (Hubbert and Rubey, 1959). The value by which uN is reduced will depend on the relative compressibilities of the aggregate and the material of the grains, given by a (Robin, 1973). The effective stress across the grain contact will thus become ]% - P,(l - a)]. The normal stresses acting across grain contacts will all be reduced by the same amount. Since the sliding friction on particle contacts is directly proportional to the normal stress acting across the contact, slip will be easier where the normal stresses are reduced by Pf. This type of pure intergranular deformation has been produced in experimentally deformed Berea Sandstone with P, equal to confining pressure. The resulting deformed textures are indistinguishable from the undeformed textures because the deformation is exclusively by independent particulate flow at such low effective stresses (Handin et al., 1963, p. 733). Independent
grain boundary
sliding of porous
aggregates
Rocks often show “tectonic” folds and yet have undeformed grains. An effective stress law may be responsible for the aggregate’s deformation and the suppression of intragranular deformation. Ephemeral dilation must accompany such grain rearrangements, and a net dilation may result (e.g., Handin et al., 1963, p. 746), so that this process is less likely to occur at high confining pressures. However, in many “slate belts” (Hobbs et al., 1976) folds do occur without noticeable grain deformation and without the formation of rock cleavage (e.g., in the Rheinisches Schiefergebirge and parts of the southwest Scottish Highlands). Other features do indicate disaggregation
(Williams, 1977), at least locally, that is attributable to liquefaction in tin. genesis of slates. Examples are tectonic sand-dikelets (Powell 1972a, 1~. 1973) and some mica films (Voll, 1960). Such microstructures indicate local. secondary disruption of beds along sheets subparallel with the first cleavage in sedimentary rocks. This occurs at the interfaces between beds of contrasting permeability in rocks which may have been deeply buried; presumably the grams did not interlock sufficiently to interfere with the particulate flow of an argillaceous sand-slurry. The particulate flow may be aided by an intergranular effective pressure principle which has been postulated for the case of natural deformation (e.g., Flinn, 1965 p. 52; Williams, 1976). The application of the effective pressure principle of the preceding section to the case of more consolidated rock requires that P, is maintained through interconnected pores of the aggregate. Under experimental conditions with strain rates faster t.han 10m7 set- ’ it is known that the permeability of granite may be too low to maintain uniform Pf at suitably high levels (Brace and Martin, 1968). However, under much slower, “normal” tectonic strain rates the permeability will probably suffice to allow an effective stress law to apply and assist penetrative particulate flow in most rocks. 3. DEPENDENT PARTICULATE ON GRAIN DEFORMATION
FLOW: GRAIN-BOUNDARY
SLIDING
DEPENDENT
There are three fundamental mechanisms or groups of mechanisms involved in crystal deformation excluding conditions of dynamic recrystallisation: fracture, crystal-plasticity (related to the motion of dislocations) and diffusion processes (Paterson, 1976). These intracrystalline components of deformation are included singly or in combination by all the well-known deformation mechanisms or multi-mechanism processes: dislocation creep, dislocation glide, twinning, diffusion-accomodated grain-boundary sliding (Nabarro-Herring or Coble creep), structural superplasticity, solution- redeposition (pressure solution) and grain fracture (cataclasis). Also where an aggregate is considered, they all involve some component of grain-boundary sliding. With the exception of cataclastic flow (an extreme form of cataclasis) and structural superplasticity, the amount of strain due to particulate flow may be quite small. This might be arbitrarily set at perhaps not more than 20% of the total strain of the aggregate, while the grains themselves take up the bulk of the strain. Fracture of grams will be discussed further under cataclastic flow, which is a deformation process involving particulate flow and extensive brittle deformation of a large number of grains spread throughout an aggregate. It is selfevident that fracturing of grains requires movement on the fractures and on grain boundaries which may involve grain rotation. Where crystals deform plastically by dislocation glide, it is theoretically conceivable that an aggregate of crystals could deform continuously without any grain sliding. If dislocation glide can operate on five independent slip
309
