How tightly does calcite e-twin constrain stress?

Mechanical twinning along calcite e-planes has been used for paleostress analyses. Since the twinning has a critical resolved shear stress at ∼10 MPa, not only principal stress axes but also differential stress can be determined from the twins. In this article, five-dimensional stress space used in plasticity theory was introduced to describe the yield loci of calcite e-twinning. The constraints to paleostress from twin and untwin data and from calcite grains twinned on 0, 1, 2 and 3 e-planes were quantified by using their information contents, which were defined in the stress space. The orientations of twinned and untwinned e-planes are known to constrain not only stress axes but also differential stress, D, but they loose the resolution of D if the twin lamellae were formed at D greater than 50–100 MPa. On the other hand, it is difficult to observe twin lamellae subparallel to a thin section. The stochastic modeling of this effect showed that 20–25% of twin lamellae can be overlooked. The degradation of the constraints by this sampling bias can be serious especially for the determination of D.     

Qualitative analysis of three-dimensional strain using twins in calcite and dolomite

Turner's (1953) technique of locating the compression (C) and tension (T) axes from the known orientations of C-axis and twin pole ([022̄1] in dolomite and [011̄2] in calcite) for each grain yields the orientation of the unique stress system when a great majority of the grains in the rock shows only singlet twins. However, since it assumes the highest possible value for the coefficient of resolved shear stress s₀ (= 0.5), application of the technique to rocks in which a large number of grains show doublet and triplet twins results in great dispersion of the C- and T-axes. In such cases the unique stress system can be established by preparing separate C-axes fabric diagrams for the untwinned grains, grains with singlet twins, grains with doublet twins and grains with triplet twins; measurement of the orientations of the twin planes becomes unnecessary.     

Structural analysis of faults related to a heterogeneous stress history: reconstruction of a dismembered gold deposit,Stawell, western Lachlan Fold Belt,Australia

In the internationally significant Victorian goldfields a complex system of faults dismembers the 5 million ounce Magdala gold deposit. These faults represent a combination of neoformed faults and inherited faults that reflect deformation associated with stress tensors of variable orientation and stress shape ratio (φ). The fault geometry is strongly controlled by the pre-existing rheology. Faults have propagated around the flanks of an antiformal basalt dome, along earlier ductile cleavages and the margins of porphyry dykes. Many of the faults do not have Andersonian geometries and there is no correlation between the orientation of the faults and the palaeostress directions. Much of the faulting is associated with the emplacement of porphyry dykes, additional gold mineralisation related to plutonism and late-stage deformation post-dating the intrusion of the Stawell pluton. Systematic mapping of extension veins associated with faults, striations and conjugate joint sets allowed the construction of a revised and more robust history of brittle deformation. This successfully predicted the offset direction of the currently mined Magdala ore body beneath the studied system of faults. The use of extension veins was a critical aspect of the analysis. If striations on the fault surfaces had solely been used, the offset direction of the new Golden Gift orebody would not have been correctly ascertained. The palaeostress history was delineated via use of compression and tension dihedra, stress inversion of slip data and calculation of theoretical resolved shear stress for faults with orientations similar to those mapped. The calculation of theoretical resolved shear stress directions highlights the importance that the intermediate stress has on the slip direction for faults whose pole does not lie in the plane containing σ₁ and σ₃.     

Deformation of dolomite single crystals from 20–800° C

Dolomite single crystals of six different crystallographic orientations were tested in compression under confining pressure at temperatures of 20 to 800° C. The chosen orientations favoured slip or twinning on particular systems. The deformed crystals were analysed by optical and high voltage transmission electron microscopy to determine activated deformation systems, dislocation behaviour, etc., and to assist in interpreting stress-strain data. It is shown that slip on c≡(0001) and on \(f \equiv (\bar 1012)\) ), and twinning on f between 300 and 600° C, are the principal modes of deformation. At low temperatures there is considerable cataclasis, and shear-fracturing must be counted as a significant deformation mechanism. The effects of climb become apparent at temperatures ?600° C. A pronounced increase in strength with testing temperature shown by some orientations of the crystals is largely associated with c slip, but f twinning also shows similar although weaker tendencies. The yield stress for f slip decreases markedly with temperature. Values of critical resolved shear stress are obtained for c and f slip, and for f twinning. Major and minor slip systems, dislocation and twin configurations generated by deformation under different regimes are documented and illustrated. Some of the characteristics of the deformation systems are attributed to the details of atomic displacements. In particular, the increase in strength with temperature for c slip is explained by friction of CO ₃ ^2? groups during dislocation movement, which is unique for c slip. This friction increases with thermal vibration, expansion and rotation of the CO ₃ ^2? groups.     

