Discrete element modeling of tool‐rock interaction I: rock cutting

Tool‐rock interaction processes can be classified as indentation or cutting depending on the direction of motion of the tool with respect to the rock surface. The modes of failure induced in the rock by an indenting or a cutting tool can be ductile and/or brittle. The ductile mode is associated with the development of a damage zone, whereas the brittle mode involves the growth of macrocracks. This is the first part of a series of two papers concerned with an analysis of the cutting and the indentation processes based on using the discrete element method. In this paper, numerical simulations of the cutting process are conducted to reproduce the transition from a ductile to a brittle failure mode with increasing depth of cut, which is observed in experiments. The numerical results provide evidence that the critical depth of cut d _* controlling the failure mode transition is related to the characteristic length ? = (K_Ic ∕ σ_c)² with K_Ic denoting the material toughness and σ_c its unconfined compressive strength. The nature of frictional contact between the cutter face and the rock in the ductile failure mode is also examined. It is shown that the inclination of the total cutting force is controlled by a multi‐directional flow mechanism ahead of the cutter that is related to the formation of a wedge of failed material, intermittently adhering to the cutter. As a result, the inclination of the total cutting force varies with the rake angle of the cutter and cannot be considered an intrinsic measure of the interfacial friction between the cutter and the rock. Copyright © 2012 John Wiley & Sons, Ltd.     

顺层路堑边坡锚杆支护稳定性的有限元模拟分析

基于理想弹塑性本构模型和Drucker-Prager准则,运用ANSYS软件和有限元数值模拟技术,建立了顺层岩体边坡的有限元分析模型。结合沪蓉国道主干线宜昌至恩施公路白氏坪-榔坪段顺层路堑高边坡工程实例,对顺层岩体路堑边坡布设锚杆支护前后的应力、变形和稳定性进行了模拟分析。分析比较表明,锚杆支护结构可以减小边坡临界状态下的最大位移、增大最危险接触面的摩擦力和提高边坡的稳定性系数,从而能有效地提高边坡的稳定性以防止顺层滑坡的发生。     

顺层岩体路堑边坡稳定性的弹塑性有限元模拟分析

基于理想弹塑性本构模型和Drucker-Prager准则,运用岩体力学理论、有限元数值模拟技术和强度折减原理,对顺层岩体路堑边坡在开挖过程中不同阶段的应力、变形、结构面上的摩擦力和边坡的稳定性等问题进行了模拟分析。分析表明,顺层岩体路堑边坡的应力场、位移场、结构面的接触状况以及边坡的稳定性明显受开挖效应的影响;在每一阶段的开挖面上,坡脚附近的水平位移量最大,最危险接触面也都集中在开挖形成的坡脚处,此处岩石最先脱落破坏;边坡的稳定性安全系数也随着开挖阶段的深入而逐渐降低。     

地下洞室围岩脆性破坏时的应力特征研究

在高应力作用下,岩爆、钻孔崩落、片帮都是地下空间硬脆围岩中常见的破坏现象,这三类现象本质上均可归于完整岩体的脆性破坏,它们分别反映了高应力作用下完整岩体不同的破坏程度。通过对前人关于岩爆判据、钻孔崩落判据和片帮应力强度比判据研究成果的类比分析可知,这些脆性破坏现象在破坏时具备相同的应力背景条件。脆性破坏的应力条件可以用地下空间周边切向最大应力与岩石单轴抗压强度之比（ / ）或者工程区最大主应力与岩石单轴抗压强度之比（ / ）来描述,两种指标本质上反映了相同的应力背景条件。对于 / , / = 0.4 ± 0.1是发生脆性破坏的应力临界条件;对于 / , / = 0.15 ± 0.05是发生脆性破坏的应力临界条件。大量的工程实例和基于Hoek-Brown强度准则的力学分析也证明了这一背景条件的正确性。这里两种指标都取了一个范围,主要是由于不同的岩体分级、岩性和工程地质条件会对指标的界定产生较为显著的影响。     

