Single layer folding in simple shear

Despite the common occurrence of simple shear deformation, laboratory and numerical simulations of folding have so far been almost exclusively in pure shear. Here we present a series of finite-element simulations of single layer folding in simple shear up to high shear strains (γ ≤ 4, and up to 75% shortening of the folding layer). In the simulations we vary the viscosity contrast between layer and its surroundings (25–100), the stress exponent (1 or 3) and the kinematics of deformation (pure- versus simple shear). In simple shear fold trains do not show a clear asymmetry, axial planes form perpendicular to the developing fold train and rotate along with the fold train. Differences in geometries between folds formed in simple and pure shear folds are thus difficult to distinguish visually, with simple shear folds slightly more irregular and with more variable axial plane orientation than in pure shear. Asymmetric refraction of an axial planar cleavage is a clearer indication of folding in simple shear. The main effect of an increase in stress exponent is an increase in effective viscosity contrast, with only a secondary effect on fold geometry. Naturally folded aplite dykes in a granodiorite are found in a shear zone in Roses, NE Spain. Comparison of the folded dykes with our numerical simulations indicates a viscosity contrast of around 25 and a stress exponent of 3. The natural folds confirm that at this moderate viscosity contrast, a significant amount of shortening (20–30%) is achieved by layer thickening instead of folding.     

Eocene simple shear and plio-quaternary pure-shear folding in the Central-Eastern Algerian Atlas

Tertiary folds of the central and eastern part of the Algerian Atlas were studied in order to assess their kinematics and regimes of deformation. Folds developed following two main phases of deformation during the Eocene and the Pliocene. The NE-SW trending Eocene folds show a clockwise rotation of fold axis with depth, noncylindrical geometry and a right-stepping en echelon configuration. Early secondary structures inside each fold are also rotated clockwise with respect to the younger folds. These data are in agreement with progressive ‘simple shear’ deformation. Pliocene folds strike E-W and display a cylindrical geometry. Associated Plio-Quaternary brittle structures show no rotational path. These observations are compatible with ‘pure shear’ style of deformation. These results, in combination with focal mechanism solutions, have important implications for the understanding of the kinematic evolution of the western segment of the African-European plate boundary. For Algeria they imply that transcurrent motion during the Paleogene was followed by coaxial shortening with a NNW direction during Neogene-Quaternary times. Comparison with published data for Morocco and Tunisia suggests that this transcurrent regime developed from west to east continuing from the Middle Jurassic through to the Miocene.     

Three-dimensional finite element analysis of the direct simple shear test

This paper investigates two aspect of the direct simple shear (DSS) using three-dimensional finite element analysis. Firstly, the different total stress paths followed by DDS devices that impose constant cross-sectional area using a stiff external boundary, and those that use a constant total stress lateral boundary condition are explored. This is done by conducting finite element analysis of a single cubic element. It is shown that this element may be subjected to perfect simple shear using four different boundary condition types. Each boundary condition type results in the same effective stress path, but different total stress paths and excess pore pressures. The boundary condition types are related to DSS devices in use. The second aspect investigated is the fact that no DSS device can impose true simple shear conditions, as they are unable to generate the required complementary shear stress on the vertical boundaries. Full three-dimensional finite element analysis of a UWA/Berkeley type simple shear device, which has a constant total stress lateral boundary, is then presented. The results are compared to the ideal solution and effects of stress non-homogeneity on the friction angle and undrained shear strength, deduced from a standard interpretation, are established.     

Dynamic stability analysis of undrained simple shear on water-saturated granular soils

Dynamic stability of undrained, simple-shear deformations on water-saturated granular soil specimens is discussed. The soil is described by a 2D-flow theory of plasticity for frictional and dilatant material. Contractant material becomes unstable (liquefies) at the state of maximum shear stress, whereas dilatant material becomes unstable after the state of maximum effective stress obliquity is reached in the softening regime of the background drained behaviour. In both cases the correct evolution equations for the growth coefficient of the instability are derived and compared with the results of the inertia-free formulation of the problem.     

Sheath fold morphology in simple shear

Sheath folds are highly non-cylindrical structures often associated with shear zones. We investigate the formation of sheath folds around a weak inclusion acting as a slip surface in simple shear by means of an analytical model. We present results for different slip surface orientations and shapes. Cross-sections perpendicular to the shear direction through the sheath fold display closed contours, so called eye-structures. The aspect ratio of the outermost closed contour is strongly dependent on the initial slip surface configuration. The center of the eye-structure is subject to change in height with respect to the upper edge of the outermost closed contour for different cross-sections perpendicular to the shear direction. This results in a large variability in layer thickness across the sheath fold length, questioning the usefulness of eye-structures as shear sense indicators. The location of the center of the eye structure is largely invariant to the initial configurations of the slip surface as well as to strain. The values of the aspect ratios of the closed contours within the eye-pattern are dependent on the strain and the cross-section location. The ratio (R′) of the aspect ratios of the outermost closed contour (R_yz) and the innermost closed contour (R_y′z′) shows values above and below 1. R′ shows dependence on the slip surface shape and orientation but not on the number of involved contours. Using R′ measurements to deduce the bulk strain type may be erroneous.     

