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.     

砂土力学性质的细观模拟

基于颗粒流理论,对砂土的室内双轴试验和砂土剪切带形成与发展进行了数值模拟,基本再现了砂土试样应力-应变关系。主要研究了颗粒粒径、颗粒摩擦系数等细观参数变化时试样宏观性质的变化情况。对比分析了室内试验和颗粒流数值模拟试验的砂土剪切带特征。同时对比研究了模型试样颗粒粒径、颗粒刚度和摩擦系数等细观参数的变化,对剪切带的形成与发展过程的影响。结果表明：通过颗粒流数值模型试验可以有效模拟砂土剪切带的形成与发展机理。     

基于颗粒流程序的真三轴应力状态下堆石体的变形和强度特性研究

采用三维颗粒流程序,模拟了堆石体的真三轴试验,不仅研究了堆石体在三维应力条件下的宏观应力变形特点,而且将细观与宏观参数联系起来,进一步完善了对堆石体的研究。试验过程采用等中主应力比路径加载。通过比较堆石体真三轴颗粒流模型试验和室内真三轴试验结果,表明颗粒流程序能较好地模拟堆石体的力学特性。颗粒流数值试验结果表明,中主应力对堆石体在三向应力状态下的强度和变形特性均有显著的影响。应力比参数b从0～1变化过程中,中主应力面先压缩后膨胀,小主应力面一直处于压缩状态;中主应力对内摩擦角、弹性模量和泊松比也均有影响。从细观上看,围压越高,b值越大,颗粒配位数越大,孔隙率越小,故从细观角度解释了堆石体的宏观应力变形现象。     

Micromechanical parameters in bonded particle method for modelling of brittle material failure

Bonded particle modelling (BPM) is nowadays being extensively used for simulating brittle material failure. In BPM, material is modelled as a dense assemblage of particles (grains) connected together by contacts (cement). This sort of modelling seriously depends on the mechanical properties of particle and contact, which are named here as micro‐parameters. However, a definite calibration methodology to obtain micro‐parameters has not been so far established; and many have reported some serious problems. In this research, a calibration procedure to find a unique set of micro‐parameters is established. To attain this purpose, discrete element code of UDEC is used to perform BPM. This code can be conveniently developed by the user. The proposed BPM is composed of rigid polygonal particles interacting at their contact points. These contacts can undergo a certain amount of tension, and their shear resistance is provided by cohesion and friction angle. The results demonstrate that each material macro‐property (i.e. Young's modulus, Poisson's ratio, internal friction angel, internal cohesion, and tensile strength) is directly originated from and distinctly related to the contact properties (i.e. normal and shear stiffness, friction angel, cohesion, and tensile strength). Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

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.     

Characterization of clastic rock using a biconcave bond model of DEM

This paper presents a biconcave bond model to investigate the effect of the cementation between grains on the mechanical behavior of rock. The proposed model considers the shape of the bonds among particles that have a biconcave cement form, based on observations of microscopic rock images. The general equations of the proposed model are based on Dvorkin theory. The accuracy and efficiency of the bond model is improved in three ways. After the biconcave bond model is implemented in the discrete element method software Particle Flow Code in 2 Dimensions, a series of numerical uniaxial compression tests were performed to investigate the relationships between the micro‐ to macro‐parameters. The simulations revealed that the biconcave bond model reflects the effect of micro‐parameters, such as the elastic modulus and Poisson's ratio of the cement, on the macroscopic deformation of cemented granular material. Variations in the bond geometry caused extremely diverse macro‐mechanical behaviors. Experimental results concerning rock demonstrate that the biconcave bond model accurately captures the mechanical behavior of intact rock and supports an innovative method for investigating the relationships between the micro‐ and macro‐parameters of cemented granular material. Copyright © 2016 John Wiley & Sons, Ltd.     

