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.     

A two‐dimensional coupled hydromechanical discontinuum model for simulating rock hydraulic fracturing

Within the framework of our discontinuous deformation analysis for rock failure algorithm, this paper presents a two‐dimensional coupled hydromechanical discontinuum model for simulating the rock hydraulic fracturing process. In the proposed approach, based on the generated joint network, the calculation of fluid mechanics is performed first to obtain the seepage pressure near the tips of existing cracks, and then the fluid pressure is treated as linearly distributed loads on corresponding block boundaries. The contribution of the hydraulic pressure to the initiation/propagation of the cracks is considered by adding the components of these blocks into the force matrix of the global equilibrium equation. Finally, failure criteria are applied at the crack tips to determine the occurrence of cracking events. Several verification examples are simulated, and the results show that this newly proposed numerical model can simulate the hydraulic fracturing process correctly and effectively. Although the numerical and experimental verifications focus on one unique preexisting crack, because of the capability of discontinuous deformation analysis in simulating block‐like structures, the proposed approach is capable of modeling rock hydraulic fracturing processes. Copyright © 2014 John Wiley & Sons, Ltd.     

Coupled flow network and discrete element modeling of injection-induced crack propagation and coalescence in brittle rock

We present a numerical analysis on injection-induced crack propagation and coalescence in brittle rock. The DEM network coupling model in PFC is modified to capture the evolution of fracture geometry. An improved fluid flow model for fractured porous media is proposed and coupled with a bond-based DEM model to simulate the interactions among cracks induced by injecting fluid in two nearby flaws at identical injection rates. The material parameters are calibrated based on the macro-properties of Lac du Bonnet granite and KGD solution. A grain-based model, which generates larger grains from assembles of particles bonded together, is calibrated to identify the microscopic mechanical and hydraulic parameters of Lac du Bonnet granite such that the DEM model yields a ratio between the compressive and tensile strength consistent with experiments. The simulations of fluid injection reveal that the initial flaw direction plays a crucial role in crack interaction and coalescence pattern. When two initial flaws are aligned, cracks generally propagate faster. Some geometrical measures from graph theory are used to analyze the geometry and connectivity of the crack network. The results reveal that initial flaws in the same direction may lead to a well-connected crack network with higher global efficiency.

     

锥形聚晶金刚石复合片齿破岩特征与机制研究

锥形聚晶金刚石复合片(polycrystalline diamond compact,PDC)齿是一种具有较强抗冲击性和耐磨性的新型PDC齿,在坚硬、强研磨性和软硬交错地层中取得了非常好的钻井提速效果。为了揭示锥形齿破碎硬岩机制,开展锥形齿破碎花岗岩试验与数值模拟研究,分析了切削深度和前倾角对锥形齿切削力和破岩比能的影响规律,采用高速摄像机和透明K9玻璃观测了锥形齿作用下岩屑形成过程及微裂纹萌生与扩展过程,通过数值模拟分析了破岩过程中岩石应力响应与损伤演化特性,结合对切削槽和大尺寸块体岩屑表面形貌及断口微观特征分析,建立了锥形齿破碎花岗岩机制模型。结果表明,锥形齿破碎花岗岩的过程可以分为挤压成核和块体崩裂两个阶段,前倾角对岩石破碎过程影响较小,切削深度的影响显著;锥形齿周围的裂纹主要由压实核、纵向裂纹和横向裂纹组成,纵向裂纹和横向裂纹扩展的最大深度分别为切削深度的6.69倍和4.53倍;齿尖周围压应力集中,岩石发生压剪破坏,压应力区外围形成弧形条带状拉应力区,并在齿尖及压应力区边界处诱导出拉伸微裂纹;微裂纹向齿前扩展形成弧形拉伸主裂纹,发生块体岩屑崩裂,提高破岩效率,向岩石内部扩展劣化...     

DEM analyses of crack propagation in flawed rock mass under uniaxial compressionEI北大核心CSCD

A contact model for rock is established and imbedded into a DEM software by summarizing the bond granule tests. DEM simulation of uniaxial compression test on the pre-cracked Lac du Bonnet granite is performed, and then stress distributions are further analyzed and compared with the theoretical results. Different fracture criteria are employed to predict the crack initiation angles that are compared with theoretical ones. The results show that the failure modes obtained from DEM simulation are similar to experimental results, and stress distributions in DEM simulation are qualitatively similar to theoretical values. When the angle of pre-crack is small, the lateral stresses are compressive and tensile. The compressive strains concentrate at two edges, resulting in the tensile strains in the up-and downward cracks. When the angle of the pre-crack is large enough, the stress concentration is unobvious, leading to a discrepancy between the DEM and theoretical results. The crack extension angle resulting from uniaxial compression measured from DEM tests are in good agreement with those acquired from experimental tests. These angles are consistent with theoretical predictions by the maximum circumferential stress criterion and the maximum energy release rate criterion.     

