粗粒料强度及变形特性的细观模拟

粗粒料是一定级配的岩石颗粒集合体,具有独特的物理力学特性。以粗粒料室内三轴固结排水试验成果为基础,基于离散元颗粒流理论,从细观角度出发,以PFC3D为工具,通过自编程及二次开发,得到按级配生成的粗粒料三轴试验数值模型。引入clump颗粒考虑颗粒形状对粗粒料强度及变形的影响,分析剪胀、颗粒形状、颗粒重排的关系。结果表明：颗粒形状是影响粗粒料强度与变形的主要因素,在其他细观参数一定的情况下,改变颗粒形状,可以显著影响粗粒料的力学行为;BPM模型的应力-应变关系只在低围压下与试验值吻合,随着围压的增大,偏差越来越大;而引入clump颗粒的PFC3D数值模型能很好地模拟粗粒料室内三轴固结排水试验的应力-应变特性,但由于BPM及clump都是刚性颗粒,没有考虑颗粒变形及破碎,造成应变剪胀偏大。     

A relationship between tensile strength and loading stress governing the onset of mode I crack propagation obtained via numerical investigations using a bonded particle model

Numerical models based on the discrete element method are used to study the fracturing process in brittle rock‐like materials under direct and indirect tension. The results demonstrate the capacity of the model to capture the essential characteristics of fracture including the onset of crack propagation, stable and unstable crack growth, arrest and reinitiation of fracturing, and crack branching. Simulations of Brazilian indirect tension tests serve to calibrate the numerical model, relating macroscopic tensile strength of specimens to their micromechanical breakage parameters. A second suite of simulations reveals a linear relationship between the tensile strength of specimens and the loading stress for which mode I tensile crack propagation ensues. Based on these results, a crack initiation criterion for brittle materials is proposed, prescribing the stressing conditions required to induce tensile failure. Such a criterion, if broadly applicable, provides a practical means to rapidly assess the failure potential of brittle materials under tensile loads.     

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。     

锦屏深埋大理岩破裂扩展的时间效应试验及特征研究

脆性岩石破裂扩展的时间效应与地下工程的长期稳定性密切相关。针对锦屏深埋大理岩易受高应力卸荷而产生初始损伤的特点,首先利用无损取样技术获得无损岩样,并利用声发射对无损岩样进行初始损伤检测,剔除初始损伤对试验结果的影响。之后利用获得的无损岩样进行一系列的长期加载的静态疲劳试验验证锦屏大理岩强度的时效特性。结果显示,锦屏大理岩表现出强度随时间衰减的特性,当应力驱动比较低时,需要的时间也相应增加,最后得到静态疲劳极限为0.48。分析证明,脆性岩石在稳定荷载作用下蠕变曲线也分为3个阶段,同时应变率也表现出相应的变化趋势,利用扩容指标阐述了岩样在静态疲劳试验中的变形特征和破坏模式。最后,利用FLAC3D计算了开挖引起的应力松弛区和应力集中区,说明了埋深对试验结果的影响。针对试验中出现的含节理岩样强度较低的问题,借助颗粒流程序PFC中的光滑节理模型进行了数值试验,结果显示,节理的存在极大地影响了岩样的整体强度,并且在加载初期,存在压缩紧密,而在残余阶段,存在一定的强化效应和延性特征。     

Fracturing and Failure Behavior of Carrara Marble in Quasistatic and Dynamic Brazilian Disc Tests

The tensile strength and fracturing behavior of Carrara marble subjected to the dynamic Brazilian disc test using the split Hopkinson pressure bar technique are determined and compared with those obtained by the conventional quasistatic Brazilian disc test. Detailed observation of the cracking processes is aided by high-speed video footage captured at a frame rate of 100,000 frames per second. The dynamic increase factor is computed, revealing a strong strain rate dependence of the Carrara marble when subjected to strain rates above 1 s^?1. Similar to the quasistatic loading tests, conspicuous white zones/patches commonly appear prior to the initiation of visible cracks in the dynamic loading tests. Identification of the white patch initiation and evolution is aided by image comparison software. Comparing the cracking and failure processes under quasistatic and dynamic loading, some distinct differences in the white patch geometry and initiation load are observed. In addition, the extent of the compressive failure zones around the contact points between the loading platens and specimens is found to increase with the strain rate.     

