中低应变率加载条件下花岗岩尺寸效应的能量特征研究

能量相互转化过程的综合作用导致了岩石破坏,而其破坏的根本原因是岩石中储存的应变能的释放。对中低应变率加载条件下岩石尺寸效应能量特征的研究结果表明：花岗岩破坏时吸收的总能量U、弹性应变能Ue以及损伤应变能Ud均随试件尺寸的增长而降低;岩石强度与岩石中储存的能量有关,尤其与弹性储能有关,即弹性应变能愈高,岩石强度越大;试件长度由50 mm 变为125 mm时,弹性储能逐渐降低,岩石破坏形态从劈裂破坏变为剪切破坏,大尺寸时局部化变形明显。能量是不同应变率加载条件下岩石破坏细微观及宏观特征存在差异的内在动力;亦是导致岩石强度存在尺寸效应的本质动因。     

泊松比对岩样破坏模式及全部变形特征的影响

利用编写的计算岩样全部变形特征的FISH函数, 采用FLAC模拟了泊松比不同时单缺陷岩石试样的破坏及全部变形特征。在峰前及峰后, 本构模型分别取为线弹性模型及莫尔库仑剪破坏与拉破坏复合的应变软化模型。高泊松比使岩样发生由单一剪切破坏向复杂破坏转变、破坏区域的面积增加、剪切带倾角降低, Coulomb、Roscoe及Arthur理论对此无法解释。不同泊松比时计算得到的峰前应力-轴向应变曲线、应力-侧向应变曲线、侧向应变-轴向应变曲线、体积应变-轴向应变曲线的线性阶段与平面应变压缩条件下的线弹性解吻合。若泊松比超过1/3, 通过计算得到的平面应变压缩泊松比可大于0.5, 这被数值模拟确认。泊松比的增加使峰后的侧向应变-轴向应变曲线、体积应变-轴向应变曲线、计算得到的泊松比-轴向应变曲线变得不陡峭, 使峰后的应力-侧向应变曲线变得陡峭, 使破坏的前兆变得不明显。      

Bifurcation and instability modelling by a multimechanism elasto‐plastic model

The bifurcation and instability conditions in geomechanics are closely related to the elasto‐plastic behaviour. In this paper the potential of a multimechanism elasto‐plastic model to predict various modes of failure is examined. First, a brief overview for the essential aspects of the constitutive model and the development of the elasto‐plastic constitutive matrix for this model are presented. Then, numerical simulations of different drained and undrained paths in the axisymmetric and plane‐strain conditions for the Hostun sand are illustrated. These examples confirm the capacity of the model to reproduce instability and strain localization phenomena. The obtained response is in agreement with experimental observations, theoretical developments and numerical analyses existing in the literature. Copyright © 2007 John Wiley & Sons, Ltd.     

单轴压缩下岩石应变局部化的应变梯度塑性解

通过在屈服函数中引入材料内部长度建立应变梯度塑性增量本构关系,对岩石材料在单轴压缩条件下应变局部化的二维情况进行了研究。首先,建立了在Mises屈服准则下平面应变情况的岩石材料应变局部化带的带宽与其倾角的关系式,讨论了其带宽的分布范围和最大值与最小值形成的条件,给出岩石材料破坏Ⅰ, Ⅱ类变形的条件,并推出破坏的临界角度;其次,对岩石材料Ⅰ类变形进行了详细地分析,讨论了在不同泊松比 和 条件下材料应变局部化带的倾角的变化范围;最后,利用所得的结论同材料破坏的库仑准则进行对比研究,对内摩擦系数给予了合理的解释。     

单轴压缩下软岩的动态力学特性试验研究

对软岩(砂浆模拟材料)进行了应变速率范围为10-5~101s-1的动单轴压缩实验。实验结果表明,试样的抗压强度随应变速率的增加有较明显的增加趋势,增加幅度大于硬岩;试样的弹性模量以及泊松比随着应变速率的增加均有增加的趋势,但幅度小于强度的增加幅度。并根据不同应变速率下试样破裂面的SEM实验结果,初步地分析了软岩动态力学特性机理。     

