Validation of discrete element method by simulating a 2D assembly of randomly packed elliptical rods

This paper aims at establishing the predictive capability of the discrete element method (DEM) by validating the simulated responses of granular systems against experimental observations at both the macroscale and the microscale. A previously published biaxial shearing test on a 2D assembly of randomly packed elliptical rods was chosen as the benchmark test. In carrying out the corresponding DEM simulations herein, the contact model was derived and then validated using finite element analysis; the associated parameters were calibrated experimentally. The flexible (membrane) boundary was modeled by a bonded-particle string with experimentally calibrated parameters. An iteration procedure was implemented to replicate the initial packing and also to satisfy the boundary conditions in the experiment. Overall, the DEM simulation is found effective in reproducing the stress–strain–volumetric response, the statistical observation on the fabric anisotropy and the strain localization. Furthermore, the closer the numerical packing is to the experimental one, the closer the response is reproduced, demonstrating the significance of the initial packing reconstruction. Still, there are some minor differences between the experiment and simulation, reflecting the limitations associated with the particle number and the measurement resolution used in the experiment when reproducing the initial packing.     

A PACKING GENERATION SCHEME FOR THE GRANULAR ASSEMBLIES WITH PLANAR ELLIPTICAL PARTICLES

In this paper, a new generator algorithm and a computer program PG2D is introduced for 2D numerical simulation of packing configuration in a granular material composed of elliptical particles of different a/b aspect ratios. Each elliptical particle is approximated by four connected arcs. The centre co-ordinates and radius of each arc and co-ordinates of connecting points can be determined from the formulae derived by entering the major axis length, 2a, and the eccentricity. The domain to be filled with particles can be a polygon of any shape. Given the size of the packing domain, geometrical information and numbers of particles to be generated, the packing location of each particle and the co-ordinates of contact points along with contact normal rose diagram can be generated as outputs. Simulation results show that this new algorithm can provide quite a reasonable packing model in accordance with the initial input required for the analysis of the mechanics of granular material. This generation scheme has the potential to cover packing generation and behaviour analysis of 3D sphere or ellipsoidal shaped granular materials. © 1997 by John Wiley & Sons, Ltd.     

Void distributions in samples of Ottawa sand

The void distribution of saturated specimens of Ottawa sand is presented. The presence of water inside the sand specimen is detected using the magnetic resonance imaging (MRI) technique. The void distribution of the sample was determined from the image. The specimen was prepared in a non-metallic triaxial cell and was put insie a MRI apparatus to obtain the image. Two sample preparation methods (wet tamping and dry pluviation) were used to illustrate the uniformity of the samples in the initial state. The void distribution along the height of the sample and the three-dimensional orientational void distribution at different locations inside the sample were analysed. The results indicate that the sample generated by the dry-pluviation method is more uniform than the sample generated by the wet-tamping method. When the wet-tamping sample preparation technique is used, the dense sample is more uniform than the loose sample. The development of voids was investigated by a sample loaded inside the MRI device under drained compression condition. The void distribution along the height of the sample at different stages was observed. This work has demonstrated the feasibility of using the MRI technique to examine void distribution in granular material.     

Deterministic and statistical size effect during shearing of granular layer within a micro‐polar hypoplasticity

The paper deals with numerical investigations of a deterministic and statistical size effect in granular bodies during quasi‐static shearing of an infinite layer under plane strain conditions, free dilatancy and constant pressure. For a simulation of the mechanical behaviour of a cohesionless granular material during a monotonous deformation path, a micro‐polar hypoplastic constitutive relation was used which takes into account particle rotations, curvatures, non‐symmetric stresses, couple stresses and the mean grain diameter as a characteristic length. The proposed model captures the essential mechanical features of granular bodies in a wide range of densities and pressures with a single set of constants. In the paper, a deterministic and statistical size effect is analysed. The deterministic calculations were carried out with an uniform distribution of the initial void ratio for four different heights of the granular layer: 5, 50, 500 and 2000 mm. To investigate the statistical size effect, the Monte Carlo method was applied. The random distribution of the initial void ratio was assumed to be spatially correlated. Truncated Gaussian random fields were generated in a granular layer using an original conditional rejection method. The sufficient number of samples was determined by analysing the convergence of the outcomes. In order to reduce the number of realizations without losing the accuracy of the calculations, stratified and Latin hypercube methods were applied. A parametric analysis of these methods was also presented. Some general conclusions were formulated. Copyright © 2007 John Wiley & Sons, Ltd.     

A visco‐elasto‐plastic model for granular materials under simple shear conditions

The numerical simulation of rapid landslides is quite complex mainly because constitutive models capable of simulating the mechanical behaviour of granular materials in the pre‐collapse and post‐collapse regimes are still missing. The goal of this paper is to introduce a constitutive model capable of capturing the response of dry granular flows from quasi‐static to dynamic conditions, in particular when the material experiences a sort of solid‐to‐fluid phase transition. An ideal assembly of identical spheres under simple shear conditions is considered. In the constitutive model, void ratio and granular temperature have been chosen as state variables, and both shear and normal stresses are computed as the sum of two contributions: the quasi‐static one and the collisional one. The former is determined by using a perfect elasto‐plastic model including the critical state concept, while the latter is derived from the kinetic theory of granular gases. The evolution of the granular temperature, fundamentally governing the material phase transition, is obtained by imposing the kinetic fluctuating energy balance. The constitutive relationship has been integrated, under both constant pressure and constant volume conditions, and the influence of shear strain rate, initial void ratio and normal pressure on the mechanical response has been investigated. Copyright © 2015 John Wiley & Sons, Ltd.     

