Examination of the Response of Regularly Packed Specimens of Spherical Particles Using Physical Tests and Discrete Element Simulations

Significant insight into the response of granular materials can be gained by coupling accurately controlled physical tests with complementary discrete element simulations. This paper discusses a series of triaxial and plane strain laboratory compression tests on steel spheres with face-centered-cubic and rhombic packings, as well as discrete element simulations of these tests. The tests were performed on specimens of uniform-sized steel balls and on specimens of steel balls with specified distributions of ball diameters. The packing configurations are ideal and differ considerably from real sand specimens, however, studies of such idealized granular materials can yield considerable insight into the response of granular materials and the capability of discrete element simulations to capture the response. The differences in response for the two packing configurations considered illustrate the importance of fabric. The numerical simulations captured the observed laboratory response well if the particle configurations, particle sizes, and boundary conditions were accurately represented. However, the postpeak response is more difficult to capture, and it is shown to be sensitive to the coefficient of friction assumed along the specimen boundaries. The simulations of the tests on the nonuniform-sized specimens demonstrated a clear correlation between strength and coordination number.     

Effect of Particle Shape on Interface Behavior of DEM‐Simulated Granular Materials

This paper presents a detailed computational investigation of the effect of particle shape on the interface shear behavior of granular materials. The discrete element method (DEM) using clusters to model rough particles is used, expanding the procedure introduced in an earlier paper by Jensen et al. [1]. Seven new cluster shapes (i.e., particle configurations) of varying degrees of roughness are presented herein, and numerical experiments simulating ring shear tests are made using these clusters. From these simulations, the effect of particle shape on void ratio (e) and interface angle of friction between soil and structure surface (δ) is reported. Particle shape characteristics include roundness, angularity, and surface roughness. The results of numerical simulations using the newly formed cluster shapes are in very good qualitative agreement with laboratory tests. Simulation results showed that the void ratio of a particle mass increased as the angularity or roughness of the particles increased. They also showed an increase in interface shear strength between perfectly round DEM particles and the more angular cluster shapes, but no systematic correlations with the various definitions of particle shape parameters was found. It may be necessary to use greater accuracy in modeling the size and shape distributions of a natural medium to further investigate the influence of particle shape on interface friction. The simulations also successfully reflected the relationship between interface friction angle and structure surface roughness as demonstrated in recent physical experiments. The simulations comparing initially “dense” media to initially “loose” media demonstrated behavior that is similar to the behavior of a natural sandy soil observed in experiments.     

Modified Direct Shear Test for Anisotropic Strength of Sand

This paper presents a simple method to estimate the directional dependency of granular soil strength using a modified shear box and a special specimen preparation procedure. This method is used to investigate the strength anisotropy of granular materials with particle shapes varying from spherical to angular. The experimental results show that the friction angle of granular materials varies with the orientation of shear plane relative to the bedding plane, and the degree of anisotropy is affected by particle shape. Comparison of the data from direct shear tests in this study with those of plane strain and torsional simple shear tests in the literature shows that direct shear using the modified direct shear box can reasonably capture the directional dependency of the friction angle for cohesionless materials.     

Behavior of Ellipsoids of Two Sizes

The influence of particle shape on granular material response is examined by using the discrete element method. Triaxial drained and undrained tests were performed on specimens of ellipsoids of two sizes. The triaxial test boundary conditions were simulated with a recently developed boundary mechanism. Different loading paths including axial compression, axial extension, lateral compression, and true extension were employed. The specimens were composed of 1,170 ellipsoids having two types of particles. The specimen is made up of 50% by weight of Type I particles that have an aspect ratio of 1.2. The aspect ratio of the Type II particles varies between 1.5 and 2. The specimens were consolidated isotropically before shearing. Comparing with the behavior of specimens of mono-size particles, a higher friction angle and a more complex particle shape effect were observed. The friction angles from the drained tests (axial extension, true extension, and lateral compression tests) were similar and the values are higher than that of the axial compression test. All simulated results are in good agreement with laboratory observation of sands.     

