Failure pattern of brittle rock governed by initial microcrack characteristics

Fracturing processes of rock are simulated using a micro- and fracture mechanical-based numerical modeling approach. The numerical model considers material heterogeneity and initial microcrack distributions. The gradual formation of macroscopic fractures by coalesced microcracks is successfully reproduced. Distinct failure modes are observed in the model under different loadings. Agreement is shown between the numerical results and laboratory observations. The influence of microcrack orientations on the fracture patterns is quantified by the numerical models. Possible mechanisms describing the splitting failure of hard brittle rocks under uniaxial compression are proposed and discussed.

     

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。     

岩石裂纹损伤及围压对剪切破坏影响研究

岩石内部细观裂纹的存在,对压缩作用下岩石剪切断裂的宏观现象有着重要的影响。然而,能够通过解析解阐释细观裂纹几何特性、围压等影响因素对压缩作用下剪切断裂面角度变化趋势的研究很少。基于Ashby模型中提出的裂纹尖端应力强度因子,提出了一种改进的考虑裂纹角度影响的应力强度因子表达式。利用该改进的应力强度因子表达式,推出了一个可以预测岩石峰值强度的裂纹扩展、应变与应力之间的本构关系。结合本构关系的峰值强度与摩尔-库仑失效准则,得到了岩石损伤与内摩擦角、黏聚力、剪切强度及失效断裂面角度之间的理论关系;讨论了围压、裂纹尺寸、角度及摩擦系数对岩石宏观剪切断裂面角度的影响,通过试验结果验证了模型合理性。结果表明：随着损伤增大,内摩擦角、黏聚力及剪切强度不断减小;随着围压增大、摩擦系数增大和初始裂纹尺寸减小,剪切断裂面角度不断增大;随着裂纹角度增大,剪切断裂纹面角度先减小后增大。     

Coupling between anisotropic damage and permeability variation in brittle rocks

In this paper, a coupled constitutive model is proposed for anisotropic damage and permeability variation in brittle rocks under deviatoric compressive stresses. The formulation of the model is based on experimental evidences and main physical mechanisms involved in the scale of microcracks are taken into account. The proposed model is expressed in the macroscopic framework and can be easily implemented for engineering application. The macroscopic free enthalpy of cracked solid is first determined by approximating crack distribution by a second‐order damage tensor. The effective elastic properties of damaged material are then derived from the free enthalpy function. The damage evolution is related to the crack growth in multiple orientations. A pragmatic approach inspired from fracture mechanics is used for the formulation of the crack propagation criterion. Compressive stress induced crack opening is taken into account and leads to macroscopic volumetric dilatancy and permeability variation. The overall permeability tensor of cracked material is determined using a micro–macro averaging procedure. Darcy's law is used for fluid flow at the macroscopic scale whereas laminar flow is assumed at the microcrack scale. Hydraulic connectivity of cracks increases with crack growth. The proposed model is applied to the Lac du Bonnet granite. Generally, good agreement is observed between numerical simulations and experimental data. Copyright © 2005 John Wiley & Sons, Ltd.     

煤体在高压水射流作用下的损伤机制

为研究高压水射流破煤的力学机制,煤体采用J-H-C含损伤本构模型,水射流采用Bridgman状态方程,用固-流耦合算法对高压水射流冲击煤体的损伤机制进行有限元数值计算,得出了煤体在不同冲击压力水射流作用下的损伤形式,模拟与现场试验结果基本一致。研究结果表明,不同水压的水射流冲击煤体形成的损伤机制存在差别,煤体在高压水射流作用下的损伤是阶梯式,煤体在高压水射流冲击下形成压缩波和拉伸波的复合作用是形成煤体损伤的主要原因,随着破煤过程的进行,压缩区和拉伸区有进一步减小的趋势;对于不同强度煤体存在临界破煤压力和最佳破煤压力。     

Crack Initiation and Crack Propagation in Heterogeneous Sulfate-Rich Clay Rocks

Brittle fracture processes were hypothesized by several researches to cause a damage zone around an underground excavation in sulfate-rich clay rock when the stress exceeds the crack initiation threshold, and may promote swelling by crystal growth in newly formed fractures. In this study, laboratory experiments such as unconfined and confined compression tests with acoustic emission monitoring, and microstructural and mineralogical analyses are used to explain brittle fracture processes in sulfate-rich clay rock from the Gipskeuper formation in Switzerland. This rock type typically shows a heterogeneous rock fabric consisting of distinct clayey layers and stiff heterogeneities such as anhydrite layers, veins or nodules. The study showed that at low deviatoric stress, the failure behavior is dominated by the strength of the clayey matrix where microcracks are initiated. With increasing deviatoric stress or strain, growing microcracks eventually are arrested at anhydrite veins, and cracks develop either aligned with the interface between clayey layers and anhydrite veins, or penetrate anhydrite veins. These cracks often link micro-fractured regions in the specimen. This study also suggest that fracture localization in sulfate-rich clay rocks, which typically show a heterogeneous rock fabric, does not take place in the pre-peak range and renders unstable crack propagation less likely. Sulfate-rich clay rocks typically contain anhydrite veins at various scales. At the scale of a tunnel, anhydrite layers or veins may arrest growing fractures and prevent the disintegration of the rock mass. The rock mass may be damaged when the threshold stress for microcrack initiation is exceeded, thus promoting swelling by crystal growth in extension fractures, but the self-supporting capacity of the rock mass may be maintained rendering the possibility for rapidly propagating instability less likely.     

