Successive development of plane noncylindrical folds in progressive deformation

In the history of superposed deformations of the iron formations at the western border of the Kolar Gold Field in S India, an important event was the successive growth of broadly coaxial plane noncylindrical folds in course of a progressive deformation concomitant with development of ductile mesoscopic shear zones. The noncylindrical folds were initiated as active folds by the creation of a buckling instability at successive stages on newly developed foliation surfaces. The nucleation of noncylindrical folds and the subsequent axial-plane folding of the tightened mature folds are explained by the mechanical inhomogeneity of the rocks and the heterogeneous character of strain. The correlation between increasing tightness and increasing noncylindricity of the folds indicates that the initial curvatures of hinge lines were accentuated by an extension parallel to the subhorizontal stretching lineation. From the patterns of deformed lineations over folds of varying tightnesses, it is concluded that the passive accentuation of hinge-line curvatures was mostly achieved when the folds had already become isoclinal or very tight.     

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.     

Structures in the banded iron-formation of the southeastern Bababudan Hills, Karnataka, India

The banded iron-formation in the southeastern Bababudan Hills display a macroscopic synformal bend gently plunging towards WNW. The bedding planes in smaller individual sectors show a cylindrical or conical pattern of folding. The dominant set of minor folds has WNW-ESE trending axial planes and the axes plunge towards WNW at gentle to moderate angles, though there is considerable variation in orientation of both axes and axial planes. A later set of sporadically observed folds has N-S trending axial planes. The macroscopic synformal bend within the study area forms the southeastern corner of a horseshoe shaped regional synformal fold closure which encompasses the entire Bababudan range. The minor folds are buckle folds modified to a varying extent by flattening. In some examples the quartzose layers appear to be more competent than the ferruginous layers; in others the reverse is true. The folds are frequently noncylindrical and the axes show curvature with branching and en echelon patterns. Such patterns are interpreted to be the result of complex linking of progressively growing folds whose initiation is controlled by the presence of original perturbations in the layers. Domes and basins have at places developed as a result of shortening along two perpendicular directions in a constrictional type of strain. Development of folds at different stages of progressive deformation has given rise to nonparallelism of fold axes and axial planes. The axes and axial planes of smaller folds developed on the limbs of a larger fold are often oriented oblique to those of the latter. Progressive deformation has caused rotation and bending of axial planes of earlier formed folds by those developed at later stages of the same deformational episode. Coaxial recumbent to nearly reclined fold locally encountered on the N-S limb of the macroscopic fold may belong to an earlier episode of deformation or to the early stage of the main deformation episode. The E-W to ESE-WNW strike of axial plane of the regional fold system in the Bababudan belt contrasts with the N-S to NNW-SSE strike of axial planes of the main fold system in the Chitradurga and other schist belts of Karnataka.     

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.     

A mathematical model for orientation data from macroscopic conical folds

Statistical techniques are developed to classify folds into one of three classes: cylindrical, conical, or neither. A translated version of Bingham's distribution on the sphere is applied to orientation data fron conical folds. Iterative least-squares techniques are used to determine the best-fitting small circle (or cone), and confidence intervals for the cone axis and half apical angle are developed. Examples of a cylindrical and a conical fold are given. Another fold is neither cylindrical nor conical and is classified as pseudoconical. Relationships between the Bingham and Fisher distributions are presented.     

A mathematical model for orientation data from macroscopic elliptical conical folds

An iterative least-squares technique to fit circular and elliptical conical surfaces to orientation data from folds is presented. A statistical model is used which assumes that each data point is an observation from a Fisher distribution. The mean of this distribution is assumed to lie on the curve to be fitted. Estimates of variances and covariances for the fitting parameters are calculated, and confidence intervals for the cone axis and half apical angle are estimated from variances and covariances. A normal test with null hypothesis that the cone angle is 90° determines if a conical model fits the data better than a cylindrical model. AnF test is used to determine whether an elliptical cone is a better model than a circular cone. In this fashion, macroscopic folds are classified into cylindrical, circular conical, or elliptical conical folds. Examples of these three types of fold are given. The Wynd Syncline near Jasper, Alberta is the first natural elliptical conical fold described as such.     

