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.     

岩体强度的各向异性研究

本文运用断裂力学理论推导了含节理岩体的初裂强度公式,定量地讨论了节理方向、长度对岩石强度的影响,阐明了节理岩体强度各向异性的实质。通过证实,本文所建立的公式具有很强的适用性和较高的可靠性,可用于实际的工程岩体稳定性评价。     

软土初始应力各向异性弹塑性模型

自然土体处于初始应力状态,其强度和应力-应变关系都呈现出各向异性,而以往广泛使用的剑桥模型是建立在重塑土试验结果的基础上的,因此,计算实际问题时有一定缺陷.在总结了一些在修正剑桥模型基础上进行扩展而得到的各向异性模型,尤其是S-CLAY1模型.然后,假定了初始屈服面的倾角为K0线,这样使S-CLAY1的计算更加简单.此外,还编制了相关程序,进行了比较计算.结果表明,该模型简单合理,参数正确,可以在实际工程中应用.     

On the effects of deformation induced anisotropy in isotropic materials

Effects of recoverable deformation induced anisotropy in the elastic stiffness of isotropic materials are described. In isotropic materials, thermodynamics predicts coupling of hydrostatic and deviatoric responses. It is shown that the coupling of the two responses is more significant than previously recognized in the literature. Properly accounting for the coupling of hydrostatic and deviatoric responses requires re‐evaluating elastic materials characterization data, allowing for the coupled response. The result is an apparent decrease in the pressure sensitivity of the elastic shear modulus. The decrease in the pressure sensitivity of the shear modulus leads to stress paths that are more tangential to the yield surface in stress space, resulting in an increase in predicted elastic strain at each step of an elastic–plastic stress update. Consequently, predicted plastic strains and, in particular, volumetric plastic strains, are smaller than if recoverable deformation induced anisotropy had been neglected. The result is an associated plasticity model, which appears to be non‐associated. Copyright © 2012 John Wiley & Sons, Ltd.     

考虑各向异性的原状软黏土微观结构变化机制研究

采用电镜扫描仪（SEM）对在复杂应力路径作用下剪切前后的黏土样进行微观观察,并从剪切前后孔隙排列、孔隙形态、孔隙尺度变化特征3方面分析宏观试验原状软黏土归一化抗剪强度各向异性的微观本质。试验表明：剪切前后孔隙排列无序,孔隙排列方向变化很小,对黏土宏观性质影响很小;当中主应力参数b=0时,剪切过程中孔隙形态的变化对剪切后黏土归一化抗剪强度表现出的各向异性贡献较大;当b =0.5时,剪切过程中孔隙尺度的变化对剪切后黏土归一化抗剪强度表现出的各向异性贡献较大。因此,当中主应力参数不同时,影响剪切后黏土归一化抗剪强度各向异性的土的微观变化因素不同。     

横观各向同性岩体中圆形巷道反分析的惟一性

惟一性研究是位移反分析的基础工作之一。推导了横观各向同性岩体中圆形巷道的位移解析解,利用参数可辨识条件对横观各向同性岩体中圆形巷道位移反分析的惟一性进行了探讨。结果表明,无论量测多少个点的位移也不能惟一地反演出所有6个参数;必须至少已知3个参数时,才有可能惟一地反演其他参数;2个地应力分量是否相等对反分析结果有明显的影响;2个地应力分量的可辨识性最好,各向同性面上的弹性模量和泊松比次之,垂直各向同性面方向的弹性模量和泊松比最差。     

致密岩石纵横波波速各向异性的比较研究

通过对板岩、千枚岩、糜棱岩和变质砂岩等4种岩石在平行和垂直层理、板理的3个正交方向上的纵、横波波速试验,提出了致密岩石纵波波速的各向异性与横波波速的各向异性普遍存在着一致性和差异性两种特征。一致性特征主要表现为致密岩石的横波各向异性随纵波各向异性的增强而增强;差异性特征主要表现为在平行和垂直层理、板理的两个方向上,纵波波速的各向异性指数大于横波,亦即纵波波速的各向异性比横波更为显著。从横观各向同性弹性介质的波速方程出发,通过具体的算例对这两种特征进行了较好的理论分析。     

碳酸盐岩中锶元素地球化学特征及其指示意义

应用锶指示古环境的方法很多,其中以锶的含量和与Sr配对的相应的元素比值作为指示剂,具有典型代表性。本文以北京下古生界碳酸盐岩为研究对象,采用ICP-MS分析技术测试了49件样品中Sr、Ba、Cu的含量。以锶的含量、Sr/Ba、Sr/Cu比值作为地化指标,深入探讨了锶的地球化学特征。系统的分析了Sr含量,Sr/Ba、Sr/Cu比值对不同的沉积环境的地质响应。指出从浅海环境到深海环境Sr含量及其相应的元素比值增加趋势明显,对沉积环境具有重要的指示作用。并且,Sr的分布还受到不同沉积旋回的影响,研究沉积作用对Sr分布的影响时,应在同一沉积旋回中进行。此外还深入研究了不同岩性、不同沉积旋回中Sr的分布特征,探讨了影响Sr分布的不同因素。归纳了锶对沉积环境的指示作用。就成岩作用对碳酸盐岩中锶分布的影响,结合前人的工作,进行了探索性的分析。     