含裂隙岩体单轴压缩裂纹扩展机制离散元分析

将由室内试验总结得到的岩石微观胶结模型嵌入离散元软件,对Lac du Bonnet花岗岩石进行预制单裂隙单轴压缩试验DEM数值模拟,分析了压缩过程中裂隙试样中应力的分布,并与理论计算结果进行对比分析,同时对各种断裂判据中裂纹起裂角的预测值进行了适用性的对比分析。结果表明,离散元模拟试样破坏形态与试验结果相近;离散元分析得到的应力分布与理论解在定性上相似;当预制角度较小时,侧向应力都处于拉压状态;由于裂隙左右两端压应变的集中造成了裂隙上下面拉应变的产生,造成了裂隙周围特殊的应力分布;当裂隙角度较大时,应力集中现象已不明显,因而,理论值与试验值有偏差;在断裂判据中最大周应力准则和最大能量释放率准则得到的裂纹扩展角与室内试验与DEM结果中的数值较为吻合。     

A three-dimensional numerical investigation of the fracture of rock specimens containing a pre-existing surface flaw

Three-dimensional surface crack initiation and propagation in two kinds of heterogeneous rocks were numerically investigated via parallel finite element analysis using a supercomputer. Numerically simulated rock specimens containing a pre-existing flaw were subjected to uniaxial compression until failure. The initiation and propagation of wing cracks, anti-wing cracks, and shell-like cracks were reproduced by numerical simulations. The numerically simulated results demonstrate that the further propagation of wing cracks and shell-like cracks stop due to their wrapping (curving) behavior in three-dimensional spaces, even if the applied loads continue to increase. Furthermore, rock heterogeneity could significantly influence crack propagation patterns and the peak uniaxial compressive strengths of rock specimens. Moreover, anti-wing cracks only appeared in relatively heterogeneous rocks, and the peak uniaxial compressive strengths of the specimens were observed to depend on the inclination of the pre-existing flaw. Finally, the mechanism of surface crack propagation is discussed in the context of numerically simulated anti-plane loading tests, wherein it was identified that Mode III loading (anti-plane loading) does not lead to Mode III fracture in rocks due to their high ratio of uniaxial compressive strength to tensile strength. This finding could explain the lateral growth of an existing flaw in its own plane, which is a phenomenon that has not been observed in laboratory experiments.     

Micromechanical analysis of the failure process of brittle rock

The failure process of brittle rock submitted to a compression state of stress with different confining pressures is investigated in this paper based on discrete element method (DEM) simulations. In the DEM model, the rock sample is represented by bonding rigid particles at their contact points. The numerical model is first calibrated by comparing the macroscopic response with the macroscopic response of Beishan granite obtained from laboratory tests. After the validation of numerical model in terms of macroscopic responses, the failure process of the DEM model under unconfined and confined compression is studied in micro‐scale in detail. The contact force network and its relation to the development of micro‐cracks and evolution of major fractures are studied. Confining pressure will prohibit the development of tensile cracks and hence alter the failure patterns. An in‐depth analysis of micro‐scale response is carried out, including the orientation distribution and probability density of stress acting on parallel bonds, the effect of particle size heterogeneity on bond breakage and the evolution of fabric tensor and coordination number of parallel bond. The proposed micromechanical analysis will allow us to extract innovative features emerged from the stresses and crack evolution in brittle rock failure process. Copyright © 2014 John Wiley & Sons, Ltd.     

Meso‐scale particle modeling of concrete deterioration caused by alkali‐aggregate reaction

