Homogenization estimates for texture evolution in halite

In this work, the recently developed “second-order” self-consistent method [Liu, Y., Ponte Castañeda, P., 2004a. Second-order estimates for the effective behavior and field fluctuations in viscoplastic polycrystals. J. Mech. Phys. Solids 52 467–495] is used to simulate texture evolution in halite polycrystals. This method makes use of a suitably optimized linear comparison polycrystal and has the distinguishing property of being exact to second order in the heterogeneity contrast. The second-order model takes into consideration the effects of hardening and of the evolution of both crystallographic and morphological texture to yield reliable predictions for the macroscopic behavior of the polycrystal. Comparisons of these predictions with full-field numerical simulations [Lebensohn, R.A., Dawson, P.R., Kern, H.M., Wenk, H.R., 2003. Heterogeneous deformation and texture development in halite polycrystals: comparison of different modeling approaches and experimental data. Tectonophysics 370 287–311], as well as with predictions resulting from the earlier “variational” and “tangent” self-consistent models, included here for comparison purposes, provide insight into how the underlying assumptions of the various models affect slip in the grains, and therefore the texture predictions in highly anisotropic and nonlinear polycrystalline materials. The “second-order” self-consistent method, while giving a softer stress-strain response than the corresponding full-field results, predicts a pattern of texture evolution that is not captured by the other homogenization models and that agrees reasonably well with the full-field predictions and with the experimental measures.     

组构数值模拟的原理及其在地学中的应用

组构是指由岩石塑性变形导致多晶体的结晶学优势取向现象。组构的存在会增加岩石的各向异性,进而可能影响到岩石的后续变形。岩石组构包含了变形类型、运动学、变形环境、流变学特征等信息,因而成为显微构造学的重要内容。组构数值模拟是近年来得到重视的一种组构研究方法,它以晶体塑性理论为基础,利用计算机技术定量地模拟多晶岩石中组构的形成和演化。在晶体塑性理论中,晶体的塑性变形是由滑移系的剪切滑动导致的,由单晶塑性本构关系表征。多晶均匀化模型包括Sachs模型、Taylor模型、自洽模型和有限元模型,它们从不同角度描述了由单晶变形组成的多晶体变形。极图、反极图和取向分布函数被用来显示多晶体中各晶粒的空间取向。目前组构数值模拟在地学中的应用主要体现在各种单相和多相岩石的组构形成、重结晶作用下的组构形成、组构对地幔和地核地震波波速各向异性的影响等方面。     

岩石低周疲劳损伤模型与损伤变量表达方法

在岩石（体）工程领域,周期荷载作用下岩石的疲劳破坏特性与岩体的长期稳定性密切相关。针对目前对混凝土疲劳损伤研究较多,但对岩石疲劳损伤研究相对较少这一现状,运用损伤力学方法对以累积塑性应变表达的损伤变量进行了分析,指出了目前常用的以累积塑性应变表达的损伤变量表达式存在的理论上的缺点,建立了一种新的岩石疲劳损伤变量表达方法。为研究岩石在疲劳荷载作用下力学性能不断劣化的过程,从连续介质损伤力学的基本理论出发,分析岩石在疲劳荷载下的损伤发展和变形规律,并考虑岩石材料的硬化特性,推导了低周疲劳损伤演化方程,经低周疲劳试验数据分析,所建模型可以较好地反映岩石的疲劳损伤演化规律,可用于岩石在低周疲劳荷载作用下的有限元分析。     

Texture development of recrystallised quartz polycrystals unravelled by orientation and misorientation characteristics

The development of microstructures and textures (i.e. crystallographic preferred orientations) during recrystallisation of naturally deformed quartz polycrystals has been studied via electron diffraction techniques in the scanning electron microscope. In the investigated sample series of quartz-rich rocks originating from different deformation regimes, the microstructural and textural changes in quartz have been significantly influenced by dynamic recrystallisation. Based on microstructural observations paired with orientation and misorientation analyses down to the scale of grains and subgrains, criteria could be established which characterise the dominant recrystallisation process and its influence on texture development. It is shown that the texture development during dynamic recrystallisation is controlled by a differential activation of slip systems in grains of ‘soft’ and ‘hard’ orientations. The analyses provide further evidence that specific grain orientations are preferred during crystal plastic deformation, recrystallisation and grain growth. The influence of twinning after the Dauphiné law was also investigated. Observations of a progressive reduction in the population of Dauphiné-twin boundaries during recrystallisation and a penetrative deformation in both hosts and twins indicate a generation prior to deformation and recrystallisation. A mechanical origin for twinning and possible influence on texture development was therefore discarded.     

