Finite-element folds of similar geometry

Model folds of similar geometry have been produced by using the finite-element method and the constitutive relations of a layer of wet quartzite embedded in a marble matrix with an initially sinusoidal configuration and a 10° limb dip. The power law for steady-state flow of Yule Marble (Heard and Raleigh, 1972) is used for the matrix and our new law for Canyon Creek quartzite deformed in the presence of water is used for the layer. The equiv- alent viscosity of the wet quartzite is highly temperature-sensitive, giving rise to a strong temperature dependence of the quartzite: marble viscosity ratio which, at a strain rate of 10⁻¹⁴/sec, drops from 543 at 200° to 0.13 at 800°C. At 375°C (η_q/η_m = 10), concentric folds develop at all strains to 80% natural shortening and stress, finite strain and viscosity distributions are somewhat similar to those found previously. Raising the temperature to 550° C (η_q/η_m = 1), at any stage of prior amplification, causes the folds to flatten with increasing strain, accompanied by attenuation of limbs and thickening of hinges, leading to folds with similar geometries and isoclinal folds at extreme strains. The effects are more pronounced at higher temperatures and at 700° C (η_q/η_m = 0.3) limb attenuation is so severe as to give rise to unrealistic geometries. At temperatures below about 600° C (η_q/η_m = 2), similar folds do not form. It thus appears as if a viscosity contrast near unity is required to produce similar folds in rocks, under the conditions simulated and different temperature dependencies of viscosities of materials in layered sequences is one important means of reducing viscosity contrasts.     

Numerical modelling of finite-amplitude similar folds developing under general deformation histories

A simple model of similar folds in homogeneous materials with anisotropic properties is proposed and it is shown that the model is applicable to a wide range of natural examples of folds. A mathematical derivation is given which allows the instantaneous deformation of the folds to be calculated for any imposed bulk deformation. A means of projecting the effects of the deformation over a finite time interval is described. The modelling is illustrated by simulations of folds observed in the Morcles nappe, western Switzerland, based on the assumption that the folds formed under simple shear bulk deformation. Folds with geometrical features remarkably similar to those natural folds are produced in the modelling by varying the parameters.     

安徽黄栗树地区流变褶皱及其构造意义

黄栗树地区位于张八岭超高压变质带东侧 ,该区变形构造可以划分为基底韧性变形带、韧脆性构造片岩带和流变褶皱带。流变褶皱构造发育于黄 (栗树 )—破 (凉亭 )断裂以东的震旦系和下古生界盖层岩系中 ,自北西向南东依次表现为翻转褶皱、平卧褶皱和倒转褶皱 ;流变褶皱与基底韧性—韧脆性变形呈渐变关系 ,并且与基底韧性—韧脆性变形具有一致的变形运动学和动力学特征 ,反映了扬子地块与华北地块碰撞造山期及折返过程的构造变形特点。     

Planar, non-planar and refolded sheath folds in the Phulad Shear Zone, Rajasthan, India

Progressive ductile shearing in the Phulad Shear Zone of Rajasthan, India has produced a complex history of folding, with development of planar, non-planar and refolded sheath folds. There are three generations of reclined folds, F₁, F₂ and F₃, with a striping lineation (L₁) parallel to the hinge lines of F₁. The planar sheath folds of F₁ have long subparallel hinge lines at the flanks joining up in hairpin curves at relatively small apices. L₁ swerves harmoniously with the curving of F₁ hinge line. There is a strong down-dip mineral lineation parallel to the striping lineation in most places, but intersecting it at apices of first generation sheath folds. Both the striping and the mineral lineation are deformed in U-patterns over the hinges of reclined F₂ and F₃. Folding of axial surfaces and hinge lines of earlier reclined folds by later folds was accompanied by very large stretching and led to the development of non-planar sheaths. The reclined folds of all the three generations were deformed by a group of subhorizontal folds. Each generation of fold initially grew with the hinge line at a very low angle with the Y-axis of bulk non-coaxial strain and was subsequently rotated towards the down-dip direction of maximum stretching. The patterns of deformed lineations indicate that the stretching along the X-direction was extremely large, much in excess of 6000 percent.     

Growing folds and sedimentation of the Gosau Group, Muttekopf, Northern Calcareous Alps, Austria

Analysis of the three-dimensional geometry of Upper Cretaceous clastics in the Muttekopf area (Northern Calcareous Alps, Austria) indicate fold and fault structures active during deposition. Coniacian continental to neritic sedimentation (Lower Gosau Subgroup) was contemporaneous with displacements on NW-trending faults and minor folding along NE-trending axes. From the Santonian onwards (sedimentation of the deep-marine Upper Gosau Subgroup) the NW-trending faults were sealed and large folds with WSW-trending axes developed. The direction of contraction changed to N-S after the end of Gosau deposition in the Danian (Paleocene). Synorogenic sedimentation patterns indicate continuous contraction from the Coniacian to the Late Maastrichtian/?Danian. Therefore, large-scale extension as observed in the central part of the Eastern Alps cannot be documented in the western parts of the Northern Calcareous Alps. A combination of subduction tectonic erosion for the frontal parts and gravitational adjustment of an unstable orogen after nappe stacking for the internal parts possibly accounts for the different development of Gosau basins in the frontal and trailing regions of the Austroalpine wedge.     

