曲折边界斜向裂陷伸展的砂箱实验模拟

根据黄骅盆地边界几何特征简化所设计的３个砂箱实验模型表明,同一裂陷伸过程可以形成不同走向的正断层,基底菜边界方向的变化可以引起裂陷内部断层走向的变化,陷盆地断瞳向受基底展边界方向和裂陷伸展方向的共同影响,裂陷边界及其附近断层走向主要受基底伸展边界方向的影响,裂陷内部、离伸展边界较远部位的断层走向主要受展方向影响,凸菜曲折边界可以引起断层转向,而凹工折边界的复合方向构成对断层走向的控制,黄骅新生代盆     

The development of folds in bedded chert and related rocks in the Malaguide Complex, southern Spain

Folds and folding mechanism in a chert sequence and related rocks of the Maláguide Complex (the uppermost tectonic unit of the Betic Zone) have been investigated. The geometric study shows that folds that developed in the chert sequence are usually angular in shape and asymmetric. Chevron and conjugate folds are common.Folding in bedded chert is explained in terms of a suggested model:

1. (1) Development of folds by kink and conjugate kinking.

2. (2) As the shortening increases, the interlimb angles decrease; in the kink folds this is caused by a reduction of the angle between the layers within the kink and the kink boundaries. There seems to be a relationship between this angle and the asymmetrical thinning-out in the limbs of many folds: the smaller is the angle between the kink boundary and the layers within the kink band, the larger is the reduction of the thickness in these layers.

Single limestone layers embedded in slate deform very probably by a buckling mechanism, implying tangential longitudinal strain and an additional flattening.     

A theory of concentric, kink and sinusoidal folding and of monoclinal flexuring of compressible, elastic multilayers: VI. Asymmetric folding and monoclinal kinking

One of the rules of thumb of structural geology is that drag folds, or minor asymmetric folds, reflect the sense of layer-parallel shear during folding of an area. According to this rule, right-lateral, layer-parallel shear is accompanied by clockwise rotation of marker surfaces and left-lateral by counterclockwise rotation. By using this rule of thumb, one is supposed to be able to examine small asymmetric folds in an outcrop and to infer the direction of axes of major folds relative to the position of the outcrop. Such inferences, however, can be misleading. Theoretical and experimental analyses of elastic multilayers show that symmetric sinusoidal folds first develop in the multilayers, if the rheological and dimensional properties favor the development of sinusoidal folds rather than kink folds, and that the folded layers will then behave much as passive markers during layerparallel shear and thus will follow the rule of thumb of drag folding. The analyses indicate, however, that multilayers whose properties favor the development of kink folds can produce monoclinal kink folds with a sense of asymmetry opposite to that predicted by the rule of thumb. Therefore, the asymmetry of folds can be an ambiguous indicator of the sense of shear.The reason for the ambiguity is that asymmetry is a result of two processes that can produce diametrically opposed results. The deformation of foliation surfaces and axial planes in a passive manner is the pure or end-member form of one process. The result of the passive deformation of fold forms is the drag fold in which the steepness of limbs and the tilt of axial planes relative to nonfolded layering are in accord with the rule of thumb.The end-member form of a second process, however, produces the opposite geometric relationships. This process involves yielding and buckling instabilities of layers with contact strength and can result in monoclinal kink bands. Right-lateral, layer-parallel shear stress produces left-lateral monoclinal kink bands and left-lateral shear stress produces right-lateral monoclinal kink bands. Actual folds do not behave as either of these ideal end members, and it is for this reason that the interpretation of the sense of layer-parallel shear stress relative to the asymmetry of folds can be ambiguous.Kink folding of a multilayer with contact strength theoretically is a result of both buckling and yielding instabilities. The theory indicates that inclination of the direction of maximum compression to layering favors either left-lateral or right-lateral kinking, and that one can predict conditions under which monoclinal kink bands will develop in elastic or elastic—plastic layers. Further, the first criterion of kink and sinusoidal folding developed in Part IV remains valid if we replace the contact shear strength with the difference between the shear strength and the initial layer-parallel shear stress.Kink folds theoretically can initiate only in layers inclined at angles less than to the direction of maximum compression. Here φ is the angle of internal friction of contacts. For higher angles of layering, slippage is stable so that the result is layer-parallel slippage rather than kink folding.The theory also provides estimates of locking angles of kink bands relative to the direction of maximum compression. The maximum locking angle between layering in a nondilating kink band and the direction of maximum compression is . The theory indicates that the inclination of the boundaries of kink bands is determined by many factors, including the contact strength between layers, the ratio of principal stresses, the thickening or thinning of layers, that is, the dilitation, within the kink band, and the orientation of the principal stresses relative to layering. If there is no dilitation within the kink band, the minimum inclination of the boundaries of the band is to the direction of maximum compression, or to the direction of nonfolded layers. Here α is the angle between the direction of maximum compression and the nonfolded layers. It is positive if clockwise.Analysis of processes in terminal regions of propagating kink bands in multilayers with frictional contact strength indicates that an essential process is dilitation, which decreases the normal stress, thereby allowing slippage and buckling even though slopes of layers are low there.     

