Pulsating strains

Pulsating strains are modelled analytically using a continuum model with a well defined heterogeneous rheology. The mechanical continuum comprises single circular cylindrical inclusions of isotropic homogeneous viscosity hosted in a less viscous matrix. The analysis concentrates on the behaviour of the competent inclusion and demonstrates that the progressive deformation of the inclusion is entirely controlled by its viscosity ratio to the host and the orientation of the far field stress. The rate of deformation is determined by the stress magnitude and the viscosity of the inclusion, but does not affect the deformation path followed. An extreme case is provided by pure shear deformations where, by definition, the shear rate vanishes from the deformation tensor. Vorticity will then be zero, and strains will develop coaxially without pulsation.     

浅变质岩石中的叠加韧性剪切带——以吉林桦甸二道甸子地区为例

吉林省桦甸市二道甸子金矿区的板岩、千枚岩中,存在着平行叠加式和垂直叠加式两个类型的韧性剪切带。它们叠加在早期变形构造之上,显示出不同的构造特征。前者以含“叶理鱼”的疙瘩状千枚岩为特征,“叶理鱼”的含量决定了其应变强度。后者以折劈构造成带状发育为特征,折劈的不同类型决定了其应变强度。     

单轴压缩岩样轴向回跳及侧向回跳理论研究

研究了单轴压缩条件下轴向回跳及侧向回跳之间的关系。在应变软化阶段,试样的弹性轴向应变及弹性侧向轴向应变由虎克定律确定;试样的轴向塑性应变及侧向塑性轴向应变由梯度塑性理论确定,它们与应力水平、剪切带倾角及宽度、软化模量及试样的尺寸有关。根据轴向应力-应变曲线及侧向应力-应变曲线软化段斜率的正负,得到了轴向回跳及侧向回跳的条件。轴向回跳的原因是轴向弹性应变的恢复快于轴向塑性应变的增加。侧向回跳的原因是侧向弹性应变的恢复快于侧向塑性应变的增加。当剪切带倾角的正切小于泊松比与试样宽高比之积时,若侧向变形发生回跳,则轴向变形就发生回跳;反之,若轴向变形发生回跳,则侧向变形就发生回跳。对于常规岩样,若侧向发生回跳,则轴向必定是回跳的。在应变软化阶段,根据轴向应变及侧向应变是否发生回跳,轴向应变与侧向应变曲线被划分为4种类型：即轴向回跳及侧向回跳情形、轴向回跳及侧向回跳情形、轴向不回跳及侧向回跳情形及轴向回跳及侧向不回跳情形,并得到了各种类型的条件。     

Strain distribution in superposed buckling folds and the problem of reorientation of early lineations

Two series of experiments were carried out with soft model-materials in order to assess the relative importance of initial homogeneous strain, external rotation and late-stage strain in reorienting early lineations during superposed buckle-folding. In the first series cylindrical buckling folds were produced in embedded planar sheets containing a “lineation”. In the second series noncylindrical folds were produced by compression of a set of cylindrical folds. The experiments indicate that the ratio of buckle shortening to layer-parallel strain is much smaller when the principal extension is parallel to the fold-axis than in the case when the principal extension is perpendicular to the fold-axis. In very competent rocks, the reorientation of old lineations is mainly by external rotation and by the associated concentric longitudinal strain. In moderately competent rocks, the orientation of early lineations always changes by initial homogeneous strain before buckling becomes significant. Because of the unlike amounts of initial strain in layers of different competences, orientations of unrolled lineations may not be parallel in disharmonically folded layers of unlike competences. Under certain conditions the early lineation may become virtually parallel to the later fold-axis. The experiments indicate that the effects of late-stage strain in buckle-folding are largely restricted to the incompetent layers of a multilayer. Hence, if orientation data of early lineations in both competent and incompetent rocks are lumped together, the pattern of orientation may become quite complex. Even for a single competent layer, the pattern of early lineations can locally become complex because of the complex nature of concentric longitudinal strain (and strain resulting from stretching of middle surface of the layer), development of conical folds, development of shear strain along hinge zones of deformed early folds and also because of the development of different orders of folds in both the first and the second deformations.     

