Discrete element modeling of the single-particle crushing test for ballast stones

In this paper, a discrete element modeling approach for the single-particle crushing test for irregularly shaped ballast stones is presented. Bonded spherical particles are used to represent test specimens. Parametric studies focusing on particle size, axial strain rate, particle aggregate size and number of bonds are performed. The selection criteria of these parameters are discussed from the perspective of railway engineering. The results indicate that the proposed modeling approach is reliable for simulating railway ballast stones and can thus be further used for simulations of ballast aggregations.     

Generation of a realistic 3D sand assembly using X‐ray micro‐computed tomography and spherical harmonic‐based principal component analysis

Three‐dimensional particle morphology is a significant problem in the discrete element modeling of granular sand. The major technical challenge is generating a realistic 3D sand assembly that is composed of a large number of random‐shaped particles containing essential morphological features of natural sands. Based on X‐ray micro‐computed tomography data collected from a series of image processing techniques, we used the spherical harmonics (SH) analysis to represent and reconstruct the multi‐scale features of real 3D particle morphologies. The SH analysis was extended to some highly complex particles with sharp corners and surface cavities. We then proposed a statistical approach for the generation of realistic particle assembly of a given type of sand based on the principle component analysis (PCA). The PCA aims to identify the major pattern of the coefficient matrix, which is made up of the SH coefficients of all the particles involved in the analysis. This approach takes into account the particle size effect on the variation of particle morphology, which is observed from the available results of micro‐computed tomography and QICPIC analyses of sand particle morphology. Using the aforementioned approach, two virtual sand samples were generated, whose statistics of morphological parameters were compared with those measured from real sand particles. The comparison shows that the proposed approach is capable of generating a realistic sand assembly that retains the major morphological features of the mother sand. Copyright © 2016 John Wiley & Sons, Ltd.     

高黏性吹填土固结过程中细颗粒迁移规律研究

软土地基在真空预压过程中,受强大的真空吸力作用,产生固结压密。其中一类软土黏粒含量较大,排水固结过程中产生细颗粒迁移现象,令土体固结的同时细颗粒也积聚在排水板四周,形成泥膜,造成后期排水通道堵塞,降低了固结效率。本研究采用室内试验模拟吹填土排水固结过程,监测颗粒分布情况,探讨细颗粒迁移规律,从颗粒空间分布特征解释高黏性吹填土固结机理。研究证实,固结条件影响细颗粒迁移现象:自重沉淤固结期间,细颗粒迁移受边界条件及渗流路径影响; 加压固结期间,细颗粒迁移受附加荷载产生的垂直压力影响,随着土体含水量的减少,黏粒迁移趋势逐渐减弱,黏粒不再表现出明显的迁移趋势,土体中细颗粒分布从竖向条带状逐步转变为水平向条带状。同时,高黏性吹填土固结过程中,将土样未加分散剂测试得到的粉粒含量称为似粉粒,随着吹填土排水固结过程的持续,吹填土似粉黏比不断地增加。固结时间越长,似粉黏比随深度增加而减小的特征越明显; 与排水管水平距离较远的土体似粉黏比有所增大。似粉黏比作为吹填土固结过程的指标,与土体强度大小成正比,可间接反应强度变化规律,为确定流塑状态及软塑状态的高黏性吹填土固结程度提供了定性指标,直观地反映出土体固结程度。研究表明,随着固结排水过程的持续,排水速度减慢,吹填土粉黏比不断增加,固结程度迅速增加。     

