Influence of Particle Shape and Surface Friction Variability on Response of Rod-Shaped Particulate Media

Discrete element methods are important tools for the investigation of the mechanics of granular materials. In two dimensions, the reliability of these numerical approaches can be explored using physical tests on rod assemblies. This work highlights the importance of representing the actual distribution of rod shapes and surface friction in numerical simulations. The sensitivity of the response of hexagonally packed rods to minor changes in particle geometry and friction is investigated using a combination of laboratory tests and discrete element simulations. Laboratory test results highlight the influence of small variations in rod geometry on the global response, with the peak friction angle decreasing significantly as the standard deviation of the rod size distribution increased. Small changes in rod shape are also seen to be important. The numerical simulations indicate that the peak friction angle decreases as the standard deviation of the distribution of particle surface friction increases. This paper illustrates the way in which laboratory tests and numerical simulations can be used in a complementary manner to better understand the micromechanics of the response of granular materials.     

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.     

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.     

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.     

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.     

Coupled Continuum-Discrete Model for Saturated Granular Soils

A coupled hydromechanical model was used to analyze the mesoscale pore fluid flow and microscale solid phase deformation of saturated granular soils. The fluid motion was idealized using averaged Navier–Stokes equations, and the discrete element method was employed to model the assemblage of solid particles. The fluid–particle interactions were quantified using established semiempirical relationships. Simulations were conducted to investigate the three-dimensional response of sandy deposits when subjected to critical and overcritical upward pore fluid flow. These simulations revealed complex response patterns after the onset of quicksand conditions and provided valuable insight into the associated mechanisms. The employed model provides an effective tool to assess the microscale mechanisms and characteristics of the partially drained response of saturated granular media.     

Algorithm to Generate a Discrete Element Specimen with Predefined Properties

The discrete element method is a powerful numerical tool in simulating the behavior of granular materials. It bridges the gap between continuum mechanics and physical modeling investigations. In spite of the significant achievements to date, some major problems are yet to be solved including the development of realistic large-scale models with initial conditions similar to those encountered in real problems. This paper introduces a computational method to generate a large-scale packing with predefined porosity and grain-size distribution in three-dimensional space based on a small initial sample packing. The developed method is implemented into an open-source computer code and used to generate specimens with known properties. The results showed that, under static condition, specimens generated using the proposed algorithm exhibited realistic behavior suitable for geotechnical applications. In addition, the controlled structure of the initial sample packing is successfully transferred to the final packing.     

Large Scale Discrete Element Modeling of Vehicle-Soil Interaction

This paper describes the current work on a large deformation soil model to demonstrate the feasibility of particle models to simulate full-scale vehicle-soil interaction problems in which the soil undergoes large excavation-like deformation. To achieve this objective, boundary conditions that accurately represent the vehicle geometry had to be incorporated into a 3D discrete element model. The approach taken was to use a finite-element grid to model the vehicle component interacting with the soil and develop routines to model the particle-grid interactions. The particle-grid interactions were more complicated than the particle-particle interactions required for the soil simulations and pose the greatest challenge to the use of computational parallelism. Two examples are presented in which vehicle components are modeled by finite elements that interact with 10 million discrete soil elements. Important theoretical issues are briefly noted concerning mechanics of granular media that are critical to acceptance of the nascent discrete element modeling technology.     

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.     

Fabric Study of Granular Materials after Compaction

Numerous micromechanical models have been developed based on assemblies of spherical particles with certain fabric distributions. Most of these distributions are hypothetical, and only very few of them can be determined experimentally. This paper presents a study to provide some useful fabric information for granular material. The discrete element method is used to study the microscopic information for granular materials after compaction. Specimens with 520 identical ellipsoidal elements are generated and compressed under different conditions. Up to six different aspect ratios are used to study their effect on the compression process. Two different compression methods and five different microfrictions between particles are used. The fabric of the specimens after compaction, including the total number of contacts, the distribution of particle orientations, the distribution of branch vectors, the distribution of the length of branch vectors, and the spatial distribution of a similar length of branch vector, is presented. The relations between these fabrics and particle shape, microfriction, and the compression process are also developed.     

