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。     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Effect of brittle fracture on the rheological structure of the lithosphere and its application in the Ordos

An empirical formula for the fracture strength of the principal rock type in the lithosphere is obtained based on the experimental data from previous studies, in which the effects of the confining pressure, size of the rock sample, temperature, strain rate and the pore pressure are taken into account, the empirical formulae for the effects of them are also presented. By comparing the frictional strength to the fracture strength calculated using the new empirical formula, it is shown that frictional sliding is dominant in the upper crust but brittle fracture is dominant in the lower part of the crust and the lithosphere beneath the crust. Therefore the fracture mechanism must be taken into account in the study of the rheological structure of the lithosphere. The empirical formula for the fracture strength is applied to study the rheological structure of the lithosphere in the Ordos block. Brittle regime in the rheological structure can be divided into two sub-regions, in one of which brittle fracture and in the other frictional sliding are dominant, respectively, unlike previous conventional studies in which frictional sliding is assumed to be the only factor; the magnitude of the rheological strength of the lithosphere calculated by the empirical formula is also lower than that obtained in previous conventional studies.     

双向压缩条件下闭合裂隙岩体断裂破坏机制及渗透压环境判定准则

在研究双向压缩条件下压剪复合型裂纹应力分布特征及断裂破坏机制基础上,考虑渗透压对初始裂隙面上有效正应力的影响,提出高低渗透压环境的判定准则,并基于滑动裂纹模型理论及最大周向拉应力破坏准则,得到不同渗透压环境下初始裂隙尖端微裂纹起裂特征与规律。研究结果表明：压剪复合应力条件下,初始裂隙尖端发育微裂纹的最优倾角与裂隙面摩擦系数直接相关,随裂隙面摩擦系数的增大,最优初始裂隙倾角由45°起逐渐增大;低渗透压条件下,渗流场的存在使裂纹面摩擦系数发生弱化,进而使得最优初始裂隙倾角向45°靠近,而渗透压直接降低裂隙面上有效正应力且与裂隙倾角无关,其仅仅影响裂隙体材料的初裂强度;高渗透压条件下,初始裂隙面由压剪复合应力状态转化为拉剪复合应力状态,并在拉剪复合应力场作用下,尖端微裂纹起裂角随KI/KII的不断增大,由70.5°逐渐趋近于0°。     

岩石摩擦滑动变形演化及声发射特征研究

进行岩石摩擦滑动变形演化过程的声发射特征试验研究。以数字散斑相关方法和声发射系统为试验监测手段,采用双面剪切模型试验方法,开展界面摩擦滑动速率与声发射振铃计数、界面摩擦滑动位移与声发射累计能量、试件变形能密度与声发射b值的对应关系研究。结果表明：（1）声发射振铃计数演化受岩石界面摩擦滑动速率影响,界面摩擦滑动速率的突变与声发射振铃计数激增有较好对应关系;（2）界面摩擦滑动位移与摩擦滑动过程中声发射累计能量演化趋势具有较好的对应关系,可以利用声发射累计能量对岩石摩擦滑动位移的变化趋势进行定性判断;（3）通过声发射b值演化分析可以得出,在剪应力缓慢增长阶段,界面摩擦滑动以随机分布的小尺度微破裂为主;在剪应力线性增长阶段后期,界面摩擦滑动以锁固段的大尺度微破裂为主;在剪应力波动增长阶段,岩石摩擦滑动失稳既可能是由小尺度微破裂为主引发的状态转化,又可能是由以锁固段大尺度微破裂为主引发的稳定状态转换。     

A yield criterion for isotropic and cross‐anisotropic cohesive‐frictional materials

This paper proposes a yield and failure criterion for cohesive and frictional materials. The function is given by the combination of a Lode dependence for the behaviour in the deviatoric plane and a meridian function for the pressure‐dependent behaviour. A variety of shapes can be achieved with the proposed criterion including Lode dependences which are able to reproduce the behaviour of isotropic and cross‐anisotropic materials in the deviatoric plane. The criterion is validated through the comparison with experimental data based on multiaxial experimental tests on clays, sands, rocks and concrete. Finally, the convexity of the criterion is analysed and discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

On the pore‐scale mechanisms leading to brittle and ductile deformation behavior of crystalline rocks

Deformation mechanisms at the pore scale are responsible for producing large strains in porous rocks. They include cataclastic flow, dislocation creep, dynamic recrystallization, diffusive mass transfer, and grain boundary sliding, among others. In this paper, we focus on two dominant pore‐scale mechanisms resulting from purely mechanical, isothermal loading: crystal plasticity and crofracturing. We examine the contributions of each mechanism to the overall behavior at a scale larger than the grains but smaller than the specimen, which is commonly referred to as the mesoscale. Crystal plasticity is assumed to occur as dislocations along the many crystallographic slip planes, whereas microfracturing entails slip and frictional sliding on microcracks. It is observed that under combined shear and tensile loading, microfracturing generates a softer response compared with crystal plasticity alone, which is attributed to slip weakening where the shear stress drops to a residual level determined by the frictional strength. For compressive loading, however, microfracturing produces a stiffer response than crystal plasticity because of the presence of frictional resistance on the slip surface. Behaviors under tensile, compressive, and shear loading invariably show that porosity plays a critical role in the initiation of the deformation mechanisms. Both crystal plasticity and microfracturing are observed to initiate at the peripheries of the pores, consistent with results of experimental studies. Copyright © 2015 John Wiley & Sons, Ltd.     

