Grain‐scale pressure variations and chemical equilibrium in high‐grade metamorphic rocks

In the classical view of metamorphic microstructures, fast viscous relaxation (and so constant pressure) is assumed, with diffusion being the limiting factor in equilibration. This contribution is focused on the only other possible scenario – fast diffusion and slow viscous relaxation – and brings an alternative interpretation of microstructures typical of high‐grade metamorphic rocks. In contrast to the pressure vessel mechanical model applied to pressure variation associated with coesite inclusions in various host minerals, a multi‐anvil mechanical model is proposed in which strong single crystals and weak grain boundaries can maintain pressure variation at geological time‐scales in a polycrystalline material. In such a mechanical context, exsolution lamellae in feldspar are used to show that feldspar can sustain large differential stresses (>10 kbar) at geological time‐scales. Furthermore, it is argued that the existence of grain‐scale pressure gradients combined with diffusional equilibrium may explain chemical zoning preserved in reaction rims. Assuming zero net flux across the microstructure, an equilibrium thermodynamic method is introduced for inferring pressure variation corresponding to the chemical zoning. This new barometric method is applied to plagioclase rims around kyanite in felsic granulite (Bohemian Massif, Czech Republic), yielding a grain‐scale pressure variation of 8 kbar. In this approach, kinetic factors are not invoked to account for mineral composition zoning preserved in rocks metamorphosed at high grade.     

车辆荷载作用下软土地基塑性变形的计算

对于低路堤公路,合理地预测车辆荷载引起的地基塑性累积变形对于低路堤公路的设计有着重要的意义。从机制上讲,可将地基的塑性应变分为塑性体积应变和塑性剪切应变。其中对于塑性体积应变,提出采用不排水条件下的残余孔压模型与一维固结理论相耦合进行计算;对于塑性剪切应变,考虑了塑性体积应变引起的土体硬化,提出了修正的塑性剪切应变计算模型。然后基于所提模型,对萧山黏土的不排水与排水条件下的动三轴试验进行模拟,初步验证了所提模型的有效性。对于实际工程问题,首先运用数值的方法求得车辆荷载在地基中引起的附加应力,然后运用所提模型计算各土层的塑性应变,再结合分层总和的方法求得地基的累积塑性变形。以日本佐贺机场1号测点为例,说明了模型在工程边值问题中的有效性。     

The origin of strain patterns resulting from contemporaneous deformation and metamorphism in the Sambagawa metamorphic belt

Abstract The magnitudes of plastic strains of 104 metacherts were determined from the deformed shape of initially spherical radiolarians in the Sambagawa high- P type metamorphic belt of Western Shikoku, Japan. The strain magnitude increases with increasing metamorphic temperature from several per cent to 250%. The a₂/a₃ ratio of strain ellipsoids in the higher metamorphic grades decreases with increasing metamorphic grade while the a₁/a₂ ratio increases rapidly. The long axis of the strain ellipsoid for every grade is nearly parallel to the length of the metamorphic belt, suggesting that the flow direction of the synmetamorphic deformation was uniform along the belt. A map of strain zones within the Sambagawa high- P type metamorphic belt reveals that the metamorphic belt underwent a progressive bulk inhomogeneous shear deformation and that the high-grade zones represent a deep-seated boundary shear zone on the accretionary wedge between a subducting oceanic plate and the immobile rigid continental plate.     

Localized failure of fibre‐reinforced elastic–plastic materials subjected to plane strain loading

We consider discontinuous bifurcations as the indicator of a localized failure for a class of composites that are characterized by elastic fibres reinforcing an elastic–plastic matrix. A macroscopic tangent stiffness tensor for the fibre‐reinforced composite is developed by consistently homogenizing the contribution of fibres in a spherical representative volume element. Analytical solutions are derived for the critical hardening modulus and corresponding bifurcation directions for the case of plane strain loading. Properties of the solutions are further illustrated on the example of the non‐associated Drucker–Prager model at onset of yielding. Results show that presence of fibres decreases the critical hardening modulus, thus inhibiting the onset of strain localization. The rate of decrease in the critical hardening modulus is the highest for pure shear, followed by uniaxial tension, uniaxial compression, biaxial tension and biaxial compression. The main fibre parameters that control the onset of strain localization are their volumetric content and their stiffness modulus whereby very stiff fibres can produce the most significant decrease in the critical hardening modulus, especially for the state of biaxial tension. The critical hardening modulus for the non‐associated Drucker–Prager model exhibits a full range of localization modes including compaction bands, dilation bands, and transition in the form of shear bands regardless of the presence of fibres. Presence of fibres affects bifurcation directions, except in the case when Poisson's ratio of the matrix is equal to 0.25. The results demonstrate stabilizing effects of fibres by which they provide the control against the onset of strain localization. Copyright © 2006 John Wiley & Sons, Ltd.     