A meso‐scale particle model is presented to simulate the expansion of concrete subjected to alkali‐aggregate reaction (AAR) and to analyze the AAR‐induced degradation of the mechanical properties. It is the first attempt to evaluate the deterioration mechanism due to AAR using the discrete‐element method. A three‐phase meso‐scale model for concrete composed of aggregates, mortar and the interface is established with the combination of a pre‐processing approach and the particle flow code, PFC2D. A homogeneous aggregate expansion approach is applied to model the AAR expansion. Uniaxial compression tests are conducted for the AAR‐affected concrete to examine the effects on the mechanical properties. Two specimens with different aggregate sizes are analyzed to consider the effects of aggregate size on AAR. The results show that the meso‐scale particle model is valid to predict the expansion and the internal micro‐cracking patterns caused by AAR. The two different specimens exhibit similar behavior. The Young's modulus and compressive strength are significantly reduced with the increase of AAR expansion. The shape of the stress–strain curves obtained from the compression tests clearly reflects the influence of internal micro‐cracks: an increased nonlinearity before the peak loading and a more gradual softening for more severely affected specimens. Similar macroscopic failure patterns of the specimens under compression are observed in terms of diagonal macroscopic cracks splitting the specimen into several triangular pieces, whereas localized micro‐cracks forming in slightly affected specimens are different from branching and diffusing cracks in severely affected ones, demonstrating different failure mechanisms. Copyright © 2012 John Wiley & Sons, Ltd.     

Analytical simulation of the dynamic compressive strength of a granite using the sliding crack model

A sliding crack model is employed to simulate rock strength under dynamic compression. It is assumed that the growth and nucleation of a sliding crack array presented results in the shear fault failure and dominate the mechanical properties of rock material. The pseudo‐tractions method is used to calculate the stress intensity factor of the sliding crack array under compression. With the utilization of a dynamic crack growth criterion, the growth of the sliding crack array is studied and the simulated strengths of a granite under dynamic compression are correspondingly obtained. It is concluded that the simulated rock strengths increase with increasing strain rates at different confining pressures, and the rising rates have a trend to decrease with increasing confining pressures. It is also indicated that the simulated rock strengths increase with increment of confining pressure at different strain rates, and the rising rates are almost identical at different strain rates. The simulation results are validated by the experimental data for the granite. Copyright © 2001 John Wiley & Sons, Ltd.     

Numerical modelling of heat shock-assisted rock fracture

This paper presents a numerical investigation on the effects of thermal shock as a pretreatment of rock prior to comminution. More specifically, the effect of heat shock-induced cracks on the uniaxial compressive strength of rock is numerically studied. The chosen constitutive model of rock employs a (strong) embedded discontinuity finite element formulation to describe cracks. The thermomechanical problem that governs the heat shock pretreatment of rocks is considered as an uncoupled problem because of a highly dominating role of the external heat influx. Two solution methods of the global problem are presented: an explicit-explicit dynamic scheme and an implicit-implicit quasi-static scheme. The model performance is tested in simulations on heterogeneous numerical rock samples subjected first to a heat shock pretreatment and then to a mechanical compression test. According to the results, the compressive strength of intact granite rock having the axial splitting failure mode can be substantially reduced by heat shock pretreatment.     

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.     

Polygonal grain‐based distinct element modeling for mechanical behavior of brittle rock

The microstructure of rock was numerically reproduced by a polygonal grain‐based model, and its mechanical behavior was examined by performing the uniaxial compression test and Brazilian tests via the Universal Distinct Element Code. The numerical results of the model demonstrated good agreement with the experimental results obtained with rock specimens in terms of the stress–strain behavior, strength characteristics, and brittle fracture phenomenon. An encouraging result is that the grain‐based model‐Universal Distinct Element Code model can reproduce a low ratio of tensile to compressive strength of 1/20 to 1/10 without the need for an additional process. This finding is ascribed to the fact that the geometrical features of polygons can effectively capture the effects of angularity, finite rotation, and interlocking of grains that exist in reality. A numerical methodology to monitor the evolution of micro‐cracks was developed, which enabled us to examine the progressive process of the failure and distinguish the contribution of tensile cracking to the process from that of shear cracking. From the observations of the micro‐cracking process in reference to the stress–strain relation, crack initiation stress, and crack damage stress, it can be concluded that the failure process of the model closely resembles the microscopic observations of rock. We also carried out a parametric study to examine the relationships between the microscopic properties and the macroscopic behavior of the model. Depending on the micro‐properties, the model exhibited a variety of responses to the external load in terms of the strength and deformation characteristics, the evolution of micro‐cracks, and the post‐peak behavior. Copyright © 2016 John Wiley & Sons, Ltd.     