Regional stress field as determined from electromagnetic radiation in a tunnel

The paper presents the results of electromagnetic radiation (EMR) measurements in the Feuerberg tunnel in southwest Germany. EMR is associated with small scale fracturing processes. The measured numbers of EMR impulses are shown to be proportional to shear stresses. From the correlation of EMR and shear stresses along the long axis of the tunnel, orientations and magnitudes of the horizontal principal stresses are determined. The major horizontal principal stress is 3.6±0.3 MPa and has an azimuth of 143±6°. The minor principal horizontal stress is 2.1±0.3 MPa. Zones in the tunnel are located where low shear stresses occur because vertical overburden and horizontal stresses are equal. In these zones also minimum radiation was detected. A possible stress accumulation close to a fault is suggested by higher EMR values in a part of the tunnel. Orientations and magnitudes of the horizontal principal stresses, which are derived from the measurements of EMR, correlate well with conventional stress measurements. It is suggested that the cross-section measuring method described in the study is used to determine regional stress fields as well as to investigate endangered zones with high stresses in underground facilities, which may be critical with regard to stability.     

真三轴条件下非饱和黄土的有效应力屈服特性

为了研究非饱和黄土在有效应力空间的屈服特性,利用真三轴仪对非饱和原状黄土进行了不排水等向净应力压缩固结和不同中主应力参数b值的剪切试验,研究了真三轴压缩条件下非饱和黄土的有效应力屈服变化规律。研究结果表明：有效应力比随着中主应力或净围压的增大而减小,中主应力的增大作用对有效球应力的影响大于广义剪应力;由有效应力比?体应变关系曲线确定的剪缩屈服曲线在有效应力空间具有良好的规律性,屈服点的有效屈服应力随着中主应力和初始吸力的增大而增大;π平面上的有效应力屈服强度面和强度破坏面与SMP强度准则稳合较好,有效球应力和初始吸力越大,屈服强度面和强度破坏面越大。提出了真三轴条件下弹性剪应变和塑性剪应变的计算公式,通过分析有效应力与塑性应变关系得出有效应力空间中不同子午平面内的塑性势面呈椭圆形,且随着中主应力的增大,椭圆屈服面增大。     

山东阜山金矿区构造应力场及其转化

在估算了阜山金矿区成岩成矿期的构造差应力值后,获得约2km2区域内的主压应力和差异应力的空间分布规律。结果表明,矿体部位往往对应于应力或应变强烈变化的区段,而非应力或应变的极高值或极低值处。依据应变测量和磁组构分析,研究了阜山金矿成岩期和成矿期的构造应变场特征,指出:阜山金矿在成岩和成矿期间构造应力场经历了由NE向挤压转为NW向挤压,构造应力场的这种转化对该区的成矿意义重大。      

高地应力下硬岩的本构模型研究

传统的本构模型在模拟高地应力下硬岩破坏的范围和深度方面并不理想。针对高应力下的拉西瓦花岗岩,通过真三轴压缩试验模拟了开挖时应力路径的演化。在摩尔-库仑强度准则、格里菲斯强度准则、德鲁克-普拉格准则、双剪统一强度理论和霍克-布朗强度准则的基础上,考虑十二面单元体主剪面上主剪应力、正应力和静水压力的共同作用,提出了一个有关高应力下硬岩的三剪强度准则。根据试验结果,利用遗传算法全局寻优的功能,搜索出了三剪强度准则的参数。预测样本和与摩尔-库仑强度准则、德鲁克-普拉格准则、双剪统一强度理论的比较表明,该三剪强度准则与试验结果吻合,适用于高地应力下的硬岩。根据试验得到的应力-应变关系曲线,建立了基于三剪强度准则和应变软化的弹-脆-塑性本构模型,并用FLAC3D提供的基于C++的用户自定义模型工具UDM,创建了用户自定义模型的动态链接库,嵌入了FLAC3D软件。采用遗传算法-FLAC方法,搜索得到了基于岩石试样和岩体的本构模型参数。计算结果与实测情况吻合,表明建立的本构模型适用于高地应力下的硬岩,为高地应力下硬岩地下工程的安全性和稳定性分析奠定了基础。     