级配碎石填料大三轴试验及累积塑性应变预测模型

级配碎石作为重载铁路基床表层的主要填料,其受列车荷载的影响最大。因此,研究级配碎石在循环荷载作用下的动力行为及累积塑性应变演化特征变得尤为重要。首先,通过制备不同细粒含量的级配碎石填料,开展一系列大型动三轴试验,探究细粒含量、围压及动应力幅值对循环荷载作用下试样累积塑性应变的耦合影响机制。其次,基于塑性安定理论,确定不同应力水平下试样的动力行为,得到考虑围压及细粒含量参数的塑性蠕变状态临界动应力计算模型。最后,结合试验数据,建立考虑应力水平及细粒含量参数的塑性蠕变动力行为累积塑性应变预测模型,并明确各参数的物理意义。其研究成果可为既有重载铁路路基健康状态评估及考虑强度、变形综合控制的路基结构设计提供参考。     

The influence of the plastic potential on plane strain failure

The influence of the shape of the plastic potential in the deviatoric plane on plane strain collapse is investigated. The most commonly employed elastic‐perfect plastic models are considered, which adopt well‐known failure criteria for defining the yield and plastic potential surfaces, namely the von Mises, the Drucker–Prager, the Tresca, the Mohr–Coulomb and the Matsuoka–Nakai criteria. Finally, the conclusions are also extended to strain hardening/softening models. For simple constitutive models based on perfect plasticity, it is shown that the value of the Lode's angle at plastic collapse in plane strain conditions strongly depends on the specific failure surface adopted for reproducing the plastic potential surface. If the value of the Lode's angle at yield coincides with the failure value prescribed by the plastic potential, the stress–strain curves exhibit the typical perfect plastic behaviour with yield coinciding with failure, otherwise the stress changes after yield and the stress‐strain curves resemble those of strain hardening/softening models. The infinite strength which is in some situations exhibited by the Drucker–Prager model in plane strain condition is investigated and explained, and it is shown that this can also affect strain hardening/softening models. Copyright © 2013 John Wiley & Sons, Ltd.     

On the pore‐scale mechanisms leading to brittle and ductile deformation behavior of crystalline rocks

Deformation mechanisms at the pore scale are responsible for producing large strains in porous rocks. They include cataclastic flow, dislocation creep, dynamic recrystallization, diffusive mass transfer, and grain boundary sliding, among others. In this paper, we focus on two dominant pore‐scale mechanisms resulting from purely mechanical, isothermal loading: crystal plasticity and crofracturing. We examine the contributions of each mechanism to the overall behavior at a scale larger than the grains but smaller than the specimen, which is commonly referred to as the mesoscale. Crystal plasticity is assumed to occur as dislocations along the many crystallographic slip planes, whereas microfracturing entails slip and frictional sliding on microcracks. It is observed that under combined shear and tensile loading, microfracturing generates a softer response compared with crystal plasticity alone, which is attributed to slip weakening where the shear stress drops to a residual level determined by the frictional strength. For compressive loading, however, microfracturing produces a stiffer response than crystal plasticity because of the presence of frictional resistance on the slip surface. Behaviors under tensile, compressive, and shear loading invariably show that porosity plays a critical role in the initiation of the deformation mechanisms. Both crystal plasticity and microfracturing are observed to initiate at the peripheries of the pores, consistent with results of experimental studies. Copyright © 2015 John Wiley & Sons, Ltd.     