分形褶皱复杂性的流变因素研究

根据Ramberg的纵弯褶皱粘性力学实验,在褶皱形态的分形分析基础上,利用分形理论和褶皱的流变学理论导出了褶皱的分数维(D)与岩层厚度(h)和粘度(μ)间的关系式,并探讨了褶皱复杂性对褶皱分数维的影响,从中获得有关复杂褶皱的流变学信息。影响分形褶皱复杂程度的因素很多,主要因素包括岩层的厚度和粘度。因此,对褶皱的分形测量和岩层厚度及粘度的分析,可以定量分析分形褶皱形成的流变机理。这一研究是褶皱的非线性流变学理论研究的一个尝试。     

Geometrical classification of multilayered folds

A new classification scheme based on the degree of fluctuation in the geometry of different layers of a multilayered fold is suggested. The classification scheme uses the degree of fluctuation in geometry in terms of the standard deviation (σ_n) of the thickness parameters t_α′ (orthogonal thickness parameter) and T_α′ (axial plane parallel thickness parameter) for n number of layers, and dip angle α. The degree of fluctuation in the geometry of a multilayered fold can be represented by σ_n(t_α′) or σ_n(T_α′) versus α plots on a Cartesian plane. In the proposed classification scheme, multilayered folds have been divided into two broad categories, namely `isodeviatoric' and `anisodeviatoric'. Isodeviatoric folds have a constant fluctuation in the geometry of different layers recorded in terms of σ_n(t_α′) or σ_n(T_α′) for α>10°. A special type of isodeviatoric fold is recognised as `analogous fold' in which each layer exhibits identical geometry [σ<sub>n</sub>(t<sub>α</sub>′) or σ<sub>n</sub>(T<sub>α</sub>′)=0]. Plots of isodeviatoric folds lie parallel to the abscissa (α) and those of analogous folds lie along the abscissa in the σ<sub>n</sub>(t<sub>α</sub>′) or σ<sub>n</sub>(T<sub>α</sub>′) (ordinate) versus α (abscissa) diagram. Analogous folds have been divided into ten varieties (1A1, 1A2, 1A3, 1B, 1C, 2, 3A, 3B, 3C and composite-analogous types). The anisodeviatoric folds do not exhibit constant fluctuation (deviation) in the geometry of different constitutive layers. Such folds have been subdivided into `peri-analogous', `sub-analogous', `sub-non-analogous', `non-analogous' and `strongly non-analogous' types. This classification scheme is applied to folds developed in low-grade metasedimentary rocks of the Mahakoshal Group and low- to medium-grade rocks of the Chhotanagpur Granite Gneiss Complex in central India.     

Strain determination from concentric folds

A new technique to determine flattening strain from initially concentric folds is described in this paper. The proposed method is simple and involves direct measurements on fold profiles. It requires measurement of the distance between the center of the fold to the middle of the layer, and this is plotted as a function of line orientation. The method needs few measurements at fixed angular spacing resulting in quick estimation of strain.     

Strain analysis in folds (Infrahelvetic complex,Central Alps)

Strain analysis based on initially uniformly oriented elliptical particles in an oolitic limestone (Blegi oolite) was used to study the homogeneity of the state of strain on various scales, kinematics of folding and deformation mechanisms. A computer (reduced means) method for strain analysis is presented which is based on deforming a population of ellipses with shape and orientation properties of measured undeformed ooids. The strain values obtained with this method are within an accuracy of about 10% (in terms of axial ratios) and are in good agreement with the ones obtained with existing graphical methods. The state of strain is homogeneous on the scale of a thin section, handspecimen and outcrop, provided that regions around relatively strong fossils and regions of marked variations in lithology are avoided. Whole rock strains and strains as indicated by ooids alone are similar. Strain patterns in folds in limestones embedded in sandstones, shales and marl are compatible with bending accompanied simultaneously with a shortening perpendicular to the axial surface. The shortening may be attributed to the shear strains related to fold asymmetry and overthrusting. Strains on the outer arcs of a competent dolomite layer compare well with theoretical and experimental fold models; strain patterns include complex contact strains and change along the fold hinge line across a transverse fault which was active during the folding process. Strains parallel to the hinge line are more or less uniform but do not necessarily represent a plane strain state. Volume change took place during deformation. It was accomplished by pressure solution processes, the pressure solved material being partly redeposited. Pressure solution accounts for only a relatively small fraction of the bulk finite strain and was accompanied by plastic flow. Intracrystalline deformation together with grain boundary sliding and/or grain boundary migration went hand in hand with recrystallization (noteably grain growth).     