The role of non‐coaxiality in the simulation of strain localization based on classical and Cosserat continua

It is normally accepted that materials inside the shear band undergo severe rotation of the principal stress direction, which causes non‐coaxiality between the principal stress and principal plastic strain rate. However, classical plasticity flow theory implicitly assumes that the principal stress and the principal plastic strain rate are coaxial; thus, it may not correctly predict the onset of the shear band. In addition, classical continuum does not contain any internal length scales; as a result, it cannot provide a reasonable shear band thickness. In this study, the original vertex non‐coaxial plastic model based on the classical continuum is extended to the Cosserat continuum. The corresponding codes are implemented via the interface of the user defined element subroutine in ABAQUS. Through a simple shear test, the effectiveness of the user's codes is verified. Through a uniaxial compression test, the influence of non‐coaxiality on the onset, the orientation, and the thickness of the shear band is investigated. Results show that the onset of the shear localization is delayed, and the thickness of the shear band is widened when the non‐coaxial degree increases, while the orientation of the shear band is little affected by the non‐coaxial degree. In addition, it is found that the non‐coaxiality can weaken the micro‐polar effect to some extent; nonetheless, the Cosserat non‐coaxial model still has its advantage over the classical non‐coaxial model in capturing the pre‐bifurcation as well as the post‐bifurcation behaviors of strain localization. Copyright © 2016 John Wiley & Sons, Ltd.     

鞍本地区前寒武纪铁建造中阳起石的变形显微构造研究

研究表明鞍山-本溪地区前寒武纪铁建造中的阳起石经受了褶皱或剪切变形作用,在相当于绿片岩相的温压条件下可形成波状消光,(001)裂理,扭折、机械双晶,重结晶等显微构造.由裂理及扭折带推导的一组滑移系为(001)[100],扭折造成的机械双晶具有S=0.57的剪切值,其双晶系统为(100)[001].     

A theory of concentric, kink and sinusoidal folding and of monoclinal flexuring of compressible, elastic multilayers: IV. Development of sinusoidal and kink folds in multilayers confined by rigid boundaries