地震作用下岩盐层套变规律研究

5.12汶川特大地震发生后,某气田在岩盐层段发现了多口井套变,为了能有效地治理,急需了解其套变的原因和规律。为此,利用真三维接触有限元分析方法研究了震前套管应力和变形分布规律,并在原有边界条件基础上,在模型的顶面进一步施加不同震级地震载荷,重新分析套管应力和变形的分布规律。对比二者分析的结果发现：无论是震前还是震后都显示岩盐层段套管的应力和变形水平明显高于套管其他部位,且基本规律是震级越高套管在岩盐层段的应力水平和变形越大。对比有限元计算震前和震后套管应力和变形的结果还发现,仅5.12特大地震载荷的竖向分量所产生的应力水平已经超过了套管的屈服强度极限,因此,可以判定此次地震是导致该气田盐岩层段出现套变的真正原因。     

基于细观变形理论的盐岩塑性本构模型研究

唯象学本构模型不能很好解决诸如夹杂含量、温度、应变速率等对盐岩力学性质的影响,更难以解释盐岩变形机制。盐岩为石岩晶体组成,其变形机制主要由多晶结构所控制,故基于固体位错理论研究方法建立的盐岩塑性本构模型更能反映盐岩的变形机制。研究表明,盐岩的塑性-蠕变交互作用机制是（亚）晶粒内部位错的滑移与（亚）晶界及其干涉面内位错的攀移运动之间的耦合。基于此,可确定亚晶（或晶粒）平均尺寸与流动应力之间的关系、（亚）晶内的位错平均密度;建立微观参量（位错、亚晶直径、亚晶界宽度等）演化模式;根据Orowan定律建立盐岩微观-宏观变形联系,从而导出盐岩塑性本构方程。导出的本构方程体现了盐岩塑性-蠕变变形的物理机制,相对于传统的塑性本构方程具有更好的物理意义。     

Structural characteristics of the halite fabric type ‘Kristallbrocken’ from the Zechstein Basin with regard to its development

The Kristallbrocken are a characteristic centimetre- to decimetre-sized, laminated halite fabric type occurring in the Stassfurt Formation in the Zechstein Basin. Up to now, the nature of the Kristallbrocken, i.e. if they are relics of fine-grained, polycrystalline halite beds or clasts of ‘single crystal-layers’, as well as the deformation mechanisms of this halite type, were not clear from the literature. Drill core material from the salt deposit Teutschenthal at the southern rim of the Zechstein Basin now allowed investigating less intensely deformed samples for the first time. The deformational behaviour of these Kristallbrocken ranges from brittle to ductile, which is evidenced by fractured Kristallbrocken on the one hand and weakly bent or even folded Kristallbrocken on the other hand. Local X-ray texture measurements demonstrated that the Kristallbrocken are definitely single crystals and that they can be regarded as relics of formerly larger ‘single crystal-layers’ of up to several dm² in size. The folded Kristallbrocken clearly display by their single grain texture characteristics that their crystal lattice is bent, which was most likely enabled by a kind of flexural-shear folding, and did not develop after deformation from a fine-grained aggregate by recrystallisation. Due to their monocrystallinity, their originally large size, and the solid inclusions forming the internal lamination, the Kristallbrocken have clearly stronger rheological properties than the surrounding fine- to coarse-grained polycrystalline rock salt, and thus also deform by fracturing.     

桩基下岩溶顶板稳定性有限元阶段分析

为了研究桩基下伏溶洞顶板的稳定性以及破坏模式,利用有限元软件DIANA进行阶段分析,模拟地基土体在溶洞不断扩大过程中渐进塑性变形及位移场特性,并以无溶洞时地基极限承载力为标准设置5个不同桩端载荷等级,对比分析荷载等级和溶洞发育对于围岩稳定性的耦合影响,并总结出溶洞发育过程中顶板的破坏模式和机理。得出如下结论:溶洞发育和桩端荷载等级均存在临界安全值。在荷载等级较小时,溶洞对地基起主要影响作用,溶洞不断发育使塑性应变沿桩基下方斜向下不断扩展。当荷载等级较大时,相同发育阶段溶洞顶板塑性应变显著增大,即使溶洞发育处于安全阶段,也可能使临界安全阶段提前,发生破坏。数值模拟较好地反应实际中溶洞随时间不断扩大演化过程中围岩的受力特点,对于岩溶顶板稳定性研究具有重要参考价值。     