Triaxial Test Simulations with Discrete Element Method and Hydrostatic Boundaries

A new boundary condition has been developed for the discrete element method. This boundary is different from the conventional periodic, rigid, or flexible boundries. This new boundary mechanism was developed to simulate triaxial tests. The new boundary, hydrostatic boundary, simulated the chamber fluid but not the rubber membrane. When a particle (ellipsoids in our simulations) contacts the hydrostatic boundary, pressure is developed. The interaction between the particle and the boundary is calculated analytically based on geometry. This hydrostatic boundary condition was implemented into an existing ellipsoidal discrete element code. Triaxial compression drained tests were performed with both periodic and hydrostatic boundaries. The result showed an increase in friction angle over the values observed from the periodic boundary mechanism. The result also closely resembles the experimental triaxial data. Thirteen specimens were generated and were used to investigate the following variables: particle shape, specimen size, and void ratio. A unique slope of the linear relationship between friction angle and void ratio was identified for monosize specimens of different particle shapes. It is found that the friction angle decreases as the aspect ratio increases provided that the void ratio of the two specimens is the same. The friction angle is linear proportional to the coordination number for monosize specimens regardless the specimen size. Also, the specimen size does not influence the behavior of two-size specimens.     

八钢COREX多粒度非球形颗粒混合堆积的研究

本文以八一钢厂COREX当地原料(球团矿、焦炭和煤)为研究对象,采用物理模拟和数值模拟方法,对多粒径非球形颗粒混合堆积行为进行了研究.首先通过物理实验确定各原料的物性参数,如粒度分布、表观密度、堆密度、静摩擦系数、恢复系数、弹性模量、剪切模量和泊松比等;其次通过物理实验和由组合球构建真实颗粒形状的数值模拟对二元混合堆积角进行研究,在两种结果相吻合的前提下,获得二元混合物之间的滚动摩擦系数,且利用该系数进一步研究三元混合堆积效果.研究结果表明:由二元混合获得的系数可成功应用在三元混合模型之上,最终模型获得了球团矿、多粒度焦炭、多粒度煤两两之间混合堆积及三者之间混合堆积的料堆休止角及内部空隙度信息,为八钢使用当地物料进行装料操作提供了详细的参考数据.     

Anisotropy-Based Failure Criterion for Interphase Systems

This paper presents a methodology for estimating the shear strength of interphase systems composed of granular materials and planar inclusions having various degrees of roughness. Existing empirical and semiempirical relationships between strength and surface roughness do not appear to be general and are unable to account for surface-particle interactions at the appropriate scales. The proposed method is based on the contact force anisotropy of those particles that touch the inclusion surface. It was developed using two-dimensional discrete element method simulations of interphase systems constructed within a direct interface shear test device. Particles consist of polydisperse and monodisperse spheres of constant median grain diameter. Surface roughness was varied by using profiles with regular and random asperities, and profiles of manufactured surfaces. Results indicate that the magnitude and direction of average contact total force at the interface controls strength. A bilinear relationship, independent of particle to surface friction coefficient, exists between the principal direction of contact total force anisotropy and strength. Results using the proposed criterion are in good agreement with laboratory results using spheres and subrounded sand.     

Micro-Macro Quantification of the Internal Structure of Granular Materials

We have attempted a multiscale quantification of the internal structure of granular materials. The internal structure of granular materials, i.e., the geometrical information on granular particles and their spatial arrangement, was described mathematically on the particle scale using Voronoi–Delaunay tessellations. These tessellations were further modified into two cell systems: a solid cell system and a void cell system, with the internal supporting structure properly reflected. By doing so, the two cell systems were geometrically and physically significant. Taking solid/void cells as the microscopic basic elements, the behavior of granular materials was expressed as the volumetric average of the microcell behavior. Macroscopically, the internal structure could be characterized by the statistical measures from the geometry of the microcells. Our approach was used to investigate the anisotropic behavior of granular materials. A study on the void cells explains how the spatial arrangement affects the strength and dilatancy of granular materials. A new anisotropic fabric tensor was defined based on the void cell anisotropy. The correlation between the anisotropic fabric tensor and the macro behavior of granular materials was verified with numerical simulations. The results showed that the new material anisotropic tensor is a more effective definition than the existing ones based on particle orientations and contact normals.     