Effects of Microparameters on Macroparameters of Flat-Jointed Bonded-Particle Materials and Suggestions on Trial-and-Error Method

The aims of this paper are to analyze the effects of microparameters on macroparameters of flat-jointed bonded-particle materials of particle flow code in two dimensions (PFC2D) and improve the efficiency of trial-and-error method in calibration of microparameters. The trial-and-error method is always used to calibrate the microparameters for a PFC2D model, but it is time-consuming and empirical. To improve the efficiency of the trial-and-error method, the effects of microparameters on macroparameters need to be analyzed. By using the trial-and-error method, a desirable set of microparameters for a uniaxial compression PFC2D model (with a flat-joint contact model as the contact model) of limestone were calibrated to match the macroscopic properties obtained from laboratory tests. Based on the calibration set of microparameters, effects of microparameters on macroparameters of the PFC2D model were studied by the orthogonal design method. On this basis, a flowchart of calibrating microparameters via trial-and-error method was proposed. This flowchart was used to calibrate the microparameters of granite. The macroparameters and failure characteristics determined from numerical simulation were very similar to those of laboratory tests, confirming the effectiveness of the proposed flowchart.     

A particle mechanics approach for the dynamic strength model of the jointed rock mass considering the joint orientation

In nature, there exist several forms of anisotropy in rock masses due to the presence of bedding planes, joints, and weak layers. It is well understood that the anisotropic properties of jointed rock masses significantly affect the stability of surface and underground excavations. However, these critical anisotropic characteristics are often ignored in existing uniaxial dynamic failure criteria. This study investigates the effect of a pre-existing persistent joint on the rate-dependent mechanical behaviours of a rock mass using a particle mechanics approach, namely, bonded particle model (BPM), to realistically replicate the mechanical response of the rock mass. Firstly, in order to capture the rate-dependent response of the jointed rock mass, the BPM model is validated using published experimental data. Then, a dynamic strength model is proposed based on the Jaeger criterion and simulation results. To further investigate the dynamic behaviours, the dynamic uniaxial compressive strength (UCS) for anisotropic rock masses with various joint orientations is investigated by subjecting the BPM models to uniaxial compression numerical tests with various strain rate. The proposed dynamic strength model is validated based on numerical simulation results. Finally, the fragmentation characteristics of the jointed rock masses are analysed, which demonstrate that the failure mode affects the dynamic UCS. This is further confirmed by the analysis of the orientations of microscopic cracks generated by the compression loading.     

Stable isotopes and archaeological geology: the Carrara marble,northern Italy

The principal marble quarries of Italy for the past 2000 years have been those of Carrara. In Roman times, the marble was exported all over the ancient world. Renaissance quarries were opened up in Seravezza; both the Seravezza and the Carrara quarries have been exploited until today. The correct identification of Carrara marble has always been a problem because it was traded so widely in Roman times and was later used to fabricate broken or lost pieces of classical statuary. Many types of geochemical analysis have been tried in order to find distinctive signatures for the recognition of classical marbles, including trace elements, ESR spectroscopy of Mn, thermoluminescence, and stable isotopic ratios. To date, the most promising has been isotopic ratio analysis of oxygen and carbon.In this study, stable isotopic signatures were investigated as a means for distinguishing: (1) the principal quarry areas of the Carrara Commune: Fossacava, Miseglia, and Torano, and the Seravezza Commune; (2) or merely the largely classical quarries of Carrara from the Renaissance quarries of Seravezza; (3) and, most important, the Carrara quarries from other quarries of Greece, Turkey, Italy, and Tunisia in the classical marble data base.Discriminant analysis (DA) of the isotopic analyses showed that the three quarry areas of a Carrara could not be told apart but that they could be told easily from Seravezza. In addition, a “mineralized” Carrara quarry at Mandria, with buff to yellow rather than white marble, was also distinctive. DA also suggests that Carrara can be told from those quarries with which it is presently confused: Paros, in the Aegean Sea; Marmara, in Turkey; and Pentelikon, near Athens.Sr isotopic analysis showed a range in the Carrara and other marbles of Hettangian (Lower Jurassic) age from 0.70778 to 0.70810 which is very different from values found in Paros and Pentelikon. This suggests that Sr might make a good third discriminator for classical marble.     

