A Discrete Element Model for Predicting Shear Strength and Degradation of Rock Joint by Using Compressive and Tensile Test Data

A discrete element model is proposed to examine rock strength and failure. The model is implemented by UDEC, which is developed for this purpose. The material is represented as a collection of irregular-sized deformable particles interacting at their cohesive boundaries. The interface between two adjacent particles is viewed as a flexible contact whose constitutive law controls the material fracture and fragmentation properties. To reproduce rock anisotropy, an orthotropic cohesive law is developed for the contacts, which allows their shear and tensile behaviors to be different from each other. Using a combination of original closed-form expressions and statistical calibrations, a unique set of the contact microparameters are found based on the uniaxial/triaxial compression and Brazilian tension test data of a plaster. Applying the obtained microparameters, joint specimens, made of the same plaster, are simulated, where the comparison of the obtained results to laboratory data shows a reasonable agreement.     

Micromechanical Model for Simulating the Fracture Process of Rock

Summary A micromechanical model is proposed to study the deformation and failure process of rock based on knowledge of heterogeneity of rock at the mesoscopic level. In this numerical model, the heterogeneity of rock at the mesoscopic level is considered by assuming the material properties in rock conform to the Weibull distribution. Elastic damage mechanics is used to describe the constitutive law of meso-level elements, the finite element method is employed as the basic stress analysis tool and the maximum tensile strain criterion as well as the Mohr-Coulomb criterion is utilized as the damage threshold. A simple method, similar to a smeared crack model, is used for tracing the crack propagation process and interaction of multiple cracks. Based on this model, a numerical simulation program named Rock Failure Process Analysis Code (RFPA) is developed. The influence of parameters that include the Weibull distribution parameters, constitutive parameters of meso-level elements and number of elements in the numerical model, are discussed in detail. It is shown that the homogeneity index is the most important factor to simulate material failure with this model. This model is able to capture the complete mechanical responses of rock, which includes the crack patterns associated with different loading stages and loading conditions, localization of deformation, stress redistribution and failure process. The numerical simulation of rock specimens under a variety of static loading conditions is presented, and the results compare well with experimental results.     

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.     

SPH procedures for modeling multiple intersecting discontinuities in geomaterial

A methodology is developed in SPH framework to analyze the behavior of preexisting multiple intersecting discontinuities or joints in rock material. The procedure does not require any additional unknowns to represent discontinuities and to capture velocity jump across them. Instead, a discontinuity is represented by a set of joint particles placed along the discontinuity plane, in which relative velocity and traction vector is evaluated, obeying the Mohr–Coulomb friction law with zero tension constrain. For failure of continuous rock material, the Drucker–Prager yield criterion with tensile cracking is employed in the elastic‐plastic constitutive model. Free‐sip, no‐slip, and symmetric boundary conditions are also implemented in SPH framework for proper representation of physical system. The paper analyzes behavior of a rock sample having a discontinuity plane under uniaxial loading and compares velocity and stress with a theoretical solution derived considering effective vertical stiffness of the joint planes. The efficacy of the proposed method is successfully demonstrated by solving another two problems of jointed rock mass under uniaxial and gravitational loading conditions.Copyright © 2014 John Wiley & Sons, Ltd.     

考虑空间相关尺度特征的细观力学模型及其应用

天然岩石材料内部存在各种缺陷,在微、细观尺度表现出高度的非均质特性。基于连续介质力学框架,采用非线性标量损伤本构关系描述岩石材料的变形与破坏行为,建立了岩石细观损伤本构模型,并在常规Weibull随机分布模型基础上,引入空间相关尺度因子以模拟实际岩石材料各项物理力学指标具有的空间相关特征。选取典型岩石单轴拉伸试验算例,分析随机场内空间相关尺度因子的变化对试样荷载-加口张开度关系曲线以及破坏行为的影响。结果表明,考虑岩石材料各项物理力学指标的空间相关尺度特征对评价其力学指标的离散性以及破坏形态特征有着较显著的影响。     