This part concerns folding of elastic multilayers subjected to principal initial stresses parallel or normal to layering and to confinement by stiff or rigid boundaries. Both sinusoidal and reverse-kink folds can be produced in multilayers subjected to these conditions, depending primarily upon the conditions of contacts between layers. The initial fold pattern is always sinusoidal under these ideal conditions, but subsequent growth of the initial folds can change the pattern. For example, if contacts between layers cannot resist shear stress or if soft elastic interbeds provide uniform resistance to shear between stiff layers, sinusoidal folds of the Biot wavelength grow most rapidly with increased shortening. Further, the Biot waves become unstable as the folds grow and are transformed into concentric-like folds and finally into chevron folds. Comparison of results of the elementary and the linearized theories of elastic folding indicates that the elementary theory can accurately predict the Biot wavelength if the multilayers contain at least ten layers and if either the soft interbeds are at most about one-fifth as stiff as the stiff layers, or there is zero contact shear strength between layers.Multilayers subjected to the same conditions of loading and confinement as discussed above, can develop kink folds also. The kink fold can be explained in terms of a theory based on three assumptions: each stiff layer folds into the same form; kinking is a buckling phenomenon, and shear stress is required to overcome contact shear strength between layers and to produce slippage locally. The theory indicates that kink forms will tend to develop in multilayers with low but finite contact shear strength relative to the average shear modulus of the multilayer. Also, the larger the initial slopes and number of layers with contact shear strength, the more is the tendency for kink folds rather than sinusoidal folds to develop. The theoretical displacement form of a layer in a kink band is the superposition of a full sine wave, with a wavelength equal to the width of the kink band, and of a linear displacement profile. The resultant form resembles a one-half sine curve but it is significantly different from this curve. The width of the kink band may be greater or less than the Biot wavelength of sinusoidal folding in the multilayer, depending upon the magnitude of the contact shear strength relative to the average shear modulus. For example, in multilayers of homogeneous layers with contact strength, the Biot wavelength is zero so that the width of the kink band in such materials is always greater than the Biot wavelength. In general, the higher the contact strength, the narrower the kink band; for simple frictional contacts, the widths of kink bands decrease with increasing confinement normal to layers. Widths of kink bands theoretically depend upon a host of parameters — initial amplitude of Biot waves, number of layers, shear strength of contacts between layers, and thickness and modulus ratios of stiff-to-soft layers — therefore, widths of kink bands probably cannot be used readily to estimate properties of rocks containing kink bands. All these theoretical predictions are consistent with observations of natural and experimental kink folds of the reverse variety.Chevron folding and kink folding can be distinctly different phenomena according to the theory. Chevron folds typically form at cores of concentric-like folds; they rarely form at intersections of kink bands. In either case, they are similar folds that develop at a late stage in the folding process. Kink folds are more nearly akin to concentric-like folds than to chevron folds because kink folds form early, commonly before the sinusoidal folds are visible. Whereas concentric-like folds develop in response to higher-order effects near boundaries of a multilayer, kink folds typically initiate in response to higher-order shear, as at inflection points near mid-depth in low-amplitude, sinusoidal fold patterns. Chevron folding and kink folding are similar in elastic multilayers in that elastic “yielding” at hinges can produce rather sharp, angular forms.     

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.     

Formation of shear bands in sand bodies as a bifurcation problem

The paper reports on the results of theoretical and experimental investigations on the spontaneous formation of shear bands in sand bodies. The phenomenon is considered as a bifurcation problem. Consequently, material response and configuration-dependent loading determine the bifurcation mode. Both Coulomb's and Roscoe's solutions of inclination of the shear band can be correct theoretically and experimentally. The first one holds for non-rotating stress axes, the second one for co-rotating stress and strain increment axes during failure. Values in between can occur if the rotation of principal stress axes is not equal to one of these limits. If Coulomb's inclination of shear band occurs, there is a thin deforming material layer separating rigid bodies. Inside the shear band non-coaxiality of strain increment and stress holds from the beginning. If Roscoe's inclination of shear band occurs, it is separating two deforming bodies. Inside the shear band strain increment and stress are coaxial at peak.     

The geometry and kinematics of a suite of conjugate kink bands, southeastern Australia

A conjugate set of subvertical kink bands is exposed in coastal outcrops of well-foliated Ordovician turbidites near Mystery Bay, Australia. All kink bands with widths exceeding 3 cm have complex internal structures including compound and parasitic kinks, stepped kink boundaries, internal crenulations, variable kink angles and prismatic voids. The kink bands are interpreted to result from rotation of short foliation segments between fixed kink planes with subsequent widening and modification by layer-parallel shear external to the kink band. Layer-parallel shear of both sinistral and dextral sense accompanied kinking and indicates a variable stress system during kink band development.Conjugate kink bands are abundant and are used to estimate bulk strain orientations. In general, the dominant kink set of a conjugate pair is inclined at a lower angle to the external foliation than the weaker set and this angular disparity increases with increasing dominance of one set. These observations are at variance with relationships described from experimental bulk pure shear deformation of anisotropic materials. It is suggested that orthogonal constraints in these experiments restrict layer-parallel shear to within a developing kink band and are, therefore, unlike many natural kink systems. Simple shear experiments can produce structures geometrically similar to natural kink bands.     

