Damage‐viscoplastic consistency model for rock fracture in heterogeneous rocks under dynamic loading

This paper presents a damage‐viscoplastic consistency model for numerical simulation of brittle fracture in heterogeneous rocks. The model is based on a combination of the recent viscoplastic consistency model by Wang and the isotropic damage concept with separate damage variables in tension and compression. This approach does not suffer from ill‐posedness, caused by strain softening, of the underlying boundary/initial value problem since viscoplasticity provides the regularization by introducing a length scale effect under dynamic loading conditions. The model uses the Mohr–Coulomb yield criterion with the Rankine criterion as a tensile cut‐off. The damage law in compression is calibrated via the degradation index concept of Fang and Harrison. Thereby, the model is able to capture the brittle‐to‐ductile transition occurring in confined compression at a certain level of confinement. The heterogeneity of rock is accounted for by the statistical approach based on the Weibull distribution. Numerical simulations of confined compression test in plane strain conditions demonstrate a good agreement with the experiments at both the material point and structural levels as the fracture modes are realistically predicted. Copyright © 2009 John Wiley & Sons, Ltd.     

3D numerical modelling of bit–rock fracture mechanisms in percussive drilling with a multiple‐button bit

This paper considers numerical modelling of rock fracture induced by dynamic bit–rock interaction in percussive drilling. The work presented here extends the author's earlier research on the topic from the axisymmetric case to 3D case. The numerical method for modelling rock fracture includes a constitutive model for rock and a contact mechanics‐based technique to simulate the bit–rock interaction. The constitutive model is based on a combination of the recent viscoplastic consistency model, the isotropic damage concept and a parabolic compression cap. This model is improved here from its earlier state by calibrating the softening laws using fracture energies G_Ic and G_IIc in tension and compression, respectively. Moreover, the viscosity modulus in tension is calibrated based on the dynamic Brazilian disc test. With these enhancements, the developed method is applied to 3D case of the bit–rock interaction problem assuming one symmetry plane. Single impact with single and multiple‐button bits is simulated. In the latter case, an initial borehole is modelled in order to simulate the usual in‐situ drilling conditions. The different failure types observed in the experiments as well as the interaction between the buttons resulting in chipping are realistically captured in the simulations. Copyright © 2012 John Wiley & Sons, Ltd.     

Numerical modelling of bit–rock fracture mechanisms in percussive drilling with a continuum approach

This paper presents a numerical method for continuum modelling of the dynamic bit–rock interaction process in percussive drilling. The method includes a constitutive model based on a combination of the recent viscoplastic consistency model, the isotropic damage concept and a parabolic compression cap. The interaction between the drill bit and rock is modelled using contact mechanics by treating the bit as a rigid body. As the bit–rock interaction in percussive drilling is a transient event, the method is implemented in explicit dynamics FEM. The rock strength heterogeneity is characterized at the mesoscopic level statistically using the Weibull distribution. The bit–rock interaction is simulated under axisymmetric conditions using cylindrical and hemispherical buttons. The choice of the quite complex constitutive model accounting, e.g. for plastic compaction, viscoplastic shear and tensile failure along with induced damage and rate dependency is justified by numerical simulations. Moreover, the quasi‐static and dynamic cases are compared in plane strain simulations. Finally, some results clarifying the discrepancy of opinions found in the literature concerning the side (lateral) crack formation are obtained. Copyright © 2010 John Wiley & Sons, Ltd.     

Granite rock fragmentation at percussive drilling – experimental and numerical investigation

The aim of this study is to numerically model the fracture system at percussive drilling. Because of the complex behavior of rock materials, a continuum approach is employed relying upon a plasticity model with yield surface locus as a quadratic function of the mean pressure in the principal stress space coupled with an anisotropic damage model. In particular, Bohus granite rock is investigated, and the material parameters are defined based on previous experiments. This includes different tests such as direct tension and compression, three‐point bending, and quasi‐oedometric tests to investigate the material behavior at both tension and confined compression stress states. The equation of motion is discretized using a finite element approach, and the explicit time integration method is employed. Edge‐on impact tests are performed, and the results are used to validate the numerical model. The percussive drilling problem is then modeled in 3D, and the bit‐rock interaction is considered using contact mechanics. The fracture mechanism in the rock and the bit penetration‐ resisting force response are realistically captured by the numerical model. Copyright © 2013 John Wiley & Sons, Ltd.     