A multi‐asperity plastic‐contact crack plane model for geomaterials

A mechanistic constitutive model for fully formed cracks in geomaterials, such as concrete and rock, is presented. A three‐dimensional characterisation of the crack morphology is employed in which the crack surface is idealised as a series of conical teeth and corresponding recesses of variable height and slope. Based on this geometrical characterisation, an effective contact function is derived to relate the contact stresses that develop on the sides of the teeth to the net stresses on a crack plane. Plastic embedment and frictional sliding are simulated using a local plasticity model in which the plastic surfaces are expressed in terms of the contact surface function in cylindrical relative displacement space. Finally, the performance of the model is assessed against several sets of experimental data from direct shear tests, and it is concluded that the model is able to capture key characteristics of the behaviour of fully formed cracks in geomaterials. Copyright © 2012 John Wiley & Sons, Ltd.     

The nanogranular origin of friction and cohesion in shale—A strength homogenization approach to interpretation of nanoindentation results

An inverse micromechanics approach allows interpretation of nanoindentation results to deliver cohesive‐frictional strength behavior of the porous clay binder phase in shale. A recently developed strength homogenization model, using the Linear Comparison Composite approach, considers porous clay as a granular material with a cohesive‐frictional solid phase. This strength homogenization model is employed in a Limit Analysis Solver to study indentation hardness responses and develop scaling relationships for indentation hardness with clay packing density. Using an inverse approach for nanoindentation on a variety of shale materials gives estimates of packing density distributions within each shale and demonstrates that there exists shale‐independent scaling relations of the cohesion and of the friction coefficient that vary with clay packing density. It is observed that the friction coefficient, which may be interpreted as a degree of pressure‐sensitivity in strength, tends to zero as clay packing density increases to one. In contrast, cohesion reaches its highest value as clay packing density increases to one. The physical origins of these phenomena are discussed, and related to fractal packing of these nanogranular materials. Copyright © 2010 John Wiley & Sons, Ltd.     

Three‐dimensional shakedown solutions for anisotropic cohesive‐frictional materials under moving surface loads

Previous work on three‐dimensional shakedown analysis of cohesive‐frictional materials under moving surface loads has been entirely for isotropic materials. As a result, the effects of anisotropy, both elastic and plastic, of soil and pavement materials are ignored. This paper will, for the first time, develop three‐dimensional shakedown solutions to allow for the variation of elastic and plastic material properties with direction. Melan's lower‐bound shakedown theorem is used to derive shakedown solutions. In particular, a generalised, anisotropic Mohr–Coulomb yield criterion and cross‐anisotropic elastic stress fields are utilised to develop anisotropic shakedown solutions. It is found that shakedown solutions for anisotropic materials are dominated by Young's modulus ratio for the cases of subsurface failure and by shear modulus ratio for the cases of surface failure. Plastic anisotropy is mainly controlled by material cohesion ratio, the rise of which increases the shakedown limit until a maximum value is reached. The anisotropic shakedown limit varies with frictional coefficient, and the peak value may not occur for the case of normal loading only. Copyright © 2013 John Wiley & Sons, Ltd.     

石灰岩裂隙摩擦滑动特性试验研究

为研究石灰岩裂隙的摩擦滑动特性,搭建了三轴试验系统,进行了劈裂石灰岩岩芯在湿润和干燥条件下的滑动-控制-滑动试验、速度步长试验和渗透试验。通过滑动-控制-滑动试验和速度步长试验分别研究了石灰岩裂隙摩擦强度的时间依赖性和滑动稳定性,并进一步分析了水对裂隙摩擦强度特性的影响,同时还通过渗透试验观察了裂隙渗透率在滑动过程中的变化。滑动-控制-滑动试验表明:裂隙的摩擦强度具有时间和应力依赖性,裂隙摩擦强度在控制时间内的下降量及重新滑动后的愈合量均与控制时长成正比,而与有效压应力成反比;此外,摩擦强度特性还明显受到水的影响。速度步长试验则表明:石灰岩裂隙摩擦强度随滑动速度的增加而增大,呈现速度强化特性。最后通过不同有效正应力下(介于1?3 MPa之间)的渗透试验发现:裂隙的渗透率不仅随有效应力的增加而急剧下降,而且在各级正应力下亦随滑动而逐渐减小。