考虑饱和黏土初始各向异性的循环边界面塑性模型

天然土体的初始各向异性通常可对其后继循环特性产生显著影响。现有考虑循环载荷作用的土体弹塑性模型,往往采用类似修正剑桥模型的椭圆形屈服面,已有研究表明,该椭圆形屈服面因其拉伸弹性区域偏大,针对天然K0固结状态的土体,其计算精度较差。基于新近提出的广义各向同性硬化准则,在边界面方程中引入初始各向异性张量,并采用空间滑动面破坏准则（SMP）的变换应力法,建立了能考虑饱和黏土初始各向异性的循环边界面塑性模型。分别针对等压和偏压固结的饱和黏土静、动三轴试验进行模拟,结果表明,该模型能合理反映土体的初始各向异性及其后继循环动力特性。     

初始应力各向异性结构性土的二元介质模型

天然岩土材料具有结构性和各向异性。在岩土破损力学的理论框架下,建立了初始应力各向异性结构性土的二元介质模型。岩土破损力学把结构性岩土材料抽象成由胶结强的胶结块（胶结元）和无胶结的软弱带（摩擦元）组成的二元结构体,变形过程中胶结块逐步破损并向软弱带转化。假定胶结块为横观各向同性的理想弹脆性体,胶结块破损后转化成的软弱带为可用邓肯-张模型描述的非线性弹性体。通过引入考虑各向异性影响的破损率和局部应变系数,建立了初始应力各向异性结构性土的二元介质本构模型,并给出了模型参数的确定方法。最后给出了模型的表现,且通过人工制备初始应力各向异性结构性土的三轴压缩试验结果验证了模型的适用性。计算结果表明,所提出的本构模型可以较好地模拟初始应力各向异性结构性土的应力-应变和体积变形特性。     

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.     

压剪应力条件下各向异性岩石损伤本构模型和渗流模型(Ⅱ)：三轴压缩应力状态下理论模型及算例

在文[1]的基础上，推导了所建立本构模型和渗流模型的三轴压缩情况下的方程，并给出了1个算例。结果表明，建立的本构模型能够反映微裂纹闭合摩擦滑移、微裂纹发生自相似扩展和微裂纹发生弯折扩展对变形的影响；建立的本构模型能够反映岩石剪胀特征；弯折微裂纹分支张开是使岩石渗流明显地增大原因     

Cross-bedding related anisotropy and its interplay with various boundary conditions in the formation and orientation of joints in an aeolian sandstone

Previous research revealed that the cross-bedding related anisotropy in Jurassic aeolian Aztec Sandstone cropping out in the Valley of Fire State Park, Nevada, affects the orientation of compaction bands, also known as anti-cracks or closing mode structures. We hypothesize that cross-bedding should have a similar influence on the orientation of the opening mode joints within the same rock at the same location. To test this hypothesis, we investigated the relationship between the orientation of cross-beds and the orientation of different categories of joint sets including cross-bed package confined joints and joint zones in the Aztec Sandstone. The field data show that the cross-bed package confined joints occur at high-angle to bedding and trend roughly parallel to the dip direction of the cross-beds. In comparison, the roughly N–S trending joint zones appear not to be influenced by the cross-beds in any significant way but frequently truncate against the dune boundaries.To characterize the anisotropy due to cross-bedding in the Aztec Sandstone, we measured the P-wave velocities parallel and perpendicular to bedding from 11 samples and determined an average P-wave anisotropy to be slightly larger than 13%. From these results, a model based on the generalized Hooke's law for anisotropic materials is used to analyze deformation of cross-bedded sandstone as a transversely isotropic material. In the analysis, the dip angle of cross-beds is assumed to be constant and the strike orientation varying from 0° to 359° in the east (x), north (y), and up (z) coordinate system. We find qualitative agreement between most of the model results and the observed field relations between cross-beds and the corresponding joint sets. The results also suggest that uniaxial extension (ε_zz > ε_xx = ε_yy = 0) and axisymmetric extension (ε_xx = ε_yy < ε_zz and ε_xx = ε_yy > ε_zz) would amplify the influence of cross-bedding associated anisotropy on the joint orientation whereas a triaxial extension (ε_xx > ε_yy > ε_zz) would mitigate this influence. We suggest that the potential implication of different categories of joint sets (i.e., cross-bed package confined joints and joint zones) forming in response to the variation of the boundary conditions (axisymmetric extension and triaxial extension, respectively) and the interplay with the rock anisotropy is significant. These results have important implications for fluid flow through aeolian sandstones in reservoirs and aquifers.     