甘肃阳山金矿区安昌河—观音坝断裂带显微构造特征及地质意义

甘肃阳山金矿是我国最大的金矿床,位于西秦岭造山带的陕甘川"金三角"地区。金矿成矿时代为早侏罗世,与燕山期斜长花岗斑岩有密切的成因联系。基于野外地质调查,本文对安昌河—观音坝断裂带构造岩进行了细致的显微构造研究,以期通过微观构造特征认识宏观断裂构造的活动规律。镜下观察表明断裂带内兼具大量的脆性与塑性显微变形,主要发育左行剪切,暗示该断裂为左行韧-脆性剪切带。断裂带内构造岩经历了高绿片岩相、低绿片岩相及低于绿片岩相的变质-变形过程,且断裂带内至少存在过三到四期构造变形,为断裂带曾发育"多期构造变形"提供依据。显微构造应力分析及岩层产状等密度图显示区域主压应力方向为NNW-NNE,是对印支期以来多期主应力方位的综合反映。据亚颗粒法及动态重结晶法计算的成矿前古应力差值为128.6～95.8 MPa,成矿期古应力差值为74.9～69.3 MPa,成矿后古应力差值为65.8 MPa。综合分析认为中—晚三叠世以来安昌河—观音坝断裂带变质相相变为高绿片岩相→低绿片岩相→低于绿片岩相,变形序列为韧性→韧-脆性→脆性,区域主应力大小发生了大→小的转变,主应力方位经历了SN向挤压→NE向挤压→NW及SN向挤压的转换。安昌河—音坝断裂带构造演化特征反映其经历了从深部到浅部逐渐抬升的过程。     

复杂应力状态下条形基础的临塑荷载公式

莫尔-库仑强度准则的临塑荷载公式由于没有考虑中主应力在强度上的作用使计算结果偏于保守。利用具有线性形式的双剪应力强度准则替换原有的莫尔-库仑强度准则,将中主应力引入临塑荷载的计算中,推导出平面应变条件下考虑中主应力影响的临塑荷载公式,并通过算例说明了新临塑荷载公式的计算结果比原有公式有较大的偏高。     

Mechanical twinning of jadeite – an indication of synseismic loading beneath the brittle–plastic transition

The orientation distribution of mechanically twinned jadeite crystals in a metagranite from the Sesia Zone, Western Alps, is evaluated to derive the orientation of the principal stress directions for a prominent stage of ductile deformation at ca. 300 to 350 °C that has been interpreted to reflect synseismic loading and postseismic creep by Küster and Stöckhert (1999). It is tested whether the orientation distribution can be used to obtain information on the magnitude of differential stress if the critical shear stress for twinning is known. Assuming that the critical shear stress of 140 MPa determined by Kollé and Blacic (1982) for mechanical twinning of clinopyroxene in the (100) [001] system holds true for jadeite, and assuming a homogeneous stress field as a first approximation, differential stresses of the order of 1-2 GPa are inferred for metagranites with ca. 15% jadeite, and of 0.5 GPa for jadeitite with 80% of jadeite. Notwithstanding the uncertainty for the critical resolved shear stress for jadeite, these unexpectedly high values are suspected to be due to a combination of the following effects: (1) an inhomogeneous stress field in the polyphase material with curved stress trajectories, (2) stress concentration in jadeite due to load transfer from the quartz matrix, and (3) minor reorientation of the jadeite crystals in the flowing quartz matrix. Hence, absolute values of differential stress cannot be derived from the orientation distribution of twinned jadeite in polyphase rocks. Notwithstanding the failure in deriving reliable absolute values, a short period with exceptionally high stress must have occurred, and is fully consistent with the microstructural record of other minerals. It is proposed that the mechanical twinning of jadeite was caused by a short-lived stress peak and flow at laboratory strain rates related to quasi-instantaneous loading of the uppermost level of the ductile lower crust during brittle failure of the brittle upper crust in a major seismic event.     