Effects of orientation on the diffusive properties of fluid-filled grain boundaries during pressure solution

An unresolved issue in the study of pressure solution in rock materials is the dependence of grain boundary structure and diffusive properties on the mutual orientation of neighbouring grain lattices. We report electrical measurements yielding the diffusivity of differently oriented halite–glass and halite–halite contacts loaded in the presence of brine. The halite–glass contact experiments show pressure solution of the halite and an effect of halite lattice orientation on grain boundary transport. Post-mortem observations show an orientation-dependent grain boundary texture controlled by the periodic bond chains in the halite structure. It is inferred that this texture determines the internal grain boundary structure and properties during pressure solution. In the halite–halite experiments neck-growth occurred, its rate depending on twist-misorientation. The results imply that deformation by pressure solution may lead to lattice-preferred orientation development, and that polymineralic rocks may deform faster at lower stresses than monomineralic rocks.     

Formation of garnet polycrystals during metamorphic crystallization

Garnet polycrystals may form throughout the metamorphic history of a rock, starting at the earliest stages of garnet growth when closely spaced nuclei coalesce. In mica schist from Townshend Dam, VT, electron back-scattered diffraction (EBSD) analysis shows that garnet polycrystals possess two or more distinct lattice orientations separated by high-angle boundaries (28–61°). The minimum rotational displacements required to bring these lattice orientations into concordance with each other are commonly normal to the same low-energy planes that occur as crystal faces of euhedral garnet. There is no evidence for intracrystalline deformation, and the polycrystals therefore probably represent individual garnet crystals that coalesced during growth. The boundaries cross-cut growth zoning and inclusion trails of the polycrystals, indicating that early-formed polycrystals, once coalesced, behave chemically and physically as single crystals. Statistical analysis of a 3D, high-resolution X-ray computed tomographic data set of a large sample (912 cm³) of a Townshend Dam schist, combined with microprobe and EBSD analyses of garnet, are consistent with a high degree of clustering at all stages of garnet growth. The formation and prevalence of polycrystals implies that garnet nuclei impinged on each other and coalesced, and that coalescence was a common feature throughout garnet growth in the rock.     

Comments on the interpretation of deformation textures in rocks

In rocks that undergo ductile deformation, preferred orientation develops as a result of intracrystalline slip and mechanical twinning. The orientation distribution is a consequence of the microscopic mechanisms and of the strain path. It can be used to get some insight into the deformation history; however it is never unique. The interpretation relies largely on polycrystal plasticity theory. The concepts of stress equilibrium and strain compatibility, which are two extreme assumptions made to model deformation, are discussed. New approaches such as the viscoplastic self-consistent theory are a compromise and may be applicable to mineral systems which display a high degree of plastic anisotropy. Important extensions allow for heterogeneous deformation in the polycrystal from grain to grain and even within grains in correspondence with microstructural observations. All these theories defy the popular notion which is becoming entrenched in the geological literature, that the microscopic slip plane normal aligns with the axis of maximum principal compressive stress, and that in simple shear the crystallographic slip plane rotates into the macroscopic shear plane and the slip direction into the macroscopic shear direction, an orientation referred to by geologists as ‘easy glide’. It is emphasized that future work on texture development of rocks should be based on rigorous physics rather than ingenious intuition, in accordance with an old recommendation of Walter Schmidt.     

Effect of plastic deformation on hydraulic fracturing with extended element method

The propagation of hydraulic fracture in elastic rocks has widely been investigated. In the paper, we shall focus on numerical modeling of hydraulic fracturing in a class of porous rocks exhibiting plastic deformation. The plastic strain of porous rocks is described by a non-associated plastic model based on Drucker–Prager criterion. The plastic deformation is coupled with fluid pressure evolution described by the lubrication theory. An extended finite element method is used for modeling the propagation of fracture. The fracture propagation criterion is based on the J-integral. The proposed numerical model is validated by comparisons with numerical and analytical results. The influence of plastic deformation on fracture propagation process is investigated.