systems in every grain, the aggregate could accomodate a general strain and retain continuity with homogeneous strain of the grains (Von Mise’s criterion). Heterogeneous strain of grains may reduce the number of necessary slip systems to four (Ashby and Verall, 1977, p. 68). The number of necessary slip systems could also be reduced if other deformation mechanisms operate or, especially in the case of metasedimentary rocks, if pore-spaces collapsed. Special types of deformation involving coaxial prolate, oblate or plane-strain histories could also relax the constraints on the number of slip systems (Flinn, 1965). Nevertheless, most rock-forming silicates have so few slip systems that the strain is generally heterogeneous. Intragranular deformations produce voids or try to produce grain-overlap if some inter-granular sliding does not take place. This has been demonstrated by computer simulation of the deformation of a polycrystal in which the crystals have only one slip system (Etchecopar, 1974). Where diffusion is important in the deformation of grains it has also been shown that grain-boundary sliding is a requirement of granular deformation, for example accompanying diffusional creep (Raj and Ashby, 1971), and the grain-boundary sliding is dependent on the creep processes (Elliot, 1973). This appears to be the case whether the diffusion path is through the grains (Nabarro-Herring creep) or along grain boundaries (Coble creep) or via a solute (solution-redeposition). It appears that some grain sliding (particulate flow) is required by and is dependent on the deformation of crystals in an aggregate especially where they deform by fracture, or plastically, and even where diffusion processes operate. Since the crystal-deformation processes are unable to adjust grain shapes to keep them fitting neatly together, voids must be produced to allow slip. 4. CONTROLLED
PARTICULATE
FLOW
It is envisaged that this is the most general way in which particulate flow operates in rocks. Grains slide past one another at rates controlled (Flinn, 1965, p. 55) by intragranular deformation as outlined in the preceding section. However, the sliding is more than would be required by, and dependent on, the intragranular deformation. It is suggested that one factor encouraging the extra component of grain sliding is the pore fluid pressure (Pi). If all the pores in a sedimentary pile were filled with fluid (water), the value of PfIPLOAD would be given by l/p where p is the density of the dry rock. For sedimentary rocks P, would be about 43% of the lithostatic load. However, sedimentary rocks and rocks undergoing low grade and middle grade metamorphism may have elevated pore-fluid pressures approaching the lithostatic load, or mean stress. (At higher grades the presence of a melt phase between rigid particles may produce the same effect).
310
5. CATACLASTIC
FLOW AND SUPERPLASTICITY
Particulate flow plays an important role in these two types of behaviour. Each comprises at least one intragranular deformation mechanism and one of the previously discussed categories of particulate flow. Cataclastic flow Reproduced in rock mechanics experiments (Borg et al., 1960; Paterson, 1978) and inferred from natural examples (Friedman, 1969) this flow is allowed by the rolling and sliding of grams on original gram boundaries and on many new surfaces produced by rupturing grams. Between 50% and 90% of the grains were fractured after experimentally simulated cataclastic flow (Borg et al., 1960). Resistance to slip is overcome by rupture of grams, thereby progressively reducing grain size. The sliding and rolling of broken grains is more sensitive to the mean stress than is fracturing, so that progressive fracturing will dominate, and particulate flow will become less dominant at higher confining pressures (Ashby and Verrall, 1977). Cataclastic flow is not sensitive to temperature but is more important at lower temperatures since crystal plasticity is more effective than fracture at higher temperature with similar differential stress. Comparison of natural textures with those of experimentally produced cam&site suggest that cataclasis is important in fault zones where large aggregate-strains are achieved. Experimental strain rates of the order of 10W4 set-’ and natural strain rates of perhaps around 10-‘” set-’ (Price, 1975; Sibson, 1977) are associated with cataclasis. Thus in nature, cataclastic flow may be common in strain-softened zones such as fault-breccia zones and other fault rocks of the “elastic0-frictional” type (Sibson, 1977) where grain-size reduction is a brittle process and not due to recovery. Cataclastic flow involves controlled (or perhaps under some circumstances dependent) particulate flow, according to Pf , at low temperatures and at high strain rate where the dominant crystal deformation mechanism is fracture . Superplastic flow Structural superplasticity is a type of behaviour achieving very large strains of aggregates at temperatures higher than half the absolute melting temperature, The process achieves large total strains involving a very large component of intercrystalline slip at strain rates relatively insensitive to stress but sensitive to inverse grain-size. It has been suggested that slip is permitted by diffusion (Nicholas and Poirier, 1976) hence the association of superplasticity with high temperature and small, equant grams. The presence of more than one phase inhibits gram growth and may help to keep the small grain-size required by super-plastic flow.