Effect of Interparticle Friction on the Cyclic Behavior of Granular Materials Using 2D DEM

This study presents the influence of the interparticle friction angle on the cyclic behavior of granular materials using the two-dimensional (2D) discrete-element method (DEM). The numerical sample was modeled with oval-shaped particles, whereas the isotropically compressed dense sample was prepared from the initial sparse sample using periodic boundaries. Biaxial cyclic shear tests were simulated with different interparticle friction angles. It was noted that the width of the stress-strain cyclic loops becomes thin when the interparticle friction angle increases. It was also noted that the induced fabric anisotropy is more pronounced during unloading than loading. Moreover, a strong correlation between macro- and microquantities was observed for strong contacts during cyclic loading.     

基于离散元的烧结梭式布料仿真

摘要：烧结梭式布料对烧结台车宽度方向上混合料的均匀分布起着重要作用,根据某钢铁企业烧结机梭式布料器的实际尺寸建立了三维模型,使用EDEM软件对带前挡板的梭式布料器的布料过程进行了仿真模拟。结果表明：梭式布料器前挡板角度为90°,梭式布料器在料仓两侧的停留时间应当尽量一致,当停留时间均为7s时,料面形状较平整,宽度方向上不同尺寸的颗粒在不同区域的质量分数标准差最低达到0.001,但颗粒在料仓两侧的质量差异较大,有可能造成烧结物料分布不均;梭式布料器前挡板的角度为60°时,颗粒在不同区域的质量分数标准差为0.006,料面形状的平整度最高,且最小粒度的颗粒在料仓两端所占比例最高,可以有效减小“气流边缘效应”,提高烧结均匀性。     

Micromechanical Analysis of the Shear Behavior of a Granular Material

A distinct element analysis of the behavior of a granular material was performed by simulating direct shear tests of a dense and a loose 2D sample of 1,050 cylinders. Macroscopic results exhibit typical features of the shear response of granular materials: a perfect plasticity state that does not depend on the initial density, a peak stress and a dilatant behavior in the case of the dense sample, and a contractant behavior of the loose sample. A micromechanical analysis of the shear behavior was carried out based on the simulation results. Using the particle displacements and rotations, a shear band is located within the sample. Special attention is focused on the evolution of particle∕particle contact orientation as well as on the direction of particle∕particle contact forces. The shear process induces a clear change of contact and contact force orientations. A strong correlation between the induced anisotropy of the microstructure and the macroscopic loading is evident in the simulation results.     

Capturing Nonspherical Shape of Granular Media with Disk Clusters

In discrete numerical modeling of granular materials, idealization of individual particles is required, as it is not practical to model a large number of particles, each with its actual shape and size. To minimize computation times, researchers often use two-dimensional, circular elements. However, biaxial and direct shear tests on such specimens result in low strengths compared to granular materials, due, in part, to excessive rolling of the perfectly circular particles. In this paper, a new particle type, disk clusters, is presented. A disk cluster is a group of circular disks permanently connected to form an irregularly shaped particle that more closely represents the shape of granular materials and has less tendency to rotate. Development and implementation of disk cluster particles into a discontinuous deformation analysis program is presented. Validations of the mechanics of a single disk cluster, biaxial shear, and anchor pullout simulations illustrate the usefulness of this new particle type.     

