DEM study of the shear behavior and formation of shear band in biaxial test

This paper aims to study the shear behavior of granular matter by DEM simulations. Granular samples are prepared by automatic clump generation algorithm to create particles of irregular shapes. Simulations of the biaxial test with membrane boundary condition are used to test the shear behavior of samples. A new method for computing sample volume in membrane boundary condition is proposed. Deviatoric stress and volumetric strain curves are plotted to describe contracting-dilatancy of granular materials during the shearing stage. Formation of the shear band is studied from particle rotation and particle displacement fields. The influence of confining pressure, initial porosity, and friction coefficient on the development of shear band are studied. Lower confining pressure, higher initial porosity can be resulted in later formation of shear bands.     

Study of the shear behavior of binary granular materials by DEM simulations and experimental triaxial tests

This paper aims at studying the shear behavior of mixtures of fine and coarse particles by classical triaxial tests. The work is performed both on experimental tests and computer simulations by discrete element method. The comparisons between experimental and simulation results on monosized and binary samples show that the DEM model can reproduce deviatoric curves satisfactorily in experimental conditions. The shear behavior of monosized and binary systems with the same initial void ratio differs significantly, suggesting that the state of compaction of the system is more influential than the initial void ratio. Comparison between compacted and uncompacted samples confirms that compaction increases the shear strength of granular matter. At the particle scale, the coordination number decreases with the augmentation of the volume fraction of coarse particles. The average rotation velocity of fine particles is higher than coarse particles, but their particle stress tensor is smaller than coarse ones.     

DEM simulation of the shear behaviour of breakable granular materials with various angularities

Particle shape is an important factor that affects particle breakage and the mechanical behaviour of granular materials. This report explored the effect of angularity on the mechanical behaviour of breakable granular materials under triaxial tests. Various angular particles are generated using the quasi-spherical polyhedron method. The angularity α is defined as the mean exterior angle of touching faces in a particle model. A breakable particle is constructed as an aggregate composed of coplanar and glued Voronoi polyhedra. After being prepared under the densest conditions, all assemblies were subjected to triaxial compression until a critical state was reached. The macroscopic characteristics, including the shear strength and dilatancy response, were investigated. Then, particle breakage characteristics, including the extent of particle breakage, breakage pattern and correlation between the particle breakage and energy input, were evaluated. Furthermore, the microscopic characteristics, including the contact force and fabric anisotropy, were examined to probe the microscopic origins of the shear strength. As α increases, the peak shear strength increases first and then remains constant, while the critical shear strength generally increases. Assemblies with larger angularity tend to cause more serious particle breakage. The relative breakage is linearly correlated with α under shear loading. Compared with unbreakable particles, the peak shear strength and the critical volumetric strain decline, and the degree of decline linearly increases with increasing α.     

Discrete element analysis for shear band modes of granular materials in triaxial tests

The discrete element method (DEM) is adopted to simulate the triaxial tests of granular materials in this study. In the DEM simulations, two different membrane-forming methods are used to generate triaxial samples. One method is to pack the internal particles first, then to generate the enclosed membrane; the other is to generate the internal particles and the enclosed membrane together. A definition of the effective strain, which combines microscopic numerical results with macroscopic expression in three-dimensional space, is presented to describe the macroscopic deformation process of granular materials. With these two membrane generation methods, the effective strain distributions in longitudinal section and transverse section of the triaxial sample are described to investigate the progressive failure and the evolution of the shear bands in granular materials. Two typical shear band failure modes in triaxial tests are observed in the DEM simulations with different membrane-forming methods. One is a single shear band like a scraper bowl, and the other is an axial symmetric shear band like two hoppers stacking as the shape of rotational “X” in triaxial sample. The characteristics of the shear bands during the failure processes are discussed in detail based on the DEM simulations.     

Influence of relative density on granular materials behavior: DEM simulations of triaxial tests

The rheological behavior of non-cohesive soils results from the arrangement and complex geometry of the grains. Numerical models based on discrete element modeling provides an opportunity to understand these phenomena while considering the discrete elements with a similar shape to that of the grains the soil is composed of. However, dealing with realistic shapes would lead to a prohibitive calculation cost. In a macroscopic modeling approach, simplification of the discrete elements’ shape can be done as long as the model can predict experimental results. Since the intrinsic non-convex geometry property of real grains seems to play a major role on the response of the granular medium, it is thus possible to keep this geometrical feature by using cluster of spherical discrete elements, which has the advantage to reduce dramatically the computation cost. Since the porosities found experimentally could not always be obtained with the numerical model—owing to the huge difference in shape, the notion of relative density, which requires a search for minimum and maximum porosities for the model, was chosen to compare the experimental and numerical results. Comparing the numerical simulations with the experimental triaxial tests conducted with relative densities and different confining pressures shows that the model is able to predict the experimental results.     