Studying the effect of non‐spherical micro‐particles on Hoek–Brown strength parameter mi using numerical true triaxial compressive tests

The strength parameter m_i in the Hoek–Brown strength criterion is empirical and was developed by trial and error. To better understand the fundamental relationship between m_i and the physical characteristics of intact rock, this paper presents a systematic study of m_i by representing intact rock as a densely packed cemented particle material and simulating its mechanical behavior using particle flow modeling. Specifically, the three‐dimensional particle flow code (PFC3D) was used to conduct numerical true triaxial compression tests on intact rock and to investigate the effect of non‐spherical micro‐particle parameters on m_i. To generate numerical intact rock specimens containing non‐spherical micro‐particles, a new genesis process was proposed, and a specific loop algorithm was used based on the efficiency of the process and the acceptability of generated specimens. Four main parameters—number, aspect ratio, size, and shape—of non‐spherical micro‐particles were studied, and the results indicated that they all have great effect on m_i. The strength parameter m_i increases when the number, aspect ratio, or size is larger or the shape becomes more irregular, mainly as a result of the higher level of interlocking between particles. This confirms the observations from engineering experience and laboratory experiments. To simulate the right strength parameter m_i, it is important to use appropriate non‐spherical micro‐particles by controlling these four parameters. This is further demonstrated by the simulation of two widely studied rocks, Lac du Bonnet granite and Carrara marble. Copyright © 2014 John Wiley & Sons, Ltd.     

Crack Coalescence in Molded Gypsum and Carrara Marble: Part 2—Microscopic Observations and Interpretation

Experimental uniaxial compression loading tests were conducted on molded gypsum and Carrara marble prismatic specimens to study the cracking and coalescence processes between pre-existing artificial flaws. The study showed that material had an influence on the cracking and coalescence processes (see the companion paper in this issue). As reported in the companion paper, one of the pronounced features as observed in the high-speed video recordings was the development of macroscopic white patches prior to the development of observable cracks in marble, but not in gypsum. This paper (part 2) deals with the microscopic aspects of the study. Specifically, the scanning electron microscope (SEM) and the environmental scanning electron microscope (ESEM) imaging techniques were used to study the microscopic development of white patches and their evolution into macroscopic tensile cracks and shear cracks in marble, and the microscopic initiation of hair-line tensile cracks and their evolution into macroscopic tensile cracks in gypsum. The microscopic imaging study in marble showed that the white patches were associated with extensive microcracking zones (process zones), while the extent of process zone development in gypsum was limited. The comparison of the macroscopic and microscopic results indicates that the different extent of microcracking zone development, related to the material textural properties, is a key factor leading to different macroscopic cracking behavior in gypsum and marble.

Modeling of dynamic cohesive fracture propagation in porous saturated media

In this paper, a mathematical model is presented for the analysis of dynamic fracture propagation in the saturated porous media. The solid behavior incorporates a discrete cohesive fracture model, coupled with the flow in porous media through the fracture network. The double‐nodded zero‐thickness cohesive interface element is employed for the mixed mode fracture behavior in tension and contact behavior in compression. The crack is automatically detected and propagated perpendicular to the maximum effective stress. The spatial discretization is continuously updated during the crack propagation. Numerical examples from the hydraulic fracturing test and the concrete gravity dam show the capability of the model to simulate dynamic fracture propagation. The comparison is performed between the quasi‐static and fully dynamic solutions, and the performance of two analyses is investigated on the values of crack length and crack mouth opening. Copyright © 2010 John Wiley & Sons, Ltd.     