A numerical method for the study of shear band propagation in soft rocks

This paper investigates the possibility of interpreting progressive shear failure in hard soils and soft rocks as the result of shear propagation of a pre‐existing natural defect. This is done through the application of the principles of fracture mechanics, a slip‐weakening model (SWM) being used to simulate the non‐linear zone at the tips of the discontinuity. A numerical implementation of the SWM in a computation method based on the boundary element technique of the displacement discontinuity method (DDM) is presented. The crack and the non‐linear zone at the advancing tip are represented through a set of elements, where the displacement discontinuity (DD) in the tangential direction is determined on the basis of a friction law. A residual friction angle is assumed on the crack elements. Shear resistance decreases on elements in the non‐linear zone from a peak value at the tip, which is characteristic of intact material, to the residual value. The simulation of a uniaxial compressive test in plane strain conditions is carried out to exemplify the numerical methodology. The results emphasize the role played by the critical DD on the mechanical behaviour of the specimen. A validation of the model is shown through the back analysis of some experimental observations. The results of this back analysis show that a non‐linear fracture mechanics approach seems very promising to simulate experimental results, in particular with regards to the shear band evolution pattern. Copyright © 2009 John Wiley & Sons, Ltd.     

DEM–SPH simulation of rock blasting

A numerical model is proposed for the simulation of rock blasting. A bonded particle system is utilized to mimic the behavior of rock. The particles interact at the contact points through normal and shear springs to simulate rock elasticity. To withstand the deviatoric stresses, the particles are glued to each other. If the applied force exceeds the contact strength, local failure occurs and microcracks are developed in the synthetic rock. For simulation of gas flow, the smooth particle hydrodynamic method is implemented. The interaction of gas particles with the rock grains is assumed to follow a perfect plastic collision model in which the initial momentum of the colliding particles is preserved. A detailed examination of the interaction of gas with blast hole is investigated. It is shown that the proposed hybrid model is capable of simulating the induced shock waves in the gas together with wave propagation in the rock material. The model successfully mimics crack propagation in rock. In particular, the crushed zone around the borehole, radial cracks, and surface spalling are all captured successfully. The results of numerical analysis suggest that gas–rock interaction can, in fact, generate a few successive compressive waves in the rock specimen, causing further extension of radial cracks with time as the weaker secondary and tertiary waves interact with the crack tips.     

Numerical 3D modeling of the effects of strain rate and confining pressure on the compressive behavior of Kuru granite

This paper deals with numerical modeling of the compressive behavior of granite rock under high strain rate dynamic loading and wide range of confining pressure. For this end, a constitutive model based on damage mechanics and viscoplasticity for rock is formulated and implemented in explicit dynamics FEM. The viscoplastic part is based on a simple power law type yield criterion that incorporates the rate-dependency with a linear viscosity term. Moreover, a Rankine type of tensile cut-off is employed. The damage part of the model is formulated with separate scalar damage variables in tension and compression. The model is calibrated for Kuru granite and validated with the experimental data from dynamic compression tests at the strain rate of 600 1/s up to 225 MPa of confining pressure. The numerical simulations demonstrate that, despite the underlying continuum modeling approach, the model captures the correct experimental failure modes, including the transition from single-to-multiple fragmentation, as well as the dynamic compressive strengths at different confining pressures.     

单轴压缩条件下含三叉裂隙类岩石试样力学特性的细观研究

三叉裂隙是自然界普遍存在的一种岩体缺陷形式,其对岩体的力学特性有重要影响。对含预制三叉裂隙的水泥砂浆试样进行室内单轴压缩试验,配合使用摄像机拍摄裂纹的起裂、扩展、贯通过程,通过数字图像技术处理获取试样的应变场云图,并结合PFC2D程序研究不同?、? 条件下试样的强度特征、裂纹模式和裂纹演化扩展规律。研究表明：三叉裂隙对试样单轴抗压强度有明显的削弱作用。当? 恒定为120°时,试样在? = 30°时达到最大抗压强度;当? 恒定为90°时,随?增大,试样抗压强度呈先减小后增大的趋势,且当? = 45°时达到最大抗压强度。试样产生的裂纹可分为3类,分别是张拉型裂纹(Ⅰ型裂纹)、剪切型裂纹(Ⅱ型裂纹)、混合型裂纹(Ⅲ型裂纹)。这3类裂纹通常从裂隙尖端开始产生,并且Ⅰ型裂纹沿加载方向扩展,通常未扩展至试样边界;Ⅱ型和Ⅲ型裂纹通常与加载方向呈一定角度扩展至试样边界。通过对裂纹的几何形态和组成宏观裂纹的微裂纹成分的分析,得知导致含三叉裂隙试样在单轴压缩条件下失效的是张拉破坏。数字图像技术得到的应变云图表明,当载荷达到一定阶段,裂隙尖端出现应力集中,微破裂开始发育并聚集成微破裂区,微破裂区扩大产生宏观裂纹。通过对主应变和剪应变云图分析,发现导致试样失效的是张拉破坏,剪应变在裂纹扩展过程中的影响较小。     