基于统一强度准则改进式的压力隧洞弹塑性应力分析

基于具有抛物线型强度包络线的统一强度准则,即对双剪双参数统一强度准则进行相应的非线性化处理,考虑了中间主应力影响,分析在渗流作用下压力隧洞弹塑性力学行为。通过分析中间主应力对压力隧洞的塑性区半径影响可知,随着中间主应力的参数的增大,塑性区半径也相应减小。通过考虑和不考虑渗流场影响的实例对比分析表明,考虑渗流场时所得塑性区半径要比不考虑时大,而且随着孔隙水压力的增大,渗流场的影响越显著。隧洞径向应力和切向应力也与中间主应力参数b和渗流场密切相关。通过与直线型统一强度准则对比分析可知,采用两种不同准则时所得结果相差较大。隧洞设计时应根据岩石强度特性合理地选择数b,为强度包络线近似于二次抛物线的围岩隧洞设计提供理论依据     

真三轴条件下Q3原状黄土的力学特性

为了模拟实际工程中黄土在不排水条件下的破坏,在控制含水率不变条件下,利用非饱和土真三轴仪对不同初始吸力非饱和原状黄土进行了等向固结试验和不同中主应力参数b值的剪切试验,研究了非饱和原状黄土的力学特性。研究结果表明：真三轴等向压缩屈服应力随着初始吸力的增大而增大,吸力随着净平均应力的增大而减小,净平均应力对吸力的影响程度随着初始吸力的增大而增大。不同 值条件下,广义剪应力和净平均应力破坏状态线近似呈平行直线关系,广义剪应力和有效净平均球应力试验点可归一为饱和土的排水剪切破坏状态线;剪切破坏时吸力随着b值的增大基本呈线性增大趋势;孔隙比和净平均应力对数临界状态线近似呈线性平行关系,其斜率比饱和土大,且大于等向压缩屈服前的斜率;非饱和土孔隙比和有效净平均球应力对数临界状态线与饱和土的临界状态线近似呈线性平行关系;不同净围压条件下,不同 值非饱和土与饱和土的破坏状态孔隙比的比值与气体饱和度的试验点分布于1.0～1.2的直线带内,但同一净有效球应力条件下可以归一为一条非线性曲线。     

A non‐coaxial critical state soil model and its application to simple shear simulations

The yield vertex non‐coaxial theory is implemented into a critical state soil model, CASM (Int. J. Numer. Anal. Meth. Geomech. 1998; 22 :621–653) to investigate the non‐coaxial influences on the stress–strain simulations of real soil behaviour in the presence of principal stress rotations. The CASM is a unified clay and sand model, developed based on the soil critical state concept and the state parameter concept. Without loss of simplicity, it is capable of simulating the behaviour of sands and clays within a wide range of densities. The non‐coaxial CASM is employed to simulate the simple shear responses of Erksak sand and Weald clay under different densities and initial stress states. Dependence of the soil behaviour on the Lode angle and different plastic flow rules in the deviatoric plane are also considered in the study of non‐coaxial influences. All the predictions indicate that the use of the non‐coaxial model makes the orientations of the principal stress and the principal strain rate different during the early stage of shearing, and they approach the same ultimate values with an increase in loading. These ultimate orientations are dependent on the density of soils, and independent of their initial stress states. The use of the non‐coaxial model also softens the shear stress evolutions, compared with the coaxial model. It is also found that the ultimate shear strengths by using the coaxial and non‐coaxial models are dependent on the plastic flow rules in the deviatoric plane. Copyright © 2006 John Wiley & Sons, Ltd.     

4D modelling of fault reactivation using complete paleostress tensors from the Cooper–Eromanga Basin,Australia

Determining fault activity through time has typically utilised high-resolution seismic data to identify stratigraphic thickness changes or displacement vs distance plots; however, this approach is not possible in regions with low-resolution seismic data. We present a new approach for determining fault reactivation (tensile and shear) through time by integrating three-dimensional seismic data, geomechanical modelling and complete paleostress tensors from calcite twin stress inversion. The Cooper–Eromanga Basin is used as a case study to model the stress conditions present during six tectonic events that have affected the basin and, in doing so, constrain the effective paleostress magnitudes through time. Results show that the likelihood of dilation and shear reactivation of individual fault sets varies through time, with N–S- and E–W-striking faults likely to have been open to fluid flow after the critical moment in the hydrocarbon system. These results have substantial implications for hydrocarbon migration pathway models and structural and stratigraphic models for the Cooper–Eromanga Basin. This approach would benefit other provinces with low-resolution seismic data preventing fault growth analysis, or in regions where hydrocarbon migration pathways are poorly defined.     

