The geometry of kink bands in crystals — a simple model

A crystallographic explanation for the geometry of kink bands in crystals is proposed and three possible types of kinking are discussed, 1. simple kinking, 2. kinking associated with a phase change and 3. kinking associated with twin formation. The angular relationships at kink band boundaries have been calculated for a number of minerals and the results compared with observations in the literature. It is proposed that the crystallography of a mineral may be the dominant control of kink band geometry rather than external stress conditions as is generally assumed, this is probably particularly true of kink bands formed under natural conditons.     

Ultimate locking angles for conjugate and monoclinal kink bands

Honea, Reches and Johnson have introduced a theory of conjugate and monoclinal kinking in rocks. A correction is required in expressions for the ultimate locking angles of kink bands.     

Nucleation and growth of kink bands

The geometric and strain properties of an ideal kink band in a perfectly plastic material with one slip surface are determined and two plausible modes by which a kink band can grow while maintaining these properties are presented. The first mode involves change in the orientation of the boundary surface of the kink band as it broadens. In the second mode the initial orientation of this boundary surface is maintained during broadening.A theoretical model is proposed for kink band formation in three stages: first, in an elastically strained material with a suitably oriented planar anisotropy; a small nucleus is either present or develops, and grows in thickness by one or the other or by both of the growth modes; second, as some critical thickness is reached, this nucleus propagates longitudinally until the excessive elastic distortion surrounding its ends is sufficiently relieved, or until the boundary of the body is reached; and third, the band widens by lateral migration of its boundaries, most probably by mode 2 growth.It is proposed that the direction of longitudinal propagation—and hence the orientation of the kink band with respect to principal normal stress—is decided by the value of a, the kink angle, in the nucleus at the time the critical thickness for propagation is reached. A further proposal is that this value of a is in turn decided by a principle of maximum plastic work: the instantaneous increment in strain or in volume within a nucleus is always the one for which the instantaneous increment in plastic work is a maximum at constant deviatoric stress.Calculations based on this theory for the two growth modes working either separately or together as competing processes yield three models of kink band nucleation in reasonable agreement with published experimental data. The most appealing of these models physically is one in which early mode 1 growth is replaced by mode 2 growth as the increments in mechanical work for the two modes become equal.     

通南巴背斜几何学、运动学与构造模型

通南巴背斜发育于四川盆地东北米仓山冲断构造带和大巴山弧形冲断构造带的构造叠合部位, 其形成与演化受到米仓山与大巴山的联合影响, 然而目前其变形特征以及变形机制认识尚且不清楚, 精细研究通南巴背斜构造几何学、运动学对于揭示背斜成因机制以及认识陆内构造变形具有积极作用.本文以覆盖通南巴背斜的三维地震资料为基础, 运用断层相关褶皱理论和平衡复原等方法, 精细刻画出通南巴背斜几何学与运动学特征, 并建立构造模型, 探讨其成因机制.研究表明, 通南巴背斜总体具有"东西分段、上下分层、早晚期构造叠加"的特征, 具体表现为: 1)受控于三叠系嘉陵江组膏盐滑脱层、志留系泥岩局部滑脱层以及前震旦系滑脱层, 通南巴背斜分为上、中、下、深4套构造层, 表现为多层滑脱变形特征, 其中, 中部构造层变形强度最大; 2)深部(前震旦系)构造楔发育于整个通南巴背斜, 其个数和几何学形态的变化直接影响了上覆背斜形态以及分段性背斜高点差异; 3)位移沿楔端点向前传递过程中, 受到川中刚性基底的阻挡, 背斜前翼旋转, 形成次级褶皱调节断层; 4)通南巴背斜晚期受大巴山向西南推覆挤压的叠加作用, 表现为中部构造层在东北段发育一系列双重构造和叠瓦构造, 并导致嘉陵江组以上地层被动变形褶皱.     

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.     

The displacement-distance method for contractional kink bands and its application to fold-thrust structures

The displacement-distance (d−x) method can be modified to study the geometry and development of contractional kink bands by dividing displacements into cartesian component vectors. Kink bands are idealised as having constant layer lengths, enabling simple trigonometry to be used to determine the displacement of one wall of the kink band relative to the other wall.

