An anisotropic damage–plasticity model for saturated quasi‐brittle materials

This article is devoted to numerical modeling of anisotropic damage and plasticity in saturated quasi‐brittle materials such as rocks and concrete. The damaged materials are represented by an isotropic poroelastic matrix containing a number of families of microcracks. Based on previous works, a discrete thermodynamic approach is proposed. Each family of microcracks exhibits frictional sliding along crack surfaces as well as crack propagation. The frictional sliding is described by a Coulomb–Mohr‐type plastic criterion by taking into account the effect of fluid pressure through a generalized effective stress concept. The damage evolution is entirely controlled by and coupled with the frictional sliding. The effective elastic properties as well as Biot's coefficients of cracked porous materials are determined as functions of induced damage. The inelastic deformation due to frictional sliding is also taken into account. The procedure for the identification of the model's parameters is presented. The proposed model is finally applied to study both mechanical and poromechanical responses of a typical porous brittle rock in drained and undrained compression tests as well as in interstitial pressure controlled tests. The main features of material behaviors are well reproduced by the model. Copyright © 2012 John Wiley & Sons, Ltd.     

Homogenization‐based analysis of anisotropic damage in brittle materials with unilateral effect and interactions between microcracks

This paper is devoted to micromechanical modeling of induced anisotropic damage in brittle geomaterials. The formulation of the model is based on a proper homogenization procedure by taking into account unilateral effects and interactions between microcracks. The homogenization procedure is developed in the framework of Eshelby's inclusion solution and Ponte‐Castaneda and Willis (J. Mech. Phys. Solids 1995; 43 :1919–1951) estimate. The homogenization technique is combined with the thermodynamics framework at microscopic level for the determination of damage evolution law. A rigorous crack opening–closure transition condition is established and an energy‐release‐rate‐based damage criterion is proposed. Computational aspects on the implementation of micromechanical model are also discussed. The proposed model is evaluated by comparing numerical predictions with experimental data for various laboratory tests on concrete. Parametric studies on unilateral effects and influences of microcracks interactions are finally performed and analyzed. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

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.     

岩石弹脆性分维损伤本构模型

本文定义岩石构元中破裂面的分维值为各向同性损伤变量,而各个方向上裂纹面的累加量定义为各向异性损伤变量,并根据裂纹发育特征提出了损伤变量演化方程,从而建立起岩石脆性变形破坏过程的分维损伤本构模型。最后,利用该模型对大理岩单轴压缩应力应变曲线进行了模拟,结果说明本文提出的模型是较为合理的。     

Micromechanics modelling for stress–strain behaviour of brittle rocks

A micromechanics model for stress–strain behaviour of brittle rocks has been developed. Microcracking is the mechanism of the non-linear deformation behaviour for brittle rocks in the pre-peak stage. The non-linear behaviour in this stage is simulated by considering the local axial splitting of microcracks. The relationships between the compressive stresses, the growth of microcracks, and the fracture-induced deformation are analytically established. In the post-peak stage the shear faulting predominates the process of deformation, which is simulated by a damage model. This micromechanics model is helpful in understanding the failure process in brittle rocks. The model can be used to simulate the complete stress–strain behaviour of rock. The model simulations are consistent with experimental results.     

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。     

A discrete thermodynamic approach for anisotropic plastic–damage modeling of cohesive‐frictional geomaterials

A discrete plastic–damage model is developed for cohesive‐frictional geomaterials subjected to compression‐dominated stresses. Macroscopic plastic strains of material are physically generated by frictional sliding along weakness planes. The evolution of damage is related to the evolution of weakness planes physically in connection with the propagation of microcracks. A discrete approach is used to account for anisotropic plastic flow and damage evolution, by introducing two stress invariants and one plastic hardening variable for each family of sliding weakness planes. Plastic flow in each family is coupled with damage evolution. The proposed model is applied to typical geomaterials and comparisons between numerical predictions and experimental data are presented. Copyright © 2009 John Wiley & Sons, Ltd.     

