On the strength of transversely isotropic rocks

Accurate prediction of strength in rocks with distinct bedding planes requires knowledge of the bedding plane orientation relative to the load direction. Thermal softening adds complexity to the problem since it is known to have significant influence on the strength and strain localization properties of rocks. In this paper, we use a recently proposed thermoplastic constitutive model appropriate for rocks exhibiting transverse isotropy in both the elastic and plastic responses to predict their strength and strain localization properties. Recognizing that laboratory‐derived strengths can be influenced by material and geometric inhomogeneities of the rock samples, we consider both stress‐point and boundary‐value problem simulations of rock strength behavior. Both plane strain and 3D loading conditions are considered. Results of the simulations of the strength of a natural Tournemire shale and a synthetic transversely isotropic rock suggest that the mechanical model can reproduce the general U‐shaped variation of rock strength with bedding plane orientation quite well. We show that this variation could depend on many factors, including the stress loading condition (plane strain versus 3D), degree of anisotropy, temperature, shear‐induced dilation versus shear‐induced compaction, specimen imperfections, and boundary restraints.     

An approach to model the mechanical behavior of transversely isotropic materials

The present work proposes an approach to adapt existing isotropic models to transversely isotropic materials. The main idea is to introduce equivalence relations between the real material and a fictitious isotropic one on which one can take all the advantages of the well‐established isotropic theory. Two applications of this approach are presented here: a failure criterion and a damage model that takes into account the load‐induced anisotropy. In both cases, theoretical predictions are in agreement with the experimental data. In the present paper, the developed approach is applied to sedimentary rock materials; nevertheless, it can be generalized to any material that exhibits transverse isotropy. Copyright © 2015 John Wiley & Sons, Ltd.     

Thermoplasticity and strain localization in transversely isotropic materials based on anisotropic critical state plasticity

Geomaterials such as soils and rocks are inherently anisotropic and sensitive to temperature changes caused by various internal and external processes. They are also susceptible to strain localization in the form of shear bands when subjected to critical loads. We present a thermoplastic framework for modeling coupled thermomechanical response and for predicting the inception of a shear band in a transversely isotropic material using the general framework of critical state plasticity and the specific framework of an anisotropic modified Cam–Clay model. The formulation incorporates anisotropy in both elastic and plastic responses under the assumption of infinitesimal deformation. The model is first calibrated using experimental data from triaxial tests to demonstrate its capability in capturing anisotropy in the mechanical response. Subsequently, stress‐point simulations of strain localization are carried out under two different conditions, namely, isothermal localization and adiabatic localization. The adiabatic formulation investigates the effect of temperature on localization via thermomechanical coupling. Numerical simulations are presented to demonstrate the important role of anisotropy, hardening, and thermal softening on strain localization inception and orientation. Copyright © 2016 John Wiley & Sons, Ltd.     

Experimental investigation on the deformation characteristics of granular materials under drained rotational shear

Rotational shear is the type of loading path where samples are subjected to cyclic rotation of principal stress directions while the magnitudes of principal stresses are maintained constant. This paper presents results from an experimental investigation on the drained deformation behaviour of saturated sand in rotational shear conducted in a hollow cylinder apparatus. Two types of granular materials, Leighton Buzzard sand and glass beads are tested. A range of influential factors are investigated including the material density, the deviatoric stress level, and the intermediate principal stress. It is observed that the volumetric strain during rotational shear is mainly contractive and most of strains are generated during the first 20 cycles. The mechanical behaviour of sand under rotational shear is generally non-coaxial, i.e., there is no coincidence between the principal axes of stress and incremental strain, and the variation of the non-coaxiality shows a periodic trend during the tests. The stress ratio has a significant effect on soil response in rotational shear. The larger the stress ratio, the more contractive behaviour and the lower degree of non-coaxiality are induced. The test also demonstrates that the effect of the intermediate principal stress, material density and particle shape on the results is pronounced.     

Evolution of anisotropy with saturation and its implications for the elastoplastic responses of clay rocks

Many clay rocks have distinct bedding planes. Experimental studies have shown that their mechanical properties evolve with the degree of saturation (DOS), often with higher stiffness and strength after drying. For transversely isotropic rocks, the effects of saturation can differ between the bed-normal (BN) and bed-parallel (BP) directions, which gives rise to saturation-dependent stiffness and strength anisotropy. Accurate prediction of the mechanical behavior of clay rocks under partially saturated conditions requires numerical models that can capture the evolving elastic and plastic anisotropy with DOS. In this study, we present an anisotropy framework for coupled solid deformation-fluid flow in unsaturated elastoplastic media. We incorporate saturation-dependent strength anisotropy into an anisotropic modified Cam-Clay (MCC) model and consider the evolving anisotropy in both the elastic and plastic responses. The model was calibrated using experimental data from triaxial tests to demonstrate its capability in capturing strength anisotropy at various levels of saturation. Through numerical simulations, we demonstrate the role of evolving stiffness and strength anisotropy in the mechanical behavior of clay rocks. Plane strain simulations of triaxial compression tests were also conducted to demonstrate the impacts of material anisotropy and DOS on the mechanical and fluid flow responses.     