A non‐coaxial and unbalanced plastic flow rule for geomaterials and its application to the shear band orientation prediction

In this paper, the non‐coaxial relation between the principal plastic strain increments and the principal stresses, which results from the internal friction in geomaterials, is analyzed, and the phenomenon of the unbalanced development of plastic flow in two conjugate directions is discussed. A non‐coaxial, unbalanced plastic flow model for Coulomb frictional materials is developed and used to determine the orientation of shear band in geomaterials. It is shown that the unbalanced index r of plastic flow has important effect on the orientation of the shear band, and the orientation determined by the conventional plastic flow theory is only a special case of the proposed model when r=0. This result soundly explains the reason that the geomaterials with the same internal friction angle and dilatancy angle can have very different shear band orientations. In addition, the difference between the intrinsic and apparent dilatancy angles is analyzed, and it is emphasized that the dilatancy angle commonly used in practice is indeed the apparent dilatancy angle. Copyright © 2010 John Wiley & Sons, Ltd.     

伸展方式对伸展构造形成特征影响的相似模拟

本文分析了三种不同基底伸展方式、具有膝状边界形态的砂箱实验模型 ,结果表明基底伸展方式的不同可以导致伸展盆地平面变形面貌和剖面构造样式上的显著差异。伸展方式对于凹形边界和凸形边界具有不同的影响。凹侧主动伸展模型在凹形边界附近形成平行边界复合方向的断层 ,在凸形边界附近则形成平行边界走向的断层。凸侧主动伸展则趋于在两侧边界附近形成近于垂直伸展方向的断层。由此可见 ,可能借助伸展盆地的断层平面变形面貌判别主动分离块体。     

Failure Loci of Some Igneous and Metamorphic Rocks

Summary Experimental evidence from true triaxial tests on dense rocks are analysed with emphasis on the failure modes of these materials under multiaxial loading, ambient temperature and external pressure. The strong dependence of the modes of fracture on the secondary components of applied stresses, and especially on the intermediate principal stress, indicated that the failure surface of these brittle materials may be appropriately described by a failure tensor polynomial criterion. As such, the elliptic paraboloid failure criterion was found to conveniently describe their mode of failure, by considering also the severe influence of anisotropy of the material.  For this purpose, a method developed recently (Theocaris and Panagiotopoulos, 1995a, 1995b) was applied, defining anisotropic hardening plasticity through an appropriate sequence of anisotropic elasticity problems. Assuming a particular path of loading or unloading, we measured the instantaneous tension and compression yield stresses along the transient principal-stress directions. These parameters completely define the instantaneous state of anisotropy of the body for the corresponding loading step, by applying the theory of the elliptic paraboloid failure locus (EPFS) (Theocaris, 1989a). A parameter identification problem was formulated on the constitutive expressions for this most general failure criterion. Then, by applying convenient constraints derived from the EPFS theory, which serve as filters throughout the whole procedure, the characteristic values of terms defining the variable components of the failure tensor polynomial were calculated, as the material was continuously loaded from the elastic into the plastic region and up to the ultimate failure load. Accurate simple tests in uniaxial tension and compression provided sufficient data for the definition of the yield loci of the material, at the considered loading step. These tests may be complemented with biaxial and triaxial modes of loading of the specimens. The results improve the accuracy and sensitivity of the method. All such data were used as input values, for establishing the mode of plastic deformation of the body during particular loading paths.  Moreover, the method employed allows the complete definition of the components of the failure, H, and the strength differential effect, h, tensors at each loading step. These quantities define completely the failure tensor polynomial for each material. Therefore, it presents the important advantage over other experimental methods by clearly indicating the parts contributed to the failure mode (either by plasticity, or by the strength differential effect) and their evolution during plastic deformation.  As convenient prototype materials for testing the method, specimens of metamorphic rocks such as Westerly granite (G), or quartzite (Q) were selected. Interesting results concerning the mechanical and especially the failure modes of such materials were obtained. Furthermore, the mechanical tests indicated clearly some basic properties of these materials as concerns the mode of their structure.     