空隙率对潜孔锤凿岩瞬态冲击过程的影响

潜孔锤的钻进过程是一个高度非线性、大变形、破碎岩石的过程,利用非线性有限元程序ANSYS/LS-DY-NA研究了在凿岩过程中,球齿凿入不同空隙率（塑性体积应变）岩石的冲击力特性。结果表明,岩石空隙率对钻头球齿与岩石之间的凿入冲击力幅值有很大影响,随着空隙率的增大,球齿凿入的冲击力显著减小,而对活塞与钻头间冲击力幅值影响甚微。通过ANSYS/LS-DYNA瞬态冲击数值模拟,形象地再现了潜孔锤钻凿系统冲击岩石发生侵入破坏的物理过程,为冲击碎岩瞬态研究提供了一个有效的分析方法。     

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 coupled chemo‐viscoplastic cap model for simulating the behavior of hydrating cemented tailings backfill under blast loading

Although the use of blasting has become a routine in contemporary mine operations, there is a lack of knowledge on the response of cement tailings backfills subjected to sudden dynamic loading. To rationally describe such a phenomenon, a new coupled chemo‐viscoplastic cap model is proposed in the present study to describe the behavior of hydrating cemented tailings backfill under blast loading. A modified Perzyna type of visco‐plasticity model is adopted to represent the rate‐dependent behavior of the cemented tailings backfill under blast loading. A modified smooth surface cap model is consequently developed to characterize the yield of the material, which also facilitates hysteresis and full compaction as well as dilation control. Then, the viscoplastic formulation is further augmented with a variable bulk modulus derived from a Mie–Gruneisen equation of state, in order to capture the nonlinear hydrostatic response of cemented backfills subjected to high pressure. Subsequently, the material properties required in the viscoplastic cap model are coupled with a chemical model, which captures and quantifies the degree of cement hydration. Thus, the behavior of hydrating cemented backfills under the impact of blast loading can be evaluated under any curing time of interest. The validation results of the developed model show a good agreement between the experimental and the predicted results. The authors believe that the proposed model will contribute to a better understanding of the performance of cemented backfills under mine blasting and contribute to evaluating and managing the risk of failure of backfill structures under such a dynamic condition. Copyright © 2015 John Wiley & Sons, Ltd.     

石灰改良膨胀土的应力-应变-强度特征与本构描述

为探讨石灰改良膨胀土的变形特征与破坏机制,以压实度为95 %的荆门石灰改良膨胀土为研究对象,开展了单轴、侧限、三轴压缩应力状态下的力学性质试验。试验结果表明：即使湿化饱和后石灰土也具有较高的刚度与强度;单轴压缩状态下,无论饱和还是非饱和状态,石灰土的破坏都为典型的脆性破坏;三轴压缩状态下石灰土破坏前剪缩,同时伴随应变强化,即将破坏时开始剪胀,随后表现为应变软化;围压对石灰土的脆性破坏与破坏后的剪胀有一定的抑制作用,但即使在200 kPa围压下,试样仍发生脆性破坏。在辨明石灰土应力、变形机制的基础上,选用Duncan模型描述其脆性破坏前表现出的压硬性、剪缩性与应变强化特性,标定了相应模型参数,通过数值模拟与平行试验的对比验证了模型的适用性与参数的可靠性。     

Numerical modeling of dynamic rock fracture with a combined 3D continuum viscodamage‐embedded discontinuity model