裂隙介质电性各向异性的研究

文中提出了一个一般介质的裂隙集中体积模型,由此导出了裂隙介质以及作为特例的EDA介质的各向异性电导率表达式。然后,从大地电磁测深法的角度,详细地推导了双层地层 (含裂隙)结构的视电阻率正演公式。最后,利用所得结果进行了数值模拟。本文的结果有助于进一步开展电性各向异性及其与地震的联合解释的研究。     

On double shearing in frictional materials

This paper evaluates the mechanical behaviour of yielding frictional geomaterials. The general Double Shearing model describes this behaviour. Non‐coaxiality of stress and plastic strain increments for plane strain conditions forms an important part of this model. The model is based on a micro‐mechanical and macro‐mechanical formulation. The stress–dilatancy theory in the model combines the mechanical behaviour on both scales. It is shown that the general Double Shearing formulation comprises other Double Shearing models. These models differ in the relation between the mobilized friction and dilatancy and in non‐coaxiality. In order to describe reversible and irreversible deformations the general Double Shearing model is extended with elasticity. The failure of soil masses is controlled by shear mechanisms. These shear mechanisms are determined by the conditions along the shear band. The shear stress ratio of a shear band depends on the orientation of the stress in the shear band. There is a difference between the peak strength and the residual strength in the shear band. While peak stress depends on strength properties only, the residual strength depends upon the yield conditions and the plastic deformation mechanisms and is generally considerably lower than the maximum strength. It is shown that non‐coaxial models give non‐unique solutions for the shear stress ratio on the shear band. The Double Shearing model is applied to various failure problems of soils such as the direct simple shear test, the biaxial test, infinite slopes, interfaces and for the calculation of the undrained shear strength. Copyright © 2006 John Wiley & Sons, Ltd.     

Simulating the effects of induced anisotropy on liquefaction potential using a new constitutive model

The effects of induced anisotropy on the undrained behaviour of very loose and saturated sands have been a subject of intensive investigation, both experimentally and theoretically, by several authors in the past few years. This paper proposes an original constitutive model well‐adapted to simulate the behaviour of sands subject to complex stress histories, in particular, the preloading cycle along the classical drained stress path in compression. The developed model belongs to the family of critical state models. Its construction is based on a few theoretical concepts taken from the theory of ‘Bounding Surface Plasticity’ developed among others by Y. Dafalias and Popov (1975), the ‘Clay And Sand Model’ (CASM) of H. Yu (2006), the CJS model (B. Cambou and K. Jafari (1988)) and the hyperelastic isotropic model of P. Lade (1987). To accurately simulate volume changes, which represent a key element in soil behaviour, a state‐dependent dilatancy rule is proposed, which can account for the influences of stress and void ratio. The current void ratio depends implicitly on the irreversible strains already accumulated hence the strain history. A kinematic hardening is combined with an isotropic hardening, involving rotation and distortion of the bounding surface, in order to capture correctly the experimental observations. Comparisons of experimental results to numerical simulations show that the model is able to simulate with a good precision the major trends of undrained responses of loose and presheared sands. It predicts correctly rapid static liquefaction at small or null drained preloading, as well as the progressive transition to a completely stable behaviour typical of dense sands, while the sample is loose in reality. At intermediate to large amplitudes of preloadings, the model also predicts correctly the temporary stage of instability when the deviatoric stress decreases slightly before rising up again. Copyright © 2013 John Wiley & Sons, Ltd.     

Description of deformation process in inherently anisotropic granular materials

The main focus in this work is on modeling of mechanical response of granular materials that display inherent anisotropy. Both the experimental and numerical investigations are described. First, the results of direct shear as well as drained/undrained triaxial tests that involve crushed limestone with elongated angular‐shaped particles are reviewed. Afterward, a mathematical framework is presented for modeling of elastic/ inelastic deformation that incorporates the multi‐laminate approach. The deformation is monitored on a set of randomly oriented planes, and the formulation incorporates the thickness of the shear band that is associated with sliding/separation process. A systematic procedure for identification of material functions/ parameters is outlined that is based on the results of direct shear tests, and the framework is later applied to simulate the behavior under triaxial conditions. The results of numerical simulations are compared with the experimental data. Copyright © 2011 John Wiley & Sons, Ltd.     