顺层岩质路堑边坡稳定性的敏感性因素分析

运用弹塑性理论和有限元法,建立了顺层岩质路堑边坡稳定性的模拟分析模型。结合沪蓉国道主干线湖北宜昌至恩施高速公路的顺层岩质路堑高边坡工程,分析了结构面强度、岩层厚度、岩层倾角等各项因素对顺层岩质路堑边坡稳定性的影响,探讨了顺层岩质路堑边坡稳定性的规律。结果表明：软弱结构面的强度参数对顺层岩质路堑边坡稳定性起主要控制作用,岩层倾角对顺层岩质路堑边坡的稳定性也有明显的影响。在该工程的地质条件下,当岩层倾角为38°左右时,顺层路堑边坡的稳定性最差。     

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 creep of asphalt mixtures

Creep tests on asphalt mixtures have been undertaken under four stress levels in the laboratory while the discrete element model (DEM) has been used to simulate the laboratory tests. A modified Burger’s model has been used to represent the time-dependent behaviour of an asphalt mixture by adding time-dependent moment and torsional resistance at contacts. Parameters were chosen to give the correct stress-strain response for constant strain rate tests in Cai et al. (2013). The stress-strain response for the laboratory creep tests and the simulations were recorded. The DEM results show reasonable agreement with the experiments. The creep simulation results proved to be dependent on both bond strength variability and positions of the particles. Bond breakage was recorded during the simulations and used to investigate the micro-mechanical deformation behaviour of the asphalt mixtures. An approach based on dimensional analysis is also presented in this paper to reduce the computational time during the creep simulation, and this analysis is also a new contribution.     

岩体裂隙模拟的扩展有限元法应用研究

岩体中普遍存在着断层﹑节理和裂隙等结构面,这些结构面的存在和发展对岩体的整体强度﹑变形及稳定性有极大的影响。因此,研究岩体中原生结构面的萌生﹑发展以及贯通演化过程对评估岩体工程安全性和可靠性具有非常重要的理论与现实意义。扩展有限元法（XFEM）作为一种求解不连续问题的有效数值方法,模拟裂隙时独立于网格,因此,在模拟岩体裂隙扩展﹑水力劈裂等方面具有独特优势。针对扩展有限元法的基本理论及其在岩体裂隙扩展模拟中的应用展开了研究,建立了扩展有限元法求解岩体裂隙摩擦接触、岩体裂隙破坏等问题的数值模型,并将计算模型应用于岩质边坡稳定性分析和重力坝坝基断裂破坏等工程问题。     

基于统计岩体力学的岩体强度特征分析

结构面的存在改变了岩体力学性质,影响了岩体强度特征。基于统计岩体力学强度判据,结合摩尔-库仑准则,得到了含单组结构面岩体破坏的4种不同方式和相应的结构面倾角范围,推导了岩体强度由结构面控制转化为应力控制的临界围压表达式。在此基础上,根据岩石和结构面参数之间的关系,将含单组结构面岩体分为4类,并探讨了可能破坏方式和发生破坏的条件。最后,举例分析了含单组结构面闪长岩的强度特征,结果表明,该岩体属于第I类岩体,在垂向受压时先沿结构面后沿岩块破坏,临界围压为9.12 MPa;从全空间分析,该岩体强度各向异性显著,围压增大可使岩体在一些方向上受力时强度由结构控制转化为应力控制。     

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.     

Three-dimensional discrete element simulation of indirect tensile behaviour of a transversely isotropic rock

This paper presents the development of a three-dimensional discrete element model using flat-joint and smooth-joint contact models to investigate the effect of anisotropy on the tensile behaviour of slate, a transversely isotropic rock, under Brazilian testing from both macro and microscales. The effect of anisotropy is further realised by exploring the influence of foliation orientations (β and ψ) on the tensile strength, fracture pattern, microcracking and stress distribution of the transversely isotropic rock. The variation of tensile strength with foliation orientation is presented. The cross-weak-plane fracture growth observed in laboratory is reproduced, and the criterion for which to form is also given from the aspect of foliation orientation. Furthermore, the proportional variations of microcracks well account for the effects of foliation orientation on the tensile strength and failure pattern. Finally, it is found that the existence of weak planes increases both the heterogeneity and the anisotropy of stress distributions within the transversely isotropic rock, with the degree of influence varying with the foliation orientation.     