Foreland- and hinterland-verging structures in fold-and-thrust belt: an example from the Variscan foreland of Sardinia

In the Variscan foreland of SW-Sardinia (Western Mediterranean sea), close to the leading edge of the nappe zone, nappe emplacement caused folding and repetition of stratigraphic successions, km-scale offset of stratigraphic boundaries and an extensive brittle-ductile shear zone. Thrusts assumed a significant role, accommodating a progressive change of shortening direction and forming complicated thrust triangle zones. During thrust emplacement of the nappes, strong penetrative deformation affected rocks beneath the basal thrust of the nappe stack and produced coeval structures with both foreland-directed and hinterland-directed (backthrusting) shear sense. Cross-cutting and overprinting relationships clearly show that the shortening direction changed progressively from N–S to E–W, producing in sequence: (1) E–W trending open folds contemporaneous with early nappe emplacement in the nearby nappe zone; (2) recumbent, quasi-isoclinal folds with axial plane foliation and widespread, “top-towards-the-SW”, penetrative shearing; (3) N–S trending folds with axial plane foliation, contemporaneous with late nappe emplacement; (4) backthrusts and related asymmetrical folds developed during the final stages of shortening, postdating foreland-verging structures. Structures at (3) and (4) occurred during the same tectonic transport “top-towards-the-E” of the nappe zone over the foreland. The several generations of folds, thrusts, and foliations with different orientations developed, result in a complex finite structural architecture, not completely explicable by the theoretical model proposed up to date.     

Geochemistry of spinel-hosted amphibole inclusions in abyssal peridotite: insight into secondary melt formation in melt–peridotite reaction

Spinel-hosted hydrous silicate mineral inclusions are often observed in dunite and troctolite as well as chromitite. Their origin has been expected as products associated with melt–peridotite reaction, based on the host rock origin. However, the systematics in mineralogical and geochemical features are not yet investigated totally. In this study, we report geochemical variations of the spinel-hosted pargasite inclusions in reacted harzburgite and olivine-rich troctolite collected from Atlantis Massif, an oceanic core complex, in the Mid-Atlantic Ridge. The studied samples are a good example to examine geochemical variations in the inclusions because the origin and geological background of the host rocks have been well constrained, such as the reaction between MORB melt and depleted residual harzburgite beneath the mid-ocean ridge spreading center. The trace-element compositions of the pargasite inclusions are characterized by not only high abundance of incompatible elements but also the LREE and HFSE enrichments. Distinctive trace-element partitioning between the pargasite inclusion and the host-rock clinopyroxene supports that the secondary melt instantaneously formed by the reaction is trapped in spinel and produces inclusion minerals. While the pargasite geochemical features can be interpreted by modal change reaction of residual harzburgite, such as combination of orthopyroxene decomposition and olivine precipitation, degree of the LREE enrichment as well as variation of HREE abundance is controlled by melt/rock ratio in the reaction. The spinel-hosted hydrous inclusion could be embedded evidence indicating melt–peridotite reaction even if reaction signatures in the host rock were hidden by other consequent reactions.     

一个韧性转换挤压带的变形分解作用：以阿尔金断裂带东段为例

变形构造研究显示阿尔金划分成具有近水平拉伸线理的韧性左行走滑变形域和具有陡角度倾伏拉伸线理的收缩变形域。在ＳＳ与ＰＳ之间的过渡区域还发现中等角度倾伏的拉伸线理。     

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).     

Application of kinematic vorticity and gold mineralization for the wall rock alterations of shear zone at Dungash gold mining,Central Eastern Desert,Egypt

The use of porphyroclasts rotating in a flowing matrix to estimate mean kinematic vorticity number (Wm) is important for quantifying the relative contributions of pure and simple shear in wall rocks alterations of shear zone at Dungash gold mine. Furthermore, it shows the relationship between the gold mineralization and deformation and also detects the orientation of rigid objects during progressive deformation. The Dungash gold mine area is situated in an EW-trending quartz vein along a shear zone in metavolcanic and metasedimentary host rocks in the Eastern Desert of Egypt. These rocks are associated with the major geologic structures which are attributed to various deformational stages of the Neoproterozoic basement rocks. We conclude that finite strain in the deformed rocks is of the same order of magnitude for all units of metavolcano-sedimentary rocks. The kinematic vorticity number for the metavolcanic and metasedimentary samples in the Dungash area range from 0.80 to 0.92, and together with the strain data suggest deviations from simple shear. It is concluded that nappe stacking occurred early during the underthrusting event probably by brittle imbrication and that ductile strain was superimposed on the nappe structure during thrusting. Furthermore, we conclude that disseminated mineralization, chloritization, carbonatization and silicification of the wall rocks are associated with fluids migrating along shearing, fracturing and foliation of the metamorphosed wall rocks.     