311
Experiments by Schmid et al. (1977) showed that the strain of an aggregate may be 66% due to grain-boundary sliding and Nicholas and Poirier suggest that as much as 90% of the total strain may be due to grain-boundary sliding during superplastic flow. This contrasts with the amount of particulate flow manifest as dependent grain sliding accompanying the plastic deformation of crystals at lower temperatures and/or in coarser-grained aggregates where only 10% of the strain may be due to particulate flow (Schmid et al., 1977). Superplastic behaviour has been reproduced experimentally in limestones (Schmid, 1976, Schmid et al., 1977) and has been inferred to have occurred in some naturally deformed rocks with “mylonite” textures (Boullier and Gueguen, 1974; White, 1977; Allison et al., 1979). However, the criteria for recognising that superplastic flow has occurred in naturally deformed rock are now not clear (Schmid et al., 1977; Etheridge and Wilkie, 1979). Superplastic flow appears to involve controlled particulate flow accompanying ductile crystaldeformation at high temperatures and fast strain rates. 6. OBSERVATIONS
ON REGIONALLY
DEFORMED
ROCKS
The following observations yield circumstantial evidence for particulate flow of low-grade metamorphic rocks. Data are derived mainly from studies of sandstones accompanying slates and schists of lower greenschist facies. Original grain shapes are recognisable in the examples discussed as recrystallisation is absent. Rock-strain exceeds grain-strain Quite large total strains have been determined for some slates and schists. Phyllites and interbedded sandstones in the southwest Scottish Highlands may have bulk principal extensions of 124%, 55% and -73% and for slates and siltstones in the Rheinisches Schiefergebirge the bulk extensions may be 48%, 48% and -66% (Borradaile, 1974, 1977). Petrographic evidence often reveals little evidence of strain. Comparable observations have been made on slates from Wales, U.K. (Knipe, reported in Williams, 1976, p. 190). Similarly, tightly folded rocks in the northern Appalachians contain undeformed fossils (Borradaile, 1978, fig. 10, 15). Petrographic observations dwell on features within grains because evidence of displacements along grain boundaries is rare. (In carbonate petrography the absence of grain deformation was formerly taken to indicate absence of diagenetic compaction for similar reasons - Bathurst, 1971; Shinn et al., 1977.) In the Scottish examples the contrast between rock-strain and grain-strain has been quantified. In the Rhinns of Islay, in a Proterozoic psammitic sequence, grains have been deformed plastically and partly cataclastically. R,/@ analyses of grain shape of groups of 30 or more grains at a large number
312
In a
0 ~wtwl4rock)
1 :;f:;;I,n b
Fig. 1. Flinn diagmm (logarithmic axes) giving mean strain data for quartz and feldspar grains and mean strain data for whole rock using multigranular strain markera from the same rocks; Islay, Scotland. (a = X/Y, b = Y/Z.)
of localities (see Fig. 1) have been averaged. The results of the analysis indicate that the total strain ellipsoid for the deformation of the grains is a flatteningdeformation ellipsoid. The average strain ellipsoid for quartz clasts shows larger strain magnitudes than for feldspar clasts but the strain ellipsoid data for quartz and feldspar are different in shape and magnitudes from the average whole rock strain. The latter is determined from the shapes of In a
In a (b)
I
05
I
,,“.?I
‘0
‘5-ln b
Fig. 2. Flinn diagram (logarithmic axea) giving data for strain of oolites and of large aand dikes in adjacent rocks. Numbers deaignete localities; Inlay, Scotland. (a = X/Y, b = Y/Z.)