Micromechanical Modeling of Anisotropic Damage-Induced Permeability Variation in Crystalline Rocks

This paper presents a study on the initiation and progress of anisotropic damage and its impact on the permeability variation of crystalline rocks of low porosity. This work was based on an existing micromechanical model considering the frictional sliding and dilatancy behaviors of microcracks and the recovery of degraded stiffness when the microcracks are closed. By virtue of an analytical ellipsoidal inclusion solution, lower bound estimates were formulated through a rigorous homogenization procedure for the damage-induced effective permeability of the microcracks-matrix system, and their predictive limitations were discussed with superconducting penny-shaped microcracks, in which the greatest lower bounds were obtained for each homogenization scheme. On this basis, an empirical upper bound estimation model was suggested to account for the influences of anisotropic damage growth, connectivity, frictional sliding, dilatancy, and normal stiffness recovery of closed microcracks, as well as tensile stress-induced microcrack opening on the permeability variation, with a small number of material parameters. The developed model was calibrated and validated by a series of existing laboratory triaxial compression tests with permeability measurements on crystalline rocks, and applied for characterizing the excavation-induced damage zone and permeability variation in the surrounding granitic rock of the TSX tunnel at the Atomic Energy of Canada Limited’s (AECL) Underground Research Laboratory (URL) in Canada, with an acceptable agreement between the predicted and measured data.     

基于分形与损伤理论的岩石声-应力相关性理论模型研究

建立单一微裂纹在单轴压缩荷载作用下的力学模型,采用宏观复合型断裂理论中的最大周向应力理论,求出单一微裂纹达到稳定时的形态尺寸.利用分形损伤理论,求出不同荷载阶段的分形维数;由分形维数的定义导出了不同荷载阶段的裂纹个数的变化情况;结合单一微裂纹的形态尺寸,求出不同荷载阶段中岩石孔隙率与荷载值之间的关系;利用目前被广泛采用的超声波纵波速度与孔隙率的关系式,最终导出单轴压缩荷载作用下岩石超声波纵波速度与应力的理论关系式.进行岩石声-应力的试验测试,根据试验成果作出声-应力曲线,并与理论声-应力曲线进行比对,结果表明,理论模型比较适合于反映岩石受载全过程中的后半部分的声-应力关系.     

Effect of inherent microcrack populations on rock tensile fracture behaviour: numerical study based on embedded discontinuity finite elements

Inherent microcrack populations have a significant effect on the fracture behaviour of natural rocks. The present study addresses this topic in numerical simulations of uniaxial tension and three-point bending tests. For this end, a rock fracture model based on multiple intersecting embedded discontinuity finite elements is developed. The inherent (pre-existing) microcrack populations are represented by pre-embedded randomly oriented discontinuity populations. Crack shielding (through spurious locking) is prevented by allowing a new crack to be introduced, upon violation of the Rankine criterion, in an element with an initial crack unfavourably oriented to the loading direction. Rock heterogeneity is accounted for by random clusters of triangular finite elements representing different minerals of granitic numerical rock. Numerical simulations demonstrate the strength lowering effect of initial microcrack populations. This effect is substantially stronger under uniaxial tension, due to the uniform stress state, than in semicircular three-point bending having a non-uniform stress state with a clear local maximum of tensile stress.

     

基于细观力学脆性岩石剪切特性演化模型研究

压缩作用下岩石内部细观裂纹扩展导致岩石产生损伤,其对岩石变形、强度等力学特性有着重要影响;然而,岩石内部裂纹扩展与剪切特性（黏聚力、内摩擦角及剪切应力）动态演化关系很少被研究。基于裂纹扩展机制推出的岩石应力-应变本构模型,并结合摩尔-库仑失效准则,推出了在岩石应力-应变关系峰值应力（对应岩石压缩强度）状态时,本构模型细观力学参数与岩石黏聚力、内摩擦角及剪切强度之间的状态关系。然后,引入岩石应力-应变本构关系塑性变形阶段服从摩尔-库仑屈服准则的力学流动规律,进而将已推出的应力-应变关系峰值状态点所满足的细观力学参数与黏聚力、内摩擦角关系,推广到岩石进入塑性变形后,岩石内部裂纹扩展（或应变）与黏聚力、内摩擦角及剪切应力动态演化的理论关系。随着裂纹扩展或应变增加,黏聚力、内摩擦角及剪切应力先增大,达到一个峰值点后减小,该结果与应力-应变本构曲线变化趋势相对应。通过试验结果验证了所提出理论结果的合理性。并讨论了初始裂纹之间摩擦系数对黏聚力、内摩擦角及剪切应力随裂纹扩展或应变演化规律的影响。     