     

混凝土面板堆石坝应力变形长期性状有限元模拟

为了获得混凝土面板堆石坝长期力学行为（尤其流变变形对混凝土面板堆石坝工作性状的影响）定量分析成果,运用ABAQUS有限元对国内某抽水蓄能电站混凝土面板堆石坝进行了数值模拟。采用考虑非线性强度的改进双屈服面流变模型描述堆石料长期力学性能,其中瞬时塑性变形采用改进双屈服面模型确定,而黏塑性流变变形采用指数衰减函数定义。有限元分析获得坝体、单元和面板在填筑期、蓄水期与运行期的应力与变形一般规律。结果表明：运行阶段堆石流变变形对混凝土面板堆石坝应力、变形性状产生显著影响。研究结论有益于进一步了解和合理预测混凝土面板的长期性能。     

Evolution of zircon deformation mechanisms in a shear zone (Lanzo massif,Western-Alps)

Magmatic zircons within two sheared gabbroic dykes from the peridotitic massif of Lanzo (Western-Alps, Italy) revealed evolution of deformation from crystal plasticity to rigid body rotation during shear zone evolution. This is the first time that multiple zircon grains have been analysed in a kinematic context in a shear zone. Zircon grains recorded crystal plastic deformation activating the commonly inferred <100>{001} and <001>{100} glide-systems to the newly identified <001>{110} glide-system. The exact selection of glide-system could be dependant of deformation conditions such as pressure, temperature, and strain rate. Moreover, the activation of one or several glide-systems within a single grain could be favoured by the primary orientation of the grains combined with a high strain rate. In these sheared gabbros, the deformation mechanisms evolve from plastic deformation at low strain rate conditions to increase strain, strain softening and localisation of deformation. The progressive shear zone development and the softening of the matrix relative to the zircon has lead to a switch from crystal-plasticity to rigid body rotation of zircon. The zircon grains rigid body rotation involved that their long axes became parallel to the lineation of the shear zone, causing reorientation and dispersion of the misorientation axes away from kinematic Y.     

Finite deformation analysis of geomaterials

The mathematical structure and numerical analysis of classical small deformation elasto–plasticity is generally well established. However, development of large deformation elastic–plastic numerical formulation for dilatant, pressure sensitive material models is still a research area. In this paper we present development of the finite element formulation and implementation for large deformation, elastic–plastic analysis of geomaterials. Our developments are based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts. A consistent linearization of the right deformation tensor together with the Newton method at the constitutive and global levels leads toward an efficient and robust numerical algorithm. The presented numerical formulation is capable of accurately modelling dilatant, pressure sensitive isotropic and anisotropic geomaterials subjected to large deformations. In particular, the formulation is capable of simulating the behaviour of geomaterials in which eigentriads of stress and strain do not coincide during the loading process. The algorithm is tested in conjunction with the novel hyperelasto–plastic model termed the B material model, which is a single surface (single yield surface, affine single ultimate surface and affine single potential surface) model for dilatant, pressure sensitive, hardening and softening geomaterials. It is specifically developed to model large deformation hyperelasto–plastic problems in geomechanics. We present an application of this formulation to numerical analysis of low confinement tests on cohesionless granular soil specimens recently performed in a SPACEHAB module aboard the Space Shuttle during the STS‐89 mission. We compare numerical modelling with test results and show the significance of added confinement by the thin hyperelastic latex membrane undergoing large stretching. Copyright © 2001 John Wiley & Sons, Ltd.     

路堑边坡施工过程离心模型试验及数值模拟研究

以粤北山区高速公路某路堑边坡为研究对象,通过离心模型试验及有限元模拟其施工过程,揭示开挖卸荷过程中的变形特性及稳定机制,探讨锚杆在边坡稳定中发挥的作用。结果表明,开挖卸荷引起松弛变形,变形量从坡顶向坡脚逐渐增大,从开挖临空面向坡体内部逐渐减小,最大值出现在坡脚,且在坡脚形成塑性区;锚杆支护后提高了加固部分土体的强度,减小了下级开挖引起的松弛变形,限制坡脚塑性区的发展。锚杆轴力沿杆体不均匀分布,其规律与锚杆长度有关,且一般下层锚杆轴力较上层大。锚杆支护不仅提高施工期的稳定,还可有效减弱应变软化对边坡长期稳定的不利影响,提高安全储备。研究成果对高速公路路堑边坡的设计及施工具有指导意义。     