313
deformed multigranular pebbles and the strain of deformed sedimentary dikelets. The multigranular structures are much more deformed than individual grains. A study of Eocambrian (Dalradian) metasediments in the southwestern Highlands also yields a similar result. From reasonably close localities with similar deformation the strain of groups of individual oolites (by R,/@ analysis) and of large sand dikes has been compared. The oolites remain entire and act as integral, single grains and have strained much less than adjacent rock aggregates in which sand dikes are considerably sheared. Comparison of oolite data versus whole rock strain data are given in Fig. 2 for two groups of localities. Removal
of granular strain fails to “unfold”
rocks
The Proterozoic sandstone sequence, referred to above, is folded in contact with gneisses. Localities near the base of the sandstones have been sampled and the strain ellipsoids responsible for the grains’ shapes have been determined. Using Ramsay’s technique for removing strains and reconstructing profiles (1969) the fold plunge-profile for the area (Fig. 3a) was “unstrained” (Fig. 3b) by applying strains reciprocal to the strain determined for the grains. The reconstruction (Borradaile, 1979) fails to restore the profile to an undeformed state because much of the strain was inter-granular and left no impression on the grains themselves. Dissipation
of discrete
surfaces
in zones of particulate
flow
In phyllites bearing crenulation cleavages and in mylonite zones. discrete
Fig. 3. a. Plunge profile of major folds of a contact between Proterozoic sandstones (above) and gneisses (below). Dots indicate localities at which strain analyses of grainshape were possible. b. Profile un-strained using the data on deformation of grains and the method of Ramsay (1969).
Fig. 4. Microfolded bedding lamination in crenulated phyllite. Where the lamination is parallel to the crenulation it is red&ad in thickness. The reduction in thickness to about one grain diameter (see arrow) is largely accomplished by derogation, for the grains are reduced in number but not in size in the thinned portion of the lamination. Mull of Oa, Islay, Scotland. Width of field of view about 1 mm; crossed nicols.
Fig. 5. Mylonitic schistosity. Numerous discrete surfaces are surfaces of shear for they cut through, and displace porphyroclasts (see arrowed surface). The surfaces disappear where they merge into grain boundaries, indicating that the grain boundaries take up the motion as particulate flow, Dog Lake, northwest Ontario.
surfaces are often present along which movements have occurred. Shear-zone type displacements of silt laminae in crenulated phyllites (Fig. 4) and sheared porphyroclasts in mylonites (Fig. 5) are evidence of this. In the case of crenulated phyllites the discrete surface becomes dissipated along grain boundaries in the silt layer, and the slip is taken up in a shearzone which thins the layer, reducing it by disaggregation rather than by dissolution, to a layer a few grains thick (Fig. 4). An experimental counterpart is presented in Friedman et al. (1980). In the case of the mylonite, slip surfaces oblique to the prominent. mylonitic schistosity turn parallel to the mylonitic schistosity and “disappear” into grain boundaries which take up this displacement. Grain-boundary sliding: a mode of discontinuous strain The examples all serve to illustrate ways in which only a part of total strain has been achieved by grain deformation. A commonly undetectable component of strain of the aggregate has achieved much strain via slip along grain boundaries. There may have been penetrative grain-sliding and rotation, or the slip may have been heterogeneous, concentrating on spaced, discrete
(a)
(b)
Fig. 6. Without deforming grains an aggregate may change shape (a-c). approximately outline a strain ellipse at each stage.
The black grains
surfaces such as some crenulation cleavage surfaces or some discrete schistosity planes in mylonites. On a suitably large scale, many times larger than individual grains, there may occur an approximately homogeneous strain arising from penetrative grain-sliding with little or no deformation of the grains (Fig. 6). 7. RELATIVE ROLES OF PARTICULATE DURING NATURAL DEFORMATION
FLOW AND I~TRAGRANULAR
STRAIN
Under the circumstances that conspire to produce dependent particulate flow, intergranular sliding is a consequence of grain deformation. ‘I’be two are then contemporary. However, grain sliding may be encouraged by factors other than grain deformation and occurs with different intensities under different circumstances, For this reason it is useful to draw attention to the degree of coupling between grain deformation and particulate flow using the terms dependent, independent and controlled. In the particular case of controlled particulate flow, the importance of grain sliding may vary with the ratio of Pr to mean normal stress. This may change; for example, decrease during tectonic dewatering, so that the controlled grain-boundary sliding may also decrease in importance. During a deformation history in which dewatering occurs the early strain will be due mostly to controlled flow and, perhaps locally, independent particulate flow may occur (tectonic sand intrusions). Subsequently, controlled grain-sliding will be less important and then strain will be due mostly to grain defo~ation with smaller component of strain due to dependent grain sliding. This sequence of events may be recognised in the deformation of many sedimentary and metasedimentary rocks. Some special features and observations which might be explained in this way are discussed below.