Shock-induced mechanical deformations in biotites from crystalline rocks of the ries crater (Southern Germany)

Mechanical deformation features in shocked biotites from crystalline rocks of the Ries crater are: kink bands, planar elements, and plastic lattice deformations as determined by X-ray investigations.Kink bands can be observed in micas of various pressure histories (stages 0, I, II and less frequently stage III of shock metamorphism). Kink bands in shocked micas are less symmetrical than kinks of static origin. Asymmetry increases with increasing dynamic pressures. Moreover, kink band width is sensitive against changing peak pressures. Distribution of kinked and undistorted micas within a rock permits to fix the shock front direction. Shock-induced kinks in micas are produced by various gliding processes in the cleavage plane (001).Planar elements seldom occur in biotites of shock stages II and III and have never been described in endogenic rocks. Up to now orientations of planar elements parallel to (111), (1¯11), (112) and (11¯2) have been determined. Planar elements are interpreted as planes of plastic lattice gliding. {[110]} is supposed to be the main gliding direction. In the same pressure region other plastic lattice deformations have been determined. They are orientated parallel to (001), (100) and (¯132) or (201) which results from single crystal X-ray investigations and may represent planes of plastic lattice gliding. The dependency of formation of gliding planes and gliding directions on increasing dynamic pressures will be discussed.     

Sequential limb rotation and kink-band migration recorded by growth strata,Almazán Basin,North Spain

The geometry of growth strata in the Almazán monocline demonstrates that limb rotation and kink-band migration can coexist as folding mechanisms. The Almazán Basin, showing an overall synclinal geometry, was one of the most actively subsiding areas during the Tertiary in the inner part of the Iberian plate, with more than 3500 m of preserved Tertiary non-marine sediments. They are arranged in five tectonosedimentary units, TSU (A1 to A5), bounded by unconformities at the basin borders. The southern basin border is defined by the WNW–ESE-trending Almazán monocline, that can be followed for 25 km along strike, with a maximum structural relief of about 2500 m. The maximum changes in thickness on both limbs of the monocline occur in units A2 and A3, which constrains the maximum deformation period to between the Middle/Upper Eocene (Headonian, top of A1) and Upper Oligocene/Lower Miocene (Agenian, base of A4). The detailed geometry of the Mesozoic, pre-growth, and the Tertiary growth strata of the Almazán monocline was determined from the analysis of six seismic reflection sections, at high angles or perpendicular with the fold axis. The average dip of the monocline changes from 15° in the east to more than 45° in the western sector, being replaced westwards by a north-verging, steeply dipping thrust. In some sections, growth strata in the dipping limb show rotational offlap–onlap syntectonic unconformities, with progressively decreasing dips from bottom to top, indicating that limb rotation took place during the first stages of folding. At the limits of the dipping limb (anticline and syncline), two kink bands appear in some of the sections, the one located on the syncline being more developed. Within each kink-band, beds show a constant dip of 30–40°. The axial surfaces of each kink band converge upwards in the third and fourth tecto-sedimentary units, being parallel in the older units. The fixed axial surface occurs in a down dip position with respect to the active axial surface. The geometry of growth strata indicates that the mechanism of folding followed a sequence of: (i) a first stage of large-scale limb rotation (wavelength larger than 5 km), with minor development of kink-bands in some sections, and (ii) a second stage of more localised kink-band migration, probably favoured by fault propagation in the basement.     