岩石化学风化时效效应的离散元模拟

微观上,岩石由晶粒和晶粒之间的联接组成。在岩石的风化过程中,晶粒之间的联接会被削弱,导致岩石微观缺陷的发展,从而表现为显著的时效效应。在已有胶结模型的基础上,将岩石的化学风化过程等效为颗粒之间胶结物质不断溶蚀进而影响颗粒之间胶结强度和刚度的过程,基于此建立了考虑化学风化的微观接触模型。随后将模型植入离散元软件,运用离散元方法（DEM）,模拟和对比分析了室内腐蚀试验与DEM模拟化学风化试验,结果表明：该模型可以反映岩石强度的化学风化时效效应,即随着反应时间增加,强度减小;可以反映单轴压缩试验中裂隙压密阶段以后变形的时效效应,即随着反应时间的增加,弹性模量、破坏时应变减小;粒间胶结的破坏,即微观缺陷的发育,是导致岩石化学风化时效效应的微观原因。同时DEM模拟风化与加载耦合的试验现象表明,施工过程中的施工速度会影响岩石的强度,施工应该选择合适的速率。     

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.     

岩石破坏非连续变形分析弹脆性本构模型的二次开发

岩石非连续变形分析方法DDARF成功实现了模拟岩体裂纹萌生、扩展、贯通、破碎的全过程,但算法只考虑了岩体的线弹性本构模型,没有分析岩体的非线性应力-应变关系。为更符合真实岩体工程,同时扩展岩石非线性本构模型的应用范围,分别采用摩尔-库仑强度准则和最大拉应力强度准则对岩体进行剪切和拉伸破坏判断;对理想弹脆性本构模型进行算法分析,并在VC++平台下程序实现;对“自定义”的岩体非连续变形分析方法弹脆性本构模型与室内单轴压缩试验进行比较分析;将岩体非连续变形分析方法弹脆性本构模型应用于大型地下洞室开挖,并与线弹性本构模型进行对比。结果表明,非连续变形分析方法中自定义岩体弹脆性本构模型是可行的,它能够反映岩体变形的非线性特征,与室内试验吻合度较好;非连续变形分析方法弹脆性本构模型应用于大型地下工程,能更安全且真实地分析洞室围岩的稳定性,进而更好地指导地下洞室的防护措施。     

基于断裂力学的岩石切削数值分析探讨

为研究岩石切削过程中刀具的力学特性以及刀具平均峰值作用力的预测,基于断裂力学和有限元理论建立了岩石切削的数值模型。模拟分析岩石对刀具的反作用过程,得到不同力学特性岩石和刀具作用条件下刀具所受的反作用力,结果表明,冲击速度在一定范围内对刀具平均峰值作用力影响较小;岩石体积呈阶跃性递减,刀具作用力大小与崩落岩石碎片体积变化一致。对模拟、实验以及已有理论计算得到的刀具平均峰值作用力进行线性回归分析,研究结果表明,数值方法计算结果与实验结果、Goktan[1]理论计算结果的线性相关系数分别为0.812、0.930,相关性较好,表明所建数值模型用于模拟岩石切削是正确和可靠的。     

Waterjet-assisted rock cutting systems — the present state of the art

Summary A review of the benefits of assisting mechanical tools, notably drag bits, with moderate pressure waterjets suitably directed with respect to the bit is given. These benefits include reduced bit forces, especially the bit normal force, reduced bit wear, reduced dust make, and reduced incidence of frictional sparking. The research work that has been conducted to date to investigate this phenomenon has been empirical in nature. Experiments are described that extend the data bank of this empirical knowledge. In addition, experiments aimed at gaining a better understanding of the fundamentals of the rock fragmentation process with this hybrid cutting method are outlined.Results from the first of these experimental series are used to make recommendations as to the position of the jet with respect to the bit, the stand-off distance between the nozzle exit and the bit/rock interface, and the jet energy. In addition, preliminary findings are reported regarding the increase necessary in the jet energy when the bit velocity is increased. Results from the second test series are discussed in the context of rock fracture behaviour induced by mechanical bits acting alone. The likely influence of waterjets on these fracture processes is analysed. It is concluded that, in terms of the bit force reductions, a dominant influence of the jets when used in conjunction with sharp drag bits, is continuous removal of the rock debris that forms ahead of the advancing bit. The observed reductions in bit wear and incidence of frictional sparking are attributed to reduced heat loading of the bit during the cutting operation. Reductions in the dust make are attributed to effective wetting of the fine rock particles before they become entrained in the airstream.     