Performance of mixed and enhanced finite elements for strain localization in hypoplasticity

Displacement and mixed finite element formulations of shear localization in materials are presented. The formulations are based on hypoplastic constitutive laws for soils and the mixed enhanced treatment involving displacement, strain and stress rates as independently varied fields. Included in these formulations are the standard displacement method, the three‐field mixed formulation, the enhanced assumed strain method and the mixed enhanced strain method. Several numerical examples demonstrating the capability and performance of the different finite element formulations are presented. The numerical results are compared with available experimental data for Hostun RF sand and numerical results for Karlsruhe sand on biaxial tests. Copyright © 2011 John Wiley & Sons, Ltd.     

Inelastic constitutive properties and shear localization in Tennessee marble

The inelastic response of Tennessee marble is modelled by an elastic plastic constitutive relation that includes pressure dependence of yield, strain‐softening and inelastic volume strain (dilatancy). Data from 12 axisymmetric compression tests at confining pressures from 0 to 100 MPa are used to determine the dependence of the yield function and plastic potential, which are different, on the first and second stress invariants and the accumulated inelastic shear strain. Because the data requires that the strain at peak stress depends on the mean stress, the locus of peak stresses is neither a yield surface nor a failure envelope, as is often assumed. Based on the constitutive model and Rudnicki and Rice criterion, localization is not predicted to occur in axisymmetric compression although faulting is observed in the tests. The discrepancy is likely due to the overly stiff response of a smooth yield surface model to abrupt changes in the pattern of straining. The constitutive model determined from the axisymmetric compression data describes well the variation of the in‐plane stress observed in a plane strain experiment. The out‐of‐plane stress is not modelled well, apparently because the inelastic normal strain in this direction is overpredicted. In plane strain, localization is predicted to occur close to peak stress, in good agreement with the experiment. Observation of localization on the rising portion of the stress–strain curve in plane strain does not, however, indicate prepeak localization. Because of the rapid increase of mean stress in plane strain, the stress–strain curve can be rising while the shear stress versus shear strain curve at constant mean stress is falling (negative hardening modulus). Copyright © 2001 John Wiley & Sons, Ltd.     

应变软化扩容对含随机缺陷岩石的渐进变形及破坏前兆特征的影响

在单轴平面应变压缩条件下, 采用FLAC模拟了剪切扩容对含随机缺陷岩石破坏前兆及变形特征的影响。密实的岩石服从莫尔库仑剪破坏与拉破坏复合的破坏准则, 破坏之后呈现应变软化-理想塑性行为。缺陷在破坏之后经历理想塑性行为。随着轴向应变的增加, 试样内部破坏的单元数目增加, 直到达到一个常数, 该常数随着扩容角的增加而增加。当扩容角较高时, 计算得到的泊松比在峰前就可以超过0.5;剪切扩容于峰前发生; 变形后试样的最终体积大于初始体积。剪切局部化(导致了毗邻块体之间的相对滑动)及剪切扩容(发生于剪切带内部)是非零扩容角试样峰后体积膨胀的原因。在峰前, 通过观察剪切应变增量、破坏的单元数目、侧向应变、计算得到的泊松比及体积应变可以发现, 扩容角越高, 试样破坏的前兆越明显。在低扩容角时, 由于弯曲的剪切带边界, 试样内部充分发展的剪切带的倾角比较分散, 剪切带的倾角更接近Arthur理论。      