Model experiments showing simultaneous development of folds and transcurrent faults

Simultaneous development of noncylindrical folds and transcurrent fractures has been studied using model techniques. A plasticine model was compressed in one direction and an initial formation of folds was followed by the initiation of conjugate sets of transcurrent fractures. It was recorded that with progressive deformation the length of each fracture and the displacement along it increase steadily and the rate of displacement varies at different stages of deformation. Individual fold geometries vary along their hinge lines and these geometrical variations appear to be due to interference of folds with the transcurrent fractures. These interference effects also change the amount of rotation of fractures. Fold structures are different on either side of the fault plane. A natural example from the Bude area, England, shows similar geometrical features.The method of determining fault displacement by comparing the positions of fold hinge lines on either side of a fault is discussed in the light of the above results.     

Noncylindrical flexural slip folds in nature and experiment

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

1. (a) each fold is noncylindrical;

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

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

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

Strains developed in the hangingwalls of thrusts due to their slip/propagation rate: A dislocation model

Fault planes propagate radially from a point source and this failure propagation process is very similar to the movement of a dislocation through a crystal lattice. An elastic strain represented by an extra half plane is necessarily imparted to the lattice at an edge dislocation, and this is equivalent to the ductile bead which accompanies the propagating tip of a thrust fault. This ductile bead migrates with the fault tip, and imparts a characteristic internal strain to the thrust sheet. A two-dimensional model is presented to illustrate the inter-relationship between fault plane slip, fault tip propagation and internal strain. In multilayered sequences, internal strain is usually represented by asymmetric folds verging in the thrust transport direction. A simple technique, the displacement/distance plot utilizes the fact that displacement dies out towards the fault tip. This plot can be used to quantify the relative stretch, measured parallel to the fault movement, which is dependent on the slip/propagation rate, and it may be used to define exactly the position of the fault tip on a cross-section. Examples of fold-thrust structures from Devon (England) and Pembrokeshire (Wales) are used to illustrate the technique.     

圆锥状褶皱的几何分析

长期以来,地质学家习惯于把不同类型和不同成因的褶皱的基本形态当作圆柱状几何性状处理,建立了褶曲构造的基本几何要素,并且以此作为划分构造均匀区段的几何准则。从最近十余年来关于区域变质造山带的大量观测研究证明,还有另一种褶皱,即圆锥状褶皱,广泛发育于褶皱复杂的变质岩系之中,在不同尺度上显示其控制作用和对区域构造格架的影响。     

A new isogon-cleavage classification and its application to natural and model fold studies

Traditional methods of studying natural folds are reviewed. A new method of describing cleavage attitude in folds is presented; the β plot. The combined graph of dip isogon angle ϕ (Hudleston 1973) and cleavage angle β is proposed as a linked classification of fold and cleavage geometry. Plots of β and βϕ are given for three natural fold examples. The classification is extended to the geometry and strain attitude (βϕ₅) of two finite-element models and the classical folding models. Results are compared and some tentative conclusions drawn on the relationship of cleavage, the XY plane of strain and dip isogons.     

An additional criterion in the aberrant fold relationship

From a re-analysis of aberrant folds in southwest Scotland the divergence of host fold axes from the regional b-axis, i.e. regional deviation, emerges as an additional factor determining the magnitude of the incongruous relationship in an assemblage of noncylindrical megascopic folding.     

甘-新北山金窝子金矿田构造控矿解析

金窝子金矿田位于中朝—塔里木板块与哈萨克斯坦板块俯冲碰撞带南缘的甘—新北山中带，是受断裂构造控制的岩浆热液型金矿床。区域构造格局控制成矿带的分布，不同构造单元具有不同的控矿构造型式。金矿田内基本构造格局是走向：NE、倾向NW的低角度逆冲断层及其伴生(派)生的同走向高角度逆冲断层、紧闭褶皱以及与其垂直的高角度横张断层组成的推覆构造体系。NE向低角度逆冲断层控制蚀变糜棱岩型金矿化(以210金矿床为代表)，NNW向高角度横张断层控制石英脉型金矿化(以金窝子金矿床为代表)，而NE向高角度逆冲断层和紧闭褶皱中无金矿化。NE向低角度断层不仅是重要的含矿构造，而且在成矿过程中起着控制成矿物理化学界面的作用。所以，金窝子金矿田2种不同金矿化类型是同一成矿作用在不同控矿构造动力学条件下的具体表现。     

GEOLOGICAL STUDIES OF METAMORPHIC ROCKS IN THE VICINITY OF M.C.T./LESSER HIMALAYAN SHEAR ZONE, PARTS OF SIKKIM HIMALAYAS

GEOLOGICAL STUDIES OF METAMORPHIC ROCKS IN THE VICINITY OF M.C.T./LESSER HIMALAYAN SHEAR ZONE, PARTS OF SIKKIM HIMALAYAS     

A novel analytical approach for predicting the noncylindrical pile penetration‐induced soil displacement in undrained soil by combining use of cavity expansion and strain path methods