复合岩层中滚刀旋转切割破岩效率试验研究

TBM掘进经常遇到复合岩层,在该地层中施工对滚刀破岩非常不利。为了提高掘进效率,降低工程造价,开展复合岩层滚刀破岩效率研究很有必要。鉴于此,采用滚刀岩机作用综合试验台对砂岩、花岗岩复合(复合比例为4(25) 6)而成的岩层进行5组刀间距下3种贯入度的3把滚刀同步旋转切割试验;试验过程中监测破岩总法向力、总扭矩,并分别收集两种岩石的岩渣进行筛分、称重;依据试验结果分析不同刀间距、贯入度下的法向力、扭矩及比能的关系。研究表明:不同刀间距时,平均法向力、平均扭矩随贯入度的增加而增大但两者的增加趋势不同,即平均法向力随着贯入度的增加几乎呈直线增大,而平均扭矩随着贯入度的增加其递增趋势减小;不同贯入度下存在不同的最优刀间距;砂岩、花岗岩切割轨迹长度比例为4:6时刀间距与贯入度的比值在14左右,破岩效率最高。     

The transition from brittle to ductile deformation in the Sambagawa metamorphic belt, Japan

The dominant deformation mechanism during the Sambagawa metamorphism changes from brittle to ductile with increasing metamorphic temperature. The magnitude of plastic strains inferred from the shapes of deformed radiolaria in metachert increases sharply across the boundary between the epidote-pumpellyite-actinolite zone and the epidote-actinolite zone. The synmetamorphic crack density of metachert is an indicator of the contemporaneous brittle strain of rocks, and it decreases sharply as the grade reaches the epidote-actinolite zone. Hence, the ratio of the ductile strain to the brittle strain of metachert decreases rapidly across the transition to the epidote-actinolite zone of the Sambagawa metamorphic belt.
The sharp change of the ductile strain magnitude also takes place at the epidote-actinolite grade in the Shimanto metamorphic belt of Japan, an example of the intermediate pressure facies series of metamorphism. It is concluded that the transition from brittle to ductile deformation takes place at about 300-400°C. and is independent of pressure of metamorphism.     

用5种圆盘试件的劈裂试验确定岩石断裂韧度

用5种不同形状的圆盘试件测定了大理岩张开型断裂韧度。5种圆盘试件分别为平台巴西圆盘、带有中心圆孔的平台巴西圆盘、人字型切槽巴西圆盘、直切槽巴西圆盘和圆孔切槽平台巴西圆盘。加载模式是对径压缩劈裂。介绍了试件的制作方法,提出了用每种圆盘确定断裂韧度的公式。结果表明,含有切槽圆盘的断裂韧度值在0.78～0.91 MPa•m1/2之间,不含切槽圆盘测得的值在1.01～1.04 MPa•m1/2之间。有3种含有切槽圆盘测得的断裂韧度值比较稳定,其中孔槽式平台巴西圆盘能够制作理想的宽度较小的切槽。     

Discrete element modelling of an underground explosion in a jointed rock mass

The purpose of this paper is to investigate the application of the discrete element program UDEC for modelling underground explosions in a jointed rock mass. A field underground explosion test has been conducted and UDEC and AUTODYN were utilised in a coupled manner to predict the rock mass response due to the underground explosion. The dynamic equation for the state of the rock material obtained from impact tests was incorporated into the calibration modelling. The comparison of modelling results with test results and empirical formulas shows that UDEC is capable of modelling explosion wave propagation in jointed rock mass with high reliability.