Numerical analysis of the effect of natural microcracks on the supercritical CO2 fracturing crack network of shale rock based on bonded particle models

The problem of predicting the geometric structure of induced fractures is highly complex and significant in the fracturing stimulation of rock reservoirs. In the traditional continuous fracturing models, the mechanical properties of reservoir rock are input as macroscopic quantities. These models neglect the microcracks and discontinuous characteristics of rock, which are important factors influencing the geometric structure of the induced fractures. In this paper, we simulate supercritical CO₂ fracturing based on the bonded particle model to investigate the effect of original natural microcracks on the induced‐fracture network distribution. The microcracks are simulated explicitly as broken bonds that form and coalesce into macroscopic fractures in the supercritical CO₂ fracturing process. A calculation method for the distribution uniformity index (DUI) is proposed. The influence of the total number and DUI of initial microcracks on the mechanical properties of the rock sample is studied. The DUI of the induced fractures of supercritical CO₂ fracturing and hydraulic fracturing for different DUIs of initial microcracks are compared, holding other conditions constant. The sensitivity of the DUI of the induced fractures to that of initial natural microcracks under different horizontal stress ratios is also probed. The numerical results indicate that the distribution of induced fractures of supercritical CO₂ fracturing is more uniform than that of common hydraulic fracturing when the horizontal stress ratio is small.     

岩石材料的三维各向异性损伤破坏模型与数值模拟

基于复合材料以及连续介质损伤理论,给出了岩石材料的各向异性损伤破坏模型。通过引入与岩石材料单轴加载行为相对应的特征模态构成的四阶对称损伤张量,描述了岩石材料的损伤演化过程,其中对不同主应变方向采用不同的损伤变量,而对同一主应变方向拉压时的损伤则采用不同的损伤变量来描述。在数值模拟岩石破坏过程的程序中,采用了张量分解的方法。将该模型编写用户材料子程序,并嵌入到大型有限元分析程序ABAQUS中,通过ABAQUS/EXPLICIT SOLVER的显式有限元算法求解。利用此程序对岩石材料的单轴压缩进行了数值模拟。     

A rate‐dependent cohesive crack model based on anisotropic damage coupled to plasticity

In quasi‐brittle material the complex process of decohesion between particles in microcracks and localization of the displacement field into macrocracks is limited to a narrow fracture zone, and it is often modelled with cohesive crack models. Since the anisotropic nature of the decohesion process in separation and sliding is essential, it is particularly focused in this paper. Moreover, for cyclic and dynamic loading the unloading, load reversal (including crack closure) and rate dependency are essential features that are included in a new model. The modelling of degradation is based on a ‘localized’ version of anisotropic continuum damage coupled to inelasticity. The concept of strain energy equivalence between the states in the effective and nominal settings is adopted in order to define the free energy of the interface. The proposed fracture criterion is of the Mohr type, with a smooth transition of the failure and kinematics (slip and dilatation) characteristics between tension and shear. The chosen potential, of the Lemaitre‐type, for evolution of the dissipative processes is additively decomposed into plastic and damage parts, and non‐associative constitutive equations are obtained. The constitutive equations are integrated by applying the backward Euler rule and by using Newton iteration. The proposed model is assessed analytically and numerically and a typical calibration procedure for concrete is proposed. Copyright © 2006 John Wiley & Sons, Ltd.     

Numerical modeling of fracturing in permeable rocks via a micromechanical continuum model

The paper presents a micromechanical approach to describe the failure of low-permeability brittle rocks as a multiscale fracturing process based on a poroelastic microcrack-damage model. Failure is formulated deep down at the fine pore scale as a material degradation phenomenon driven by microcrack growth that also impacts upon hydromechanical properties. A set of damage tensors describes the effect of dual-scale porosities (nanopores and microcracks) on both the hydraulic and poroelastic rock properties. Essentially, the multiscale model reconstructs the coupling effect of hydromechanical forces at the continuum level from the ground up through the upscaling of multiphase interactions at the fundamental structural level of the material. As a result, many macroscopic characteristics emerge naturally such as friction angle, fracture properties, and most importantly, Biot's coefficient taking on a tensorial form that is generally anisotropic. The model is validated within the framework of finite elements to illustrate various baseline constitutive features such as the effect of microcrack growth on the nonlinear stress-strain response and the induced anisotropy in the context of lab experimental tests and boundary value problems. Heterogeneities of the rock samples were incorporated by choosing material properties to be stochastic following Weibull and lognormal distributions. Numerical results appropriately replicated typical experimental observations where fracture localization and propagation are shown to be a multiscale phenomenon emerging from microcrack growth and coalescence at the microscale, with concomitant enhancement in fluid conductivity.     

