Deformation path concepts in strain analysis: Applications for study of ductile shear zones

The internal fabric of a deformed rock represents the state of finite strain. In some special cases the fabrics also record the strain history of the deformed body. These special cases can profitably be utilized to compare the predictions of dynamic models and strain paths in natural deformations. In this contribution, the concept of deformation path in the study of ductile shear zones has been demonstrated.     

弥散性走滑条件下底辟构造特征研究:以莺歌海盆地为例

实验以莺歌海底辟构造为典型实例设计3组砂箱物理模型,探讨弧形弥散性基底走滑与上覆同构造沉积对底辟构造样式及演化过程的影响。砂箱物理模拟表明:物质变形主要集中在弥散性剪切带内、且断裂特征与底辟带形成演化具有一定耦合性。底辟带断裂欠发育、以塑性应变为主,仅在底辟翼部和顶部分别形成小型逆冲断层和放射状裂隙;但底辟带外缘普遍发育高角度弥散性走滑断裂体系。沿弧形走滑剪切方向,底辟物质斜向生长由倾向外弧逐渐转变为倾向内弧,导致其平面上为非对称结构形态。同构造沉积地层与底辟相互作用控制了底辟生长结构及上覆地层的变形,底辟通过逐渐减小刺穿以响应上覆沉积载荷的增加。基于比例模型模拟结果与莺歌海盆地典型底辟带构造特征具有一定相似性,揭示出莺歌海盆地底辟构造及分布特征受红河断裂带弥散性走滑与同构造沉积过程共同控制。     

Removal of finite deformation using strain trajectories

A technique is described for removing the effects of finite deformation, given the principal values and orientations of strain at a number of points throughout a deformed body.Using the principal orientations, strain trajectories are constructed for the deformed state. The body is divided into finite elements bounded by these trajectories. Each element is then unstrained without changing its orientation or position. This process creates artificial voids and overlaps, which are minimized by imparting rigid translations and rotations to the elements according to a least squares method.The result is the pattern of strain trajectories for the undeformed state. It is shown that the trajectories for the deformed and undeformed states may be used as reference coordinates in order to map the change in shape of any body as it passes from the deformed to the undeformed state or vice versa. The technique is tested using models of a folded layer and a shear zone. It is suggested that the technique is versatile enough to allow for errors in original strain data. Although the technique has so far been applied to two-dimensional deformations, a similar method should be usable in three dimensions.     

Strain distribution within arcuate diapiric ridges of silicone putty

Twenty crescent-shaped diapiric models of silicone putty were made in two high-capacity centrifuges. The strain distribution within the models was studied by means of coloured rectangular elements, a method which led to large errors at random locations. Most elements affected by large errors could be identified in repeated experiments.The deformation pattern within the central segment of the diapiric ridges is dominated by two large regions of contrasting principal strain normal to the radial symmetry plane (axial plane of the crescents). This principal strain is tensile near the concave boundary of a ridge and compressive near the convex boundary of a ridge.Within the radial symmetry plane, the orientation pattern of long axes of the total-strain ellipses resembles an open fan which diverges toward the crest of the diapiric ridge. In the high-amplitude models, there is a narrow crestal region in which the long axes are subhorizontal. A similar region has been noted in comparable models of cylindrical diapiric ridges.In one of our models (WMS 20), the arcuate hinge line has pronounced culminations at both ends of the diapiric ridge. This results in a strong crestal depression at the radial symmetry plane where the strain analysis was performed. Accordingly, the characteristic region of tensile normal strain occupies most of the radial section.     

Influence of pre- or post-diapiric deformation on the foliation and strain pattern of a diapiric ridge

Foliation and total strain patterns of diapiric structures are very sensitive to pre- or post-diapiric deformation. This is illustrated quantitatively by superimposing homogeneous pure and simple shear on Mareschal and West's (1977) finite-element model of an antiformal diapiric ridge.