Numerical analysis of slope stability based on the gravity increase method

A micromechanical model is proposed for studying the stability and failure process of slopes based on the gravity increase method (GIM). In this numerical model the heterogeneity of rock at a mesoscopic level is considered by assuming that the material properties conform to the Weibull distribution. Elastic damage mechanics is a method used for describing the constitutive law of the meso-level element, the finite element method (FEM) is employed as the basic stress analysis tool, and the maximum tensile strain criterion and the Mohr–Coulomb criterion are utilised as the damage threshold. The numerical model is implemented into the Realistic Failure Process Analysis (RFPA) code using finite element programming, and an extended version of RFPA, i.e., RFPA-GIM, is developed to analyse the failure process and stability of slopes. In the numerical modelling with RFPA-GIM, the critical failure surface of slopes is obtained by increasing the gravity gradually but keeping material properties constant. The acoustic emission (AE) event rate is employed as the criterion for slope failure. The salient feature of the RFPA-GIM in stability analysis of slopes is that the critical failure surface as well as the safety factor can be obtained without any presumption for the shape and location of the failure surface. Several numerical tests have been conducted to demonstrate the feasibility of RFPA-GIM. Numerical results agree well with experimental results and those predicted using the FEM strength reduction method and conventional limit equilibrium analysis. Furthermore it is shown that selection of the AE rate as the criterion for slope failure is reasonable and effective. Finally, the RFPA-GIM is applied to several more complex cases, including slopes in jointed rock masses and layered rock formations. The results indicate that the RFPA-GIM is capable of capturing the mechanism of slope failure and has the potential for application in a larger range of geo-engineering.     

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.     

On the role of pre-existing discontinuities on the micromechanical behavior of confined rock samples: a numerical study

The deformation process and failure mechanism of rock mass with increased density of initial joints subjected to confined stress state are investigated in this study using discrete element method (DEM). A numerical model of standard size granite samples is developed and validated using experimental data for both intact and jointed rocks. The micro-parameters of the rock material are first determined, and the effects of the rock discontinuity on strength, deformability, stress–strain relationship, and failure modes are then investigated at the macro-scale level. Analyses are also performed to examine the tensile and shear crack distributions, fragmentation characteristics, particle kinematics, and energy dissipation to advance the current understanding of the deformation processes and failure mechanisms of jointed rock masses. The microscopic evolutions in the fabric and force anisotropy during loading and distributions of contact forces provide insights into the influence of increasing initial jointing on the macroscopic deformational behavior of the rock. The results show how the deceleration in the growth of fabric and contact force anisotropies develops and confirms that the increase in initial jointing and the associated changes in microstructure can restrain the development of anisotropy, thereby reducing significantly the strength of the rock samples.

     

多块体形状堆石体碾压颗粒破碎数值模拟

通过6种典型堆石块体的形状近似,分别采用两种接触本构模型建立了多块体形状堆石体离散元数值模型,研究堆石体在碾压荷载作用下的颗粒破碎过程,建立颗粒破碎的量化计算方法,分析碾压前、后堆石级配曲线的变化,讨论接触本构模型和颗粒形状对块体破碎的影响。模拟结果显示,碾压荷载下堆石颗粒以张拉破碎为主,随着碾压遍数的增加,局部开始出现剪切破碎;提出的颗粒破碎量化计算方法,在大粒径范围对粒径变化幅度预测偏大,但级配曲线整体趋势与实测结果比较吻合;相比较于接触连接模型,平行连接模型与现场碾压试验结果更接近。6种块体形状的数值结果显示,随着形状系数的增加,在其他条件不变的情况下颗粒破碎率逐渐降低,其中类长方形块体在碾压荷载作用下颗粒破碎最明显。相比较于纯圆颗粒或者单一非圆颗粒,采用的6种颗粒形状建立的堆石体振动碾压离散元模型,更接近现场实际情况。     

颗粒配比对岩石力学特征影响的数值模拟研究

岩石是矿物颗粒的集合体同时也是一种重要的非均质材料,了解它的力学特征对岩土工程及矿产开采都具有重要的指导作用。作为典型的颗粒材料,颗粒单元体的粒径分布配比必然影响着岩石的宏观力学表现。通过设置不同体积配比下的颗粒材料单元体,利用PCF2D软件模拟了相同颗粒材料单元体不同配比下岩石模型的力学特征。模拟结果表明颗粒单元体配比对岩石的力学特征有明显的影响。在模拟过程中大颗粒的配比显著影响着岩石的抗压强度,大颗粒含量相对越高,抗压强度越大。而细颗粒的配比影响着岩石的抗拉强度,细颗粒含量相对越高,抗拉强度越大,但是过多的细颗粒会降低岩石的抗拉强度。考虑岩石压缩过程中裂缝形态的影响。结果表明均匀分布、5:2:3、7:2:1的颗粒配比形成了贯穿裂缝,而1:2:7和3:2:5的颗粒配比未能形成贯穿裂缝,且细颗粒配比越高,裂缝数目出现高值的概率也越大。      