Regional shear variation in relation to diapirism and folding

Regional structural trends in the Lévézou area (southern Massif Central, France) delineate an antiformal structure. Deformed granitoids display changes along strike in S---C plane relationships, and therefore in sense of shear. These variations are interpreted to be strain accommodation features that developed during the diapiric emplacement and folding of the granitoid sheets, and so cannot be used as kinematic indicators on a regional scale.     

Kinematic hardening of soft clay in simple shear

In a separate paper, the authors have proposed a normalized, non-degrading form of the shear stress–shear strain relationship for undrained, cyclic simple shear of soft clay. This relationship is described in the present paper, and it is seen to include a single fatigue parameter—the mean effective stress. Application of the relationship therefore requires knowledge of the history of the mean effective stress during any loading history. The present paper proposes an effective stress path model which may be used for prediction of this history. The model is developed within the framework of bounding surface kinematic and isotropic hardening plasticity. It incorporates an isotropic hardening bounding surface, and a kinematic hardening yield surface, in which the elastic region vanishes, and so the yield surface reduces to the stress point. The normalized shear stress–shear strain relationship, developed on the basis of Iwan's model, is used to establish the shape of the cap of the bounding surface. A new translation rule is also incorporated in the model, allowing improved prediction of stress path development within the bounding surface during regular or irregular cyclic loading. Use of the proposed model to simulate the behaviour of soft clay in laboratory undrained cyclic simple shear tests shows excellent qualitative agreement, with most of the major features of the actual behaviour being predicted.     

橡胶砂应力-应变特性三轴-单剪联合试验研究

橡胶砂作为一种环保的岩土材料有广泛的应用前景。应用三轴和单剪两种试验方法对2种固结压力下、7种配比橡胶砂的应力-应变特性、体变特性和模量衰减特性进行了对比研究,结果表明：随着橡胶颗粒含量的增加,橡胶砂模量降低,应力-应变曲线向应变硬化型转变,线性关系增强;随着橡胶颗粒含量的增加,橡胶砂剪胀特性减弱,剪缩增大;橡胶砂应力-应变关系可用扩展邓肯-张模型进行模拟,模型参数受橡胶颗粒含量影响的规律明显;随着橡胶颗粒含量的增加,橡胶砂的静剪切模量Gs与剪应变? 曲线降低,而橡胶砂模量衰减曲线Gs /G0 -?（G0为初始剪切模量）向大应变方向偏移;三轴和单剪两种试验方法得到的橡胶砂应力-应变特性、体应变-剪应变规律类似,但试验参数明显受应力状态和应力路径的影响,两者的差异主要表现为三轴试验得到的应力-应变曲线和模量曲线高于单剪试验,产生这种差异的主要原因是由于前者的平均应力相对较大。试验还得到了橡胶砂初始模量随橡胶颗粒含量降低的经验关系。     

一种控制直剪蠕变试验剪应力的简易装置

土的蠕变是指土在保持应力不变的条件下,应变随时间延长而增加的现象。研究土的蠕变性质对于确定土的长期强度有重要意义,土的蠕变研究也是近几年的研究热点。然而,土的蠕变试验周期特别长,因此简便、易行又有一定可信度的蠕变试验仪器,对于土蠕变性质的研究有较大的推动意义。直剪蠕变试验是研究确定土的蠕变性质的一种最简单、最直观的试验方法。但由于该试验只是控制剪切力不变,剪切过程中,试样受剪面积逐渐减小,剪应力持续增大,整个过程并不是蠕变。通过在传统仪器上附加一个简单装置,利用液体的浮力来控制试验剪切力,从而使得试样在剪切过程中的剪应力不变。在对仪器进行相应改进后,做了对比试验,检验该装置对剪应力的控制效果,试验结果表明,该简易装置可在一定程度上控制剪应力。     

土与混凝土接触面反向剪切单剪试验

土与混凝土接触面的力学行为是土与结构共同作用研究中的一个主要课题。进行了17 %、20 %、24 %共3组含水率的土与混凝土接触面正反向单剪试验,每组试验分别考虑5个法向应力和4个正向剪切比。试验结果表明,在正向剪切比和含水率一定时,接触面反向剪切破坏仍遵循摩尔-库仑破坏准则。当正向剪切比为0.50、0.75、1.00时,对应反向剪切强度分别为各自正向初始强度的90 %、75 %、55 %,对应的反向剪切黏聚力约为初始正向剪切黏聚力的95 %、80 %、54 %,反向剪切摩擦角约为初始正向剪切摩擦角的90 %、76 %、57 %。试验结果可供相关工程数值分析参考。     