This paper deals with numerical modeling of dynamic failure phenomena in rate‐sensitive quasi‐brittle materials, such as rocks, with initial microcrack populations. To this end, a continuum viscodamage‐embedded discontinuity model is developed and tested in full 3D setting. The model describes the pre‐peak nonlinear and rate‐sensitive hardening response of the material behavior, representing the fracture‐process zone creation, by a rate‐dependent continuum damage model. The post‐peak response, involving the macrocrack creation accompanied by exponential softening, is formulated by using an embedded displacement discontinuity model. The finite element implementation of this model relies upon the linear tetrahedral element, which seems appropriate for explicit dynamic analyses involving stress wave propagation. The problems of crack locking and spreading typical of embedded discontinuity models are addressed in this paper. A combination of two remedies, the inclusion of viscosity in the spirit of Wang's viscoplastic consistency approach and introduction of isotropic damaging into the embedded discontinuity model, is shown to be effective in the present explicit dynamics setting. The model performance is illustrated by several numerical simulations. In particular, the dynamic Brazilian disc test and the Kalthoff–Winkler experiment show that the present model provides realistic predictions with the correct failure modes and rate‐dependent tensile strengths of rock at different loading rates. The ability of initial embedded discontinuity populations to model the initial microcrack populations in rocks is also successfully tested. Copyright © 2016 John Wiley & Sons, Ltd.     

Thermodynamic‐based model for coupling temperature‐dependent viscoelastic,viscoplastic, and viscodamage constitutive behavior of asphalt mixtures

Based on the continuum damage mechanics, a general and comprehensive thermodynamic‐based framework for coupling the temperature‐dependent viscoelastic, viscoplastic, and viscodamage behaviors of bituminous materials is presented. This general framework derives systematically Schapery‐type nonlinear viscoelasticity, Perzyna‐type viscoplasticity, and a viscodamage model analogous to the Perzyna‐type viscoplasticity. The resulting constitutive equations are implemented in the well‐known finite element code Abaqus via the user material subroutine UMAT. A systematic procedure for identifying the model parameters is discussed. Finally, the model is validated by comparing the model predictions with a comprehensive set of experimental data on hot mix asphalt that include creep‐recovery, creep, uniaxial constant strain rate, and repeated creep‐recovery tests in both tension and compression over a range of temperatures, stress levels, and strain rates. Comparisons between model predictions and experimental measurements show that the presented constitutive model is capable of predicting the nonlinear behavior of asphaltic mixes under different loading conditions. Copyright © 2011 John Wiley & Sons, Ltd.     

双向加载煤岩变形与声发射特性颗粒流研究

为了明确煤岩双向应力状态下的强度和损伤特性,通过煤岩的单轴试验测得其力学参数,然后利用颗粒流和fish程序结合试验结果获得煤岩细观力学参数,进行了煤岩双向加载下的强度、变形和损伤声发射特征的研究。获得以下主要结论:双向加载煤岩变形破坏过程中,中间主应力对屈服阶段影响最显著,而对峰后软化阶段基本没有影响,这与三向加载下围压对峰后软化阶段的影响不同,从而表明双向加载条件下煤岩峰后基本不存在脆性-延性转化的特征。双向加载下煤岩的体变经历线性体缩、非线性扩容和线性扩容阶段,中间主应力对非线性扩容阶段影响显著,而对其他两个阶段基本没有影响。煤岩损伤破坏过程中,在弹性阶段声发射呈线性增加趋势但增速较小,屈服阶段声发射进入非线性快速增加阶段,在峰值附近增速最快,峰后初期达到最大强度,随后声发射强度急剧减小。声发射最大强度有一定的滞后效应,随着中间主应力的增大,最大声发射强度的滞后效应相对减弱,且随着中间主应力的增大,声发射最大强度持续时间段明显延长。     

Characterisation of confinement effect on jointed rock pillars using a Synthetic Rock Mass approach

Confinement effect on jointed rock pillars is numerically characterised in this research using a Synthetic Rock Mass (SRM) approach. The SRM is an integrated model incorporating a discrete fracture network within a Particle Flow Code 3D particle assembly. In this paper, the confinement effect on a 3D jointed pillar SRM model is investigated in a series of simulations, including biaxial compression tests and true and conventional triaxial compression tests. The numerical results suggest that the applied confining stresses generally result in higher pillar strengths and ductile post‐peak responses. More brittle post‐peak behaviour is simulated in the biaxial and true triaxial tests when the pillar is confined by a high stress in one lateral direction and by a zero/low stress in the other lateral direction. This phenomenon is attributed to significant lateral pillar dilation in the less confined direction. Detailed pillar failure modes are monitored in the uniaxial and triaxial tests. Axial splitting fractures and long shear zones cutting through the pillar are simulated when the pillar is able to dilate in the direction of least confinement. Localised shearing along joints and failed rock blocks is the dominant failure mode when the pillar dilation is resisted by the applied confining stresses. The pillar remains relatively intact with limited cracking in the pillar core in the highly confined triaxial tests. Copyright © 2016 John Wiley & Sons, Ltd.     