堆石料湿化变形特性试验研究

湿化变形是土石坝的主要后期变形之一,对坝体的应力变形性状具有显著影响。采用糯扎渡高心墙堆石坝的弱风化花岗岩堆石料进行了常规三轴试验、不同围压和应力水平条件下的流变-湿化组合试验和快速湿化三轴试验等,分析了流变-湿化组合试验各阶段的变形特征,重点研究了堆石料湿化变形的过程、特性及发生机制。结果表明,可将堆石料湿化变形划分为湿化瞬时变形和湿态流变变形两个部分。其中,湿化瞬时变形是堆石料随浸水饱和过程发生的变形,其应变增量的方向平行于相应应力状态下应力加载应变增量的方向,且具有非硬化特性;湿态流变变形是堆石料试样在饱和浸水完成后发生的随时间的变形,和一般堆石料的流变变形具有相类似的特性。湿化变形是堆石料浸水后所导致的物态弱化变形。可将堆石料湿化看作一种广义的荷载。     

激发极化法在淮南六方堤稳性检测中的应用

在淮南六方堤稳定性研究中,应用激电异常结合累计Σρ_S曲线解释[2],地质效果良好,为堤坝稳定性分析提供了依据。      

大功率激电在双阳煤田找矿应用

大功率激电法在双阳煤田找煤的应用中,证实了山河推覆构造的存在;在充分研究工作区的地质、地球物理特征前提下,恰当地选用了方法技术,并正确理解异常的地质、地球物理意义,取得了较好的找煤效果,在Ⅰ号剖面的激电异常上经钻探和坑探证实磨盘山组灰岩下存在质量较好的可采煤层。     

On equilibrium in non‐hydrostatic metamorphic systems

Metamorphic geology has accumulated a huge body of observation on mineral assemblages that reveal strong patterns in occurrence, summarized, for example, in the idea of metamorphic facies. On the realization that such patterns needed a simple explanation, there has been considerable a posteriori success from adopting the idea that equilibrium thermodynamics can be used on mineral assemblages to make sense of the patterns in terms of, for example, the pressure and temperature of formation of mineral assemblages. In doing so, a particularly simple implicit assumption is made, that mineral assemblages operate essentially hydrostatically. Structural geologists have studied the same rocks for different ends, but, remarkably, the phenomena they are interested in depend on non‐hydrostatic stress. We look at the effect of such behaviour on mineral equilibria. With adoption of some plausible assumptions about how metamorphism in the crust works, the consequence of minerals being non‐hydrostatically stressed is commonly second order in equilibrium calculations.     

兰州Q4黄土各向异性的初步研究

水敏感性和结构性是黄土区别于其他类型土的主要特点,得到了广泛的研究,但大多数试验研究都采用垂直方向制备的试样,仅考虑了黄土垂直方向的力学特性,这对于以承受上部垂直荷载为主的黄土地基基础等工程类型来说是合理和准确的,而对于受力状态较为复杂的边坡和隧道及地下结构等工程类型,黄土力学性质的各向异性可能更为重要。分别从垂直向和水平向制取兰州Q4黄土的原状土试样,通过三轴剪切试验研究了其抗剪强度和变形参数在不同围压下和不同方向上的差异性,并与直剪试验获得的强度参数进行对比。结果表明：兰州Q4黄土力学性质的各向异性是较为显著的,强度方面的差异主要体现在黏聚力,而内摩擦角的差异性较小;变形特征具有随围压增加而从脆性向塑性转化的特点,垂直方向的变形模量比水平方向的变形模量平均要大2倍左右。用黄土的结构性强度及其形成机制解释了试验结果,认为黄土力学性质的各向异性特点是其结构性的另一种表现方式,应重视黄土在不同方向上强度和变形特征的差异性,以获得更安全合理的参数。     

青藏高原东部及其邻区力学耦合的岩石圈变形模式

根据青藏高原东部及其邻区布设的143个宽频带固定和流动地震台站的远震记录的SKS波分裂分析获得了各台站的快波偏振方向和快慢波之间的时间延迟。SKS分裂分析结果总体上反映了高原东部的上地幔物质流动方向,即高原内部表现为环绕喜马拉雅东构造结的顺时针旋转。在造山运动过程中有关岩石圈地壳和地幔力学耦合的造山变形方式,用从GPS和第四纪断裂滑动速率数据确定的地面变形场和由地震波各向异性数据推断的地幔变形场联合分析来定量求得。在青藏高原东部和云南、四川等地区新近快速增加的GPS和SKS波分裂观测数据,提供了对青藏高原岩石圈地幔实际变形方式的检验。这些新的数据不仅加强了高原内部力学耦合岩石圈的证据,而且也解释了高原外部相同的耦合特征。文中引入简单剪切变形和纯剪切变形的概念,用于解释高原内外不同的耦合变形特征。青藏高原和周围区域力学耦合岩石圈的垂直连贯变形有两个方面的大陆动力学含义:第一,岩石圈垂直强度剖面被一个重要的条件所约束,即要求与重力势能变化相关的应力能够从地壳传递到地幔;第二,青藏高原各向异性的空间变化反映了一个岩石圈变形的大尺度模式,以及从高原内部的简单剪切变形向高原外部的纯剪切变形的过渡带。文中提出的力学耦合岩石圈变形模型与当前已有的多种造山运动变形模型具有不同的变形含义,因此,地幔变形在青藏高原隆升过程中起主要作用。     