Influence of particle shape on the shear behavior of superellipsoids by discrete element method in 3D

This paper aims to study the influence of particle shape on the shear strength of superellipsoidal particles by Discrete Element Method (DEM) simulations of triaxial tests in 3D. A total of forty-nine types of equiaxed superellipsoidal particles from three evolution paths have been created. The definition of effective porosity has been proposed. Our findings show that both the particle sphericity and roundness affect the shear strength of the superellipsoidal particle system. Under the mutual impact of initial porosity and particle shape, the simulation results of shear strength and volumetric strains present a trend of initially decreasing and subsequently increasing. The microstructure evolution of superellipsoidal particles during the shearing process is observed microscopically. The anisotropy of fabric reveals the mechanism of effective porosity and sphericity influencing the macroscopic shear strength at the particle scale.     

Experimental and numerical study of cylindrical triaxial test on mono-sized glass beads under quasi-static loading condition

This paper aims at studying the shear behavior of homogeneous granular materials by conventional triaxial test. The work is performed both in laboratory tests and by discrete element method simulations. Conventional triaxial tests are performed on glass beads packing, while a cylindrical rigid wall boundary condition based on lame formula and a series of procedures are proposed to simulate the conventional triaxial test. The experimental results on dry and saturated glass beads samples have been studied to find out the effect of saturation condition on the shear behavior. The comparisons between experimental and numerical results show that the numerical model can reproduce deviatoric curves satisfactorily in experimental conditions as long as experimental sample remains cylindrical. It correctly describes the volumetric strains of a numerical sample up to the peak value. Additionally, a parametric study on the influence of main micromechanical parameters has been carried out, which has been compared to experimental tests with glass beads of different textures. The comparison highlights the significant effect of friction coefficients and rolling resistance coefficients on global behavior of granular materials.     

Analysis of the influence of crushing on the behavior of granular materials under shear

The behavior of granular materials mainly depends on the mechanical and engineering properties of particles in its structural matrix. Crushing or breakage of granular materials under compression or shear occurs when the energy available is sufficient to overcome the resistance of the material. Relatively little systematic research has been conducted regarding how to evaluate or quantify particle crushing and how it effects the engineering properties of the granular materials. The aim of this study is to investigate the effect of crushing on the bulk behavior of granular materials by using manufactured granular materials (MGM) rather than using a naturally occurring cohesionless granular material. MGM allow changing only one particle parameter, namely the “crushing strength”. Four different categories of MGM (with different crushing strength) are used to study the effect on the bulk shear strength, stiffness modulus, friction and dilatancy angle “engineering properties”. A substantial influence on the stress–strain behavior and engineering properties of granular materials is observed. Higher confining stress causes some non-uniformity (strong variations/jumps) in volumetric strain and a constant volumetric strain is not always observed under large shear deformations due to crushing, i.e. there is no critical state with flow regime (with constant volumetric strain).     

DEM calibration of cohesive material in the ring shear test by applying a genetic algorithm framework

This research demonstrates capturing different stress states and history dependency in a cohesive bulk material by DEM simulations. An automated calibration procedure, based on the Non-dominated Sorting Genetic Algorithm, is applied. It searches for the appropriate simulation parameters of an Elasto-Plastic Adhesive contact model such that its response is best fitted to the shear stress measured in experiments. Using this calibration procedure, the optimal set of DEM input parameters are successfully found to reproduce the measured shear stresses of the cohesive coal sample in two different pre-consolidation levels. The calibrated simulation resembles the stress history dependent values of shear stress, bulk density and wall friction. Through the case study of the ring shear tester, this research demonstrates the robustness and accuracy of the calibration framework using multi-objective optimization on multi-variable calibration problems irrespective of the chosen contact model.     

Forces in piles of granular material: an analytic and 3D DEM study

We investigate the stress distribution at the base of a conical sandpile using both analytic calculations and a three dimensional discrete element code. In particular, we study how a minimum in the normal stress can occur under the highest part of the sandpile. It is found that piles composed of particles with the same size do not show a minimum in the normal stress. A stress minimum is only observed when the piles are composed of particles with different sizes, where the particles are size segregated in an ordered, symmetric, circular fashion, around the central axis of the sandpile. If a pile is composed of particles with different sizes, where the particles are randomly distributed throughout the pile, then no stress dip is observed. These results suggest that the stress dip is due to ordered, force contacts between equiheight particles which direct stress to the outer parts of the pile. Received: 14 June 2000     

Quantifying the effects of elongation and flatness on the shear behavior of realistic 3D rock aggregates based on DEM modeling