Microscopic Evaluation of Strain Distribution in Granular Materials during Shear

The evolution of local strains during shear of particles of a granular material is presented in this paper. A cylindrical specimen composed of 6.5-mm spherical plastic particles was loaded under an axisymmetric triaxial loading condition. Computed tomography (CT) was used to acquire three-dimensional images of the specimen at three shearing stages. The high-resolution CT images were used to identify the 3D coordinates of 400 particles. Nine strain components (normal, shear, and rotation), rotation angles, and local dilatancy angles for particle groups were calculated, and their frequency distribution histograms are presented and discussed. It was found that there is no preferred shear direction, and the standard deviation values for shear strain components (εxy, εxz, and εyz) were almost equal for the specific test shearing stage. Shear strains as high as 25.6% were recorded for some particle groups. Furthermore, granular particle groups rotated in the 3D space with almost equal amounts of rotation strains when loaded under axisymmetric triaxial condition. Rotation strain values are very close to the corresponding shear strains. Compared to particle sliding, rotation plays a major role in the shearing resistance of granular materials. The cumulative vertical rotation angles can be as high as 38° and the horizontal rotation angles have values as high as 60°. The statistical distributions of the local dilatancy angle (ψ1) of particle groups were calculated and found to be increasing as shearing continues. The “global” dilatancy angle value is very close to the mean local ψ1 during the first stage of shearing (i.e, when global εz = ?7.3%)     

Constriction-Based Retention Criterion for Granular Filter Design

The filter design criteria in practice are currently based on laboratory tests that were carried out on uniform base soil and filter materials. These criteria mostly involve specific particle size ratios, where the system of base soil and filter is represented by some characteristic particle sizes. Consequently, these criteria have limitations when applied to nonuniform materials. In filters, it is the constriction size rather than the particle size that affects filtration. In this paper, a mathematical procedure to determine the controlling constriction size is introduced, and subsequently, a constriction-based retention criterion for granular filters is presented. The model also incorporates the effect of nonuniformity of base soil in terms of its particle size distribution, considering the surface area of the particles. The proposed retention criterion is verified based on experimental data taken from past studies plus large-scale filtration tests carried out by the authors. The model successfully and distinctly demarcates the boundary between effective and ineffective filters in the case of cohensionless base soils.     

Visualization and Analysis of Microstructure in Three-Dimensional Discrete Numerical Models

A computer program has been developed to allow for the virtual slicing of irregularly spaced and irregularly shaped three-dimensional image data. The program was used to virtually slice three-dimensional particle assemblies from discrete element method (DEM) simulations, allowing, for the first time, direct comparison to two-dimensional slices extracted from solidified physical specimens. Based on slices obtained from the numerical specimens, it is possible to compare quantitatively numerical microstructure directly to its physical analog, which should lead to greatly improved calibrations of granular mechanics models, and could facilitate the calibration of models across all scales of interest rather than solely at specimen boundaries. Improved confidence in the ability of the DEM to realistically simulate the microstructure of granular assemblies (through improved multiscale calibration) should result in increased confidence in microstructural parameters measurable in numerical simulations but inaccessible in the laboratory. Algorithm development within the framework of the open-source Visualization Toolkit is described and performance of the algorithm is quantified for two platforms. Results from virtual slices of a test assembly with regular particle packing are verified against known analytical solutions. A slice of a more complex assembly comprised of nearly 40,000 spheres is quantified statistically and compared to an analogous slice from a physical specimen of uniform sand.     

Stochastic Modeling of Load-Induced Settlement in Loose Granular Materials

The response of loose cohesionless granular material to surface applied loads is investigated from the viewpoint of probabilistic mechanics of particulate media. A model is proposed that is based on the combined propagation of intergranular forces and an excess volume of voids. In this regard, it provides a bridge between earlier theories developed independently for the diffusion of stresses and for the propagation of settlements. In its general formulation, the theory can model three-dimensional, transient effects. However, the model is believed to be limited to normally consolidated or noncompacted, fully drained or dry, granular materials that do not exhibit dilatancy effects. The derived numerical modeling of steady state deflection patterns under a rigid footing is found to be in good agreement with x-ray images of laboratory model tests using noncompacted silt. The proposed theory recognizes the discrete and inherently random nature of natural granular materials such as cohesionless soils and builds upon these fundamental characteristics to predict responses of such materials to boundary applied load. This is achieved by modeling intergranular force and excess pore volume propagation as Markovian diffusion-advection processes. This approach, which departs from traditional continuum mechanics models, seems to have potential for addressing some of the challenging aspects of granular material mechanics in lunar or Martian environments.     