Large strain similarity solution for a spherical or circular opening excavated in elastic‐perfectly plastic media

This paper deals with the unloading problem of a spherical or circular opening excavated in elastic‐perfectly plastic media with a nonassociated Mohr–Coulomb yield criterion. A large strain similarity solution, using incremental velocity approach, is presented by replacing partial differential equations from stress equilibrium, constitutive law, consistency condition, and displacement equation with first‐order ordinary differential equations. The classical Runge–Kutta method is used to solve the first‐order ordinary differential equations. Comparisons among small and large strain solutions are made using some data sets of soil and rock. The results show that the displacements by large strain similarity solution are smaller than those by exact small strain solution and somewhat larger than those by large strain solution using total strain approach. Copyright © 2014 John Wiley & Sons, Ltd.     

Usage of strain and vorticity analyses to interpret large‐scale fold mechanisms along the Sanandaj–Sirjan HP‐LT metamorphic belt,SW Iran

3D finite strain analyses and kinematic vorticity measurements were carried out on the Loghon Anticline within the HP‐LT Sanandaj–Sirjan metamorphic belt (Neyriz area, SW Iran). Rƒ/φ and Fry methods were used on the strain markers (e.g. deformed fossils) to interpret geometric relationships between the fold axis, strain ellipsoid axes and shear zone boundaries. The results indicate the predominance of prolate strain in the anticline. Quantitative kinematic analyses show that the W_k parameter is 0. 67 ± 0. 06 (i.e. pure‐shear dominated non‐coaxial flow). This study quantitatively supports the establishment of a dextral transpressive system, which is responsible for the development of the large‐scale right‐lateral shear zones that strike sub‐parallel to the major folds. Flexural shear combined with regional dextral‐shear is suggested to be the most common mechanism of folding in this area. Copyright © 2011 John Wiley & Sons, Ltd.     

Elasto‐plastic model for cement‐treated sand

This paper presents an elasto‐plastic model for non‐linear analyses of cement‐treated sand. Various laboratory tests were systematically carried out to investigate the pre‐peak and post‐peak behaviours of a cement‐treated sand. On the basis of these experimental results, the new model was built within the framework of a relatively simple elasto‐plastic theory. Two failure criteria are employed to express tensile and shear failure characteristics observed in the experimental results of the cement‐treated sand. The proposed model can describe strain‐hardening and strain‐softening responses under both failure modes. In the strain‐softening rules, the smeared crack concept is used, and a characteristic length is considered to avoid the issue of mesh‐size dependency. Since the failure criterion and strain‐hardening/softening rules are based on the experimental evidences, the model is relatively easy to understand and the parameters used in the model have clear physical meaning. The proposed model was applied to simulate the behaviour of cement‐treated sand in various laboratory tests, allowing for a reasonable comprehensive evaluation. It was demonstrated that the proposed model is suitable for describing both the tensile and shear failure behaviours of cement‐treated sand. Copyright © 2006 John Wiley & Sons, Ltd.     

The recognition of former melt flux through high‐strain zones

High‐strain zones are potential pathways of melt migration through the crust. However, the identification of melt‐present high‐strain deformation is commonly limited to cases where the interpreted volume of melt “frozen” within the high‐strain zone is high (>10%). In this contribution, we examine high‐strain zones in the Pembroke Granulite, an otherwise low‐strain outcrop of volcanic arc lower crust exposed in Fiordland, New Zealand. These high‐strain zones display compositional layering, flaser‐shaped mineral grains, and closely spaced foliation planes indicative of high‐strain deformation. Asymmetric leucosome surrounding peritectic garnet grains suggest deformation was synchronous with minor amounts of in situ partial melting. High‐strain zones lack typical mylonite microstructures and instead display typical equilibrium microstructures, such as straight grain boundaries, 120° triple junctions, and subhedral grain shapes. We identify five key microstructures indicative of the former presence of melt within the high‐strain zones: (a) small dihedral angles of interstitial phases; (b) elongate interstitial grains; (c) small aggregates of quartz grains with xenomorphic plagioclase grains connected in three dimensions; (d) fine‐grained, K‐feldspar bearing, multiphase aggregates with or without augite rims; and (e) mm‐ to cm‐scale felsic dykelets. Preservation of key microstructures indicates that deformation ceased as conditions crossed the solidus, breaking the positive feedback loop between deformation and the presence of melt. We propose that microstructures indicative of the former presence of melt, such as the five identified above, may be used as a tool for recognising rocks formed during melt‐present high‐strain deformation where low (<5%) volumes of leucosome are “frozen” within the high‐strain zone.     