It is significant for industrial production and engineering practice to study the macro and micromechanical behaviors of realistic particles in nature. Based on the rock aggregates database obtained by 3D scanning, this study investigated the effect of particle shape on the shear behaviors of particles by discrete element method (DEM) modeling. First, 1200 rock particle models were acquired by white-light scanning, and the elongation index (EI) and flatness index (FI) of the 1200 particles were calculated. After initial dense samples were created for particles with specific EI and FI values by the isotropic compression method, all the samples were sheared in drained triaxial compression tests under a quasi-static condition. Then, the mechanical behaviors of the samples at the peak and critical states were analyzed. Meanwhile, the evolution of internal mechanical behaviors during the shearing of samples with different EI and FI values was evaluated. Finally, through the analysis of the stress-force-fabric relationship, the underlying mechanism explaining why the macroscale mechanical behaviors of samples were dominated by particle shape was revealed from the perspective of fabric anisotropy.     

Investigation on instability modes of sand under biaxial shearing accounting various specimen generation techniques in DEM

Instabilities in granular material usually initiate at the microscale due to the presence of internal heterogeneity arising from variation in the particle packing arrangement. The present work elucidates the effect of various specimen generation techniques adopted in DEM on the initial sample heterogeneity and its subsequent influence on the instability response of sand under biaxial shearing. Dense and loose specimens are prepared using five different specimen generation techniques and homogeneity within the specimens has been analyzed in terms of spatial variation of porosity, anisotropy in the contact force and fabric structure. The initiation and subsequent evolution of different instability modes during shearing have been examined based on the spatial porosity distribution, relative particle displacement and particle rotation. Localized instability mode has been observed to emerge in dense specimens in form of cross-type shear bands with varying inclination and thickness for these different specimen generation techniques. Porosity and particle rotation based instability prediction indicate a delayed onset of shear band in comparison to identifications from relative particle displacement and bifurcation of local strains. The loose specimen exhibits bulging type diffused instability accompanied by large relative particle displacement and rotation scattered across the specimen.     

The effects of tensile residual stress and sliding boundary on measuring the adhesion work of membrane by pull-off test

The adhesion work of flexible film, such as membrane, is always measured by pull-off test. In this kind of experiment, the tensile residual stress due to pretension during sample preparation and the sliding of the punch have a critical influence on the experimental results. Our study aims to examine the effects of tensile residual stress and sliding boundary. The analytical expressions for the effect parameters are obtained based on the energy criterion. From our quantitative analysis, we find that these effects should be taken into account in the future experiments.     

Determining a lower boundary of elasticity modulus used in the discrete element method (DEM) in simulation of tumbling mills

Discrete Element Method (DEM) simulations of industrial tumbling mills could involve millions of particles. Even with the considerable increase in the computational power, the simulations still require a large amount of time. Reducing the computational load by selecting a small value for the particle elasticity modulus to increase the time step has become a common approach. As the elasticity modulus decreases, the overlap required to provide the rebound force increases. The appropriate value of overlap is application-dependent and requires a detailed study to ascertain that the accuracy of the results do not adversely affected. In this study, a relationship incorporating particle density and mill diameter was proposed between the elasticity modulus and the interparticle overlap for tumbling mills. The effect of interparticle overlap on the accuracy of the simulated charge shape (i.e. toe and shoulder positions) by DEM was then investigated. A model tumbling mill (100 cm by 21 cm) with a transparent end wall was used to measure the actual charge trajectory by photography. A comparison of the DEM simulations with the model mill charge shape showed that when the overlap was assumed to be lower than the particle radius, the error was negligible. When the interparticle overlap became equal to the particle radius, the lower boundary of elasticity modulus and the maximum simulation speed was achieved. The speed was 102 times of the speed of simulation when an overlap equal to 0.01 of the particle radius was chosen.     

Improvement of pressure distribution to arbitrary geometry with boundary condition represented by polygons in particle method

The boundary condition represented by polygons in the moving particle semi‐implicit method can accurately represent geometries and treat complex geometry with high efficiency. However, inaccurate wall contribution to the Poisson's equation leads to drastic numerical oscillation. To address this issue, in this research, we analyzed the problems of the Poisson's equation used in the boundary condition represented by polygons. The new Poisson's equation is proposed based on the improved source term (Tanaka and Masunaga, Trans Jpn Soc Comput Eng Sci, 2008). The asymmetric gradient model (Khayyer and Gotoh, Coastal Engineering Journal, 2008) is also adopted to further suppress the numerical oscillation of fluid particles. The proposed method can dramatically improve the pressure distribution to arbitrary geometry in three dimensions and keep the efficiency. Four examples including the hydrostatic simulation, dam break simulation, and two complex geometries are verified to show the general applicability of the proposed method. Copyright © 2017 John Wiley & Sons, Ltd.     