Numerical simulation of the fracture process in cutting heterogeneous brittle material

The process of cutting homogeneous soft material has been investigated extensively. However, there are not so many studies on cutting heterogeneous brittle material. In this paper, R‐T^2D (Rock and Tool interaction), based on the rock failure process analysis model, is developed to simulate the fracture process in cutting heterogeneous brittle material. The simulated results reproduce the process involved in the fragmentation of rock or rock‐like material under mechanical tools: the build‐up of the stress field, the formation of the crushed zone, surface chipping, and the formation of the crater and subsurface cracks. Due to the inclusion of heterogeneity in the model, some new features in cutting brittle material are revealed. Firstly, macroscopic cracks sprout at the two edges of the cutter in a tensile mode. Then with the tensile cracks releasing the confining pressure, the rock in the initially high confining pressure zone is compressed into failure and the crushed zone gradually comes into being. The cracked zone near the crushed zone is always available, which makes the boundary of the crushed zone vague. Some cracks propagate to form chipping cracks and some dip into the rock to form subsurface cracks. The chipping cracks are mainly driven to propagate in a tensile mode or a mixed tensile and shear mode, following curvilinear paths, and finally intersect with the free surface to form chips. According to the simulated results, some qualitative and quantitative analyses are performed. It is found that the back rake angle of the cutter has an important effect on the cutting efficiency. Although the quantitative analysis needs more research work, it is not difficult to see the promise that the numerical method holds. It can be utilized to improve our understanding of tool–rock interaction and rock failure mechanisms under the action of mechanical tools, which, in turn, will be useful in assisting the design of fragmentation equipment and fragmentation operations. Copyright © 2002 John Wiley & Sons, Ltd.     

Discrete element modelling of rock cutting: from ductile to brittle transition

It is well accepted that there is a transition of failure mode from ductile to brittle with increasing depth of cut during rock cutting process. Rock failure modes affect cutting efficiency, and knowledge of the failure transition is essential to the determination of optimum cutting parameters. The critical transition depth can be linked with rock properties. In this study, an attempt was made to model rock cutting process and to check the dependence of the critical failure mode transition depth on the brittleness of rock. For this purpose, dimensional analysis was first performed to establish the correlations between rock macro‐properties and micro‐parameters for discrete element simulations. Following the specimen calibration procedure, two types of synthetic rocks having approximately the same uniaxial compressive strength were generated as the synthetic specimens for simulating the rock cutting process. The first specimen was created using conventional model construction method with identical bond strengths between particles, giving rise to undesirably high indirect tensile strength. The second specimen was created using a proposed clustering algorithm such that the ratio between the tensile and compressive strength matches reasonably well with that of real rocks. The results of rock cutting simulations demonstrate that failure mode transition took place in both models, but for the clustered model the transition emerged at a shallower cutting depth. A further exploration was made to derive the critical depth for this transition based on the simulations performed on the clustered models. The derived relationship indicates that the critical transition depth decreases as strength ratio or brittleness of the rock increases. This provides a very useful tool for predicting the critical depth which can be used to help cutting tool design and cutting parameter optimisations. Copyright © 2015 John Wiley & Sons, Ltd.     

基于数字图像处理技术的溶蚀岩体细观变形破坏机制模拟研究

通过数字图像处理技术对广泛发育于岩溶地区的溶蚀岩体的溶蚀特征进行提取,构建离散元溶蚀岩体模型,并模拟单轴压缩试验研究溶蚀岩体的细观变形破坏机制,以分析溶蚀岩体的变形破坏特征和裂隙演化规律。结果表明:溶蚀岩体模型能够很好地表征岩体的溶蚀特征,对真实的溶蚀形态具有较好的还原作用;溶蚀岩体的累计破坏数曲线呈现“S”型变化特征,即分为裂隙不发育阶段、稳定发育阶段和不稳定发育阶段,溶蚀岩体的破坏具有累进性特点;由于溶蚀孔洞的存在,使得溶蚀岩体接触力力链表现出各向异性特征,随着加载的进行,岩体骨架为抵抗外部荷载的作用,导致接触力在岩体骨架内集中,表现为接触力力链线条变粗;随着应变的增加,试样发生起源于溶蚀孔洞周围的破坏,破坏区域发生卸荷作用,接触力力链被淡化,最终试样发生破坏,力链消失,溶蚀岩体应力应变关系是试样内部接触力变化规律的宏观表现。      