Effect of Model Scale and Particle Size Distribution on PFC3D Simulation Results

This paper investigates the effect of model scale and particle size distribution on the simulated macroscopic mechanical properties, unconfined compressive strength (UCS), Young’s modulus and Poisson’s ratio, using the three-dimensional particle flow code (PFC3D). Four different maximum to minimum particle size (d _max/d _min) ratios, all having a continuous uniform size distribution, were considered and seven model (specimen) diameter to median particle size ratios (L/d) were studied for each d _max/d _min ratio. The results indicate that the coefficients of variation (COVs) of the simulated macroscopic mechanical properties using PFC3D decrease significantly as L/d increases. The results also indicate that the simulated mechanical properties using PFC3D show much lower COVs than those in PFC2D at all model scales. The average simulated UCS and Young’s modulus using the default PFC3D procedure keep increasing with larger L/d, although the rate of increase decreases with larger L/d. This is mainly caused by the decrease of model porosity with larger L/d associated with the default PFC3D method and the better balanced contact force chains at larger L/d. After the effect of model porosity is eliminated, the results on the net model scale effect indicate that the average simulated UCS still increases with larger L/d but the rate is much smaller, the average simulated Young’s modulus decreases with larger L/d instead, and the average simulated Poisson’s ratio versus L/d relationship remains about the same. Particle size distribution also affects the simulated macroscopic mechanical properties, larger d _max/d _min leading to greater average simulated UCS and Young’s modulus and smaller average simulated Poisson’s ratio, and the changing rates become smaller at larger d _max/d _min. This study shows that it is important to properly consider the effect of model scale and particle size distribution in PFC3D simulations.     

DEM modeling of pullout behavior of geogrid reinforced ballast: The effect of particle shape

The performance of a geogrid reinforced system depends heavily on the properties of interface between the interacting components (i.e., backfill soil and geogrid inclusion). The comprehensive understanding of soil-geogrid interaction requires proper consideration of the true aperture geometry and the discontinuous nature of backfill soil. Based on the calibrated parameters, this paper presents a simulation procedure using PFC3D to reproduce the realistic pull-out behaviors of a triaxial geogrid embedded in various ballast aggregates with diverse particle shapes. The load transfer behaviors across the interacting components have been visualized in terms of the evolution of bond forces along the geogrid and the evolution of contact forces across the particle assembly. Meanwhile, the inherent microscopic changes accounting for the regression of macroscopic strength and the correlation between macro pull-out force and micro anisotropy parameters have been addressed. In addition, the differences in macro performance and the particle responses produced by different shapes of particles are also systematically discussed to justify the significant role of particle geometry. The findings obtained in this study are expected to provide better understanding of soil-geogrid interaction and the improved interlocking caused by irregular ballast geometry.     

Prediction of surface crown pillar stability using artificial neural networks

A relatively novel technique, artificial neural networks (ANN), is used in predicting the stability of crown pillars left over large excavations. Data for the training and verification of the networks were obtained from the literature. Four artificial networks, based on two different architectures, were used. The networks used different numbers of input parameters to predict the stability or failure of crown pillars. Multi‐layer perceptron networks using mine type, dip of orebody, overburden thickness, pillar thickness, pillar length, stope height, backfill height, Rock Mass Rating (RMR) of the host rock and RMR of the orebody showed excellent performance in training and verification. Adding three more variables, namely pillar width, rock density and pillar thickness to width ratio, showed symptoms of over‐learning without degrading performance significantly. Radial basis function networks were capable of predicting crown pillar behaviour on the basis of few input functions. It was shown that mine type, dip and pillar thickness to width ratio can be used for a preliminary estimation of stability. Copyright © 2006 John Wiley & Sons, Ltd.     