The origin of strain patterns resulting from contemporaneous deformation and metamorphism in the Sambagawa metamorphic belt

Abstract The magnitudes of plastic strains of 104 metacherts were determined from the deformed shape of initially spherical radiolarians in the Sambagawa high- P type metamorphic belt of Western Shikoku, Japan. The strain magnitude increases with increasing metamorphic temperature from several per cent to 250%. The a₂/a₃ ratio of strain ellipsoids in the higher metamorphic grades decreases with increasing metamorphic grade while the a₁/a₂ ratio increases rapidly. The long axis of the strain ellipsoid for every grade is nearly parallel to the length of the metamorphic belt, suggesting that the flow direction of the synmetamorphic deformation was uniform along the belt. A map of strain zones within the Sambagawa high- P type metamorphic belt reveals that the metamorphic belt underwent a progressive bulk inhomogeneous shear deformation and that the high-grade zones represent a deep-seated boundary shear zone on the accretionary wedge between a subducting oceanic plate and the immobile rigid continental plate.     

Influence of object concentration on finite strain and effective viscosity contrast: insights from naturally deformed packstones

Deformed conglomerates and ooidal/oncoidal packstones are commonly used to evaluate finite strain in deformed sedimentary successions. In order to obtain a correct estimate of finite strain, it is necessary to consider not only the different behaviour of matrix and objects, but also object concentration. The analysis of two-component rocks characterised by high values of packing commonly results in a substantial underestimate of bulk strain and of viscosity contrast between objects and matrix. In this study, the effects of the volumetric fraction of competent inclusions on both object and bulk measured finite strain, as well as on apparent viscosity contrast, have been investigated in naturally deformed packstones characterised by variable object concentration on the scale of the hand specimen (and hence for homogenous viscosity contrast). Object finite strain has been obtained by Rf/ analysis, whereas the Fry method provides a measure of whole-rock strain that is also a function of inclusion concentration. Therefore, the finite strain measured by the Fry method is better termed effective bulk strain. In order to investigate the role of object concentration, this parameter has been plotted against object and effective bulk strain, and also against viscosity contrast. These diagrams show that: (i) for high values of packing, measured object and effective bulk strain show values that are significantly lower with respect to the calculated maximum value (that would result in the ideal case of no particle interaction and represents therefore the real bulk strain of the samples); (ii) the viscosity contrast shows lower values with respect to the calculated maximum one (that is equal for the three principal sections of the finite strain ellipsoid), and as packing reaches the maximum value, the viscosity contrast approaches a unit value. Empirical equations have also been found that link object concentration with both object and effective bulk finite strain.     

Rheological and kinematical responses to flow of two-phase rocks

Numerical simulations have been performed to investigate the strain-dependent behaviour of rheological and kinematical responses to flow of two-phase rocks using the commercial finite-difference program FLAC2D. It was assumed that the two phases have Maxwell rheology. Plane strain and velocity boundary condition, which produces a simple shear deformation, were also assumed. Two types of geometries were considered: strong phase supported (SPS) and weak phase supported (WPS). We calculated strain-dependent variations of effective viscosity and partitioning of strain rate, vorticity and kinematic vorticity number during deformation in both SPS and WPS structure models.The results show that the strain-dependent behaviour is largely influenced by the geometry of the composite. SPS models show both strain hardening and strain softening during the simulations, with strain hardening preceding strain softening. A critical shear strain is necessary to begin the strain softening behaviour. Strain hardening and strain softening are accompanied by a reduction and an increase of the partition of strain rate into the weak phase, respectively. On the other hand, WPS models show only weak strain hardening and strain softening, being the strain-dependent behaviour close to a steady state flow. In addition, the following results are obtained on vorticity and kinematic vorticity number; (1) in both SPS and WPS models the partition of vorticity into weak phase increases with progressive shear strain, i.e. the strong phase becomes less rotational, (2) in SPS models weak inclusions changes from sub-simple shear to super-simple shear with progressive strain, whereas the strong matrix changes from super-simple shear to sub-simple shear, (3) in WPS models the strong inclusions with high viscosity contrasts are less rotational but can be in super-simple shear condition to high strains.The observed strain-dependent behaviours have been compared with previous proposed analytical models. The degree of agreement is variable. Balshin and Ryshkewitch–Duckworth models are only applicable to SPS models. Ji-generalized mixture rule model is applicable to both models.The results suggest that polyphase rocks with SPS structure during ductile shear deformation respond as strain softening materials, after an initial strain hardening stage that may drive to the strain localization into the material.     