Visco-damage tension model for rocks in ground-shock applications

A simple rate-dependent tension model, tailored primarily for rocks in ground-shock calculations, has been constructed. It is formulated as an internal state variable theory with spherical void development taken to approximate the underlying dissipative micromechanism. This simplifying assumption of ductile, rather than brittle, damage growth has been made to enhance the practicality of the model for large-scale problems. The model has been restated within the fromework of (strain-softening) viscoplastcity to associate it with the desirable mathematical properties of the latter theory. The tension option, extended to include healing in the post-damage compressive phase, has been implemented in a standard cap constitutive routine and is referred to as the visco-damage tension model. Model parameters are selected for a shale-like material. Results of uniaxial shock-loading strain-rate calculations exhibit desired characteristics in tension. Damage-related hysteretic effects are illustrated through cyclic loading calculations. It is planned to develop more effecient computational procedures to facilitate adoption of the model into large-scale ground shock calculations. Anisotropic extensions of the model will then be considered.     

A macroscopic damage‐plastic constitutive law for modeling quasi‐brittle fracture and ductile behavior of concrete

A new phenomenological macroscopic constitutive model for the numerical simulation of quasi‐brittle fracture and ductile concrete behavior, under general triaxial stress conditions, is presented. The model is particularly addressed to simulate a wide range of confinement stress states, as also, to capture the strong influence of the mean stress value in the concrete failure mechanisms. The model is based on a two‐surface damage‐plastic formulation. The mechanical behavior in different domains of the stress space is separately described by means of a quasi‐brittle or ductile material response:

相似文献   

脆性岩石破坏数值模拟研究的两个问题

应用数值模拟方法,对脆性岩石单轴压缩情况下破坏规律进行了初步研究,主要讨论了脆性岩石的破坏机理、脆性岩石破坏数值模拟试验中的端部效应问题,并得出了一些初步的结论。在单轴压缩试验中,脆性岩石破坏过程主要以拉伸破坏为主。端部效应则是除了岩石试件本身所具有的材料非均匀性外影响岩石试件破坏形式的另一个重要因素。总体上存在这样的规律,即端部约束越大,岩石试件破坏型式越趋近于“X”型剪胀破坏,端部约束越小,则岩石试件破坏型式越趋近于张拉破坏。     

基于梯度塑性理论的岩样拉压剪破坏统一失稳判据

提出了单轴拉伸,直剪及单轴压缩剪切破坏失稳判据的统一形式。首先对de Borst R及Muhlhaus H B关于单轴拉伸试件梯度塑性理论解析解方面的开创性工作进行了回顾、评论,并指出了他们工作的缺憾。受de Borst R等工作的启发,对直接剪切试件进行了分析,得到了快速回跳条件。并发现:岩样的快速回跳条件就是系统(由剪切带及带外弹性岩石构成)的失稳判据。又对单轴压缩岩样剪切破坏进行了分析,得到了其失稳判据。通过对单轴拉伸失稳判据、直接剪切失稳判据及单轴压缩剪切破坏失稳判据的类比,得到了失稳判据的统一形式。统一失稳判据表明:岩石材料的局部化带宽度及压缩或剪切弹性模量越小,软化模量及等效试件高度越大,试件越容易发生失稳破坏。     

A generalized rigid particle contact model for fracture analysis

Rigid particle models taking directly into consideration the physical mechanisms and the influence of the material meso‐structure have recently been developed for fracture studies of quasi‐brittle material such as concrete. The formulation of a generalized contact model for rigid particle simulations is presented in which the contact discretization is a model parameter. The contact model performance for different discretizations is evaluated for uniaxial tensile tests, for uniaxial compression tests and for a notched beam in mode I. Copyright © 2005 John Wiley & Sons, Ltd.     