粗粒料多边形表征及二维FEM/DEM分析

考虑到颗粒形状对粗粒料的力学特性有重大影响,提出了一种新的表征颗粒形状的方法,即在椭圆上随机选取一系列点连接成多边形颗粒,表征狭长扁平的颗粒。新方法较圆上取点的方法能代表更多类型的颗粒形状,适用范围更广。提出了一种新的粗粒料投放算法,即先缩小颗粒,然采用随机算法将缩小的颗粒投放至给定区域,对颗粒划分好网格后,将颗粒放大到原来的大小,然后采用有限元-离散元(FEM/DEM)方法计算稳定后即生成了相应的试样。通过将上述颗粒生成及投放算法与FEM/DEM结合,应用于粗粒料的数值模拟。分析表明,FEM/DEM是研究粗粒料力学性质的较好方法,对复杂的颗粒形状也可简单建模,且因在颗粒内部划分了有限元网格,复杂的接触判断及接触力计算转化为标准统一的三角形和三角形之间的接触判断及接触力计算,所有的计算均可标准化、统一化。同时因为颗粒是可以变形的,依然保留了连续介质力学中应力和应变的概念,无须像PFC那样需通过测量圆来间接表示某点的应力、应变。最后,通过粗粒料的侧限压缩试验的数值模拟,展现了文中提出的一整套解决方案在模拟粗粒料方面的巨大潜力。     

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.     

延安新区马兰黄土湿陷特性的PFC2D模拟

为了深入了解延安新区马兰黄土的粒间作用,揭示其湿陷机理。首先利用扫描电子显微镜观察了黄土的微观结构特征,并且利用IPP图像处理软件对黄土颗粒定量分析,论证了PFC2D软件模拟黄土粒间作用的可行性。然后,基于离散元理论,利用颗粒流PFC2D程序模拟了延安新区不同埋深原状黄土颗粒的分布情况及颗粒间相互作用,以一种直观的方法再现了天然黄土的微观结构特征。对比分析了不同深度黄土颗粒分布及接触力分布与湿陷性的关系。结果表明:骨架颗粒间的作用决定了土体的结构强度,尤其以团粒结构的接触力为主。随着深度的增加,黄土骨架颗粒由点接触方式逐渐过渡到团粒重叠接触,粒间接触力明显增强。PFC2D模拟方法为黄土湿陷性成因机理研究提供了新的思路。      

砂土颗粒三维形态的定量表征方法

颗粒形态是影响砂土力学特性的重要因素,特别是影响砂土在低应力状态下的抗剪强度、剪胀效应和临界状态行为,以及高应力状态下的颗粒破碎行为。因此,准确地重构砂粒的三维形态,并量化计算其形态表征参数是研究砂粒形态效应的前提工作。借助于高精度的CT扫描技术和图像处理技术,获得近海石英砂和风化花岗岩残积砂这两类砂土颗粒的三维形态信息。采用球谐函数序列实现两种砂颗粒三维形态的准确重构,并通过球谐函数分析计算砂土颗粒的体积来验证该方法的有效性。基于球谐重构的三维砂粒表面,提出了实用性的方法来计算砂粒的表面积、表面曲率和三维尺寸等,进而计算砂粒的三维球度、圆度和伸长率等形态表征参数。结果表明,当球谐函数阶达到15时,其重构的砂粒基本形状和表面纹理均与真实砂粒非常接近;近海石英砂在水流搬运和磨蚀的作用下颗粒形态较为规则和圆滑,球度和圆度较大,而风化花岗岩残积砂则在物理风化和剥蚀作用下颗粒形态较为复杂和粗糙,球度和圆度较小;而这两种地质作用对砂土颗粒的伸长率则没有明显的影响。     

石灰岩发育土壤团聚体形成机制研究

土壤团聚体是土壤最基本的结构单元。为了解岩溶地区石灰岩发育土壤团聚体的形成机制,选择贵阳市花溪区花溪水库石灰岩所发育的土壤为材料,采用干、湿筛法,分析团聚体颗粒的分级情况,并比较拆分有机质与钙镁铁铝离子间连接后四种离子含量的变化以及团聚体各粒级含量的变化。结果显示:团聚体是由细小颗粒在胶结物质有机质与钙镁铁铝离子结合下形成微团聚体,进一步形成更大粒级的团聚体,最后在分子力的作用下粘结土粒或者其他团聚体形成完整的团聚体结构;有机质与钙离子的结合是团聚体形成的主要胶结物质,其次为有机质与镁铁离子的结合,有机制与铝离子的结合作用不大,这与石灰岩矿物主要是碳酸钙有关;研究区发育土壤大粒级水稳性团聚体含量相对较高,土壤抗蚀性好,抵抗侵蚀能力强。      