内蒙古中部大青山地区推覆构造系统及与断层相关的褶皱

对内蒙古大青山地区西部推覆构造及与断层相关的褶皱的研究表明，大青山构造系统自南向北分为根部逆冲推覆岩席带、中部斜歪倒转褶皱一逆冲断层带和前缘断层相关褶皱带，变形强度由根带向前缘带逐渐减弱，前缘带发育典型的断层转折褶皱和断层传播褶皱。推覆构造运动方向由SSE向NNW推覆，主要形成于中侏罗世末期，推覆距离达10～20km，其形成可能与鄂霍次克洋在燕山期的闭合有关。     

Geometry of sheath folds and related fabrics at the Luikonlahti mine,Svecokarelides, eastern Finland

The Luikonlahti Cu-Co-Zn sulphide ore deposit is hosted by metasediments associated with serpentinites in the 1.97 Ga old Outokumpu assemblage in the Svecokarelides of eastern Finland. Polyphase deformation of the host rocks, a history shared by the ore body, includes a phase of sheath fold propagation. A modified vergence rule, utilizing only the intersection geometry of planar fabric elements, permits recognition of these extremely curvilinear folds in poorly exposed terrain. The detailed geometry of these rocks is independently resolved from borehole and underground stope records. Sheath fold propagation occurred during D₂, the second phase of regional deformation. In the Kaavi district D₂ major structures are either thrusts or thrust-related. The Luikonlahti sheaths are located in a steeply dipping shear zone formed during this deformation episode.     

The geometry and kinematics of flow perturbation folds

Minor folds formed synchronous with ductile deformation in high strain zones can preserve a record of the scale and kinematics of heterogeneous flow. Using structures associated with WNW-directed Caledonian thrusting in N Scotland, we show that localised perturbations in flow resulted in the generation of predominantly cylindrical minor folds with hinges lying at low angles to the transport direction. These define a series of larger-scale fold culminations (reflecting ‘surging flow’) or depressions (reflecting ‘slackening flow’) that are bisected by transport-parallel culmination and depression surfaces. The fold patterns suggest a dominance of layer-normal differential shearing due to gradients in shear strain normal to transport. Culmination surfaces are marked by along-strike reversals in the polarity of structural facing and vergence of minor folds which, contrary to classic fold patterns, define reverse asymmetric relationships. Culmination surfaces separate folding in to clockwise (Z folds) and anticlockwise (S folds) domains relative to the transport lineation. The dip of fold axial planes systematically increases as their strike becomes sub-parallel to transport resulting in a 3D statistical fanning arrangement centred about the transport direction. Thus, mean S- and Z-fold axial planes intersect precisely parallel to the transport lineation and potentially provide a means of determining transport directions in cases where lineations are poorly preserved. Culminations display convergent fold patterns with fold hinges becoming sub-parallel to transport towards the culmination surface and underlying detachment, whilst axial planes define overall concave up listric geometries which are bisected by the culmination surface. Thus, around culminations and depressions there are ordered, scale-independent relationships between transport direction, shear sense, fold facing, vergence and hinge/axial plane orientations. The techniques described here can be applied and used predictively within any kinematically coherent system of ductile flow.     

Noncylindrical flexural slip folds in nature and experiment

Some naturally formed folds in North Cornwall, England, show the following geometrical features:

1. (a) each fold is noncylindrical;

2. (b) the profile shape varies along the hinge-line (chevron-shaped at culmination, rounded at terminations);

3. (c) hinge-lines and axial surfaces of some folds curve strongly in certain restricted areas. Micro-structures indicate that the folds formed by geometric bending and flexural slip.

The progressive development of folds like these has been simulated by subjecting multilayered plasticine models to layer-parallel compression in coaxial stages. This technique allows folds to be observed and measured after each deformation stage. The folds initiate at irregularities in the layering or stress-field. As each fold amplifies, it acquires a characteristic three-dimensional shape: generally the profile is chevron-shaped at the point of maximum amplitude and is rounded at the terminations. Growth of a fold also involves a lengthening of the hinge-line by propagation of the terminations (e.g. into areas of previously unfolded layering). Individual folds also tend to trigger the development of new folds at either side, eventually forming a fold complex with regular wavelength. Propagating fold complexes may interfere by processes of linking and blocking that are not strictly the same as interference effects in other wavelike processes. The interference of fold complexes is described with reference to layer surfaces and crosssections. Causes of noncylindricity are examined. Geometrical aspects of naturally formed folds are analyzed in the light of the experimental findings.     