延脆性变化对隧道掘进机刀具破岩过程及其破坏模式影响的颗粒元模拟分析

在全断面岩石掘进机（TBM）刀具破岩的颗粒元模拟中颗粒参数的选取至关重要,其中颗粒间平行黏结切向、法向强度是关键控制性参数之一,它们之间的比值关系直接决定所模拟试样的延脆性质,影响刀具破岩过程及其破岩效果。为探讨延脆性对刀具破岩模式的影响,（1）建立9种采用不同平行黏结强度比值的数值模型,分别进行单轴压缩及巴西劈裂模拟,研究不同延脆性试样的力学行为及破坏模式的变化。（2）对9种模型进行双刀破岩,并监控其裂缝的发展情况及刀具的受力状况。（3）为减小随机性对模拟结果的影响,通过改变随机数,每种模型重复模拟5次,综合分析5次的计算结果。模拟分析发现,随着切向和法向黏结强度比值( )的增大,试样的脆性增加,破坏模式逐渐从剪切破坏转变为脆性张拉破坏,刀具破岩压碎区范围减小,张拉裂缝更容易在刀具间贯通延伸从而切割出块体更大的岩渣;随着试样脆性的增加,归一化比能减小,刀具破岩的效率增加;平行黏结强度比值相同的条件下采用不同随机数种子生成的模型中,试样的具体破坏情况有一定的差别,但总体破坏模式相似。     

Study on the particle breakage of ballast based on a GPU accelerated discrete element method

Breakage of particles will have greatly influence on mechanical behavior of granular material(GM)under external loads,such as ballast,rockfill and sand.The discrete element method(DEM)is one of the most popular methods for simulating GM as each particle is represented on its own.To study breakage mechanism of particle breakage,a cohesive contact mode is developed based on the GPU accelerated DEM code-Blaze-DEM.A database of the 3D geometry model of rock blocks is established based on the 3D scanning method.And an agglomerate describing the rock block with a series of non-overlapping spherical particles is used to build the DEM numerical model of a railway ballast sample,which is used to the DEM oedometric test to study the particles’breakage characteristics of the sample under external load.Furthermore,to obtain the meso-mechanical parameters used in DEM,a black-analysis method is used based on the laboratory tests of the rock sample.Based on the DEM numerical tests,the particle breakage process and mechanisms of the railway ballast are studied.All results show that the developed code can better used for large scale simulation of the particle breakage analysis of granular material.     

三维梁-颗粒模型在岩石材料破坏模拟中的应用

用三维梁-颗粒模型BPM3D(beam-particlemodelinthreedimensions)对岩石类非均质脆性材料的力学性质和破坏过程进行了数值模拟。梁-颗粒模型是在离散单元法基础上,结合有限单元法中的网格模型提出的用于模拟岩石类材料损伤破坏过程的数值模型。在模型中,材料在细观层次上被离散为颗粒单元集合体,相邻颗粒单元由有限单元法中的弹脆性梁单元联结。梁单元的力学性质均按韦伯(Weibull)分布随机赋值,以模拟岩石类材料力学参数的空间变异性。材料内部裂纹通过断开梁单元来模拟。通过自动生成的非均质材料模型对岩石类材料的破坏机理进行研究。岩石类非均质脆性材料在单轴压缩状态下破坏过程细观数值模拟结果显示,岩石材料宏观破坏是由于其内部细观裂纹产生、扩展、贯通的结果。通过数值模拟结果之间的对比分析,揭示出岩石试样宏观破坏模式随细观层次上韦伯分布参数的变化而不同。与实际矿柱破坏形态的对比分析表明了模型的适用性。根据数值模拟结果对岩石类非均质材料的破坏机理进行了探讨。     

Constitutive model for soft rocks considering structural healing and decay

The behavior of soft rock depends on the contact area between mineral particles and the tensile strength of the interparticle cementation, which are usually referred to as structures. We investigated the effects of structural decay and healing on the behavior of soft rock through monotonic and slide-hold-slide triaxial tests under the drained condition with constant effective confining pressure. We developed a constitutive model for soft rocks incorporating structural healing and decay in the context of the extended critical state theory. The model was validated via laboratory tests and captured the behavior of soft rock, including the healing and decay phenomena.     