Modeling 3D thermal fracture propagation by transient cooling using virtual multidimensional internal bonds

Thermal fracturing can play an important role in development of unconventional petroleum and geothermal resources. Thermal fractures can result from the nonlinear deformation of the rock in response to thermal stress related to cold water injection as well as heating. Before the rock reaches the final failure stage, material softening and bulk modulus degradation can cause changes in the thermo‐mechanical properties of the solid. In order to capture this aspect of the rock fracture, a virtual multidimensional internal bond‐based thermo‐mechanical model is derived to track elastic, softening, and the failure stages of the rock in response to the temporal changes of its temperature field. The variations in thermo‐mechanical properties of the rock are derived from a nonlinear constitutive model. To represent the thermo‐mechanical behavior of pre‐existing fractures, the element partition method is employed. Using the model, numerical simulation of 3D thermal fracture propagation in brittle rock is carried out. Results of numerical simulations provide evidence of model verification and illustrate nonlinear thermal response and fracture development in rock under uniform cooling. In addition, fracture coalescence in a cluster of fractures under thermal stress is illustrated, and the process of thermal fracturing from a wellbore is captured. Results underscore the importance of thermal stress in reservoir stimulation and show the effectiveness of the model to predict 3D thermal fracturing. Copyright © 2016 John Wiley & Sons, Ltd.     

Modeling the particle breakage of rockfill materials with the cohesive crack model

A practical combined finite–discrete element method was developed to simulate the breakage of irregularly shaped particles in granular geomaterials, e.g., rockfill. Using this method, each particle is discretized into a finite element mesh. The potential fracture paths are represented by pre-inserted cohesive interface elements (CIEs) with a progressive damage model. The Mohr–Coulomb model with a tension cut-off is employed as the damage initiation criterion to rupture the predominant failure mode occurs at the particle scale. Two series of biaxial tests were simulated for both the breakable and unbreakable particle assemblies. The two assemblies have identical configurations, with the exception that the former is inserted with CIEs and is breakable. The simulated stress–strain–dilation responses obtained for both assemblies are in agreement with experimental observations. We present a comprehensive study of the role of particle breakage on the mechanical behavior of rockfill materials at both the macroscopic and microscopic scales. The underlying mechanism of particle breakage can be explained by the force chain in the assemblies.     

岩石拉伸剪切破裂试验研究

岩石拉伸剪切破裂是一类特殊应力状态条件下的破裂形式,属于同时受垂直于破裂面的法向拉应力和平行于破裂面的剪应力作用的复合破裂模式。在研制的DSC-800电液伺服测控岩石拉伸剪切试验仪的基础上,进行了大量花岗闪长岩和砂岩的拉伸剪切试验,开展了配套的破裂断口三维激光扫描、扫描电子显微镜（SEM）、岩石物理力学性质试验、颗粒流离散元（PFC）数值模拟等相关试验,利用分形理论研究了岩石拉剪破裂面特征,研究了岩石拉剪-压剪全区破裂准则、剪切速率对岩石拉剪破裂强度的影响,采用颗粒流离散元研究了岩石拉剪破裂过程。研究结论如下：（1）岩石拉剪破裂面的宏观与微观分形维数即粗糙度随着拉应力的增加而增大;（2）岩石的微观断裂形式是拉伸破坏和剪切破坏的结合。当拉应力较小时,岩石的微观断裂形式主要表现为剪切破坏,并且随着拉应力的增加,岩石的拉伸破坏形式表现得更加明显;（3）岩石在拉伸剪切区的破裂拉应力与剪应力成线性负相关关系,在拉伸剪切应力区的岩石破裂线斜率比压缩剪切区大,岩石在拉伸剪切应力条件下比压缩剪切应力条件下容易破裂;（4）在岩石拉伸剪切条件下,剪切速率与剪切强度成非线性反相关关系,随着剪切速率的增加,岩石拉剪破裂面粗糙度增加;（5）建立了岩石拉伸剪切PFC数值试验模型,模拟了岩石拉伸剪切破裂过程中的力链演化以及剪切速率对拉剪破裂面粗糙度的影响,获得了与实验室试验一致的结果。     