In models with post-diapiric homogeneous deformation (type 1) the foliation patterns typical for diapirism are obliterated. In models with pre-diapiric homogeneous deformation (type 2) diapiric deformation was too weak to overprint pre-diapiric foliation patterns. However, total strain patterns can be used successfully for identifying a diapiric component in the deformation history of both type 1 and type 2 models provided post- or pre-diapiric deformation is not too high.     

北京西山房山岩体岩浆底辟构造及其地质意义

运用底辟构造的理论和模型, 通过对北京西山房山岩体边缘围岩构造、变形和应变的研究, 厘定出岩体边缘的高温剪切带、周缘向斜、呈穹状分布陡倾的线理和面理, 并结合对西山区域构造事件分析后提出房山岩体为典型的岩浆底辟构造(HotStokesDiapir).这项研究成果不仅在世界上首次证实了岩浆底辟的存在, 而且对理清北京西山地区的地质构造格架和演化序列具有十分重要的意义.研究认为房山地区可能不存在变质核杂岩; 房山岩体边缘的关坻太古宙杂岩是基底岩石随岩体底辟流动上升带到地壳上部的; 原先确定的一些印支期“剥离断层”是房山岩体岩浆底辟的刺穿构造或围岩高温剪切作用造成的地层缺失; 太平山和凤凰山等向斜是岩体底辟过程中在围岩拖曳下形成的周缘向斜.      

Strain in an Archean greenstone belt of Minnesota

We measured strain at more than 60 locations in metasedimentary and metavolcanic rocks of the Vermilion district, an E-W trending Archean greenstone belt in Minnesota. Strain ellipsoid orientations and shapes correlate strongly with N-S location in the belt, but magnitudes do not. Flattening strains occur near the present Vermilion fault (which bounds the greenstone belt to the north) with constrictional strains to the south. The observed strain patterns can be mathematically modeled by deformation paths which produce the flattening strains (with west plunging λ₁ axes) by dextral shear of the constrictional strains (with east plunging λ₁ axes). Using reasonable geologic constraints, the shear plane must dip to the north with a subhorizontal shear direction. Structures throughout the district also indicate dextral shear. A geometrical finite element program uses the measured strains to destrain the rocks and find the configuration which most closely satisfies strain compatibility equations. The linear E-W strain patterns and minor rotations about horizontal axes during the deformation preclude origin of the greenstone belt by infolding and shear off the flanks of a rising granitic diapir. By accounting for rotations which result in the (deformed) curvature of the original surface, a true estimate of 50% N-S shortening across the belt can be made. The data and deformation models favor the origin of the Vermilion district rocks at a convergent margin, most likely as a N-dipping subduction zone complex with shallow slab dip. The origin of the constrictional strains remains enigmatic.     

Calculation of finite incremental deformations in ductile geological materials and structural models

Although the total continuous deformation of rocks can be the net result of several tectonic pulses (finite increments), it will be assumed that there are only two. It is further assumed that differential displacements are unknown, but that two generations of rotation gauges are available in a rock body, together with two respective generations of strain gauges. A mathematical procedure is outlined herein for calculating the first or second deformation increment in natural structures and putty models with elliptical markers. To illustrate their practical value, one set of equations is used to determine the pattern of large incremental strain associated with the lateral spreading of a mature model diapir. This model pattern may help to interpret igneous fabric patterns of undeformed granitoid plutons.     

库车前陆冲断带克拉苏构造带变形影响因素分析——基于离散元数值模拟研究

在解释库车前陆冲断带克拉苏构造带三维地震剖面的基础上,采用离散元数值模拟手段、单因素变量控制方法,通过六组模拟对比实验,探讨挤压背景下应变速率大小和作用时间、盐岩展布形态、先存盐底辟、基底先存断裂以及基底古隆起等因素,对库车前陆冲断带克拉苏构造带变形的影响。离散元数值模拟结果表明:相比于应变速率大小,应力作用时间对冲断带变形的影响更为显著,变形缩短率相同时导致挤压隆升幅度更大,可达70.25%,向前传播距离均更远,横向上变形范围可达73.82%,盐下层叠瓦状逆冲断裂倾角更小。先存底辟主要影响挤压端垂向变形规模,使得隆升幅度更大。先存断裂主要影响挤压端水平方向变形范围,挤压变形水平传播更远。基底古隆起和盐岩展布形态对克拉苏构造带变形也具有重要影响,基底隆起前沿形成应力集中带,盐岩在此聚集形成构造三角带。由于盐岩的分隔作用,盐上层变形相对较弱,靠近挤压端发育背斜和冲断构造,向盆地方向逐渐变为宽缓的向斜构造。     