In a consideration of several applications of the d−x method for kink bands, it is shown that displacement is transferred between conjugate and overstepping kink bands in a similar way to displacement transfer between conjugate and overstepping faults and extension fractures. The several different models of kink band formation are shown to each have different displacement characteristics. The d−x method can also be used to study the geometry and evolution of folds related to thrust-propagation and ramps, which are often modelled as having kink band geometries. For instance, the d−x method can be used to show how fault-tip and fault-bend folds cause or accommodate thrust displacement variations, and to estimate displacement rates from the amounts of deformation in different syn-thrust sedimentary layers.     

Geochemistry of a peraluminous granitoid suite from North-eastern Victoria,South-eastern Australia

The Koetong Suite of Silurian, 2-mica granitoids was derived from a metasedimentary source and emplaced into Ordovician sediments and metasediments along the eastern margin of the Western Metamorphic Belt of South-eastern Australia. Whole-rock geochemical considerations preclude derivation of the magmas represented by the granitoids from exposed Ordovician metasediments. The magmas were generated by partial melting of material similar in composition to garnet-cordierite gneisses exposed in the adjacent metamorphic belt. Melting at pressures in excess of 5 Kb and temperatures about 750°C produced peraluminous magmas and, when the degree of partial melting approached 25–30%, these magmas became mobile and moved vertically into the overlying Ordovician sediments. During movement from the source region to the zone of emplacement, separation of the melt and refractory residue components of the magma resulted in a range of compositions so that whole-rock analyses of the granitoids are linearly related on major and trace element variation diagrams. Processes such as crystal fractionation and crystal accumulation may have operated locally. The magmas were largely composed of solid material throughout their emplacement histories and the amount of melt may not have exceeded 30–45% at any stage. Metasedimentary inclusions are a reflection of source heterogeneity.After emplacement of the magmas, in situ crystallization of a relatively anhydrous assemblage of minerals led to water contents in residual, intercrystalline, melts sufficiently high for muscovite to begin crystallization at pressures around 4 Kb. Subsequent saturation of intercrystalline residual melt and loss of the resultant volatile phase caused the development of eutectoid intergrowths involving muscovitebiotite-quartz and alkali feldspar.     

准噶尔盆地西北缘红3 井东侧断层构造几何学、运动学模型

红3井东侧断层的成因与中拐凸起的形成与演化密切相关,解析其构造几何学与运动学特征对于揭示中拐凸起自晚古生代以来的构造变形具有积极作用,并对于研究区的油气勘探具有重要意义。本文利用断层相关褶皱理论,不整合面识别及平衡剖面的方法,对红3井东侧断层进行精细的构造解析、建模与构造复原。中拐凸起发育白垩系-侏罗系、侏罗系-三叠系、三叠系-上乌尔禾组、上乌尔禾组底界及佳木河组-石炭系5个区域不整合面。研究认为,红3井东侧断层为一断层传播褶皱模型,发育生长三角,平面上分为北段、中段和南段。受海西晚期及燕山期的区域挤压作用的影响,红3井东侧断层在早二叠世末期（P₁f末期）至中二叠世晚期（P₂w）及早侏罗世晚期（J₁s）至晚侏罗世发生两期传播活动,并在中段发生分支,分支断层的断距较小。早期的断层活动在中段最强,南段其次,北段最弱。中-下二叠统被抬升,遭受大面积剥蚀,地层缩短量约为3.8 km。晚期的断层活动微弱,且只发生在中段和北段,地层缩短量约为200 m。红3井东侧断层自北东向南西方向的传播、推覆作用控制了中拐凸起的主体构造形态,整体具有“南北分段、早晚期构造叠加”的特征。     

Thrust kinematics and transposition fabrics from a basal detachment zone, eastern Australia

Emplacement of an upper crustal, leading imbricate-fan thrust belt in the Lachlan Fold Belt of eastern Australia was accomplished along a 0.5–1 km thick zone of heterogeneously deformed, low grade phyllonite in pelitic rock. Continuous recrystallization and neocrystallization of mica in a zone of transposition layering has provided a weak zone at the base of a 100 km wide × 150 km exposed length × 10 km thick thrust system. The basal deformation zone is characterized by a low-moderately dipping, strong-intense transposition foliation enclosing elongate fault-bounded slices (up to 20 km long × 5 km wide in map view) of disrupted Cambrian metavolcanics and Upper Ordovician black shales and slates. These are derived from a structurally lower zone of duplexing or from the overturned limbs of anticlinorial structures. The detachment zone is a 10–15 km wide zone of intense deformation showing a transition from open, upright folds with weak cleavage to inclined, tightisoclinal folds with strong axial surface cleavage. The intensity of minor faults also increases into the zone. Leading imbricate fan thrust belts show maximum deformation effects along the basal detachment which forms the frontal or leading fault. The leading imbricate geometry is due to emplacement of the basal detachment zone up the lowest and last formed imbricate thrust. Movement is along a relatively ductile, low viscosity ‘layer’ at the base where strain softening occurs with development of transposition layering. This enables confined ‘flow’ along the basal zone with transport and emplacement of the fold system and duplex zone to higher structural levels. Reaction-enhanced ductility and grain boundary sliding may be important deformation mechanisms responsible for this flow. Localized polydeformation, marked by mesofolds and crenulation cleavage, reflects the interaction between thrust sheets and the movement on faults.     