Discrete numerical modeling of particle transport in granular filters

Granular filters are an essential component in earth dams to protect the dam core from seepage erosion. This paper uses the particle flow method (PFM) to study the mechanism of particle transport in a base soil–filter system. The distributions of the eroded base-soil particles in different filters are traced and analyzed. The eroded mass and intruding depth of the eroded particles into the filters are obtained under different times and hydraulic gradients. The simulation results show that the eroded mass and intruding depth of the base-soil particles into the filter are related to the representative particle size ratio of the base soil to the filter, hydraulic gradient and erosion time. The numerical predictions are also compared with the empirical filter design criterion. The results show that the particle flow model provides an effective approach for studying the filtration micro-property and the erosion mechanism in a base soil–filter system, which is useful for filter design.     

颗粒体双轴加载双向流动力链演化光弹试验研究

颗粒集合体在外力作用下,颗粒间产生复杂的接触力链效应。为了揭示和描述颗粒集合体力链形成、发展过程以及力链分布形态,基于光弹材料受力产生光学条纹图像的原理,研发出能够使颗粒实现双轴加载和双向流动的颗粒光弹试验装置。通过不同工况条件下的颗粒流动光弹试验,初步反映出颗粒集合体流动产生力链的发育过程和分布形态,即经过颗粒集合体的流动其流动口上部会形成一个拱结构,其可以对上部颗粒体进行支撑以保持上部结构的稳定。为研究不同背景条件下颗粒流力链结构和颗粒集合体细观力学行为,特别是颗粒双向可流动性设计为实际工程应用提供了基础试验方法。     

A new fractal modification of ultrasonic attenuation model for measuring particle size in mineral slurries

Weight percentages of different size incremental particles in a mineral slurry is integrated into the ultrasonic attenuation model to derive a relation between ultrasonic attenuation and particle sizes. However, in the inertial and scattering regimes of frequency–radius space, irregularity and aggregation of particles can results in values of ultrasonic attenuation that are significantly different from those predicted by the derived model, which is based on the assumption of separated smooth spherical particles in mineral slurries. Experimental attenuation data obtained previously from mineral slurries of iron ores particles are compared with predicted values. It is shown that there is a negligible difference between predictions and experimental data. A new modification of theoretical model for ultrasonic attenuation is derived. The theory uses ωτ_v or κR as a fractal scale. It requires an empirical determination of the difference between the fractal dimension of the measured mineral slurry and that of a hypothetical slurry of spheres with the same particle size distribution. The new fractal modification of ultrasonic attenuation model is found to enable better agreement with measured attenuation as a function concentration for irregular particles than the theoretical model. Moreover, the fractal approach is found to discriminate between the effects of particle irregularity and aggregation.     

含石量和颗粒破碎对土石混合料强度的影响研究

The characteristics of particle breakage and shear strength of soil-rock aggregate with six rock contents under six normal pressures were studied from macro and mecro perspectives by large-scale direct shear test, particle observation test and particle sieving test. The relationship between macroscopic shear strength properties and mecroscopic particle breakage characteristics was established, thus further revealing the influence mechanism of rock content and particle breakage on the shear strength characteristics of soil-rock aggregate. The results showed that particle breakage mainly occurred near the shear plane. The breakage morphology can be divided into surface grinding, local fracture, complete fracture and complete breakage, resulting from the stress concentration caused by uneven contact forces between particles. Due to particle breakage, the content of fine particles increased, coarse grains decreased, and intermediate grains fluctuated. The relative particle breakage Br increased with the increase of normal pressure ?n or rock content P5, which accorded with the function of two variables. With the increase of normal pressure ?n, the shear strength τ increased nonlinearly and met the modified M-C strength criterion. When the rock content P5 increased, the cohesive force c0 of soil-rock aggregate decreased, the internal friction angle ?0 of soil-rock aggregate increased, and the non-linear parameter Δ? increased. Particle breakage was the direct cause of non-linear strength characteristics of soil-rock aggregate.     