A general deformation matrix for three-dimensions

A deformation that is obtained by any simultaneous combination of two steady-state progressive deformations: simple shearing and a coaxial progressive deformation, involving or not a volume change, can be expressed by a single transformation, or deformation matrix. In the general situation of simple shearing in a direction non-orthogonal with the principal strains of the coaxial progressive deformation, this deformation matrix is a function of the strain components and the orientation of shearing. In this example, two coordinate systems are defined: one for the coaxial progressive deformation (x_i system), where the principal and intermediate strains are two horizontal coordinate axes, and another for the simple shear (x _i ^t’ system), with any orientation in space. For steady-state progressive deformations, from the direction cosines matrix that defines the orientation of shear strains in the x_i coordinate system, an asymmetric finite-deformation matrix is derived. From this deformation matrix, the orientation and ellipticity of the strain ellipse, or the strain ellipsoid for three-dimensional deformations, can be determined. This deformation matrix also can be described as a combination of a rigid-body rotation and a stretching represented by a general coaxial progressive deformation. The kinematic vorticity number (W _k is derived for the general deformation matrix to characterize the non-coaxiality of the three-dimensional deformation. An application of the deformation matrix concept is given as an example, analyzing the changes in orientation and stretching that variously-oriented passive linear markers undergo after a general two-dimensional deformation. The influence of the kinematic vorticity number, the simple and pure shear strains, and the obliquity between the two deformation components, on the linear marker distribution after deformation is discussed.     

A new approach to modeling perpendicular fabrics in porphyritic plutonic rocks using the finite element method

A growing body of field evidence indicates that hypersolidus fabrics preserved in syntectonic plutons are likely to have formed in highly crystallized ‘rigid sponge’ magma. This paper demonstrates that such magma could be idealized as a rheological solid and that the development of non-coaxial fabrics in plutonic rocks can very conveniently be modeled in the framework of solid mechanics. Using the finite element method (FEM), we modeled two strain regimes of small magnitudes (plane-strain horizontal simple shear with the shear strain γ of up to 0.30 and plane-strain pure shear of up to 15% shortening) superposed onto vertically oriented and variously spaced elastic phenocrysts set in the viscoelastic matrix. In the simple shear regime, the phenocrysts slightly rotate toward the shear plane, while the principal strain directions in the matrix are instantaneously oriented at an angle of about 45° or less to the phenocryst fabric. Simple shear thus can only lead to the formation of oblique phenocryst and matrix fabrics. By contrast, the vertical phenocryst fabric is maintained in the pure shear regime, and a new horizontal fabric can develop almost instantaneously in the matrix even for small amounts of superposed shortening (5% shortening after 10 ky in our model). We conclude that such a mechanism can easily produce perpendicular hypersolidus fabrics in plutonic rocks and that only a very short time span (first thousands of years) is required to develop magmatic fabric in a pluton for ‘normal’ rates (10⁻¹⁵ to 10⁻¹³ s⁻¹) of tectonic deformation.     

Lack of porphyroblast rotation in the Otago schists, New Zealand: implications for crenulation cleavage development, folding and deformation partitioning

Porphyroblasts of garnet and plagioclase in the Otago schists have not rotated relative to geographic coordinates during non-coaxial deformation that post-dates their growth. Inclusion trails in most of the porphyroblasts are oriented near-vertical and near-horizontal, and the strike of near-vertical inclusion trails is consistent over 3000 km². Microstructural relationships indicate that the porphyroblasts grew in zones of progressive shortening strain, and that the sense of shear affecting the geometry of porphyroblast inclusion trails on the long limbs of folds is the same as the bulk sense of displacement of fold closures. This is contrary to the sense of shear inferred when porphyroblasts are interpreted as having rotated during folding.
Several crenulation cleavage/fold models have previously been developed to accommodate the apparent sense of rotation of porphyroblasts that grew during folding. In the light of accumulating evidence that porphyroblasts do not generally rotate, the applicability of these models to deformed rocks is questionable.
Whether or not porphyroblasts rotate depends on how deformation is partitioned. Lack of rotation requires that progressive shearing strain (rotational deformation) be partitioned around rigid heterogeneities, such as porphyroblasts, which occupy zones of progressive shortening or no strain (non-rotational deformation). Therefore, processes operating at the porphyroblast/matrix boundary are important considerations. Five qualitative models are presented that accommodate stress and strain energy at the boundary without rotating the porphyroblast: (a) a thin layer of fluid at the porphyroblast boundary; (2) grain-boundary sliding; (3) a locked porphyroblast/matrix boundary; (4) dissolution at the porphyroblast/matrix boundary, and (5) an ellipsoidal porphyroblast/shadow unit.     