IV级软弱围岩相似材料的试验研究

以IV级围岩为参照对象,研制可用于隧道围岩稳定性物理模型试验的软弱围岩相似材料。采用的5种原材料（重晶石粉、石膏、细砂、洗衣液和水）,通过直剪试验、无侧限抗压强度试验及三轴压缩试验测得所配相似材料的强度特征和物理力学参数,包括黏聚力c、内摩擦角?、单轴抗压强度Rc、弹性模量E和泊松比?。首先,通过试验分析每种原材料的不同比例对所配相似材料强度特征及物理力学参数的影响,选择适合于模拟IV级围岩相似材料的原材料配比;其次,针对优选的材料配比所配制的相似材料,开展大量的三轴压缩试验,研究在不同围压下该相似材料的强度及其破坏特征。结果表明,含水率减少或石膏含量增加导致Rc、E和c明显增大,而?降低不明显;增加砂含量可增大E 和?,但Rc值减少;石膏含量对相似材料的脆性和延性影响最明显,而含水率对相似材料的强度影响最为突出。试验结果还表明,相似材料在低围压时呈现脆性,在高围压时呈延性;就破坏准则而言,试验所得结果小于Mohr-Coulomb准则,略大于Hoek-Brown准则,但更符合Hoek-Brown准则。研制软岩相似材料的试验数据可为下一步拟开展的隧道围岩稳定性模型试验和数值模拟提供重要的参考和依据。     

A Strain Rate Dependent Constitutive Model for the Lower Silurian Longmaxi Formation Shale in the Fuling Gas Field of the Sichuan Basin,China

Shale, as a kind of brittle rock, often exhibits different nonlinear stress-strain behavior, failure and time-dependent behavior under different strain rates. To capture these features, this work conducted triaxial compression tests under axial strain rates ranging from 5×10?6 s?1 to 1×10?3 s?1. The results show that both elastic modulus and peak strength have a positive correlation relationship with strain rates. These strain rate-dependent mechanical behaviors of shale are originated from damage growth, which is described by a damage parameter. When axial strain is the same, the damage parameter is positively correlated with strain rate. When strain rate is the same, with an increase of axial strain, the damage parameter decreases firstly from an initial value (about 0.1 to 0.2), soon reaches its minimum (about 0.1), and then increases to an asymptotic value of 0.8. Based on the experimental results, taking yield stress as the cut-off point and considering damage variable evolution, a new measure of micro-mechanical strength is proposed. Based on the Lemaitre’s equivalent strain assumption and the new measure of micro-mechanical strength, a statistical strain-rate dependent damage constitutive model for shale that couples physically meaningful model parameters was established. Numerical back-calculations of these triaxial compression tests results demonstrate the ability of the model to reproduce the primary features of the strain rate dependent mechanical behavior of shale.     

Simulating fracture propagation in rock and concrete by an augmented virtual internal bond method

This paper develops a practical approach to simulating fracture propagation in rock and concrete based on an augmented virtual internal bond (VIB) method in which the cohesion of solid is modeled as material particles interconnected by a network of randomized virtual micro bonds described by the Xu–Needleman potential. The micro bond potential is used to derive macroscale constitutive relations via the Cauchy–Born rule. By incorporating different energy contributions due to stretch and shearing, as well as different energy levels under tension and compression of each micro bond, the derived macro constitutive laws are particularly useful for modeling quasi‐brittle materials such as rock and concrete which usually have different Poisson ratios and much higher compressive strength than tensile strength. The mesh‐size sensitivity associated with strain‐softening in the present constitutive model is addressed by adjusting material constants near the crack tip so that the biJ‐integral is kept equal to the intrinsic fracture energy of the material. Numerical examples demonstrate that the proposed VIB method is capable of simulating mixed mode fracture propagation in rock and concrete with results in consistency with relevant experimental observations. Copyright © 2011 John Wiley & Sons, Ltd.