Since development of cavity expansion theory and strain path method, almost all the conventional analyses of pile penetration problem have been based on circular cross section penetrometer. However, noncylindrical pile (with noncircular cross section) is also required in geotechnical engineering such as rectangular cross‐sectional pile, X‐sectional cast‐in‐place concrete pile, H‐shaped steel pile, prefabricated vertical drains, and flat dilatometer. This paper presents a novel and general analytical approach for capturing the soil deformation mechanism around the pile with arbitrary cross section. The penetration problem is simulated by a new 2‐dimensional (radial and circumferential) cavity expansion model. Based on the theoretical framework of strain path method, the kinematics (velocity field) of the noncylindrical cavity expansion is reduced to solve the Laplace equation with arbitrary velocity boundary conditions by using the conformal mapping technique. Then, solutions for the strain and displacement, which could consider the large deformation effect, are obtained by the integration of the strain rate and velocity along the streamline. The analytical solution is validated by comparing the degenerate solution of this study with conventional circular (cylindrical) cavity expansion theory. Subsequently, typical numerical examples for the deformation mechanism of elliptical and rectangular cavity expansion are presented to prove the advantage of the proposed new solution particularly in capturing the noncylindrical symmetric displacement field. A brief application of the proposed new analytical solution to the interpretation of the smear effect of prefabricated vertical drain installation confirms its useful in geotechnical engineering.     

沁水盆地北端中生代构造变形与构造应力场特征

在对沁水盆地北端发育的中生代褶皱、断层和节理等构造研究的基础上,分析并总结了区内的构造变形及构造应力场特征,。结果表明:研究区西部构造线以NE-SW向为主;东部构造线以近SN或NW-SE向为主;两者之间的构造线方向主要表现为近EW向。研究区内的褶皱、断裂、节理以及水系的发育特征均表明:本区在晚古生代—中生代经历过一期近SN向的挤压作用,其最大主应力方位为161°~174°,倾角在10°以内,这期挤压作用可能是对印支期构造活动的响应;此外,在距今165±5 Ma至136 Ma期间,本区可能还经历过一期NW–SE向的挤压作用,其最大主应力方位为152°,倾角1°。      

Hinge migration as a mechanism of superimposed folding

Paraffin wax analogue modelling of superimposed folding shows how early fold shape and orientation determine fold-axis orientation, type of interference pattern and mechanism of superposed folding. During two successive deformations, the behaviour depends on the angle between the first and second compression directions. (i) When they are perpendicular to each other, classic superposed folding with either domes and basins, or folds with vertical axes develop, depending on whether the earlier folds were open or closed. (ii) When the two compression directions are oblique, the earlier folds rotate. The degree of rotation depends on the angle between the first folds and the later compression direction and is proportional to the amount of strain. The orientations of the new folds are close to those of the earlier open folds. The final deformation pattern consists of domains where the orientations of the axes depend on whether the early folds were previously either open or closed. Many early folds are reused to become later folds by the mechanism of hinge migration.These results are consistent with the pattern of superimposed folding observed in the Devoluy structure of the French Alps. They show that simply by studying the directions of fold axes in areas of superposed folding, it is not possible to define compression directions. Moreover there is the possibility that superposed folding may go unnoticed if hinge migration has occurred.     

三角模糊数型边坡支护方案评价模型及其应用

由于边坡支护方案评价时掌握的信息不充分,资料不全,加之问题本身的复杂性、不确定性以及人类思维的模糊性,方案的评价值往往难以精确表达,用三角模糊数的形式表示更合理。针对属性值用三角模糊数表示的边坡支护方案优选问题,提出了一种基于集对分析联系数的三角模糊数型方案综合评价模型。首先,根据集对分析中的联系数理论,利用三角模糊数的中值及上下确界所限定的取值区间,将三角模糊数转化为联系数;然后,根据联系数的加法和乘法定义,建立了联系数决策模型;按照综合决策值大小即可得到最优方案。该模型既考虑了三角模糊数的中值,又兼顾了三角模糊数的上下确界,即联系数的差异度,更具有客观性、合理性。实例应用表明,该模型算理清晰,计算简便,结论与实际相符。     

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

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