Strain‐softening analysis of a spherical cavity

This paper studies the excavation of a spherical cavity subjected to hydrostatic initial stresses in the infinite homogeneous and isotropic rock mass with strain‐softening Mohr–Coulomb (M‐C) and Hoek–Brown (H‐B) behaviors. Numerical solutions of the spherical cavity are obtained and the application to determining stress–strain curve of strain‐softening M‐C and H‐B rock mass is studied. A closed‐form solution for the elastic–brittle–plastic medium is introduced first, and then a numerical procedure that simplifies the strain‐softening process into a series of brittle–plastic ones is presented. The approach is validated against the facts that the strain‐softening process evolves into a brittle–plastic one when the softening slope is very steep, whereas it evolves into an elasto‐plastic one when the softening slope approaches zero. Numerical solutions for the prediction of displacements and stresses around the spherical cavity in the strain‐softening M‐C and H‐B rock mass are presented. On the basis of the analysis of the spherical cavity in strain‐softening rock mass, the stress–strain relationship at an infinitesimal cube around the cavity is obtained and discussed with different evolution laws for the strength parameters considered. Copyright © 2011 John Wiley & Sons, Ltd.     

基于复合损伤的节理岩体动态本构模型研究

基于运用霍普金森压杆（SHPB）装置对节理岩体动载试验得出的数据,从节理面倾角、贯通度、厚度、组数、填充物及应变率等不同方面分析各因素对节理岩体力学特性的影响,通过对节理岩体在高应变率下的损伤机制和破坏形式进行分析的基础上,基于复合损伤理论,对广义Bingham模型进行改进,构造了节理岩体材料在不同应变率下动态响应的本构模型,对模型计算和试验结果的比较表明,该模型能够很好地描述节理岩体动荷载下初始弹性变形阶段、稳态塑性变形阶段和加速变形破坏阶段的应力-应变关系,并且理论与试验结果吻合较好,从而证明了该模型的正确性和合理性。     

Numerical modeling of plastic deformation and failure around a wellbore in compaction and dilation modes

In many wellbore stability analyses, the ability to forecast both the occurrence and extent of plastic deformation and failure hinges upon a fundamental understanding of deformation mode and failure mechanism in the reservoir rock. This study focuses on analyzing plastic zones, localized deformations, and failures around a borehole drilled overbalanced or underbalanced through a highly porous rock formation. Based on several laboratory experiments, porous rocks are prone to deform under both shear-induced dilation and shear-enhanced compaction mechanisms depending on the stress state. The shapes of the deformation and failure patterns around the borehole are shown, depending on the initial stress state and the local stress paths. The inquiry of the local stress paths in the near-wellbore zone facilitates the understanding of the reasons for different types of failure mechanisms, including the mixed-mode and the plastic deformation structures. The modification of the 2D plane strain condition by imitating third stress in the numerical scheme helps us bring the stress paths closer to the real state of loading conditions. Our modeling reveals that the transition from isotropic to anisotropic stress state is accompanied by an increase in the deviatoric part of effective shear tensor that leads to the development of inelastic deformation, degradation, and subsequent rock failure. Particular interest is devoted to the modeling of strain localization especially in compaction mode around a wellbore and computing the amount of stress concentration at the tips of dog-eared breakouts. Stress concentration can result in a change in irreversible deformation mode from dilatancy to compaction, elucidating the formation of the shear-enhanced compaction phenomenon at the failure tips in the direction of the minimum horizontal stress.     

Comparison of continuous and discontinuous constitutive models to simulate concrete behaviour under mixed‐mode failure conditions

The paper presents detailed FE simulation results of concrete elements under mixed‐mode failure conditions according to the so‐called shear‐tension test by Nooru‐Mohamed, characterized by curved cracks. A continuous and discontinuous numerical two‐dimensional approach was used. In order to describe the concrete's behaviour within continuum mechanics, two different constitutive models were used. First, an elasto‐plastic model with isotropic hardening and softening was assumed. In a compression regime, a Drucker–Prager criterion with a non‐associated flow rule was used. In turn, in a tensile regime, a Rankine criterion with an associated flow rule was adopted. Second, an isotropic damage constitutive model was applied with a single scalar damage parameter and different definitions of the equivalent strain. Both constitutive laws were enriched by a characteristic length of micro‐structure to capture properly strain localization. As an alternative approach, the extended finite element method was used. Our results were compared with the experimental ones and with results of other FE simulations reported in the literature. Copyright © 2015 John Wiley & Sons, Ltd.     