Mica Inclusions inside Host Mica Grains from the Sutlej Section of the Higher Himalayan Crystallines, India—Morphology and Constrains in Genesis

Abstract: Biotite and muscovite inclusions inside mica host minerals from the Sutlej section of the Higher Himalayan Crystalline were studied under an optical microscope. These inclusions formed possibly by local recrystallization of mica grains during regional prograde metamorphism, with some affected by top-to-SW shear leading to parallelogram shapes. Recrystallization may have been assisted by solution transfer along the cleavage planes of the host grains. The relative competency of deformed phyllosilicate inclusions with the same or different composition to the host depends on the size and orientation of (001) cleavage planes of the inclusions relative to the host. Shearing of mica inclusions led to their parallelogram geometries within the contained mica inclusions. Some of the sheared inclusions deflect cleavage planes in the host minerals and define flanking microstructures. Trapezoid-shaped inclusions are a new finding that deserves more attention for their genesis. These structurally anisotropic inclusions did not originate from sub-grains, secondary infillings or retrogression. These inclusions are also not related to pseudomorphism, isomorphism, folding of the bulk rock etc. Some of the inclusions formed by recrystallization of the host mineral during top-to-SW ductile shear.     

Strain distribution across an experimental single-layer fold

Experiments have been carried out to study the effects of progressive deformation on the shape of folds and the variation in two-dimensional strains on cross-sections of singlelayer folds in a less competent matrix, in a pure-shear plane-strain deformation box with no volume change. The layer shortening continues after buckling has set in, leading to thickening of the fold hinge and with progressive buckling the layer elongates. During the layer elongation stage of folding the hinges continue to thicken, whereas the limbs thin out. Concentric folds are a combination of Class 1a type in the outer arc which gradually change to Class Ib type and then to Class 3 folds of Ramsay (1967) in the inner arc. Tangential longitudinal strains and shearing strains predominate in the fold-hinge zone and in the fold limbs of the buckling layer, respectively. Initially, uniform layer-flattening strains perpendicular to the layering develop which become extensive strains in the outer fold arc and compressive strains in the inner fold arc with progressive buckling. In the outer fold arc the extensive strains are distributed laterally over a wider zone and are of a lower magnitude than the compressive strains which are restricted to a narrow zone in the inner fold arc. The neutral surface first appears when the initial layer-flattening strains are removed due to extensive strains on the outer arc and with progressive buckling migrates towards the inner fold arc and extends laterally on the outer fold arc.     

Kinematics and geochronology of Early Cretaceous thrusting in the northwestern paleozoic of Graz (Eastern Alps)

Abstract

The multiply deformed Upper Austro-Alpine nappe pile of the Graz area is built up of low-grade metamorphosed Paleozoic rocks which are discordantly overlain by sediments of Santonian (Late Cretaceous) age (“Gosau” formation). Slices of Permo-Mesozoic rocks are absent. Analyses of structures, microfabrics, strain and shear directions were used to decipher the kinematic history; geochronological investigations to date the age of thrusting. K/Ar and Rb/Sr ages of synkinematically grown mica suggest an eo-Alpine (Early Cretaceous) age for the major deformation D1. D1 is characterized by non-coaxial rock flow which caused SW- to W directed nappe imbrication. Incremental strain measurements indicate the progressive superposition of D2 over Dl. In the higher nappe (Rannach Nappe) nappe imbrication continued during D2 changing the direction of nappe transport from SW to NW. Enhanced flattening strain in the deeper nappe (Schöckel Nappe) led to recumbent folds in all scales during D2. This study emphasized two interpretations : (1) The Alpine deformation in the Upper Austro-Alpine nappe pile of the Paleozoic of Graz started in the Earliest Cretaceous (about 125 Ma.). (2) The emplacement of nappes followed a curved translation path in the studied area.     

鄂东南铁山梯形石香肠构造基质层中的应变测量与分析

鄂东南铁山是全球第二个梯形石香肠构造的发现点。以该区成层分布、形态相近的梯形石香肠构造为研究对象,利用惯量椭圆法对其基质层进行有限应变测量,获得真应变差、岩层厚度比、运动学涡度分布等。结合梯形石香肠几何形态学、岩石学特征,对所得数据综合分析研究表明:剪切带中垂直剪切方向的厚度比值与其所受真应变差趋于负相关;该梯形石香肠构造是由其上、下相邻基质层厚度差异,基质层中总体上的纯剪切,局部相对集中的简单剪切及相对富集于张裂隙处角岩层中的热液流体等综合作用形成的;发育成层分布且形态相近的梯形石香肠构造所需特征性条件是能干层上、下相邻基质层厚度相差较大,且受总体上持续的平行层面拉伸、垂直层面压缩的纯剪切与局部的简单剪切共同作用。该类石香肠构造是较好的岩石流变学标志。