Direct Shear Tests on JSC-1A Lunar Regolith Simulant

A series of direct shear tests were conducted on the JSC-1A lunar regolith simulant in a 101.6-mm- (4-in.-) diameter container. The direct shear test provides a unique mode of failure that aids the development of excavation tools for the Moon. Relative density and normal load were varied to study the strength behavior of such granular material at peak and critical state conditions. The values of the internal friction angle ranged from 30 to 70°. A relationship between the internal friction angle of the direct shear and the published triaxial compression test results is presented. Additionally, the measured dilatancy angle is related to the difference in peak and critical state stress friction angles.     

基于PEM-JFEM方法的节理岩质边坡稳定性评价

以赞比亚一露天铜矿南帮边坡(矿体下盘)为研究对象,将Rosenbluth点估计方法与节理有限元方法相结合应用于该节理发育的岩质边坡稳定性评价中.建立以边坡岩体材料强度参数(内摩擦角和黏聚力)为输入变量,安全系数为输出变量的概率模型,点估计状态函数的求解过程引入节理有限元方法.通过现场节理及结构面调查,建立边坡节理有限元模型求解边坡安全系数,得到基于安全系数的边坡变形破坏概率统计指标,对边坡稳定性进行了概率分析,分析结果与现场失稳情况一致.该方法既考虑了岩体材料参数在赋值过程中实际存在的不确定性,同时也考虑了节理岩质边坡的节理属性,充分体现了岩层接触作用的非线性关系,使得对节理岩质边坡的稳定性评价更加合理.      

Effect of Particle Grading on the Response of an Idealized Granular Assemblage

The effects of particle-size distribution on a granular assemblage’s mechanical response were studied through a series of numerical triaxial tests using the three-dimensional (3D) discrete-element method. An assemblage was formed by spherical particles of various sizes. A simple linear contact model was adopted with the crucial consideration of varying contact stiffness with particle diameter. Numerical triaxial tests were mimicked by imposing axial compression under constant lateral pressure and constant volume condition, respectively. It was found that an assemblage with a wider particle grading gives more contractive response and behaves toward strain hardening upon shearing. Its critical state locates at a lower position in a void ratio versus mean normal stress plot. Nevertheless, no obvious difference in the critical stress ratio was shown. Model constants in a simple but efficient phenomenologically based granular material model within the framework of critical-state soil mechanics were calibrated from the numerical test results. Results show that some model constants exhibit linear variation with the coefficient of uniformity whereas others are almost independent of particle grading. This investigation provides an opportunity to better understand the implications and meanings of model constants in a phenomenologically based model from the microscale perspective.     

DEM Simulation of Particle Damage in Granular Media — Structure Interfaces

Using the discrete element method (DEM) with clustering, a novel means of numerically modeling damage of particles is presented. Damage, such as grain crushing, is treated by allowing clusters to break apart according to a failure criterion based upon sliding work. If the accumulated work done on an individual DEM particle of a cluster exceeds a threshold, that particle is allowed to break from the cluster. A value for the critical energy density is determined by comparing the degree of particle breakage from numerical simulations to data from laboratory tests. Numerical simulations were also conducted to determine the impact of particle damage on interface behavior. It was found that a very distinct shear zone was evident when particle damage was considered and that this occurred without significant reduction of the maximum shear strength of the medium. Also, the degree of damage was shown to be related to the angularity of the clusters.