Statistical classification of macroscopic folds as cylindrical, circular conical, or elliptical conical

A folded surface can be represented by the orientation of normals to the surface measured at several locations. When plotted on the unit sphere, the pattern of normals determines the type of fold. Poles from a cylindrical fold give a great circle on the unit sphere, whereas poles of a circular conical fold give a small circle, and poles from an elliptical conical fold give the projection of an ellipse onto the surface of the sphere. Several statistical tests that appear in the literature for classifying folds are discussed and compared. All but one of the tests use quantities obtained from an iterative least-squares procedure that fits the appropriate curve on the sphere. The classification procedure is illustrated with folds from the Canadian Rocky Mountains and uses for examples a cylindrical fold and a circular conical fold from the Smoky River coal field near Grande Cache, Alberta, and an elliptical conical fold near Jasper, Alberta. This methodology has resulted in new coal reserves in the Grande Cache area.This paper was presented at Emerging Concepts, MGUS-87 Conference, Redwood City, California, 13–15 April 1987.     

The geometrical classification of noncylindrical folds

The majority of naturally occurring folds are noncylindrical if definitions are strictly applied. A new classification of noncylindrical folds using a triangular plot and based on measurements of interlimb angle and hinge angle is proposed. The end-members of the triangular plot are planes, cylindrical isoclines, and isoclinal domes. An infinite range of cylindrical and noncylindrical plane fold shapes may be represented. Noncylindrical nonplane folds may be represented on the plot using proportional circles to signify the degree of non-planarity. The triangular diagram is used to classify large-scale folds from north Norway and their origin is discussed.     

Eye-type folds at the Palmi shear zone (Calabria,Italy)

International Journal of Earth Sciences -     

Wavelength-amplitude characteristics of polyphase folds in the Precambrian bundelkhand complex, India

On the basis of wavelength-amplitude measurements on minor folds in a Precambrian complex of Central India, it is demonstrated that the folds related to a particular generation are characterised by some definite values of their wavelength/amplitude ratio. The wavelength-amplitude plots show that the folds related to a particular generation are all confined to certain definite fields.     

Mass transfer and preferred orientation development during extensional microcracking in slate-belt folds, Elura Mine, Australia

Microstructures in slate belt rocks at the Elura Mine, near Cobar, south-eastern Australia, indicate that volume loss by syntectonic dissolution is coupled with mass accretion by reprecipitation of the dissolved material in dilational sites. The mass accretion is sustained primarily by repetitive tensile microfracturing at high pore-fluid pressures. Oriented growth in the inter- and intragranular microcracks is locally host-controlled, creating lattice- and shape-preferred orientations. The grain-scale crack-seal features throughout the rock reflect rhythmic fluid pressure fluctuations; a balance is achieved between the fracture-induced permeability (and consequent flushing rates), and the rate of fluid build-up in a relatively sealed environment.
Instability in the balancing factors can lead to localization and intensification of tensile failure (and hence, tension vein formation) in the grain aggregate. Growth of veins by crack-seal also reflects a steady state, but with more localized fluctuations of fluid flow on the aggregate scale. Still larger imbalances between flushing and fluid accumulation (i.e. pressure variations) induce breccia veining. The larger pressure gradients over greater distances, associated with dilation localization (from pervasive microfracturing to spaced breccia domains), allow fluid channelling with an increased potential for chemical fluid/rock disequilibrium. Therefore, large breccia vein systems tend to be sites of extensive fluid/rock interaction and replacement, as spectacularly illustrated by the syntectonic sulphide orebodies at Elura. The huge amounts of silicate, carbonate and sulphide accumulated during folding at Elura illustrate the large scale of source and sink couples possible in solute mass transfer.     

The sheath folds in the Tananao Group between Tienshiang and Tailuko, east-west cross-island highway, Taiwan

Sheath folds or “eye” folds on decimetric to metric scales are well-developed in the metachert-marble-green rock interlayers of the Changchun Formation and in the marble lens of the Tienhsiang Formation, within the Tananao Group between Tienhsiang and Tailuko, along E-W cross-island highway of Taiwan. Closely associated with the sheath folds are the tight to isoclinal folds with rectilinear axes which are parallel to the hinge line of the “eyes”, and the directions of these folds range from N-S to N30°E with gentle plunges to the north or south.The sheath folds are believed to have been formed during the second phase of deformation in this region. The traces of the earlier folding can generally be found at the hinges or limbs of these sheath folds.The explanation presented here is that the sheath fold might be generated episodically during the F₂ deformational phase throughout the entire history of progressive shearing as a result of episodic instability of the flow with successive refolding of metamorphic fabric, during Plio-Pleistocene deformation of Taiwan.