A self‐consistent approach for micro–macro modeling of elastic–plastic deformation in polycrystalline geomaterials

This paper is devoted to multi‐scale modeling of elastic–plastic deformation of a class of geomaterials with a polycrystalline microstructure. We have extended and improved the simplified polycrystalline model presented in [Zeng T. et al., 2014. Mech. Mater. 69 (1):132–145]. A rigorous and fully consistent self‐consistent (SC) scheme is proposed to describe the interaction among plastic mineral grains. We have also deeply discussed the numerical issues related to the numerical implementation of the proposed micromechanical model. The efficiency of the proposed model and the related numerical procedure is evaluated in several representative cases. We have compared the numerical results respectively obtained from the fully SC model and two simplified ones. It is found that the SC model produces a softer stress–strain response than that of the simplified models. The comparisons between the estimation of overall behavior of a granite in different loading conditions and experimental data are also conducted. Copyright © 2015 John Wiley & Sons, Ltd.     

Plastic Deformation and Recrystallization of Garnet: A Mechanism to Facilitate Diffusion Creep

Elongate and deformed garnets from Glenelg, NW Scotland, occurwithin a thin shear zone transecting an eclogite body that hasundergone partial retrogression to amphibolite facies at circa700°C. Optical microscopy, back-scattered electron imaging,electron probe microanalysis and electron back-scatter diffractionreveal garnet sub-structures that are developed as a functionof strain. Subgrains with low-angle misorientation boundariesoccur at low strain and garnet orientations are dispersed, aroundrational crystallographic axes, across these boundaries. Towardshigh-strain areas, boundary misorientations increase and thereis a loss of crystallographic control on misorientations, whichtend towards random. In high-strain areas, a polygonal garnetmicrostructure is developed. The garnet orientations are randomlydispersed around the original single-crystal orientation. Somegarnet grains are elongate and Ca-rich garnet occurs on thefaces of elongate grains oriented normal to the foliation. Commonly,the garnet grains are admixed with matrix minerals, and, wherein contact with other phases, garnet is well faceted. We suggestthat individual garnet porphyroclasts record an evolution fromlow-strain conditions, where dislocation creep and recoveryaccommodated deformation, through increasing strain, where dynamicrecrystallization occurred by subgrain rotation, to higheststrains, where recrystallized grains were able to deform bydiffusion creep assisted grain boundary sliding with associatedrotations. KEY WORDS: diffusion creep; EBSD; garnet; plastic deformation; recrystallization     

大理岩破坏阶段Biot系数研究

在流固耦合研究中经常采用有效应力原理,Biot系数的确定为其中困难之一。为了研究含裂纹大理岩中Biot系数演化规律,在三轴压缩塑性变形后期阶段的不同轴向变形条件下,进行轴向压力加卸载循环;并在轴向压力卸载末期对岩样施加孔隙水压力。通过记录试样的变形,在Shao提出的Biot系数计算方法的基础上,计算轴向和侧向Biot系数。得到了不同围压条件下轴向和侧向Biot系数随轴向变形的演化规律,并对此进行了深入分析。结果表明：（1）Biot系数表现为各向异性,三轴压缩试验时,试样中大部分裂纹沿最大正应力方向扩展,是造成这种现象的直接原因;（2）轴向和侧向Biot系数随着轴向变形的增大而增大,轴向变形的增大引起岩样中裂纹扩展,导致Biot系数增大;（3）低围压条件下轴向和侧向Biot系数均比高围压条件下的值大,这是由于破坏方式不同引起的。     

边坡大变形弹塑性有限元分析[Ⅱ]

本文应用Ｕｐｄａｔｅｄ Ｌａｇｒａｎｇｉａｎ有限元分析理论,分析了石龙庙滑坡的稳定性,其中包括滑坡的大变形,初始应力和超孔隙水压力。根据土的工程地质性质,滑坡体分为四层,土层被视为是弹塑性的,土的塑性屈服采用Ｄｒｕｃｋｅｒ－Ｐｒａｇｅｒ理想塑性屈服准则,挡土墙建成前后的滑坡应力和变形被分别分析和讨论,最后根据这些分析结果,提出了滑坡的整治方案。     