Progressive development of s-type flanking folds in simple shear

Flanking structures are deflections of planar or linear fabric elements in a rock alongside a crosscutting element (CE), e.g. a vein or fault. This study provides new results from analogue experiments, which test and extend recent numerical models of flanking structures. A linear viscous matrix material (PDMS) was deformed in a ring shear rig that allows continuous observation to large values of shear strain. Rotational behaviour, offset and deflection of marker lines around a predefined, lubricated CE were monitored for different initial orientations of the fault with respect to the shear zone boundary, and the results were compared with numerical results and natural examples. At high initial angles to the shear zone boundary (>135°), a structure previously described as an ‘s-type flanking fold’ develops. During progressive deformation, an initially straight marker line passing through the centre of the CE is offset in a sense synthetic with the bulk sense of shear and shows a shortening displacement across the CE. Simultaneously, this central marker line is deflected and forms symmetrical folds, which are convex in the direction of shear along the CE (i.e. normal drag). Both offset and deflection of the marker lines decrease towards the tips of the fault. Natural examples of s-type flanking folds, directly comparable with the model results, are more common than is generally appreciated.     

On the evolution of simple shear in saturated soils

Development of shear bands in saturated soils is a multi-stage process based on the theoretical and numerical investigations in this paper. The soil is initially in homogenous shear strain state, and the instability can be characterized by a dimensionless number D. The inhomogenous distribution of shear strains appears when D>1, and the shear band will initiate and develop gradually. Numerical solutions show that only single shear band that is finally formed in the central region of the specimen even several disturbances (distributed along the specimen) appear in the beginning. Copyright © 2004 John Wiley & Sons, Ltd.     

The transition from upright to recumbent folding in the Variscan fold belt of southwest England: a model based on the kinematics of simple shear

A transition from upright folds, at high structural levels, to recumbent folds at depth is described from the Variscan fold belt in southwest England. The folds tighten and cleavage intensifies progressively as the axial plane dip decreases. A simple shear model is developed in which the shortening of a multilayer and its folding produces initially upright open folds which tighten as they rotate during increasing shear strain. The model predicts the observed relationship between interlimb angle and axial plane dip and is used to discuss the development of the structure of north Cornwall.     

单剪条件下主应力大小及主应力轴方向

对单剪条件下的应力莫尔圆变化过程进行详细分析,将莫尔圆从初始状态到破坏状态的大、小主应力变化过程看做由若干个等增量步组成,从而推导出任意剪应力状态与初始状态对应的小主应力差值与两者大主应力差值的比为一常数,该常数可以根据初始状态莫尔圆和破坏时对应的莫尔圆确定。推导出单剪条件下任意剪应力对应的大、小主应力及主应力轴方向的表达式。讨论了土体材料参数及法向应力对主应力轴偏转过程的影响以及大、小主应力与剪应力的关系。结果表明：在土体材料参数一定的条件下,主应力轴方向由应力比唯一确定;法向应力一定,土体的摩擦角越小,相同剪应力对应的主应力偏转角越大;剪切起始阶段,主应力变化缓慢,随着剪应力增大,主应力急剧变化至土样破坏时保持不变。     

On stress and strain in a continuous-discontinuous shear zone undergoing simple shear and volume loss

I summarise observations within a continuous-discontinuous shear zone to discuss the local stress and strain conditions experienced within a mixed rheology shear zone undergoing volume loss and deformation approximating simple shear. The Chrystalls Beach Complex, New Zealand, comprises phacoids formed from dismembered beds by layer-parallel extension, enclosed within a relatively incompetent matrix. Local extension is generally subparallel to the regional direction of shortening, and overall it appears that layer-parallel extension is a geometrical necessity in low angle shear zones where significant flattening occurs in response to simple shear accompanied by volume loss.Preferential stress loading of phacoids is predicted by fibre-loading theory, and the failure of phacoids by brittle fracture is thereby governed by fibre stresses transferred from the matrix. The principal stress orientations in a phacoid are likely rotated relative to the matrix, and either parallel or perpendicular to the phacoid-matrix interface. As preferential loading of phacoids decreases the stress level in the matrix, an increased volume fraction of phacoids increases the strength of the shear zone as a whole. However, only small matrix volume fractions are required for the composite to act nearly as weak as the matrix.     

