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.     

A discrete approach for anisotropic plasticity and damage in semi-brittle rocks

In this paper, we propose an anisotropic plastic damage model for semi-brittle geomaterials based on a discrete thermodynamic approach. The macroscopic plastic deformation is generated by frictional sliding of weakness planes. The evolution of damage is related to growth of such weakness planes. The local frictional sliding in each family of weakness planes is described by a non-associated plastic model taking into account material softening and volumetric dilatancy. The damage evolution is coupled with plastic deformation and modelled by an isotropic damage criterion. The proposed model is applied to modelling mechanical responses of typical sandstone under different loading paths. There is good agreement between numerical predictions and experimental data. Further, the anisotropic distributions of plastic deformation and induced damage are analysed and discussed.     

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.     

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.     

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。     

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。     

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。     

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.     

压剪应力条件下板岩细观力学本构模型

为了研究板岩力学性质,采用细观力学方法对板岩建模进行了研究,并建立了板岩损伤本构模型。在模型中增加了对剪胀变形机制和渗流对变形影响的内容,使得模型能够更好地表述板岩的变形特性。所建立模型能够考虑微裂纹闭合、摩擦滑移、自相似扩展等过程。理论与试验对比结果表明本文模型是适用的。     

A critical state framework for modelling bonded geomaterials

A simple unified critical state constitutive model for bonded geomaterials is presented in this paper. The model, which is called CASM-n, is an enhancement of an existing unified critical state model for reconstituted geomaterials (CASM). Characteristic behaviours of a bonded geomaterial such as the pre-yield higher strength and stiffness and the cohesive–frictional shearing mode in the post-yield region are taken into account and included in the reference model. The salient feature of the proposed model is the incorporation of cohesive component into the stress–dilatancy relationship. Consideration of the contribution of cohesion to plastic flow allows the modelling of delayed dilatancy and softening–contraction behaviour, which are two interesting phenomena observed in bonded geomaterials.     

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     

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.     

A micromechanics-based elastoplastic damage model for quasi-brittle rocks

This paper presents a micromechanics-based elastoplastic damage model for quasi-brittle rocks under a compressive stress state. The plastic strain is considered to be related to frictional sliding along micro-cracks, and it is coupled inherently with damage evolution. By following a homogenization procedure, we determine the free energy of the matrix-cracks system. The thermodynamic force associated with the inelastic strain contains a back stress, which controls material hardening. Next, in order to determine plastic flow and crack propagation, we propose a Coulomb-type friction criterion, which is used as the plastic yielding function, and a damage criterion based on strain energy release rate. These thermodynamic formulations with a micro–macro scale change allow reducing significantly the number of model parameters, as compared to phenomenological models. Our model is applied to simulate triaxial compression tests on two sets of diabase samples. The first sample set is cored from a fresh diabase rock mass, and the second from a slightly weathered one. Comparisons between numerical predictions and test data are presented.     

Mechanism of frictional fusion in fault zones

Spherulitic pseudotachylytes from the Arunta Block formed by frictional fusion of mylonitic parent rocks during high-level reactivation of a previously ductile fault zone. Fusion occurred preferentially in mica-rich domains due to release of water through disruption of the mica lattice by frictional sliding. This generated selective localised melting of mica during frictional heating, with the production of initial pseudotachylyte melts enriched in water and ferromagnesian components. Subsequent fusion of adjacent salic phases, promoted by the high water content of the existing melt, would tend to shift the trend of later melts towards a total melt composition. Therefore, under conditions of frictional sliding, fusion appears to be favoured in crystalline quartzofeldspathic rocks possessing both a high shear strength, and a significant water content locked up in the lattices of hydrous minerals, principally biotite.The presence or pre-existence of glass in many pseudotachylytes demands that they cooled in a near-surface environment, i.e. at depths of less than about 5 km. Thus glassy pseudotachylytes must postdate associated mylonite series rocks, generally forming subsequent to exhumation of the mylonites to a higher level in the crust. Some non-glassy pseudotachylytes, however, may possibly form towards the end of movements in a ductile regime, as strain hardening sets in.     