循环荷载下饱和软黏土的累积塑性应变试验研究

通过以交通荷载为背景的饱和重塑软黏土室内不排水动三轴试验,研究了循环荷载作用下饱和重塑软黏土的累积塑性应变发展形态,可分为3种类型：稳定型、破坏型和临界型。根据稳定型累积塑性应变发展曲线特点,提出了饱和软黏土的稳定累积塑性应变方程,并通过试验结果分析了该方程中各拟合参数与动应力幅值、固结围压和静偏应力的变化规律,同时提出了求解无静偏应力条件下软黏土临界动应力的解析方法。通过动三轴试验结果,提出了含动应力幅值、固结围压、静偏应力和循环周次等影响因素的累积塑性应变拟合模型。     

Image‐based modelling and analysis of microstructures for two‐scale problems in geomechanics

This paper focuses on the geometry modelling and numerical analysis of microstructures of geomaterials employing the concept of image‐based engineering. The novel modelling and analysis techniques with digital images are incorporated with the mathematical homogenization method to study the interaction between individual phases, each of whose shape and spatial distribution are irregular. Owing to the distinctive features of these computational techniques, the evaluation of homogenized properties for geomaterials provides the reliable information about the micro‐ or macroscopic mechanical behaviours for engineering practice. It is, naturally, inevitable that engineers' demands on safety and efficient design place emphasis on quantitative estimates for these values. Thus, calibration accompanied with actual measurements comes within the scope of this study so that these properties would be realistic and practical from the engineering viewpoints. Copyright © 2002 John Wiley & Sons, Ltd.     

Capturing strain localization behind a geosynthetic‐reinforced soil wall

This paper presents the results of finite element (FE) analyses of shear strain localization that occurred in cohesionless soils supported by a geosynthetic‐reinforced retaining wall. The innovative aspects of the analyses include capturing of the localized deformation and the accompanying collapse mechanism using a recently developed embedded strong discontinuity model. The case study analysed, reported in previous publications, consists of a 3.5‐m tall, full‐scale reinforced wall model deforming in plane strain and loaded by surcharge at the surface to failure. Results of the analysis suggest strain localization developing from the toe of the wall and propagating upward to the ground surface, forming a curved failure surface. This is in agreement with a well‐documented failure mechanism experienced by the physical wall model showing internal failure surfaces developing behind the wall as a result of the surface loading. Important features of the analyses include mesh sensitivity studies and a comparison of the localization properties predicted by different pre‐localization constitutive models, including a family of three‐invariant elastoplastic constitutive models appropriate for frictional/dilatant materials. Results of the analysis demonstrate the potential of the enhanced FE method for capturing a collapse mechanism characterized by the presence of a failure, or slip, surface through earthen materials. Copyright © 2003 John Wiley & Sons, Ltd.     

The effect of pre‐tectonic reaction and annealing extent on behaviour during subsequent deformation: insights from paired shear zones in the lower crust of Fiordland,New Zealand

Granulite facies pargasite orthogneiss is partially to completely reacted to garnet granulite either side of narrow (<20 mm) felsic dykes, in Fiordland, New Zealand, forming ~10–80 mm wide garnet reaction zones. The metamorphic reaction changed the abundance of minerals, and their shape and grain size distribution. The extent of reaction and annealing (temperature‐related coarsening and nucleation) is greatest close to the dykes, whereas further away the reaction is incomplete. As a consequence, grain size and the abundance of garnet decreases away from the felsic dykes over a few centimetres. The aspect ratios of clusters of S1 pyroxene and pargasite in the orthogneiss, which are variably reacted to post‐S1 garnet, decrease from high in the host, to near equidimensional close to the dyke. Post‐reaction deformation localized in the fine‐grained partially reacted areas. This produced a pattern of ‘paired’ shear zones located at the outer parts of the garnet reaction zone. Our study shows that grain size sensitive deformation occurs where the grain size is sufficiently reduced by metamorphic reaction. The weakening of the rock due to the change in grain size distribution outweighs the addition of nominally stronger garnet to the assemblage.