伯格斯模型参数调试与岩石蠕变特性颗粒流分析

岩石作为地下工程的主要研究对象,其物质组成和所赋存的复杂地质环境使其具有明显的流变特性。基于三维颗粒流程序(PFC3D),采用由开尔文模型和马克斯伟尔模型串联组成的伯格斯（Burgers）流变模型,通过控制变量法,分析了伯格斯模型中弹性系数(Em和Ek)、黏性系数(?m和?k)和摩擦因数f对瞬时强度特性和流变特性的影响;分析得出数值试样的瞬时强度特性主要受马克斯伟尔体弹性系数Em和摩擦因数f影响：弹性模量和单轴抗压强度与Em和f均呈正相关,泊松比与Em呈正相关,与f呈负相关;而流变特性与各参数均呈现负相关性。在此基础上,进行了红页岩分级增量蠕变试验的模拟,通过与室内蠕变试验结果的对比,验证了PFC3D中的伯格斯模型用于岩石蠕变试验模拟的可行性,并将该方法用于分级增量循环加卸载蠕变试验和三轴蠕变试验数值研究。该研究内容是利用离散单元法研究岩石流变特性的一种新的尝试。     

基于颗粒元模拟的含软弱夹层类土质边坡变形破坏过程分析

采用基于离散单元法的颗粒元程序,引用平行连接模型,通过数值试验,确定土体细观参数与宏观力学性质的关系,并据此建立含软弱夹层的类土质边坡模型。通过路堑开挖卸荷过程模拟,再现了大变形条件下坡体渐进性破坏的完整过程,并对裂隙的发展演化过程进行实时监测。模拟结果显示,含软弱夹层类土质边坡的破坏过程历经裂隙的形成、扩大、发展直至贯通,最终发生大规模滑移破坏;裂隙从滑坡体前缘和软弱层面开始,范围逐步扩大,呈现典型的类土质边坡的渐进性破坏形式;滑坡发生后,土体结构破坏严重,承载能力大幅下降。边坡滑移过程模拟和最终滑移结果与现场滑坡状况完全吻合,表明该方法适用于类土质边坡变形破坏过程分析及其机理研究。     

贵阳既有地基红黏土蠕变特性试验研究

为了准确地掌握喀斯特发育地区岩溶作用对红黏土的结构影响,以及红黏土地基的蠕变特性,以贵州铝厂既有地基红黏土为研究对象,采用分别加载法进行了室内单轴蠕变固结试验和三轴蠕变试验,建立单轴蠕变经验方程以及Singh-Mitchell模型。结果表明:贵州铝厂红黏土的单向固结有线性规律,表现在t/ε和t存在高度的线性相关性,其单向固结经验方程中的一个参数b可用于预测试样在单向固结下的最终沉降量。所建立的Singh-Mitchell三参数的蠕变模型较好表达了试验土体在25%~100%偏应力水平范围内的应力-应变-时间三者的关系特性。同时,SEM图片表明随着竖向压力不断地增大,单轴固结试验下该红黏土的孔隙面积和微观颗粒数减小,颗粒面积变大,三维孔隙率增加,说明能用孔隙变化的微观规律来反映宏观现象。      

基于软硬石模板库的土石混合体细观损伤与力学特性分析

为了探究含软、硬两种岩性碎块石土石混合体的变形破坏过程与力学性质,发展了一种基于软硬石模板库的土石混合体建模方法。通过在PFC2D中建立符合原位结构特征的软硬石模板库,利用此模板库生成了不同含石量土石混合体颗粒流模型,对土石混合体进行了单轴压缩颗粒流模拟。结果表明：土石混合体破坏始于土-石接触面,土石介质分离大多因剪切破坏导致,加载前期微裂纹迅速增长,中、后期微裂纹增长速率减缓,但宏观变形渐趋显著;随着含石量的增加,土石混合体单轴抗压强度逐渐降低,块石的转动与侧向移动会加剧土石混合体的整体破坏;相同含石量下,随着软石比例的增加,单轴抗压强度呈下降趋势,试验后试样破裂率与单个软石颗粒的破裂程度均保持在较高水平,软石颗粒破裂是引起土石混合体单轴抗压强度降低的重要原因。     

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.     