The geometry of ductile conjugate fold systems in the Ardnamurchan Moine,Scotland

Four ductile phases of superimposed deformation are regionally mappable in the Ardnamurchan Moine in the Western Highlands of Scotland. These deformations are recognized on the basis of their individual geometrical characteristics and are named, in ascending order, the Kentra phase (D₁), the Ardtoe phase (D₂), the Glenmore phase (D₃), and the Claish phase (D₄). Non-systematic earlier structures (pre-D₁), possibly coeval with the climactic metamorphism, are locally observable. Folds and fabrics produced by the D₂, D₁, and D₄ deformations, however, developed as conjugate sets. There is a significant spatial variation in the distribution and intensity of each of the D₁-D₄ phases. The regional deformation of the Moine schists is notably inhomogeneous due to the nature of the D₁-D₄ incremental strains. In the areas affected by large finite strains, pervasive, normally composite LS-fabrics are developed. In the areas that persistently suffered negligible strain increments, right-way-up rocks commonly display several mineral foliations lying at various angles to bedding. The conjugate systems of folds and fabrics appear to be related to the evolution of a ductile shear belt in Ardnamurchan.     

玉树断裂带左旋走滑活动标志及其几何学 与运动学特征

玉树断裂带位于甘孜-玉树断裂带北西段,是一条总体呈NWW向展布的左旋走滑活动断裂带.沿断裂带发育错断水系与冲沟、拉分盆地、地震地表破裂与断裂破碎带等一系列反映玉树断裂带左旋走滑活动的典型地质-地貌标志.在室内遥感解译的基础上,结合最新的野外实地调查成果,对沿玉树断裂带上反映其左旋走滑活动的地质-地貌标志进行了总结,并对断裂带的几何学与运动学特征进行了综合分析.结果表明,玉树断裂带总长约150km,总体走向120～130°,自西向东可划分为呈左阶雁列分布的陇蒙达-结隆段、结隆-结古段和结古-查那扣段3段.沿该断裂带发育的串珠状拉分断陷盆地规模的大小反映出玉树断裂带自西向东拉张效应逐渐减弱、挤压效应逐渐增强的特点.玉树2010年7.1级地震的宏观震中处于晚第四纪活动性最为显著的中段,而仪器震中恰好处于该断裂带的不连续部位,进一步证明雁列走滑活动断裂带上的不连续部位通常是强震活动的初始破裂区域.     

Automated mapping of rock slope geometry,kinematics and stability with RSS-GIS

A GIS-implemented, deterministic approach for the automated spatial evaluation of geometrical and kinematical properties of rock slope terrains is presented. Based on spatially distributed directional information on planar geological fabrics and DEM-derived topographic attribute data, the internal geometry of rock slopes can be characterized on a grid cell basis. For such computations, different approaches for the analysis and regionalization of available structural directional information applicable in specific tectonic settings are demonstrated and implemented in a GIS environment. Simple kinematical testing procedures based on feasibility criteria can be conducted on a pixel basis to determine which failure mechanisms are likely to occur at particular terrain locations. In combination with hydraulic and strength data on geological discontinuities, scenario-based rock slope stability evaluations can be performed. For conceptual investigations on rock slope failure processes, a GIS-based specification tool for a 2-D distinct element code (UDEC) was designed to operate with the GIS-encoded spatially distributed rock slope data. The concepts of the proposed methodology for rock slope hazard assessments are demonstrated at three different test sites in Germany.     

About three sets of kink bands near Herbeumont (Belgian Ardennes)

In the area studied, three differently oriented sets of kink bands occur. The geometry of these structures is described. One particular set with mean kink angles of about 70 shows statistically that the interlimb angles are bisected by the kink band boundary planes. In the author's opinion it reflects the mechanism of formation.