层状盐岩力学和变形特性数值试验研究

对含泥岩夹层层状盐岩力学和变形特性进行有限元分析。首先,用数值试验方法预测含泥岩夹层层状盐岩体宏观等效弹性力学参数,然后,建立层状盐岩复合体细观有限元模型,研究其在单轴和三轴压缩荷载下盐岩、泥岩以及界面细观应力应变场分布特征、应力集中问题,并将上述研究与已有的理论和试验成果进行对比。结果表明,运用细观有限元方法预测层状盐岩宏观弹性力学参数是一种直观有效的方法;泥岩和盐岩力学特性上的不匹配导致在层状盐岩的泥岩夹层中以及界面边缘处存在较为明显的应力集中和差异变形。单轴压缩时,泥岩体由于侧向变形能力差会受到横向拉伸应力作用而盐岩层则相应的受到横向压应力作用,三轴压缩时因围压和偏应力大小不同层状盐岩细观应力应变场分布特征则更为复杂;此方法能更为直观的分析层状盐岩的变形和破损特征,这一分析结果对进一步进行层状盐岩体内油（气）储库硐室稳定性分析提供了理论基础。     

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.     

The mechanism of magma ascent through the solid lithosphere and relation between mantle and crustal diapirism: numerical modeling and natural examples

Diapirism can be regarded as the main mechanism of transport through the lithosphere for both felsic and mafic/ultramafic magmas. However, the lack of field observations makes it difficult to identify the key mechanism responsible for the formation of dome-shaped structures. In this study, emplacement of natural diapirs is reconstructed by numerical experiments handling realistic rheological and petrological models for the crust and mantle lithosphere. Three different regimes of diapiric ascent were established depending on the chosen model rheology: (1) single-stage diapir ascent; (2) pulsating ascent of successive batches of mantle-derived magma to the base of the crust with a periodicity of 2-3 Myr; (3) emplacement of extensive magma bodies in the form of sills either beneath the base of the crust (underplating) or to deeper mantle levels. The timescale of 30 Myr for a heat source at the base of the lithosphere is sufficient to initiate the ascent of a diapir through the mantle and crust. The study provides the estimates of rheological properties of the lithosphere and partially molten material at which diapiric ascent through the mantle and crust can occur.     

莺歌海盆地D1-1底辟区天然气成藏过程与分布差异

通过对莺歌海盆地D1-1底辟区中深层高温超压带与浅层正常压力带、压力过渡带天然气的组成、碳同位素特征差异的对比分析,结合底辟活动特征,研究了天然气藏的形成过程和天然气组分的分布规律。研究结果表明：(1)D1-1底辟核部区和底辟波及区中深层天然气成藏过程有差异,主要受底辟活动影响程度的控制。底辟核部区中深层气藏的形成过程为早期成藏、后期破坏并再次充注;底辟波及区中深层气藏的形成则为早期成藏,后期改造较弱,成熟煤型原生气藏保存较好。(2)D1-1底辟核部区和底辟波及区中深层天然气组分、碳同位素分布有明显规律;随距底辟核部距离的增大,其甲烷含量升高,二氧化碳含量降低,甲烷碳同位素变轻(成熟度降低),二氧化碳碳同位素也变轻,底辟核部区富集无机成因CO₂,至底辟波及区则以有机成因CO₂为主。     