Evaluation of image analysis methods used for quantification of particle angularity

Angularity is an important parameter in the characterization of particle morphology that is used to interpret the transport history of particles in sedimentary deposits. In the past, visual classification using silhouette charts was widely used to determine particle angularity, but this approach is subjective and time‐consuming. With advances in modern image analysis techniques and low‐cost software packages, it is possible to rapidly quantify particle angularity more objectively than using visual classification methods. This study re‐examines the performance of three existing image analysis methods and one new image analysis procedure, applied to six rock and sediment samples that were visually different in angularity. To facilitate comparison between the angularity results, measurements were reduced to rankings for each aggregate sample. These results show that the four image analysis methods rank the angularity of the samples differently, and that none rank the mean angularity index in the same order as the angularity ranking using visual classification. Therefore, further research is needed to develop an image analysis method that can quantify the angularity of sedimentary particles more precisely.     

A non-linear numerical model for soil mechanics

A new computer program (CONBAL-2) is developed for 2D numerical simulations of granular soil by random arrays of spheres. CONBAL-2 uses the discrete-element method and is based on 3D program TRUBAL, previously presented by Cundall. As in TRUBAL, the new program models a random array of elastic spheres in a periodic space. The main modification of TRUBAL is the implementation by the authors of a rigorous solution for the force–displacement relation at the interparticle contacts. This force-displacement relation is a function of the elastic constants, friction coefficient and sizes of the spheres, with the properties of quartz used to simulate sand. Other specific features of CONBAL-2 include its 2D character, the lack of particle rotation and its capability to simulate shear loading on any plane. Simulated laboratory test results are presented using CONBAL-2 and several random arrays of 531 spheres having two particle sizes. These simulations include monotonic loading drained and undrained (constant volume) ‘triaxial’ experiments, as well as a cyclic-loading, constant-volume ‘torsional shear’ test. The stress–strain curves, effective stress paths, volume changes, as well as the ‘pore water pressure’ build-up behaviour obtained in the simulations compare favourably—qualitatively and in some aspects quantitatively—with similar laboratory results on sands. However, the simulated soil is somewhat stiffer and stronger due to the perfectly rounded particles, limited range of grain sizes, lack of particle rotation and 2D character of the model.     

The use of the fractal dimension to quantify the morphology of irregular-shaped particles

For several decades, sedimentologists have had difficulty in obtaining an efficient index of particle form that can be used to specify adequately irregular morphology of sedimentary particles. Mandelbrot has suggested the use of the fractal dimension as a single value estimate of form, in order to characterize morphologically closed loops of an irregular nature. The concept of fractal dimension derives from Richardson's unpublished suggestion that a stable linear relationship appears when the logarithm of the perimeter estimate of an irregular outline is plotted against the logarithm of the unit of measurement (step length). Decreases in step length result in an increase in perimeter by a constant weight (b) for particles whose morphological variations are the same at all measurement scales (self-similarity). The fractal dimension (D) equals 1.0-(b), where b is the slope coefficient of the best-fitting linear regression of the plot. The value of D lies between 1.0 and 2.0, with increasing values of D correlating with increasing irregularity of the outline. In practice, particle outline morphology is not always self-similar, such that two or possibly more fractal elements can occur for many outlines. Two fractal elements reflect the morphological difference between micro-scale edge textural effects (D₁) and macro-scale particle structural effects (D₂) generated by the presence of crenellate-edge morphology (re-entrants). Fractal calibration on a range of regular/irregular particle outline morphologies, plus examination of carbonate beach, pyroclastic and weathered quartz particles indicates that this type of analysis is best suited for morphological characterization of irregular and crenellate particles. In this respect, fractal analysis appears as the complementary analytical technique to harmonic form analysis in order to achieve an adequate specification of all types of particles on a continuum of irregular to regular morphology.     