考虑残余体应变的土石坝地震永久变形分析

地震永久变形是评价土石坝抗震稳定性的一个重要依据,其合理计算需要同时考虑材料的残余体积应变和残余剪切应变的影响。因此,在过去提出的永久变形等效节点力计算方法的基础上,通过考虑剪切压缩耦合作用来反映残余体积应变对地震永久变形的影响,并推导了相应的模量矩阵,明确了参数选择和计算步骤。对典型单元体的残余变形模式进行了分析,计算得到的剪切应变和体积应变大小均与理论值相符,验证了模量矩阵的可靠性。在此基础上,对心墙堆石坝和面板堆石坝的算例进行了计算,重点分析了竖直向、顺河向和横河向3个方向永久变形分布,并与实测规律进行比较。计算结果表明,考虑残余体应变之后,所提方法能够反映土石坝地震永久变形以沉降为主、水平变形相对较小的特点,可更为合理地反映地震永久变形的规律。     

基于岩石圈厚度和地幔横向黏度变化的地幔对流模型重估云南地区剪切波各向异性源的深度

在已有模型的基础上,考虑岩石圈厚度和软流层横向黏度的变化,本文建立了更接近地球实际情形的地幔对流模型,然后重新推测了导致云南地区剪切波各向异性的软流层源的深度.结果 表明:岩石圈厚度和软流层横向黏度变化对云南地区的软流层各向异性源的深度及软流层的变形程度和机制具有重要影响;软流层各向异性对云南西南部区域、东部区域北纬2...     

The effects of stress on reactions in the Earth: Sometimes rather mean,usually normal,always important

Stress affects chemical processes on all scales in the Earth but the magnitude of its effect is debated. Here, I give a new synthesis of the theory that describes the effects of stress on chemistry, elaborating upon work in Materials Science which is built from fundamental thermodynamic laws, and show its significance in Earth Science. There are separate but compatible relationships describing what happens (1) at interfaces and (2) within grains. (1) The main chemical effects of stress in the Earth are due to variations in normal stress along grain interfaces and between interfaces with different orientations. For reactions involving diffusion these variations give effects on mineral stability broadly equivalent to pressure changes of (molar volume)/(molar volume change during reaction) × (stress variation). The volume ratio is generally large and so the effects of normal stress variations are always important since all stressed rocks have interfaces supporting different normal stresses. There is no global chemical equilibrium in a stressed system, so reaction kinetics contribute to ongoing evolution until stresses relax: this evolution can include deformation by diffusion creep and pressure solution, possibly with new mineral growth. These effects are relevant for predicting the conditions for reactions involving fluids, such as serpentinite formation and breakdown (relevant for the Earth's volatile cycles) and for other reactions such as ringwoodite breakdown (relevant for understanding the 660 km mantle discontinuity). (2) Within stressed solid solution grains it is not possible to define chemical potentials of all chemical components since one has to be specified as “immobile.” The chemical potential of a “mobile” component such as an exchange vector can be defined. It depends on the “partial molar strain,” a second rank tensor defining the variation in unit cell geometry with composition. In cubic crystals the partial molar strain is isotropic and the chemical potential of a mobile component depends on mean stress. In other crystal systems the partial molar strain is anisotropic and the chemical potential depends on a “weighted” mean stress; orientation as well as magnitude of stress has an influence. I propose “chemical palaeopiezometry”—the possibility of measuring past stress levels via chemistry. Examples show that stress variations in hundreds of MPa to GPa are required to produce 2% variations in composition but high stresses and/or precise chemical analyses will allow this proposal to be tested. High stresses around inclusions and dislocations could be targeted. So, the weighted mean stress inside grains has an effect which is relatively minor although potentially valuable in explaining chemical variations; the normal stress at interfaces plays the main role in chemical processes and its effects are of significant magnitude.     

激发极化法在东溪金矿接替资源勘查中的应用

东溪金矿是北淮阳构造带东段最早被发现、最早被开采的金矿,因矿石缺乏硫化物,激电测量是否有效曾有争议.通过电阻率测量,辅以极化率测量,发现这些常用的物探技术在贫硫化物的东溪-南关岭金矿接替资源勘查中有效,视电阻率异常指示含金石英(碳酸盐)脉,视极化率异常可能暗示与成矿有关的脉岩及断裂构造.激电测量为探求控矿构造,尤其为实施钻探工程提供了强有力证据.