Monitoring the state of microfracturing in rock salt during deformation by combined measurements of permeability and P- and S- wave velocities

Rock salt formations are prime candidates for underground cavities or radioactive waste disposal sites, primarily because of their extremely low permeabilities. Combined gas-permeability and P- and S-wave velocity measurements were carried out on natural rock salt samples in order to investigate the transport properties of rock salt under mechanical stresses. Experiments were done at temperatures up to 60 °C under conditions of hydrostatic compaction and triaxial compressive and extensional strain. The crack-sensitivity of P- and S-wave velocities is used for monitoring the in situ state of the microcracking during deformation. Triaxial deformation of the compacted rock salt samples is accompanied by the onset of dilatancy, that is, the opening of microcracks. The orientation of cracks is controlled by the symmetry of the applied stress field (compressive or extensional). Cracks are mostly oriented parallel to the maximum principal stress direction leading to an anisotropic crack array within the samples. A marked permeability increase is observed under compressive strain because in this case an interconnecting permeability network is generated parallel to the deformation and measuring axis. The inversions of P- and S-wave velocities are used to define the boundary between the dilatant and compressive domains (dilatancy boundary). The results confirm the equation for the dilatancy boundary given by Cristescu & Hunsche (1998).     

A micro–macro approach of permeability evolution in rocks excavation damaged zones

Excavation damaged zone, with significant irreversible deformations and nonnegligible changes in flow and transport properties generally occurs in indurated clay around underground structures. The stress perturbation around the excavation could lead to a significant increase of the permeability physically due to diffuse and/or localized microcracks growth in the material. In the present study, we investigate microcracks-induced damage processes together with the subsequent modification in permeability. The proposed approach is based on a homogenization-based upper bound extended to the context of microcracked media in presence of initial stress. Application of this approach is done on a borehole excavation problem related to the Selfrac in situ experiments on Opalinus Clay. Although, the model fails to quantitatively account for the in situ permeability change (which may also originated from existing macrofractures), its prediction shows a significant evolution of the material permeability around the borehole. This is in qualitative agreement with available data.     

Observation of Pore Spaces and Microcracks Using a Fluorescent Technique in Some Reservoir Rocks of Oil, Gas and Geothermal Fields in the Green Tuff Region, Japan

Abstract: Pore spaces and microcracks in representative oil, gas and geothermal reservoir rocks from the Green Tuff region, Japan, were examined using a fluorescent technique. This technique was developed to visualize microscopically pore spaces and microcracks filled with synthetic resin mixed with fluorescent paint under ultraviolet light. Various morphology of pore spaces and microcracks was clearly identified. Spaces in studied reservoir rocks are classified into following three types: pore spaces in matrix, pore spaces in particles, and microcracks. It is observed that valuable oil and gas reservoir rocks relatively include many pore spaces, while microcracks are important for geothermal rocks. Correlation between textural characteristics and porosity or permeability was found in the oil reservoir rocks. Effective permeability depends upon pore spaces in matrix more than upon other components such as pore spaces in particles and microcracks. Looseness in matrix caused by larger grain size of particles is strongly correlated with permeability. Pore spaces play an important role as a reservoir in oil and gas fields, but are less important in geothermal field. Instead, microcracks are important for geothermal reservoir system.     

Homogenized constitutive laws for rocks with elastoplastic fractures

This work deals with the development of a constitutive law for fractured rocks. Fractures are considered as penny‐shaped inclusions, whose constitutive law is deduced from an interface law and a regularization procedure. Such a method is applied to linear and non‐linear interface behaviours in order to reproduce effects such as an increase in stiffness during fracture closing, dilatancy or asperity surface degradation. Then, considering the fractured rock as a composite material, we use a Mori–Tanaka method to estimate the homogenized properties of the rock. Numerical experiments illustrate the interest of the proposed homogenization procedure. Copyright © 2007 John Wiley & Sons, Ltd.