锦屏大理岩蠕变损伤演化细观力学特征的数值模拟研究

岩石的蠕变损伤和断裂是岩石流变效应的重要表现形式,但其损伤演化过程往往难以直观观测,为此,采用二维颗粒流数值模拟方法(PFC2D)对岩石的蠕变损伤和断裂的细观力学机制进行了分析。在锦屏大理岩室内试验基础上,利用颗粒流应力腐蚀模型(PSC),建立了能反映其短期和长期强度特征的柱状岩样数值模型,并开展了大量数值试验。结果表明,蠕变损伤的演化过程与暂态的损伤演化过程具有明显的差异。在岩样蠕变损伤过程中,其内部微裂纹多沿加载方向开裂且分布均匀,先快速增加再稳定扩展,最后则发生快速断裂。当荷载较小时,岩样宏观上呈现劈裂破坏特征,当荷载较大时,岩样呈现剪切破坏特征。在岩样蠕变损伤初始和稳定演化阶段的前期,荷载大小对岩样的损伤演化过程影响不大;在稳定演化阶段的后期至断裂过程中,低荷载下岩样的损伤增速比高荷载下快。     

Physical and numerical investigation of a cemented granular assembly of steel spheres

In this paper, steel spheres embedded in a cement matrix were studied using numerical and physical ISRM testing procedures. A challenge in discrete element simulations is to select appropriate micro‐mechanical models and parameters, to recover the observed macro‐mechanical behavior. An ideal experiment on cohesive granular assemblies constructed identical to numerical ones would validate these micro models for a set of measured micro‐parameters. The first part of the paper summarizes the previous studies in this area, outlines such experimental methodology and depicts the steps followed for the preparation and the testing of cemented granular assemblies together with the derivation of micro‐parameters. The second part discusses the results of numerical and physical ISRM standard tests including uniaxial and triaxial compression, Brazilian tensile and shear box tests. Physical samples were prepared using steel balls bonded with Portland cement, cured under controlled laboratory conditions and tested in compression, tension and shearing. Acoustic emissions were monitored in uniaxial tests to characterize the damage thresholds relative to volumetric strains. Numerical simulations were conducted with PFC 3D using micro‐mechanical parameters derived from physical testing. Parametric sensitivity studies were carried out to look into the dependency of macroscopic responses on the parameters. The results from both numerical and physical tests showed good correspondence in macroscopic behavior i.e. peak strength, stages of damage, mode of failures. However, the numerical simulations reflected a stiffer mechanical response than physical assemblies. Copyright © 2010 John Wiley & Sons, Ltd.     

页岩水力压裂过程的态型近场动力学模拟研究

水力压裂技术广泛使用于页岩气开采工程中。为了分析压裂过程中多裂缝扩展形成复杂裂缝网的机制,尝试将态型近场动力学理论引入页岩水平井水力压裂过程的力学建模与数值仿真,在物质点间相互作用力模型中加入等效水压力项以实现在新生裂缝面上跟踪施加水压力,建立了水力压裂过程的近场动力学分析模型。通过模拟页岩储层的水力压裂过程,可得到复杂的裂缝扩展路径、裂缝网络的形成过程以及裂缝扩展受射孔间距及页岩天然裂缝和层理的影响。研究结果表明:射孔间距过小会造成起裂干扰,使中心射孔的裂缝扩展受到抑制;在压裂压力一定的情况下适当增大射孔间距,可以显著增强页岩压裂形成裂缝网的能力;压裂过程中水平层理面可能张开形成水平裂缝,且天然裂缝会诱导形成更复杂的垂直裂缝。模型和方法可为页岩水力压裂过程和机制研究及工程实践提供参考。     

循环荷载下砂土液化特性颗粒流数值模拟

利用PFC2D常体积循环双轴试验条件,对砂土在不排水循环荷载作用下的液化特性进行了颗粒流数值模拟,数值模拟按等应力幅加荷方式进行。颗粒流数值模拟的优点在于得到试样液化宏观力学表现的同时,通过不同循环加荷时刻试样内细观组构参量（包括配位数、接触法向分布、粒间法向接触力、粒间切向接触力）的演化规律,分析砂土液化过程中细观组构变化与宏观力学响应之间的内在联系,从而可进一步探讨砂土液化的细观力学机制。数值模拟研究结果表明,砂土液化现象在宏观力学表现上反映为超静孔隙水压力的累积上升和平均有效主应力的不断减小,在细观组构上对应于配位数的累积损失和粒间接触力的不断减小。砂土液化细观机制分析表明,试样配位数的减少与循环加荷过程中组构各向异性滞后于应力各向异性有关。     

油气藏水力压裂计算模拟技术研究现状与展望

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