A phenomenological constitutive model for rocks with shear failure mode

In this paper, a phenomenological constitutive model is proposed to simulate the stress–strain behaviours of intact rocks with shear failure mode. The model captures a wide range of behaviours of rock material such as elastic, plastic, strain softening, ‘Class II’, strain localization, elastic modulus degradation, etc. The sensitivity of the stress–strain relation on the parameters is also investigated. Typical results obtained by testing a number of granite and marble specimens are used to validate the proposed model. Copyright © 2001 John Wiley & Sons, Ltd.     

基于应变空间硅藻质软岩的软化本构模型

三轴试验结果表明,软岩具有显著的应变软化特征。正常固结软岩表现为峰值后较缓的软化特征,而超固结软岩峰值强度后的应力-应变曲线呈陡降软化特征。应变空间表述的弹塑性理论在解决大应变和软化问题时比应力空间表述的弹塑性理论更具有优越性。基于应变空间的基本的弹塑性本构方程式,采用Mises剪切屈服准则及相关联流动法则,导出固结不排水三轴条件下的应力-应变本构关系式,并采用不同的硬化函数表达式对软岩在不同围压下的应力-应变曲线进行数值模拟。结果表明,应变空间的弹塑性理论能较好地模拟软岩应变软化特征,其中硬化函数的确定是关键问题之一。通过研究,提出了用于固结不排水状态下正常固结软岩的硬化函数形式。     

高应力软岩巷道围岩与支护结构相互作用分析

基于Mohr-Coulomb应变软化模型,将收敛-约束法应用于高应力软岩巷道围岩-支护相互作用分析中,构建典型支护结构特征曲线。以FLAC3D数值模拟软件为工具,分析应变软化模型、剪胀角及不同巷道断面类型对围岩-支护相互作用的影响,并对支护系统稳定性进行评价。研究结果表明：考虑应变软化行为的围岩所需支护压力与Mohr-Coulomb模型计算结果相差较大,剪胀角对围岩应力释放过程及围岩-支护相互作用影响较小,巷道不同断面形式及断面不同位置点围岩所需支护压力有一定差异性;初期支护系统的稳定性是围岩与支护系统最终稳定的关键,采用收敛-约束法评价高应力软岩巷道初期支护系统的稳定性,对高应力软岩巷道的支护结构设计及施工具有一定指导意义。     

岩爆、冲击地压的定义、机制、分类及其定量预测模型

引述了若干国际权威学者关于岩爆的机制和定义的论述,在此基础上,依据岩爆发生的不同机制,将岩爆分为断层滑移或者剪切断裂所导致的断裂滑移型和岩石破坏导致的应变型岩爆,并结合事故案例,分析了应变型和滑移型两类岩爆及冲击地压的发生机制和特点。在机制分析的基础上,介绍了岩（煤）柱应变型岩爆和围岩应变型岩爆以及断裂滑移型岩爆定量预测的研究成果,其中,包括作者利用非欧几何模型研究非协调变形影响后对应变型岩爆进行了定量预测和数值模拟的新研究成果。     

Modelling strain localization in granular materials using micropolar theory: numerical implementation and verification

Implementation and applications for a constitutive numerical model on F‐75 silica sand, course silica sand and two sizes of glass beads compressed under plane strain conditions are presented in this work. The numerical model is used to predict the stress versus axial strain and volumetric strain versus axial strain relationships of those materials; moreover, comparisons between measured and predicted shear band thickness and inclination angles are discussed and the numerical results compare well with the experimental measurements. The numerical model is found to respond to the changes in confining pressure and the initial relative density of a given granular material. The mean particle size is used as an internal length scale. Increasing the confining pressure and the initial density is found to decrease the shear band thickness and increase the inclination angle. The micropolar or Cosserat theory is found to be effective in capturing strain localization in granular materials. The finite element formulations and the solution method for the boundary value problem in the updated Lagrangian frame (UP) are discussed in the companion paper. Copyright © 2006 John Wiley & Sons, Ltd.     