掺砾黏土拉伸断裂细观特性研究

掺砾黏土在高心墙堆石坝工程中的应用越来越广泛,其拉伸断裂特性对心墙的安全至关重要。将掺砾黏土视作四相复合材料,基于图像处理和随机投放建立了考虑真实砾石形态的细观数值模型,结合物理试验的结果验证了其有效性,并分析了掺砾黏土拉伸断裂的宏细观特性。应力位移曲线的宏观非线性是细观非均质性的体现,砾石的掺入大幅减低了抗拉强度,但提高了峰后抗拉性能;土石界面是微裂缝发展的源头,拉伸断裂是一个微裂缝萌生、扩展以至汇集形成宏观裂缝的过程;拉伸断裂发生在一个区域,即断裂过程区,该区域的形成与砾石的随机分布有关。最后,采用数值试验分析了随机砾石投放和掺砾量对掺砾黏土宏细观力学行为的影响。     

Modelling of anisotropic damage in brittle rocks under compression dominated stresses

A new model for describing induced anisotropic damage in brittle rocks is proposed. Although phenomenological, the model is based on physical grounds of micromechanical analysis. Induced damage is represented by a second rank tensor, which is related to the density and orientation of microcracks. Damage evolution is related to the propagation condition of microcracks. The onset of microcrack coalescence leading to softening behaviour is also considered. The effective elastic compliance of the damaged material is obtained from a specific form of Gibbs potential. Irreversible damage‐related strains due to residual opening of microcracks after unloading are also captured. All the model's parameters could be determined from conventional triaxial compression tests. The proposed model is applied to a typical brittle rock. Comparison between test data and numerical simulations shows an overall good agreement. The proposed model is able to describe the main features related to induced microcracks in brittle geomaterials. Copyright © 2002 John Wiley & Sons, Ltd.     

深埋隧洞爆破开挖荷载诱发围岩损伤特性

深埋隧洞爆破开挖荷载构成复杂,对围岩损伤区的孕育发展具有重要影响。利用颗粒流程序（PFC）软件,讨论了不同初始地应力状态下爆炸荷载及地应力瞬态卸载所分别诱发围岩损伤的特性,并通过锦屏2级水电站引水隧洞爆破开挖损伤区检测数据对数值模拟的结果进行了验证。研究表明,爆炸荷载和地应力瞬态卸载所诱发的围岩损伤程度和范围均随地应力量级的提高而显著增大;爆炸荷载作用条件下损伤区的分布有随着侧压力系数的增大而向应力集中区发展的趋势,而地应力瞬态卸荷所产生的围岩破坏以受拉破坏为主,表层损伤区沿开挖呈轮廓均匀分布的趋势;在相同的初始地应力状态下,爆炸荷载和地应力瞬态卸荷所分别诱发的围岩损伤区深度均明显小于实测值,考虑二者的耦合效应后,计算值与实测值基本吻合。这说明这两种荷载是高应力条件下爆破开挖荷载的主要成分,但二者耦合作用对围岩的损伤大于它们单独作用效应的线性叠加。     

Evaluation of coal longwall caving characteristics using an innovative UDEC Trigon approach

The paper presents an innovative numerical approach to simulate progressive caving of strata above a longwall coal mining panel. A proposed Trigon logic is incorporated within UDEC to successfully capture the progressive caving of strata which is characterized by fracture generation and subsequent propagation. A new damage index, D, is proposed that can quantify regions of both compressive shear and tensile failure within the modelled longwall. Many features of progressive caving are reproduced in the model and found to fit reasonably well with field observations taken from a case study in the Ruhr coalfield. The modelling study reveals that compressive shear failure, rather than tensile failure, is the dominant failure mechanism in the caved strata above the mined-out area. The immediate roof beds act like beams and can collapse in beam bending when vertical stress is dominant or in beam shear fracture when horizontal stress is dominant. The proposed numerical approach can be used to guide the design of longwall panel layout and rock support mechanisms.     