Small-Strain Behavior of Granular Soils. I: Model for Cemented and Uncemented Sands and Gravels

A simple formulation is presented that predicts the nonlinear small strain behavior of cemented and uncemented granular soils. Its performance is evaluated through the comparison of model predictions to results from laboratory tests. A companion paper evaluates the performance of this model implemented in a site response analysis code through comparison with the measured response at two sites. The formulation for the maximum shear modulus, Gmax, which is selected through the evaluation of existing formulations and data, is presented with the hysteretic model developed to describe the shear modulus reduction and damping increase with increasing strains. Few parameters are needed to predict the small strain response, and correlations between model parameters and index properties of granular materials are presented when possible. The model, SimSoil, is shown to capture the cyclic response for sands and gravels with varying densities over a wide range of pressures measured in laboratory tests, including cases when cementation is present.     

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.     

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.     

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.     

Degradation of a Granular Base under a Flexible Pavement: DEM Simulation

Flexible pavements are composed by an asphalt concrete layer, granular base and subbase layers, and a natural subgrade. The granular materials forming part of the granular layers are subjected to static and dynamic loads during their engineering life. As a result of these loads particle crushing may occur depending on the strength of the particles forming the granular layers. Particle crushing is important since it is associated with several detrimental effects such as settlements and a reduction in hydraulic conductivity. A computer simulation using the discrete element method (DEM) is presented in order to understand and visualize how crushing initiates and develops inside a simulated pavement structure.     

Micromechanical Aspects of Liquefaction-Induced Lateral Spreading

This paper reports the results of model-based simulations of 1-g shake table tests of level and sloping saturated granular soils subject to seismic excitations. The simulations utilize a transient fully coupled continuum-fluid discrete-particle model of water-saturated soils. The fluid (water) phase is idealized at a mesoscale using an averaged form of Navier-Stokes equations. The solid particles are modeled at the microscale as an assemblage of discrete spheres using the discrete element method (DEM). The interphase momentum transfer is accounted for using an established relationship. The employed model reproduced a number of response patterns observed in the 1-g experiments. In addition, the simulation results provided valuable information on the mechanics of liquefaction initiation and subsequent occurrence of lateral spreading in sloping ground. Specifically, the simulations captured sliding block failure instances at different depth locations. The DEM simulation also quantified the impact of void redistribution during shaking on the developed water pressure and lateral spreading. Near the surface, the particles dilated and produced an increase in volume, while the particles at deeper depth locations experienced a decrease in volume during shaking.     

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.     

回转窑内二元颗粒物料的径向混合

研究了颗粒尺寸差异和密度差异对二元物料在回转窑内混合的影响.采用离散单元法建立颗粒物料的运动模型,模拟滚落运动模式下二元物料在回转窑内的径向混合过程;通过颗粒接触数定义混合程度评价指数,结合Hong的渗流与凝聚竞争理论分析颗粒体积比σ和密度比η对二元物料混合程度的影响.结果表明:增大体积比σ会增强渗流作用,增大密度比η会增强凝聚作用,无论渗流或凝聚占据主导作用,均会导致物料在混合过程中产生径向分离,使混合程度降低;对σ与η进行配置后,可以使渗流与凝聚两种机理彼此平衡,达到物料混合均匀的目的;物料的渗流-凝聚平衡曲线中,σ与η呈幂函数关系.      

Computer Vision Technique for Tracking Bed Load Movement

An advanced image analysis system, called Khoros, was used to investigate the bed load movement of sediment particles in a laboratory flume. Incipient flow conditions prevailed throughout the experiments. Painted glass balls of identical diameter and density were used to simulate the sediment particles. They were uniformly placed on top of a tightly packed flat porous bed. Experiments were performed with two distinct surface packing configurations. A video camera was used to monitor their motion within a specified area of view. The resulting video record was converted to digital images using a frame grabber. These digital images were downloaded to a workstation for analysis. The outcome of this analysis provided quantitative information about the frequency of the entrainment of the glass beads, their displacement distance, and the mode of their motion. Such information, when used in conjunction with laser Doppler velocimeter measurements of the fluid velocity, can elucidate the physical mechanisms that are responsible for the entrainment of sediment. During the analysis of the tests, it was observed that the displacement of the beads was sporadic and occurred typically by rolling. The glass beads moved predominately along the flow direction, while on some occasions they were displaced in the transverse direction. For the two packing density tests that were examined, the minimum traveling distance in the longitudinal direction was found to be equal to one bead diameter and the maximum was equal to 10 bead diameters. In the transverse direction, the maximum particle traveling distance was equal to four bead diameters. Finally, it is shown that the existing imaging workspace can be used to accurately identify the displacements of small particles, which are typically encountered near incipient flow conditions and are not easily detectable with the bare eye. The imaging method described here is dynamic in nature and may prove to be a valuable tool for studying two-phase flows, as well as for visualizing flow structures taking place near the boundary in turbulent flows.     

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.