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.

     

花岗岩隧道脆性破坏的温度效应研究

目前深埋硬岩隧道的岩爆等脆性破坏研究还较少考虑到温度的作用效应。采用精细网格数值模型,提出热-脆性-精细力学计算方法,应用能反映高地应力下硬岩脆性破坏特点的岩体劣化模型,结合能量计算指标,开展了不同温度作用下隧道硬岩脆性破坏的热力耦合分析。以瑞典APSE花岗岩隧洞岩柱为例,进行不同地温下隧道破坏区、能量释放值和应力指标的定量化对比研究。研究结果表明,隧道地温的增加将使岩体产生附加温度应力,进而增大其脆性破坏程度,计算结果与隧道现场的破坏规律基本一致。热-脆性-精细力学计算能合理描述硬岩的损伤和渐进破坏过程,计算结果较好地揭示了花岗岩等硬岩深埋隧道脆性破坏的温度作用效应,对于高应力、高地温下深部工程的稳定性评价具有指导意义。     

脆性颗粒材料的动态多尺度模型研究

脆性颗粒材料的多尺度模型一般包含微观尺度的基本粒子、细观尺度的颗粒和宏观尺度的颗粒堆积体3个尺度。基于离散元方法（DEM）构建多尺度模型,并将该模型应用于动态加载。首先,对多尺度模型所涉及的两种接触模型和两种黏结模型的参数进行分析,详细讨论微细观模型参数与宏观材料常数之间的联系。然后,选用Hertz-Mindlin接触模型[1]和平行键黏结模型,建造石英砂的动态多尺度模型。通过选择合适的强度和局部阻尼参数发现,模型宏细观尺度上的动态压缩响应与对石英砂的相关试验结果吻合很好。利用多尺度模型和选定的参数,探讨与动态加载密切相关的局部阻尼机制对多尺度模型各个尺度上力学响应的影响。结果表明,阻尼越大则颗粒材料对波的衰减能力越强,但过高的阻尼会使团簇强度和模型的宏观压缩曲线都表现出异常的加载速度效应（后者实际是阻尼引起的微惯性效应）。另外,高阻尼会过度衰减颗粒破碎过程产生的应力波,从而阻碍颗粒破碎。最后,应用改进的动态多尺度模型,对脆性颗粒材料的动态破碎特性进行研究,发现该模型不但能给出与试验相吻合的颗粒级配曲线,还能揭示出颗粒破碎过程中微裂纹分布的空间不均匀性,即颗粒破碎过程中波的产生机制和衰减机制相互作用导致的微裂纹聚团分布的现象。     

岩土应变损伤变量测度研究

岩土材料变形破坏损伤测度关系到其稳定性计算结果的可靠性。在考虑了现有岩土损伤模型不完备性的基础上,分析了岩土材料的损伤值存在上限1的非可达性,提出了以应变对线弹性本构曲线的偏离量（差应变）与应变的比值作为损伤量度的方法。根据试验结果进行计算分析表明,其可对初始损伤和临界损伤进行准确计算。同时,根据岩石脆性破坏试验,指出岩石在由弹性阶段向非弹性阶段过渡时存在材料损伤度的陡增区间,其与岩石材料内部微裂纹的扩展与相互屏蔽作用有关,在这个区间岩石的应变和损伤会出现局部化集中。      

Study of desaturation and resaturation in brittle rock with anisotropic damage

This paper deals with numerical modelling of anisotropic damage induced by desaturation and resaturation processes in a brittle rock. This study is conducted in the framework of geological barrier safety analysis for deep disposal of nuclear waste. A non-linear poroelastic model coupled with anisotropic damage is proposed for constitutive modelling of unsaturated rock. A fully coupled FEM method is used for modelling of hydromechanical coupling problems. Instantaneous phase change without dissipation between water liquid phase and vapour is included. Parametric studies are performed to investigate influences of main factors involved in such processes. Rock damage induced by excavation, desaturation and resaturation is evaluated. Finally, we analyse the importance of taking into account the correlation between induced damage and rock permeability.