On the validity condition of the chi-squared test in 2×2 tables

A 2×2 contingency table is usually analyzed by using the chi-squared asymptotic test, with Yates' continuity correction (c=n/2, wheren is the total size of sample). This correction is the correct one when the chi-squared test is an approximation to Fisher's exact (conditional) test. When the chi-squared test is used as an approximation to Barnard's exact (unconditional) test for comparing two independent proportions (two samples of sizen ₁ andn ₂) or for contrasting independence (one sample with a size ofn), the correctionc is different (c=1 ifn ₁≠n ₂ orc=2 ifn ₁=n ₂ in the first case;c=0.5 in the second). Whatever the case, it is traditional to affirm that the asymptotic test is valid whenE>5, whereE is the minimum expected quantity. Today it is recognized that this condition is too general and may not be appropriate. In the case of Yates' correction. Martín Andrés and Herranz Tejedor (2000) proved that the validity condition must be of the typeE>E ^* —whereE ^* is a known function depending on the marginals of the table—and that checking the validity of the asymptotic test is equivalent to checking the asymmetry of the base statistic (a hypergeometric random variable). In the present article the authors prove that this argument is valid for the other two continuity corrections, and moreover, that the valueE ^* is obtained for all three cases. Given that the functionE ^* reaches an absolute maximum, it can be affirmed that the three chisquared tests referred to are valid whenE<19.2, 14.9 or 6.2 (orE>8.1, 7.7 or 3.9 ifn≤500) respectively for the three previous models (although for the first model and the two-tailed testE>0 is sufficient). This research was supported by the Dirección General de Investigación (Spain). Grant BFM2000-1472.     

On the Cauchy principal value of the surface integral in the boundary integral equation of 3D elasticity

A simple demonstration of the existence of the Cauchy principal value (CPV) of the strongly singular surface integral in the Somigliana Identity at a non-smooth boundary point is presented. First a regularization of the strongly singular integral by analytical integration of the singular term in the radial direction in pre-image planes of smooth surface patches is carried out. Then it is shown that the sum of the angular integrals of the characteristic of the tractions of the Kelvin fundamental solution is zero, a formula for the transformation of angles between the tangent plane of a suface patch and the pre-image plane at smooth mapping of the surface patch being derived for this purpose.     

三维编织复合材料弹性性能数值预测及细观应力分析

基于考虑纤维束面接触的细观结构模型, 引入周期性位移边界条件, 采用细观有限元方法建立了材料的弹性性能预报模型。模型数值结果与试件实测数据吻合较好, 证明了该模型的合理有效性。经详细分析单胞在典型工况载荷作用下的细观应力分布及变形, 表明模型体现了周期性相邻单胞表面力和位移的连续性, 能获得单胞更为合理的细观应力应变场。      

Study of the origin of shear zones in quasi-static vertical chute flows by using discrete particle simulations

We perform discrete-particle simulations of vertical chute flows in the quasi-static regime using disk-like particles. The velocity profiles show a plug flow in the central region and shear zones next to the walls approximately 6 particle diameters wide regardless of bin width, as was observed experimentally. The stress distributions are in good agreement with the predictions of the continuum mechanics equations even for small systems (15 and 20 particle diameters wide) as those studied in the present work. Large stress fluctuations in space and time have been observed, these are mainly due to the inhomogeneity of the force network. It is observed in the simulations that the wall friction does not act homogeneously but it is concentrated at certain points on the wall depending on the local arrangement of the packing. Large stress zones or arches appear at these points of the wall. It is the formation and the way these arches collapse that seems to generate the shear zones. Based on this, a simple mechanism to explain the formation of the shear zone is proposed. The simulations have revealed other interesting features of the flow, particularly the presence of macroscopic fluctuations of velocity, in which large blocks of material move together showing sudden accelerations (corresponding to the collapse of the arches) and sudden decelerations (corresponding to the formation of the arches).     

Investigation of anti-plane shear behavior of a Griffith permeable crack in functionally graded piezoelectric materials by use of the non-local theory

In this paper, the non-local theory of elasticity is applied to obtain the behavior of a Griffith crack in functionally graded piezoelectric materials under the anti-plane shear loading for the permeable electric boundary conditions. To make the analysis tractable, it is assumed that the material properties vary exponentially with coordinate vertical to the crack. By means of the Fourier transform, the problem can be solved with the help of a pair of dual-integral equations that the unknown variable is the jump of the displacement across the crack surfaces. These equations are solved by use of the Schmidt method. Numerical examples are provided. Unlike the classical elasticity solutions, it is found that no stress and electric displacement singularities are present near the crack tips. The non-local elastic solutions yield a finite hoop stress at the crack tips, thus allows us to using the maximum stress as a fracture criterion. The finite hoop stresses at the crack tips depend on the crack length, the functionally graded parameter and the lattice parameter of the materials, respectively.