缅甸翡翠显微构造的研究

翡翠的显微构造是矿物在应力作用下发生脆性或塑性变形产生的各种变形形迹。常见的显微构造有显微裂隙、波状消光、带状消光、扭折带、变形纹、机械双晶、镶嵌构造、核幔构造及出溶条纹等。它们有着不同的特征。反映了不同的形成条件,涉及到不同的变形机制。     

Geometrical adjustments during rotation of a Jura fold limb

Jura folds do not resemble models of continuously distributed buckling; they are never sinusoidal. Rather, they may be approximated by discrete, externally rotated conjugate kink bands with rounded hinges. Observational details are confusing, and good outcrops are limited; however, several types of geometrical adjustments necessary during growth (particularly external rotation) of a variety of elementary kink models may be plausibly correlated with observed features. The suitable way to the modeling of fold growth and an explanation of observations on different scales seems to be through synthesis of different modes of rotation and adjustment mixed in varying degrees to fit individual folds. A dominant role is played by incompetent beds of variable importance giving rise to several types of disharmonic folding.     

Vein arrays as kinematic indicators in kinked anisotropic materials

Vein arrays associated with natural kink bands have been, even recently, used by some workers as kinematic markers to distinguish between the migration and the rotation models of kink band mechanics.In an outcrop of schistose meta-agglomerate, conjugate kinks and synthetic sinistral shears are associated with a component of sinistral slip along the foliation. Discordant scalariform vein arrays form in association with the shears, but not the kinks. Tension gash elements of the arrays form by combined layer-parallel slip and layer-parallel extension along the rotated schistosity. They are only kinematically significant at the scale of the length of the rotated segment anisotropy.Applying this analysis to kink bands elsewhere, it is concluded that discordant vein arrays are not diagnostic of the rotational kink band model, or of high resolved shear stress on kink boundaries.     

Explicit solutions for the instantaneous undrained contraction of hollow cylinders and spheres in porous elastoplastic medium

In this article we present closed‐form solutions for the undrained variations in stress, pore pressure, deformation and displacement inside hollow cylinders and hollow spheres subjected to uniform mechanical pressure instantaneously applied to their external and internal boundary surfaces. The material is assumed to be a saturated porous medium obeying a Mohr–Coulomb model failure criterion, exhibiting dilatant plastic deformation according to a non‐associated flow rule which accounts for isotropically strain hardening or softening. The instantaneous response of a porous medium submitted to an instantaneous loading is undrained, i.e. without any fluid mass exchange. The short‐term equilibrium problem to be solved is now formally identical to a problem of elastoplasticity where the constitutive equations involve the undrained elastic moduli and particular equivalent plastic parameters. The response of the model is presented (i) for extension and compression undrained triaxial tests, and (ii) for unloading problems of hollow cylinders and spheres through the use of appropriately developed closed‐form solutions. Numerical results are presented for a plastic clay stone with strain hardening and an argilite with strain softening. The effects of plastic dilation, of the strain softening law and also of geometry of the cavity on the behaviour of the porous medium have been underlined. Analytical solutions provide valuable benchmarks enabling various numerical methods in undrained conditions with a finite boundary to be verified. Copyright © 2002 John Wiley & Sons, Ltd.     

On the stability of a coupled ocean atmosphere system in the presence of wave-CISK

The stability of a simple coupled ocean-atmosphere system similar to the one studied by Hirst with general ocean thermodynamics is investigated in which the atmospheric heating is determined by sea surface temperature anomalies as well as the convergence feedback (low level moisture convergence by the waves themselves). It is shown that the unstable coupled mode found by Hirst (UH mode) is profoundly modified by the convergence feedback. The feedback increases the unstable range of the UH mode and can increase its growth rate several folds. The maximally growing UH mode can become westward propagating for certain strength of convergence feedback. If the convergence feedback strength exceeds a critical value, several new unstable intraseasonal modes are also introduced. These modes are basically ‘advective’ modes. For relatively weak strengths of the convergence feedback the growth rates of these modes are smaller than that of the UH mode. As the atmosphere approaches ‘moist neutral’ state, the growth rates of these modes could become comparable or even larger than that of the UH mode. It is argued that these results explain why the El Nino and Southern Oscillation (ENSO) signal is clear in the eastern Pacific but not so in the western Pacific and they may also explain some of the differences between individual ENSO events. Our results also explain the aperiodic behaviour of some coupled numerical models. Importance of this process in explaining the observed aperiodicity of the ENSO phenomenon is indicated.