基于CT-CA的天然裂隙岩石受拉破坏特性研究

岩石内部存在的裂隙、孔洞等天然损伤对岩石的力学性能和破坏过程有重要影响,依据细胞自动机理论结合CT无损识别技术实现了含天然裂隙岩石在劈裂条件下裂纹扩展和贯通全过程及其力学性能变化规律的研究。从裂隙砂岩的真实细观结构出发,构建了天然裂隙岩石的数值计算模型,运用CASRock数值计算软件完成了含不同裂隙倾角的砂岩劈裂破坏的数值试验,分析了裂隙倾角对砂岩的力学特性、裂纹扩展过程及能量演化的影响规律。研究表明:(1)天然裂隙砂岩的抗拉强度与裂隙倾角密切相关,随着裂隙倾角的增加,其抗拉强度呈现先减小后增加的趋势;(2)裂隙起裂于天然裂隙尖端,当裂隙倾角0°≤θ<48°时,岩样的破坏是由错开型裂纹引起,裂纹沿着与天然裂隙近垂直方向扩展;当裂隙倾角48°≤θ<94°时,岩样的破坏是由张开型裂纹引起,裂纹沿着与天然裂隙近平行方向扩展;(3)劈裂过程中裂纹尖端应力场存在拉应力区和压应力区,拉应力造成翼裂纹由天然裂隙尖端沿加载端方向萌生扩展,而压应力则引发次生裂纹沿天然裂隙方向扩展;(4)含天然裂隙砂岩劈裂破坏过程能量演化可划分为4个阶段,随裂隙倾角的增大,峰值点处的总能量密度、弹性能密度先缓慢减少再迅速增加,但对岩样耗散能影响不大。     

On the role of joint roughness on the micromechanics of rock fracturing process: a numerical study

The deformation process and failure mechanism of rock mass with increased joint roughness subjected to unconfined compression are investigated in this study using discrete element method. A numerical model is developed using soft-bonded particle and validated to realistically replicate the mechanical response of the rock mass. The micro-parameters of the rock material are first determined, and the effects of the joint roughness on the macromechanical response and fracture growth mechanism are then investigated. Analyses are also performed to examine the tensile and shear crack distributions, acoustic emission (AE) characteristics, coordination number, and crack anisotropy to advance the current understanding of the role of joint roughness on the mechanical behavior and deformability of rock mass. The results show that strength and deformability of the jointed rocks are highly dependent on the joint orientation and roughness. Joint roughness is found to restrain the propagation and coalescence of microcracks and AE events from the interlocking of asperities. In addition, the spatial distribution of the contact forces allows for better understanding of the effect of joint inclination angle on the response of the investigated rock samples.

     

全断面岩石掘进机滚刀最优刀间距计算公式研究

基于剪切与张拉破岩机制,提出拉剪综合失效机制假设;建立了非协同切削与协同切削体积模型,推导了协同切削模式的滚刀比能耗理论模型;通过离散元仿真得到滚刀侵入岩石裂纹长度与贯入度的映射关系;推导出滚刀最优刀间距理论公式;以全断面岩石掘进机（TBM）回转切削试验台为基础,水泥模拟料为切削对象,通过多次压痕试验得到滚刀贯入度和岩石裂纹长度的趋势曲线,验证了仿真结果;通过滚刀滚动破岩进行了12组不同贯入度与刀间距的物理切削试验,统计滚刀做功与岩石破碎体积,拟合得到比能耗关系曲线,验证了最优刀间距理论公式的结论。研究表明：TBM滚刀最优刀间距计算公式综合考虑了岩石特性与滚刀结构特性,适应性较广泛;刀间距超过滚刀协同工作距离时,滚刀破岩以剪切破碎为主;刀间距小于2倍岩石裂纹长度时,张拉破碎的影响更加明显;随着贯入度的增加,最优刀间距逐渐增大,而最优滚刀间距S与贯入度P之比（S/P）值则逐渐减小。