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。     

泥石流浆体与大颗粒冲击力特征的试验研究

开展了密度为1 400～2 200 kg/m3的泥石流浆体、浆体与大颗粒混合流体的冲击力试验,获取了流速为2.8～4.9 m/s条件下31组冲击力试验数据。采用小波分析方法有效地去除了冲击力数据中的噪声信号,依据离散傅里叶变换（FFT）为基础的频谱分析结果,将低频泥石流浆体冲击和高频大颗粒冲击的临界频率值界定为2 Hz,实现了浆体和大颗粒冲击信号的分离。目前水动力学公式中待定系数α缺乏统一的确定方法,以不同地区157组泥石流观测和试验数据为基础,建立了待定系数?与流体Fr数的幂函数关系,形成可表征不同流态,且弱化尺度效应的浆体动压力计算公式。与泥石流浆体平滑信号相比,大颗粒冲击压力具有一定随机性。泥石流大颗粒冲击次数与频率随大颗粒的质量比增加而增大,其质量比从0.05增至0.21时,冲击总次数从1 305次增至2 838次,冲击频率从82次/s增至195次/s,且龙头段大颗粒的冲击频率高于后续泥石流体。测得大颗粒的压力约为60 kPa,是相同密度和流速下浆体动压力的3倍。随着大颗粒比例的增加,上部1#和2#传感器测得大颗粒冲击频率增加量明显高于下部3#～6#。说明随着流体中大颗粒比例上升,颗粒物质多集中于泥石流上部或表层运动,也佐证了泥石流运动中大颗粒多集中在龙头顶部的认识。对大颗粒和浆体冲击规律的分析可为固液两相流运动机制研究和防治工程设计以及承灾体易损性定量评估提供合理参数。     

How basin model results enable the study of multi-layer aquifer response to pumping: the Paris Basin, France

The Albian aquifer of the Paris Basin (France) has been exploited since 1841 and shows drastic drawdown. A three-dimensional (3D) groundwater flow model is used to study the hydrodynamic response of the multi-layered aquifers to pumping activity in the Albian, at basin scale over 167 years. This 3D flow model uses geometry and hydrodynamic parameter distributions that are inherited from a genetic approach through basin modelling, the basin model creating a geometric pattern of hydrodynamic properties constrained by geological history. The paper aims to promote the use of the basin model approach (long time scale, 248 Ma) for the study of deep-aquifer response to anthropogenic perturbation (short time scale, 167 years) in situations for which hydrodynamic data are scarce but geological data are numerous. The results show that parameter distribution is insufficient to reproduce the Albian aquifer behaviour, notably highlighting a different meaning of the specific storage coefficient between basin modelling and groundwater-flow modelling. Dividing the storage coefficient by 100 and including available transmissivity data significantly improved the model/data comparison. The potential impact on a deep aquitard is then discussed. This study sheds light on the advantages and limitations of the basin model approach for groundwater-flow modelling in 3D.     

Population balance in confined comminution using a physically based probabilistic approach for polydisperse granular materials

A novel, simplified approach is presented in order to compute variations of grading in granular assemblies during confined comminution under quasi‐static compression. The method is based on a population balance equation and requires a breakage probability, considered here as a probabilistic phenomenon that takes into account the particle strength and the loading condition of individual grains. Under basic assumptions, a simple breakage probability can be defined in order to get a valuable result for engineering applications and powder technology. The size effect in the strength of individual particles is introduced according to Weibull's theory. The particle loading and the cushioning effect in the granular packing are accounted for by considering the orientations of the contact forces obtained from 3D discrete element method simulations of highly polydisperse materials. The method proposed could have a value for engineering purposes in powder technology and geomechanics and gives a general framework for further research developments based on population balance. Copyright © 2016 John Wiley & Sons, Ltd.     

Structure of sediments of kaolinite

In an assembly of clay particles placed in a fluid, each particle is typically subjected to: (1) double-layer repulsive forces; (2) van der Waals attractive forces; and (3) contact mechanical forces. The study presented here concerns an approximate, quantitative analysis of clay suspensions, with considerations to the first two - the physico-chemical forces. Using recent theories to calculate the physico-chemical forces between two clay particles in an approximate model of an assembly, the equilibrium void ratio of a clay suspension is computed. The mechanical forces are ignored in the analysis. The results serve to verify the validity of physico-chemical theories employed and help interpret experimental data more fundamentally in terms of the system variables.