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Zusammenfassung Im Untersuchungsgebiet gibt es drei verschieden orientierte Gruppen von KnickbÄndern. Die Geometrie dieser Strukturen wird beschrieben. Eine der Gruppen mit Knickwinkeln von etwa 70 zeigt nach statistischer Prüfung, da\ die Winkel zwischen den Flanken der Strukturen von den KnickbandbegrenzungsflÄchen geteilt werden. Diese Daten spiegeln nach Meinung des Autors die Bildungsweise dieser Strukturen wider.

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Résumé Dans la région étudiée, il y a trois systèmes de «kink bands» distingués par leurs orientations. La géométrie de ces structures est décrite. Un des systèmes avec un angle de kink de 70 environ, indique que l'angle entre les flancs des structures est partagé par le milieu par les plans limites des kinks. Il est supposé que ces données reflètent la génèse des structures.

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The impact of analogue material properties on the geometry,kinematics, and dynamics of convergent sand wedges

Simulation of geodynamic processes in sandbox experiments requires analogue materials with a deformation behaviour that reproduces the deformation mechanisms of typical crustal rocks. We present data on the frictional strength of different sand types employing static and dynamic shear tests. The sand types analysed are characterised by an elastic/frictional plastic mechanical behaviour with a transient strain-hardening and strain-softening phase prior to transition to stable sliding. This is in conflict with the standard assumption of an ideal cohesionless Coulomb-material with constant frictional properties. The influence of the identified transient material properties on the kinematics, growth mechanisms, and internal deformation patterns of convergent sand wedges results in characteristic wedge segments which vary—depending on material compaction—between wedges with well defined segments (i.e. frontal-deformation zone, frontal-imbrication zone and internal-accumulation zone) with straight slopes and wedges with a continuous convex topographic profile. For most materials, only the frontal part of the wedge is critical during experimental runs. Taper and strength of the wedge segments can be shown to be controlled by the frictional properties of active faults. Wedge segmentation is controlled by a bulk-strength increase toward the rear of the wedge due to fault rotation in mechanically less-favourable orientations and plastic material hardening. The limit between the frontal critical parts of a wedge and internal stable parts is largely controlled by a critical state of stress upon which either renewed failure or fault inactivation occurs. On this basis, we suggest that critical-taper analysis of wedges must be restricted to specific kinematic segments. Comparison of the experimental results with the Nankai accretionary wedge suggests that our interpretation also applies to natural convergent wedges. Moreover, we provide constraints for the selection of adequate granular analogue materials to simulate typical crustal rocks in natural convergent wedges.     

Late Quaternary palaeoecology of Wyrie Swamp,southeastern South Australia

Pollen analysis of two radiocarbon-dated cores provides a history of Wyrie Swamp and the surrounding vegetation, and the result compares with other palynological data from southeastern South Australia. Eucalypt (Eucalyptus) forest or woodland with a scrub understory was the major element before about 50,000 years BP, between ca. 40,000 and 30,000 BP, and after ca. 11,000 BP. More open woodland prevailed between ca. 50,000 and 40,000 BP, and between ca. 26,000 and 11,000 BP. Casuarina stricta, common on sand dunes, migrated to the area about 10,500 years ago and remained as a dominant species until the time of European settlement at about 1840 ad. Postglacial expansion of this species implies that the climate since 10,500 years ago has been warmer than in the preceding period. It probably was drier during the period from 50,000 to 10,500 BP than in the Holocene. The driest period was from 26,000 to 11,000 BP, perhaps corresponding to the time of the last glaciation in Australia. The site is archaeologically important, as a number of wood and stone artifacts that date between 10,200 and 8000 BP have been recovered from the swamp sediments.     

Carbonate mud sedimentation on a temperate shelf: Bass Basin, southeastern Australia

Bass Basin (66,000 km²) is unusual as a carbonate-dominated basin because calcitic carbonate muds are accumulating in relatively shallow (70–85 m) water depths in the central part of the basin (20,000 km²). The carbonate muds are produced by the primary accumulation and disintegration of nannoplankton, as well as through the biodegradation of skeletal carbonate grains accumulating on the sea floor. The muds are transported to the south of the basin to the end of tidal current transport paths, where they accumulate in the lowest-energy environment available in enclosed Bass Basin, although they are still subject to periodic reworking by storm energy. The basin margins consist of coarser, partially palimpsest, carbonate sands, whereas the central muds overlie a Late Pleistocene disequilibrium surface. In cores these muds are up to 1 m thick and thin away from the centre towards the margins. Bioturbation is important in modifying the textural character of the muds by increasing the grain size as faecal pellets, and therefore creating a sea floor not in equilibrium with modern hydrodynamic conditions. Radiocarbon dates for an early post-glacial marine transgression embayment facies in the basin gave ages of 10,290 ± 250 to 11,660 ± 300 years B.P. An age of 8700 ± 710 years B.P. was obtained for the base of the modern strait facies. These ages and facies thicknesses were used to establish Holocene sedimentation rates of < 12 cm/1000 y for the basin centre, falling to < 6 cm/1000 y towards the margins.     