循环单剪下珊瑚钙质砂和普通硅质砂剪切特性对比研究

对普通硅质砂和西沙群岛珊瑚钙质砂开展多级正应力下循环单剪试验,对比多循环周期下两种砂土剪切性质和颗粒破碎的差异。研究发现,两种砂样在循环剪切下体积变化都比较微弱,剪切过程中存在阶段性剪胀,使得试样的轴向位移呈波动变化;循环单剪下剪应力峰值包络线可以用联合型指数函数表达;剪应力随循环周期变化分为同步阶段和差异阶段,两个阶段转变节点对应的循环周期数随着正应力的增大而迅速减小;同步增长阶段珊瑚钙质砂和普通硅质砂的剪应力变化一致,在差异阶段普通硅质砂的剪应力要高出珊瑚钙质砂。两种砂剪应力差异程度随试验正应力不同而变化,普通硅质砂剪应力最大可高出珊瑚钙质砂14.7%;珊瑚钙质砂和普通硅质砂的颗粒破碎存在明显差异,珊瑚钙质砂全粒径范围内颗粒破碎分布更均衡,普通硅质砂在特定粒径区间内出现了剧烈的颗粒破碎,颗粒级配曲线存在明显拐点。普通硅质砂和珊瑚钙质砂滞回曲线的形状及随循环次数的变化规律有显著差异,是两种砂样剪切性质不同的重要体现。     

一种大型循环单剪试验装置研究

循环单剪试验被认为是研究地震场地中土体动力特性最合适的方法。为减小尺寸效应影响及解决工程中广泛存在的加筋土及粗颗粒土动力特性测试问题,研究大尺寸循环单剪试验方法具有重要意义。基于此,介绍了一种大型循环单剪试验装置,采用竖向线性滑动轨道约束上加载板和采用水平滑动轨道约束下加载板,确保前者仅发生竖向平动,后者仅发生水平平动,采用层叠的、带层间橡胶膜、分离式4点支撑的钢筋环构成的柔性剪切箱为试验提供侧向边界约束,确保了对单剪土样加载边界条件的真实模拟。针对土工格室加筋橡胶砂的测试结果表明：大型循环单剪试验装置得到的土动应力-动应变关系较好地反映了土在循环荷载作用下的滞回性、非线性和棘轮特性,大型循环单剪试验装置得到的 - 和 - 曲线变化规律与常规尺寸试验基本一致,证明其具有可行性;大尺寸试验得到的动剪模量特性与常规尺寸试验之间的差异,与单剪试验尺寸效应结论相符;试验中阻尼比特性受尺寸效应影响的规律性不明显。     

Theoretical and natural strain patterns in ductile simple shear zones

A simple empirical model representing the variation of shear strain throughout a simple shear zone allows us to determine the evolution of finite strain as well as the progressive shape changes of passive markers. Theoretical strain patterns (intensity and orientation of finite strain trajectories, deformed shapes of initially planar, equidimensional and non-equidimensional passive markers) compare remarkably well with patterns observed in natural and experimental zones of ductile simple shear (intensity and orientation of schistosity, shape changes of markers, foliation developed by deformation of markers).The deformed shapes of initially equidimensional and non-equidimensional passive markers is controlled by a coefficient P, the product of

1. (1) the ratio between marker size and shear zone thickness

2. (2) the shear gradient across the zone.

For small values of P (approximately P < 2), the original markers change nearly into ellipses, while large values of P lead to “ retort” shaped markers.This theoretical study also allows us to predict, throughout a simple shear zone, various relationships between the principal finite strain trajectory, planar passive markers and foliations developed by deformation of initially equidimensional passive markers.     

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.     

Analysis of simple shear tests with cell pressure confinement

The high cost of offshore infrastructure provides continuous encouragement for optimisation of design practices. Development of a more rational method to interpret results from simple shear tests with cell pressure confinement can reduce costs and improve reliability of offshore infrastructure. This paper addresses a commonly overlooked issue affecting design parameter selection: specimen shape varies from right cylinder to oblique cylinder after loading along a single shearing direction. Thus, horizontal stresses are not always equal to the cell pressure and their magnitude varies throughout the specimen’s lateral surface. An analysis is proposed that accounts for changing specimen geometry and lateral surface area during shearing and for the actual effect of cell pressure during testing. The analysis also describes how the intermediate principal stress can be assessed. Test results for medium dense silica sand are interpreted following de Josselin de Jong’s alternative shearing mechanism hypothesis. Conventional interpretation methods yield conservative design parameters for this soil. Failure states develop when the intermediate principal effective stress is halfway between major and minor principal effective stresses. Typical results for the soil tested show equipment performance meets standard direct simple shear requirements for shear strain rate, vertical stress and specimen height control.