317
Formation
of cleavage and particulate
flow
Unambiguous examples of cleavage oblique to the axial surfaces of coeval folds (“transected folds”) are relatively rare (Hamilton, 1961; Ramsay, 1963; Plessmann, 1965; Tobisch and Glover, 1971; Powell, 1974; Cook, 1975; Davies and Cave, 1976; Borradaile, 1978). Similarly, first phase tectonic cleavages oblique to XY of the total strain ellipsoid are not commonly recorded (Borradaile, 1977, 1979). Nevertheless, their occurrence draws attention to processes that must accompany cleavage formation in less exotic examples. Especially in early stages of deformation of sedimentary rocks, considerable deformal;ion may be achieved by grain sliding, enhanced by high P,. In some instances deformation may proceed no further: folds and deformed sedimentary structures occur frequently without any rock cleavage or schistosity and consequently with little evidence of grain deformation. However, some grain deformation usually does occur. In some of the examples cited in Section 6, this was by pressure solution which produced stylolitic cleavage or by plastic deformation processes producing a penetrative cleavage defined as a weak alignment of grain shapes. Because initially high P, promoted controlled particulate flow and at the same time inhibits grain deformation by producing low effective intragranular stresses, a dichotomy in rock behaviour may be expected. As the rock de-waters, effective stresses will build up to the value expected in a dry aggregate and eventually grain deformation processes (with dependent particulate flow) will replace controlled particulate flow as the deformation progresses. Strains usually accumulate non-coaxially in deforming rock so that structures produced in the early part of the strain history, largely by grain sliding, may be asymmetrically disposed with respect to the cleavage or schistosity largely formed by grain deformation in response to later strain increments. In Fig. 7 a sequence of events is indicated that explains “non-principal plane” cleavage and transected folds. Consider the case of cleavage which forms relatively late in a deformation episode. It may be a “principal plane cleavage” in as much that it formed parallel to the principal plane of the later incremental strain ellipsoids (Fig. 7D). But, because the rock started deforming before cleavage was generated, the principal plane of the total strain ellipsoid (as determined by the “sanddike test”: Fig. 7B) will be oblique to cleavage (cf. Fig. 7B with Fig. 7D). Similarly, folds may begin to form before cleavage (cf. Fig. 7C with Fig. 7D). When controlled particulate flow ceases to be the dominant mode of straining the aggregate, grain deformation takes over. Grain deformation constitutes the main cleavage-forming process and is accompanied by a small component of dependent particulate flow. Because the cleavage only forms in response to later increments of strain, it transects the fold (cf. Fig. 7D and Fig. 7C). It is believed that partition of strain between intergranular deformation and intragranular deformation is similar for the formation of both transected
k -fs:YYElTEF:L%2 rI-
-
-
CONTlWLWF’&RTKULATE
-
-CEPEN~ENT&RTICULATE
- -
cumuhltiw stroln
E
Fig. 7. A strain history in which particulate flow dominates the earlier stages and where grain deformation dominates at later stages. Cleavage formed by deformation of grains may thus cause cleavage to develop oblique to the fl plane of the total strain ellipsoid and transect folds formed in the same strain history. A. Successive finite strain ellipses in a noncoaxial strain history. B. Deformation of sanddikes and bedding: the XY plane lies in the acute dihedral angle between deformed dikes and bedding. C. Formation of fold. D. Grain deformation partly suppressed until later stages of strain history. Grain deformation responds to later incremental strain ellipses and produced cleavage oblique to XY of the total strain ellipsoid-and transecting the fold. E. Partition of cumulative total strain between grain strain and particulate flow.
319
folds and cleavage cated schematically
oblique to XY of the total strain ellipsoid. This is indiin a graph of cumulative strain versus time (Fig. 7E).
9. REMARKS
Emphasis has been given to the discontinuous aspects of rock behaviour. This does not imply that continuum mechanics concepts are inapplicable to natural rock deformation. Applied carefully, studies considering rock as a continuum on a suitable scale can provide useful data on finite, though not necessarily total, strains. Indeed, the very application of finite-strain concepts can allow the component of grain sliding to be identified in naturally deformed rock. The most useful strain study should use grain-scale and multigranular strain markers since these both contribute to the magnitude and to the orientation of the total strain ellipsoid. In porous aggregates the contributions of the granular and intergranular components of strain differ in emphasis with time, producing special features such as transected folds and graindeformation fabrics (e.g. cleavage) not simply related to the total strain ellipsoid. ACKNOWLEDGEMENTS
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