Physical Meaning of Stress Difference for Fault-Slip Analysis

Recent stress tensor inversion methods for fault-slip analysis are used to distinguish between multiple stress states to elucidate spatiotemporal change of the earth’s crustal tectonics. An estimator named the stress difference has been a practicable tool to measure the difference between stress solutions of inversion analysis. This measure corresponds to the expected difference in shear stress direction on a randomly oriented fault plane, which is, however, an approximation including several degrees of deviation. This study investigated the formula of stress difference and found the exact physical meaning, specifically the expected difference in shear stress vector which carries information on magnitude as well as direction. The present discovery is based on the analytical proportionality between the second invariant of stress tensor and the root mean square magnitude of shear stress for all orientation of fault planes. The meaningless difference in non-dimensional shear stress magnitude was found to be incorporated into the value of stress difference. This fact is not convenient for fault-slip analysis dealing only with orientations.     

Influence of Randomly Distributed Coir Fibers on Shear Strength of Clay

The use of natural fibers such as coir for soil improvement is highly attractive in countries where such materials are locally and economically obtainable, in view of the preservation of natural environment and cost effectiveness. This paper discusses shear strength of clay reinforced with randomly distributed coir fibers based on a series of consolidated undrained triaxial compression tests. Test results show that major principal stress at failure for clay-coir fiber matrix increases with increase in fiber content (W _f ) and fiber aspect ratio (A _r ). For all the combinations of fiber contents and aspect ratios, failure principal stress envelope exhibits a curvilinear variation with a transition at a confining stress, known as critical confining stress. Separate regression analyses have been performed for observations below and above critical confining stress to develop mathematical models, which consider fiber content, aspect ratio, confining stress and plain soil characteristics as the input parameter, to predict major principal stress at failure for the clay-fiber composite. In general, the study identifies that the inclusion of discrete coir fibers in random fashion significantly improves the shear strength of clay and hence could be effectively used for the cases where in-place mixing of soil with fibers is possible (e.g., pavement sub-grade, landfill liner, small embankment). The developed regression models may be used in the design phase for the rough estimation of shear strength of the composite.     

基于统一强度理论深埋圆形隧道围岩的剪胀分析

基于连续介质理论中岩体的剪胀角与围压和塑性剪切应变密切相关,隧洞周边岩体的应力状态因开挖卸荷而发生应力重分布,迫使其围压由原地应力逐渐衰减,塑性剪切应变不断增加,引起剪胀效应呈非线性变化。首先,基于统一强度理论和非关联流动法则,将潜在塑性区围岩按等围压释放划分为若干同心圆,提出了考虑中间主应力和非线性剪胀性的有限差分法,计算应变软化围岩的力学问题,并以实例验证其正确性。其次,通过参数分析,研究塑性区内岩体的剪胀角受中间主应力、临界软化系数和支护力的影响规律。研究结果表明,中间主应力主要影响剪胀角的峰值,随着中间主应力效应增加,剪胀峰值增加;临界软化系数主要影响剪胀角的变化率,随着临界软化系数的增加,剪胀角变化缓慢;中间主应力和临界软化系数共同影响塑性区剪胀角的变化;随着支护力的增加,洞壁处的剪胀角增加;双剪强度理论计算的位移值较小,应谨慎采用,同时采用Mohr-Coulomb强度准则时可以适当考虑围岩的承载潜力。     

剪节理发育地区球状风化物的成因分析

在系统总结国内外关于球状风化物成因研究已有认识的基础上, 针对其中存在的一些值得商榷的问题,结合大量野外图片以及标本分析,对剪节理发育地区球状风化物的成因展开重点研究。提出由于应力作用使岩石内部产生球状细微剪切变动,之后受风化作用的影响形成了球状风化产物的新观点。以此为基础,分析了其他类型球状风化物的形成与力作用的关系。