Influence of Lode angle‐dependent failure criteria on shear localization analysis in sand

Geotechnical experiments show that Lode angle‐dependent constitutive formulations are appropriate to describe the failure of geomaterials. In the present study, we have adopted one such class of failure criteria along with a versatile constitutive relationship to theoretically analyze the effects of Lode angle on localized shear deformation or shear band formation in loose sand for both drained and undrained conditions. We determine the variation in the possible stress states for shear localization due to the introduction of Lode angle by considering the localized deformation as a bifurcation problem. Further, similar bifurcation analysis is performed for the stress states along a specific loading path, namely, plane strain compression at the constitutive level. In addition, the plane strain compression tests have been simulated as a boundary value finite element problem to see how Lode angle affects the post‐localization response. Results show that the inclusion of a Lode angle parameter within the failure criterion has considerable effects on the onset, plastic strain, and propagation of shear localization in loose sand specimens. For drained condition, we notice early inception of shear localization and multiple band formation when the Lode angle‐dependent failure criterion is used. Undrained localization characteristics, however, found to be independent of Lode angle consideration.     

层状盐岩力学和变形特性数值试验研究

对含泥岩夹层层状盐岩力学和变形特性进行有限元分析。首先,用数值试验方法预测含泥岩夹层层状盐岩体宏观等效弹性力学参数,然后,建立层状盐岩复合体细观有限元模型,研究其在单轴和三轴压缩荷载下盐岩、泥岩以及界面细观应力应变场分布特征、应力集中问题,并将上述研究与已有的理论和试验成果进行对比。结果表明,运用细观有限元方法预测层状盐岩宏观弹性力学参数是一种直观有效的方法;泥岩和盐岩力学特性上的不匹配导致在层状盐岩的泥岩夹层中以及界面边缘处存在较为明显的应力集中和差异变形。单轴压缩时,泥岩体由于侧向变形能力差会受到横向拉伸应力作用而盐岩层则相应的受到横向压应力作用,三轴压缩时因围压和偏应力大小不同层状盐岩细观应力应变场分布特征则更为复杂;此方法能更为直观的分析层状盐岩的变形和破损特征,这一分析结果对进一步进行层状盐岩体内油（气）储库硐室稳定性分析提供了理论基础。     

Simulation of localization failure with strain‐gradient‐enhanced damage mechanics

Strain gradient implies an important characteristic in localized damage deformation, which can be observed in the softening state of brittle materials, and strain gradients constitute the basic behaviours of localization failure area of the materials. The most important point in strain gradient is its damaging function including an internal length scale, which can be used to express the scale effects of mechanical responses of brittle rock mass. By extending the strain gradient theory and introducing an intrinsic material length scale into the constitutive law, the authors develop an isotropic damage model as well as a micro‐crack‐based anisotropic damage model for rock‐like materials in this paper. The proposed models were used to simulate the damage localization under uniaxial tension and plain strain compression, respectively. The simulated results well illustrated the potential of these models in dealing with the well‐known mesh‐sensitivity problem in FEM. In the computation, elements with C₁ continuity have been implemented to incorporate the proposed models for failure localization. When regular rectangle elements are encountered, the coupling between finite difference method (FDM) and conventional finite element method (FEM) is used to avoid large modification to the existing FEM code, and to obtain relatively higher efficiency and reasonably good accuracy. Application of the anisotropic model to the 3D‐non‐linear FEM analysis of Ertan arch dam has been conducted and the results of its numerical simulation coincide well with those from the failure behaviours obtained by Ertan geophysical model test. In this paper, new applications of gradient theories and models for a feasible approach to simulate localized damage in brittle materials are presented. Copyright © 2002 John Wiley & Sons, Ltd.