Estimation of rock mass strength and deformability in 3-D for a 30 m cube at a depth of 485 m at Äspö Hard Rock Laboratory

The rock fracture data provided by Swedish Nuclear Fuel and Waste Management Company were used to develop a 3-D stochastic fracture network model for a 30 m cube of Äspö diorite located at a depth of 485 m at Äspö Hard Rock Laboratory, Sweden. This fracture network model was validated. A new procedure is developed to estimate rock block strength and deformability in three-dimensions allowing for the anisotropy and incorporating the inherently statistical fracture geometry for the selected cube. The mean rock mass strength was found to be 47% of the mean intact rock strength of 297 MPa at 485 m depth. The mean rock mass modulus was found to be 51% of the intact rock Young's modulus of 73 GPa. The rock mass Poisson's ratio was found to be 21% higher than the intact rock Poisson's ratio of 0.28. These percentages indicate the level of weakening of the rock mass due to the presence of fractures. The ratio of mean major principal rock mass strength/mean minor principal rock mass strength turned out to be 1.28. The ratio of mean major principal rock mass modulus/mean minor principal rock mass modulus turned out to be 1.21.     

压剪应力条件下各向异性岩石损伤本构模型和渗流模型(Ⅰ)：理论模型

采用细观力学研究了岩石损伤变形过程和渗流过程。在本构模型中增加了对剪胀变形机理和渗流对变形影响的内容,同时按照微裂纹发展过程建立了考虑微裂纹扩展、变形和渗透压影响的岩石各向异性渗流模型,使得模型能够更好地表述岩石的变形特性和渗流特性。所建立的模型能够考虑微裂纹闭合摩擦滑移、微裂纹发生自相似扩展和微裂纹发生弯折扩展等过程。     

拉应力条件下岩石细观力学本构模型和渗透系数张量研究(Ⅱ):各向异性渗透系数张量及算例

建立了同时考虑微裂纹发展过程、渗透压和变形影响的岩石各向异性渗透系数张量,推导了所建立本构模型和渗透系数张量的单轴拉伸方程,并和实验结果进行了对比。结果表明,建立的本构模型能够反映岩石的弹性阶段、非线性强化阶段、应力跌落阶段和应变软化阶段的特征;能够很好地反映有渗流时岩石抗拉强度降低等渗流岩石力学特征;建立的渗透系数张量正确反映了随着岩石损伤的发展岩石中渗流的各向异性规律。该模型也适用于岩体。     

土体三维卸荷弹塑性模型及其试验验证

天然土体经历开挖卸荷应力路径后,其应力变形特性与常规加载应力路径条件下规律存在较大差异。目前常用土体本构模型大多建立在等向固结单向加载三轴试验基础上,没有考虑初始K0固结和开挖卸荷应力路径的影响。以剑桥模型为基础,借鉴关口-太田模型的建模思想,通过引入新的应力比参数,对p-q平面上屈服轨迹硬化轴进行旋转,调整弹性区范围,以反映初始K0固结的影响;再运用变换应力法将模型三维化处理,从而使模型可以描述土体三向不等向应力状态,最终得到一个能综合反映土体K0固结开挖卸荷应力-应变特性的三维弹塑性本构模型。通过和典型室内应力路径试验结果进行对比,验证了模型的合理性。     

Magnetocrystalline anisotropy of rocks and massive ores: A mathematical model study and its fabric implications

A simple mathematical model has been used to evaluate the influence of grain magnetocrystalline anisotropy and the scatter of crystallographic axes of grains on the magnetic anisotropy of rocks and massive ores whose carrier of magnetism is a magnetically uniaxial mineral of the type of pyrrhotite or hematite. The variation in magnetic anisotropy of rocks and ores whose carrier of magnetism displays the magnetocrystalline anisotropy greater than 100 is due to the variation in the preferred orientations of crystallographic axes, while the influence of the variation in the grain anisotropy on the rock (ore) anisotropy can be neglected.     

张八岭群火山岩地球化学特征及其构造学意义

安徽滁州张八岭地区的张八岭群分为2组。一是下部北将军组,以千枚岩和片岩为主;二是上部西冷岩组,主要为一套变质火山岩系。张八岭岩群的细碧-石英角斑岩系主要发育于西冷岩组中,具多旋回特点。细碧-石英角斑岩系以石英角斑岩为主,细碧岩次之,角斑岩类稀少。该岩系的火山岩富碱、富钠,具双峰值特征,其主量元素、微量元素和稀土元素地球化学特征表明,它形成于非造山张性环境,为裂陷槽,是与晚元古代罗迪尼亚(Rodinia)超大陆裂解有关的岩浆作用的产物。     

拉应力条件下岩石细观力学本构模型和渗透系数张量研究(I):各向异性损伤本构模型

在拉应力作用下的考虑渗流的岩石本构模型研究尚且很少。采用细观力学研究了岩石损伤变形过程,考虑了渗流过程。由于选用了新的微裂纹扩展准则,提高了解方程效率;采用细观力学成果建立了考虑渗流的微裂纹面不连续变形对岩石变形影响规律,并采用断裂力学成果建立了考虑渗流的微裂纹应力强度因子;建立了同时考虑微裂纹扩展过程和渗流过程的岩石各向异性损伤本构模型,该模型也适用于岩体。