基于强度折减的土质边坡破坏及稳定分析

边坡的破坏过程是由土体局部破坏向整体失稳发展的过程,其塑性区的开展及其水平位移增量的变化较完美地展现了这个过程。根据边坡的实际破坏和有限元数值模拟情况,提出了以特征点位移增量的突变及塑性区贯通作为边坡的失稳判断准则;并以此为判据,采用基于强度折减的大变形有限元方法分析了土质边坡的破坏及稳定性。研究表明,采用强度折减有限元法可有效分析边坡的破坏及其稳定性;此外还分析了带有软弱夹层黏土边坡的破坏性状及其稳定性,并比较了大、小变形有限元的计算结果,结果表明,带有软弱夹层黏土边坡的破坏性状随软弱夹层土体性质的变化而变化,由大小变形有限元分析得到的边坡稳定安全系数较为一致,但边坡的破坏机制随软弱夹层土体性质变化的转变点不同。     

Garnet polycrystals and the significance of clustered crystallization

Polycrystalline garnets are common in metamorphic rocks and may form as a result of close spacing of nuclei (if clustering is early) or impingement of larger grains (if clustering occurs later in the growth history). The timing of clustering relative to garnet growth is relevant to understanding the formation and evolution of porphyroblasts and evaluating the significance (if any) of clustering. Electron backscattered diffraction (EBSD) analysis of garnet-bearing metamorphic rocks reveals the presence of polycrystalline garnet in nine localities examined in this study: the northern Appalachians (Vermont, Maine, New York, USA); North American Cordillera (North Cascades Range, Washington; Snake Range, Nevada, USA); western Rocky Mountains (British Columbia, Canada); southern Menderes Massif (Turkey); Santander Massif (Colombia); and the Sanandaj–Sirjan zone (Hamadan, Iran). In some samples, polycrystals comprise ~20–30% of garnets analyzed, and chemical and textural evidence suggests that early coalescence of garnet polycrystals is common. Some early-coalescing polycrystals exhibit growth zoning that is concentric about the geometric center of the polycrystal. In thin section, these garnets may be undetectable as polycrystals based on morphology or zoning. In some polycrystals, zoning is unrelated to the location of internal grain boundaries; in others, Fe–Mn–Mg zoning has a different pattern than that of Ca; zoning patterns may vary on the scale of a single thin section. In addition, some polycrystals are characterized by high-angle misorientation boundaries that may be in special (non-random) orientations, an observation that indicates that these polycrystals are not random clusters of grains. The presence of internal grain boundaries may affect diffusion pathways and length scales, and may facilitate communication of porphyroblast interiors with matrix phases, thereby influencing reaction history of the rock and the composition/zoning of garnet.     

数值模拟在沉积盆地褶皱冲断构造变形研究中的应用与发展

数值模拟是一种利用电子计算机,通过数值计算和图像显示的方法,研究工程问题、物理问题乃至自然界各类问题的方法。随着高性能计算的不断发展,数值模拟方法在沉积盆地构造变形研究中的应用不断扩大,学术界和工业界将数值模拟方法广泛应用于盆地构造变形特征与变形机制的定量研究,取得了丰硕的成果。本文在系统分析前人数值模拟成果的基础上,阐述了有限元、有限差分、边界元和离散元四种常用数值模拟实验方法的特征和应用。同时,本文对近年来数值模拟方法在沉积盆地褶皱冲断构造变形中的研究进展进行了分类总结,重点介绍这一方法在构造特征与变形机制研究中取得的成果,为数值模拟方法在盆地构造变形领域应用的不断扩大和深入提供参考。最后,本文对数值模拟技术在目前应用中面临的问题和未来的发展方向提出了一些看法和建议。     

An examination of the elasticity of hot-pressed MgO

The elastic properties of polycrystalline as well as single crystal MgO have been measured extensively. New measurements on four hot-pressed magnesium oxide samples are presented and compared to existing data. Discrepancies are noted between the properties determined for the different polycrystalline MgO samples; the magnitude of these differences is as much as ±6% for the reported bulk modulus. X-ray and electron microscopy techniques were applied to the four hot-pressed specimens and revealed the presence of residual strains, plastic deformation and a preferred orientation of grains with respect to hot pressing directions. Scanning electron micrographs also indicated that a non-homogeneous pore distribution existed. The results suggest that the data obtained from polycrystalline materials may not truly reflect the intrinsic elasticity of the material but rather some combination of the elasticity of the material and the state of aggregation of the polycrystal.