The importance of unsaturated zone biogeochemical processes in determining groundwater composition, southeastern Australia

Analysis of soil, soil water and groundwater in the Mount William Creek catchment, southeastern Australia, shows that Mg²⁺ and Ca²⁺ within infiltrating rainfall are rapidly depleted by plant uptake and adsorption on clay minerals. Na⁺ and K⁺ may exhibit minor enrichment at shallow depths but are quickly readsorbed, so that cation/Cl^– ratios typical of groundwater are observed in soil water within the upper 200 cm of the soil profile for all species. The concentrations of K⁺ and Ca²⁺ in soil and groundwater are more depleted than Na⁺ and Mg²⁺ due to preferential uptake by vegetation. Removal of organic matter results in a continuing, long-term export of all major cations from the soil profiles. The processes of biogeochemical fractionation within the unsaturated zone rapidly modify the cation/Cl^– ratios of infiltrating rainfall to values characteristic of seawater. These mechanisms may have reached steady state, because groundwaters with seawater ion/Cl^– ratios are thousands of years old; the exchange sites on the soil clays are probably saturated, so cations supplied in rainfall are exported in organic matter and incorporated into recharge infiltrating into the groundwater. Much of the chemical evolution of groundwater traditionally attributed to processes within the aquifer is complete by the time recharge occurs; this evolutionary model may have broad application.     

Development of conjugate shear bands during bulk simple shearing

In rocks possessing a strong planar fabric, shear bands of constant shear sense and oriented at an oblique angle to the foliation are considered by many authors to be characteristic of a non-coaxial bulk deformation history, whereas conjugate shear bands are considered to indicate coaxial shortening. However, in two areas where bulk deformation history appears to be non-coaxial (Cap Corse, Corsica and Ile de Groix, Brittany), conjugate shear bands are observed. In order to investigate this problem, experiments were performed by bulk simple shearing using Plasticine as a rock analogue. When slip between layers of the model is permitted, shear bands of normal-fault geometry form with both the same and opposite shear sense as the bulk simple shearing at approximately the same angle with the layering (40°) irrespective of layer orientation in the undeformed state (for initial orientations of 50, 30 and 15°). Shear bands are initially formed within individual layers and may propagate across layer interfaces when further movement along these is inhibited. The existence of conjugate shear bands in Corsica and Ile de Groix is therefore not incompatible with a model of bulk simple shearing for these two regions. In field studies, one should perhaps exercise care in using shear bands to determine the kind of motion or the sense of bulk shearing.     

Dynamic analysis and two types of kink bands in quartz veins deformed under subgreenschist conditions

In order to clarify deformation mechanisms and behaviours of quartz in a low-temperature regime in the earth's crust, microstructural analyses, particularly on kink bands have been carried out for quartz veins moderately deformed under subgreenschist conditions. Both the dominance of subbasal deformation lamellae and geometry of kink bands suggest that basal (0001) slip was the sole active slip system in the deformed quartz. On a morphological basis, kink bands in the quartz were classified into two types: type I is characterized by conjugate and narrow bands with angular hinge zones, and type II by a wide monoclinal band. Dynamic analyses using deformation lamellae and kink bands have revealed that type I kink bands were formed in grains with basal plane (sub-)parallel to the compression axis, whereas type II kink bands were formed in grains with basal planes inclined to it. Using a numerical model of kinking of elastic multilayers modified after Honea and Johnson (Tectonophysics 30, 197–239, 1976), changes of the level of yielding stress for kinking and the width of kink bands as a function of the angle θ between the slip plane and the compression axis have been examined. The theory predicts that type I kink bands were formed at a higher stress level than type II kink bands, and hence occurrence of type I kink bands suggests that a significant strain hardening occurred in the deformed quartz veins. The theory also well explains the fact that the width of type I kink bands (θ=0 to 10°) is narrower by an order of magnitude than type II kink bands (θ=10 to 80°).