安徽董岭花岗岩类的构造特征及侵位机制

安徽怀宁董岭花岗岩类底辟滑覆构造体系是长江中下游地域独特的构造形式。花岗岩底辟构造是在中生代华北地块与扬子地块碰撞背景下通过气球膨胀机制侵位至盖层内(燕山期),形成了围绕董岭几何中心的环状或半环状接触变质和韧性变形岩块。该花岗岩类其内部变形明显,岩相分带、分期清晰,围岩顶盖保存完好,围岩变质均匀,变形强烈,滑覆断层发育,糜棱岩典型等为特征,是一个罕见的盖层中花岗岩类底辟构造。后期在其北侧和东侧被月山—白子山冲断岩块所超覆。     

Strain analysis in Jurassic argillites of the Monte Sirino area (Lagonegro Zone,southern Apennines,Italy) and implications for deformation paths in pelitic rocks

Analysis of strain in Jurassic argillites forming part of the folded and thrusted sedimentary succession of the Lagonegro basin (southern Italian Apennines) has been carried out using ellipsoid-shaped reduction spots as strain markers. Most of the determined finite strain ellipsoids are of oblate type and show a peculiar distribution of the maximum extension direction (X), with maxima either subparallel or subperpendicular to the local fold axes. Using the strain matrix method, two different deformation histories have been considered to assist the interpretation of the observed finite strain pattern. A first deformation history involved vertical compaction followed by horizontal shortening (occurring by a combination of true tectonic strain and volume loss), whereby all strain is coaxial and there is no change in the intermediate axis of the strain ellipsoid. By this type of deformation sequence, which produces a deformation path where total strain moves from the oblate to the prolate strain field and back to the oblate field, prolate strain ellipsoids can be generated and may be recorded where tectonic deformation has not been large enough to reverse pretectonic compaction. This type of deformation history may be of local importance within the study area (i.e. it may characterize some fold hinge regions) and, more generally, is probably of limited occurrence in deformed pelitic rocks. A second deformation sequence considered the superposition of pre-tectonic compaction and tectonic strain consisting of initial layer-parallel shortening followed by layer-parallel shear (related to flexural folding). Also in this instance, volume change during tectonic deformation and tectonic plane strain have been assumed. For geologically reasonable amounts of volume loss due to compaction and of initial layer-parallel shortening, this type of deformation history is capable of producing a deformation path entirely lying within the oblate strain field, but still characterized by a changeover, during deformation, of the maximum extension axis (X) from a position parallel to the fold axis to one perpendicular to it. This type of deformation sequence may explain the main strain features observed in the study area, where most of the measured finite strain ellipsoids, determined from the limb regions of flexural folds, display an oblate shape, irrespective of the orientation of their maximum extension direction (X) with respect to the local structural trends. More generally, this type of deformation history provides a mechanism to account for the predominance of oblate strains in deformed pelitic rocks.     

泥底辟输导流体机制及其与天然气水合物成藏的关系

摘要：详细阐述不同成因的泥底辟流体输导模式,探讨了泥底辟输导体系的演化与天然气水合物成藏之间的关系,并分析神狐海域泥底辟输导体系对天然气水合物成藏的影响。底辟核外部伴生断裂、底辟核内部流体压裂裂缝和边缘裂缝带均可作为输导流体的通道。根据运移通道和动力等差异性,提出泥底辟输导流体的2种端元模式：超压-流体压裂输导型和边缘构造裂缝输导型。在此基础上,讨论了泥底辟(泥火山)的不同演化阶段对水合物的形成、富集和分解的影响。早期阶段,泥底辟形成的运移通道可能未延伸到水合物稳定带,导致气源供给不够充分;中期阶段,水合物成藏条件匹配良好,利于天然气水合物生成;晚期阶段,泥火山喷发引起水合物稳定带的热异常,可能导致水合物分解,直至泥火山活动平静期,水合物再次成藏。神狐海域内泥底辟分为花冠状和穹顶状两类,花冠状泥底辟以超压-流体压裂输导型为主;穹顶状泥底辟以底辟边缘裂缝输导型为主。泥底辟输导体系的差异性可能是神狐海域天然气水合物非均质分布的影响因素之一。 关键词：泥底辟;输导体系;天然气水合物;成藏机制;神狐海域     