Poroelastic behaviour of saturated brittle rock with anisotropic damage

A new anisotropic poroelastic damage model is proposed for saturated brittle porous materials. The model is formulated in the framework of the continuum damage mechanics. A second‐rank symmetric tensor is used to characterize material damage due to oriented microcracks. The classic Biot poroelastic theory is then extended to include poroelastic damage coupling. Both the deterioration of elastic properties and poroelastic coefficients is taken into account. A suitable procedure for determination of model parameters from standard laboratory tests is presented. The validity of the model is tested through comparison between numerical predictions and experimental data in various loading conditions. The overall performance of the model is evaluated. The choice of relevant effective stress for the microcrack propagation criterion in saturated cohesive geomaterials is discussed. Copyright © 2000 John Wiley & Sons, Ltd.     

基于塑性损伤的黏土岩力学特性研究

一系列三轴压缩试验表明,黏土岩的力学特性与其应力状态相关。主要表现为：围压越大,黏土岩试样应力峰值越大,且峰值出现得越晚。这是因为高围压试样内部微裂纹闭合趋势更加明显,从而对于微裂纹的发展具有一定的抑制作用。但在软化过程中应力的跌落程度受围压影响不大,这是因为软化过程中,不同围压作用下试样内部的微裂纹均逐渐贯通,并发展成同类型的剪切面,对试样力学性能的削弱大致相同。在试验研究基础上,以微裂纹作为损伤基元,引入受应力状态影响的损伤演化方程（因微裂纹的发展受应力变化影响）,建立新的本构模型,通过Abaqus及子程序对新模型进行数值实现。模拟结果与试验结果对比表明,该模型可以有效地描述黏土岩的力学特性。研究成果为黏土岩相关地下工程施工提供了更可靠的理论指导。     

锦屏大理岩蠕变损伤演化细观力学特征的数值模拟研究

岩石的蠕变损伤和断裂是岩石流变效应的重要表现形式,但其损伤演化过程往往难以直观观测,为此,采用二维颗粒流数值模拟方法(PFC2D)对岩石的蠕变损伤和断裂的细观力学机制进行了分析。在锦屏大理岩室内试验基础上,利用颗粒流应力腐蚀模型(PSC),建立了能反映其短期和长期强度特征的柱状岩样数值模型,并开展了大量数值试验。结果表明,蠕变损伤的演化过程与暂态的损伤演化过程具有明显的差异。在岩样蠕变损伤过程中,其内部微裂纹多沿加载方向开裂且分布均匀,先快速增加再稳定扩展,最后则发生快速断裂。当荷载较小时,岩样宏观上呈现劈裂破坏特征,当荷载较大时,岩样呈现剪切破坏特征。在岩样蠕变损伤初始和稳定演化阶段的前期,荷载大小对岩样的损伤演化过程影响不大;在稳定演化阶段的后期至断裂过程中,低荷载下岩样的损伤增速比高荷载下快。     

基于微裂隙变形与扩展的岩石冻融损伤本构模型研究

在冻融条件下岩石微裂隙中的水发生相变,体积膨胀,对微裂隙产生很大的冻胀力,当冻胀力超过岩石的抗拉强度时,微裂隙扩展。温度升高时,水又进入新的微裂隙,如此反复循环造成了岩石的损伤。据此,将岩石中的微裂隙等效为扁平状椭圆裂隙,基于断裂力学建立了单条微裂隙下裂隙扩展长度与冻胀力的关系,考虑岩石中微裂隙的分布,将岩石冻融条件下的应变分解为初始损伤应变、附加损伤应变和塑性应变,建立了弹塑性冻融损伤本构模型。最后,通过岩石冻融试验对该模型的合理性进行了验证,结果表明,该模型能够较好地模拟岩石在不同冻融次数下的应力-应变关系曲线。     

西藏贡觉粉砂质泥岩工程地质特性与蠕变强度研究

川藏铁路在穿越西藏贡觉地区时遇到三叠系粉砂质泥岩,在高地应力条件下容易发生大变形等危害。文章开展了不同围压下的岩石三轴压缩和和三轴蠕变试验,结合PFC数值模拟,研究了粉砂质泥岩在不同围压下的蠕变特性和长期强度研究,结果表明:贡觉粉砂质泥岩流变具有西原蠕变模型特征,蠕变与常规三轴试验条件下,随着围压不断增大,粉砂质泥岩试样均由拉-剪破坏向单剪破坏过渡,剪切破裂面与水平线的夹角逐渐减小,微裂纹数量减少;蠕变试验相较于常规三轴试验,由拉应力引起的压碎带影响范围更广;在高围压条件下,粉砂质泥岩更容易发生流变,随着围压的增大,轴向应变、侧向应变和体积应变均增大,微裂纹数量呈下降趋势;瞬时弹性模量及黏弹性系数与围压呈线性递增关系,黏弹性模量与围压呈对数型增长关系,黏塑性系数与围压呈指数型增长关系。在荷载长期作用下,岩石长期强度低于瞬时强度。     

锥形聚晶金刚石复合片齿破岩特征与机制研究

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