含预制单裂隙花岗岩的真三轴单面临空岩爆试验研究

通过开展含预制单裂隙花岗岩的真三轴单面临空岩爆试验,并利用高速摄像系统和声发射（acoustic emission,简称AE）系统监测岩爆过程,探究了不同产状裂隙岩石的破坏模式、强度变形和声发射演化特性,分析了裂隙产状与岩爆过程及弹射动能之间的关系,对比了含裂隙岩石岩爆发生机制与无裂隙完整岩石的差异。有关力学特性的分析表明,随着裂隙倾角的减小,岩样破坏模式大体呈现由“内剪外劈”向“Z型斜剪”变化的趋势,裂隙对岩石强度的削弱作用不断增大。当裂隙倾角小于30°时,岩石峰值应力普遍仅为完整岩样的一半左右;小倾角裂隙的长度越大,岩样岩板劈裂现象变得显著,形成岩爆坑略微变大,且强度折减幅度越大,峰值轴向应变相应变小;裂隙位置向临空面靠近会加剧岩板的劈裂效应,塑性阶段普遍会产生较大变形并萌生大量裂纹,当裂隙已出露且切断临空面将不易形成岩爆坑。有关岩爆过程及弹射动能的分析表明,随着裂隙倾角的减小,岩样弹射动能呈现先显著降低后小幅回升的变化规律,30°倾角为转变拐点;岩样内部裂隙距临空面越近,裂隙岩样的弹射动能越小;树脂填充裂隙使得岩样弹射动能极大提升,而水泥填充的则无明显提升。有关声发射特征的分析表...     

基于考虑动力本构的连续−非连续方法的单轴压缩岩样开裂过程模拟

动载作用下岩石的破坏规律研究对于众多地质灾害的机制分析和预防具有重要的理论及实际意义。鉴于数值模拟研究的优势,应大力发展适于岩石动力断裂过程模拟的数值方法。在自主开发的拉格朗日元与离散元耦合连续−非连续方法的基础上,采用朱−王−唐本构模型取代了广义胡克定律,发展了考虑动力本构的连续−非连续方法,其正确性通过模拟不同加载速度时砂岩试样的单轴压缩试验进行了验证。通过统计裂缝区段数目随着岩样的纵向应变的演化规律,并监测岩样左、右对称线上多个测点的最小主应力的演化规律,开展了不同加载速度时单轴压缩花岗岩试样的变形−开裂过程研究,阐明了岩样的开裂机制。研究发现,剪裂缝以雁列式展布,整体上形成剪切带。随着时步数目的增加,各测点的最小主应力均呈波动下降−震荡上升的变化趋势。震荡上升阶段对应岩样的应变软化阶段。测点分离后最小主应力的震荡幅度较大,这是由于节点分离和单元接触激发了较大的应力波。剪切带尖端的最小主应力集中会使测点发生剪切分离。当岩样的三角块向下楔入时,下方测点的应力状态类似于紧凑拉伸试验进而发生拉伸分离。     

Micromechanical modeling for rate‐dependent behavior of salt rock under cyclic loading

The dependence of rock behavior on the deformation rate is still not well understood. In salt rock, the fundamental mechanisms that drive the accumulation of irreversible deformation, the reduction of stiffness, and the development of hysteresis during cyclic loading are usually attributed to intracrystalline plasticity and diffusion. We hypothesize that at low pressure and low temperature, the rate‐dependent behavior of salt rock is governed by water‐assisted diffusion along grain boundaries. Accordingly, a chemo‐mechanical homogenization framework is proposed in which the representative elementary volume (REV) is viewed as a homogeneous polycrystalline matrix that contains sliding grain‐boundary cracks. The slip is related to the mass of salt ions that diffuse along the crack surface. The relationship between fluid inclusion‐scale and REV‐scale stresses and strains is established by using the Mori–Tanaka homogenization scheme. It is noted from the model that a lower strain rate and a larger number of sliding cracks enhance stiffness reduction and hysteresis. Thinner sliding cracks (i.e., thinner brine films) promote stiffness reduction and accelerate stress redistributions. The larger the volume fraction of the crack inclusions, the larger the REV deformation and the larger the hysteresis. Results presented in this study shed light on the mechanical behavior of salt rock that is pertinent to the design of geological storage facilities that undergo cyclic unloading, which could help optimize the energy production cycle with low carbon emissions.