Numerical modeling of vertical drains with advanced constitutive models

The water flow into a vertical drain under an embankment loading is axisymmetric problem and therefore, the vertical drain system must be converted into equivalent plane strain model. The matching is achieved by manipulating the drain spacing and/or soil permeability according to relatively simple rules. This paper investigates the verification of matching approaches by comparing 2D plane strain and 3D unit cell results when complex constitutive models are used in the finite element analyses. The numerical results showed that the match was found to be satisfactory but not perfect. A full-scale plane strain analysis is subsequently applied to an embankment case history taken from Haarajoki, Finland, stabilized vertical drains and compared with field measurements.     

老挝万象平原钾盐矿床沉积特征地震解释

老挝万象平原钾盐矿具有典型的底辟构造特征,次级盐隆起和盐凹陷规模较小,但十分发育,仅依靠钻探工作,难以控制次级盐构造的范围,而地震勘探能对不同的底辟构造样式都有明显的反映,对于探明次级盐构造,以及盐构造与钾盐矿的厚度变化关系,寻找有利钾盐矿开采靶区具有重要意义。     

Small-scale ductile shear zones as transposed rheologically weak domains: A numerical modeling investigation and practical application

We test the hypothesis that small ductile shear zones are developed from initial rheologically weak domains. We regard weak domains as ellipsoidal inhomogeneities and apply Eshelby's formalism extended for power-law viscous materials to investigate the kinematics and finite strain evolution of the partitioned flow fields in weak domains. We show that, under an imposed bulk flow field, weak domains, regardless of their initial shapes and orientations, deform into zone-like features at relatively small bulk strains and the deformation paths inside weak domains have all characteristics expected in ductile shear zones. We apply our model to the Cap de Creus area Spain, where abundant small ductile shear zones exist. To relate the fabrics inside these shear zones with the regional deformation, we take a multi-scale approach. We assume that the area contained many weak domains which were randomly shaped and oriented initially and were deformed into shear zones eventually in response to the regional flow. We constrain the regional flow field by the fabric patterns across the area and compute numerically the partitioned flow fields in individual weak domains. The latter are related to fabrics inside shear zones. Our model reproduces first-order features of field-observed fabrics. Although the deformation path of each shear zone was close to simple shearing, the deformation of the whole belt was not. Our approach also resolves the strain compatibility problem for a finite-sized shear zone embedded in a far less deformed country rock.     

The analysis of deformed belemnites

Deformed belemnites are important strain markers because they allow calculation of actual length changes in deformed rocks. They have been studied in the deformed Lower Lias sequence of part of the French Alps by measuring the orientation of about 100 belemnites at each locality, recording the amount of extension of as many as possible, and locating the sector of arc on the bedding plane occupied by extended belemnites. For comparison, studies on a similar but undeformed Lower Lias sequence in southern England show that dispersed belemnites have no strong initial preferred orientation, and that a proportion of undeformed belemnites show cross-fractures that would allow extension of the rostra from the onset of deformation.Graphs of frequency vs orientation for belemnites at locations deformed by irrotational strain lead directly to an estimate of two-dimensional strain ratio and orientation. Non-random initial distributions and rotational strain produce more complex graphs, which are treated only qualitatively. Extension-orientation graphs show that many deformed belemnites lie within the sector of extension of the strain ellipse. These graphs provide estimates of 1 + e₁ and 1 + e₂, which can be cross-checked using the orientation of the lines of no finite longitudinal strain derived from measuring the maximum sector of arc occupied by extended belemnites.Examples from the French Alps show how the rotational and irrotational strain of initially random samples may be distinguished, and how the more complex case of deformation of non-random samples differs from these. The direction of rotation of the strain ellipse can be derived from the geometry of the graphs of frequency and elongation.