考虑不均质度的岩石声发射数值模拟研究

利用离散元颗粒流软件模拟了岩石单轴压缩破坏过程,采用内嵌FISH语言,通过设置随机缺陷来建立不同均质度的岩石数值试样对岩石的声发射规律进行了研究。结果表明,不均质度对于岩石声发射特性有着重要影响,随不均质度的增加,试样的峰值强度下降,声发射总数大幅增加,空间分布也更为分散,声发射出现时间更早,持续时间更长,峰值后的声发射保持更高的强度;单轴应力状态下声发射最大强度出现时间相比峰值破坏时间有不同程度滞后,不均质度越高,滞后效应越明显,显示岩石破坏要早于声发射峰值出现时间。     

Microparameter Prediction for a Triaxial Compression PFC3D Model of Rock Using Full Factorial Designs and Artificial Neural Networks

This paper presents an integrated approach that predicts the microparameters of the particle flow code in three dimensions (PFC3D) model in triaxial compression simulations. The new approach combines a full factorial design (FFD) with an artificial neural network (ANN). The ANN model maps the input factors (triaxial compressive strength, Poisson’s ratio, and Young’s modulus) onto output variables, which are microparameters that affect the macroscopic responses in a PFC3D model. Emphasis is placed on data collection and optimization of the ANN model using FFD. The data for training and testing the ANN model were obtained from laboratory experiments and numerical simulations of a PFC3D model according to the principles of FFD. Using a backpropagation artificial neural network (BPNN) optimized with FFD principles, the object of the current study (to reliably predict the microparameters for a PFC3D model) has been achieved because the predicting data obtained by the BPNN model were in excellent agreement with the testing data.     

Prediction of Elastic Modulus of Jointed Rock Mass Using Artificial Neural Networks

Two artificial neural network models for the prediction of elastic modulus of jointed rock mass from the elastic modulus of corresponding intact rock and joint parameters have been demonstrated in this paper. The data collected from uniaxial and triaxial compression tests on different rocks with different joint configurations and different confining pressure conditions, reported in the literature are used as input for training the networks. Important joint properties like joint frequency, joint inclination and roughness of joints are considered separately for making the network more versatile. Two different techniques of artificial neural networks namely feed forward back propagation (FFBP) and radial basis function (RBF) are used to predict the elastic modulus ratio.     

基于BP神经网络的岩土体细观力学参数研究

目前颗粒流计算方法中所采用的细观力学参数,均需根据岩土体宏观力学参数试验结果反复调试获取,调试效率很低且有较大的盲目性,因此,急需引入一种新方法,建立岩土体宏观力学参数与细观力学参数的关系。基于PFC3D程序,采用BP(back propagation)神经网络方法,建立宏观力学参数与细观力学参数的非线性模型,通过输入宏观力学参数,即可快速、准确地反演岩土体细观力学参数。研究结果表明：(1)根据BP神经网络模型反演确定的细观力学参数,输入数值模型计算其宏观力学参数,结果与试验值相比,精度一般高于90%;(2)当模型最小尺度上的颗粒数RES = 10、隐含层含6个神经元时,BP神经网络模型的反演性能最佳。实例计算表明,BP神经网络模型对于岩土体细观力学参数的确定具有良好的反演性能,该方法为颗粒流理论的推广应用提供了新的技术手段。     

基于PFC2D模拟的矿物粒径非均质效应研究

岩石作为矿物颗粒的集合体,矿物粒径非均质性对其宏观力学特性影响比较明显。基于颗粒流程序PFC2D,通过设置不同种类粒径组合及粒径比来体现粒径非均质性,研究了粒径非均质性对岩石材料宏观力学特性（弹性模量、峰值强度、泊松比）的影响。研究中设计了6种粒径组合方案,粒径种类数分别为:连续粒径、10种、8种、5种、3种、2种,每种方案下设置5种平均粒径及4种粒径比,进行单轴压缩试验。结果表明,岩石内部存在颗粒尺寸效应和粒径非均质效应,岩石弹性模量和峰值强度随粒径增大均呈减小的趋势,随粒径非均质性的提高整体上也呈减小的趋势,但局部变化阶段受模型中细颗粒含量及数量的影响会呈增大的趋势。粒径对弹性模量的作用机制主要是通过影响模型孔隙率实现的。研究结果揭示了岩石宏观特性的变化是模型内颗粒尺寸效应和粒径非均质性效应共同作用的结果,为掌握矿物粒径对岩石强度及变形特性的影响提供了一定依据。