Effects of soil fabric on behaviors of granular soils: Microscopic modeling

The effects of initial soil fabric on behaviors of granular soils are investigated by using Distinct Element Method (DEM) numerical simulation. Soil specimens are represented by an assembly of non-uniform sized spheres with different initial contact normal distributions. Isotropically consolidated triaxial compression loading and extension unloading in both undrained and drained conditions are simulated for vertically- and horizontally-sheared specimens. The numerical simulation results are compared qualitatively with the published experimental data and the effects of initial soil fabric on resulting soil behaviors are discussed, including the effects of specimen reconstitution methods, effects of large preshearing, and anisotropic characteristics in undrained and drained conditions. The effects of initial soil fabric and mode of shearing on the quasi-steady state line are also investigated. The numerical simulation results can systematically explain that the observed experimental behaviors of granular soils are due principally to their conditions of the initial soil fabric. This outcome provides insights into the observed phenomena in microscopic view.     

Numerical study of retention efficiency of a flexible barrier in mitigating granular flow comparing with large-scale physical modeling test data

Retention behavior of a flexible barrier in mitigating a granular flow is still an open problem not fully understood, especially due to the complexity of the granular material and the flexible barrier. Understanding the retention mechanism and quantifying the influencing factors of retention efficiency are desirable for optimizing the design and minimizing the maintenance cost of a debris-resisting flexible barrier. In this paper, a numerical model, based on the discrete element method, is presented, calibrated, and validated to analyze the interaction between a granular flow and a flexible net. A full-scale numerical simulation is first performed to compare with a large-scale physical modeling test in the literature and validate the applied parameters in the simulation. The interaction and deposition characteristics of the granular flow interacting with a flexible net are revealed. Afterward, parametric study is performed to investigate the effects of the internal friction angle (φ) of debris material and the relative mesh size of flexible net on the retention efficiency and clogging mechanism of a flexible barrier. The simulation results illustrate that the particle passing ratio (P) increases with increment of the friction angle of particles and enlargement of the mesh size of a flexible net. Both parameters have critical effects on the retention efficiency of a flexible barrier in intercepting a granular flow. Therefore, the friction angle and the particle size distribution characteristics of the debris material are suggested being used for optimization of the mesh size and more efficient design of debris-resisting flexible barriers.

     

The role of constitutive models in MPM simulations of granular column collapses

The granular column collapse is a well-established experiment which consists of having a vertical column of granular material on a flat surface and letting it collapse by gravity. Despite its simplicity in execution, the numerical modelling of a column collapse remains challenging. So far, much attention has been dedicated in assessing the ability of various numerical methods in modelling the large deformation and little to the role of the constitutive model on both the triggering mechanism and the flow behaviour. Furthermore, the influence of the initial density, and its associated dilatancy and strength characteristics, have never been included in the analyses. Most past numerical investigations had relied on simple constitutive relations which do not consider the softening behaviours. The aim of this study is to illustrate the influence of the constitutive model on the on-set of failure, the flow behaviour and the deposition profile using the material point method. Three constitutive models were used to simulate the collapse of two granular columns with different geometries and for two densities. The results of the simulations showed that the constitutive model had a twofold influence on the collapse behaviour. It defined the volume of the mobilised mass which spread along the flat surface and controlled the dissipation of its energy. The initial density was found to enhance the failure angle and flow behaviours and was more significant for small columns than for larger ones. The analysis of the potential energy of the mobilised mass explained the existence of two collapse regimes.     

Finite element study of patterns of shear zones in granular bodies during plane strain compression

Numerical investigations of patterns of shear zones in granular bodies obtained during quasi-static plane strain compression tests were performed. The effect of a spatially correlated stochastic distribution of the initial void ratio and roughness of horizontal plates was analyzed. To describe a mechanical behavior of a cohesionless granular material during a monotonic deformation path in a plane strain compression test, a micro-polar hypoplastic constitutive model was used. FE calculations were carried out with both initially dense and initially loose cohesionless sand. A Latin hypercube method was applied to generate Gaussian truncated random fields of initial void ratio in a granular specimen. A weak correlation of the initial void ratio in both directions and its large standard deviation were assumed for all specimens. The horizontal boundaries were either ideally smooth or very rough. The FE results show similar patterns of shear zones as compared to experiments.     

Micromechanical analysis of cyclic and asymptotic behaviors of a granular backfill

The paper examines the mechanics and physics of granular material responses at the macroscopic and microscopic levels during both monotonic and cyclic loadings. A numerical analysis referring to a long retaining wall is conducted using a two-dimensional discrete element model representing a granular system with a free top surface. On one of the lateral boundaries referring to the retaining wall, both active and passive loadings were applied monotonically as well as cyclically. First, the development of sheared zones and classic failure wedges resulting from active and passive monotonic displacements are discussed with respect to Rankine’s and Roscoe’s solution angles. Then, a series of loading cycles were performed using slow small-amplitude displacements at different stress states chosen before the occurrence of failure along the passive monotonic stress response curve. Particular interest is focused on the ultimate asymptotic cyclic response of the granular system, the occurrence of a high-mobility (convective) zone and a detailed macroscopic and microscopic analysis. Finally, major kinematical features that are displayed during cyclic loading from different starting stresses to eventually reach the same asymptotic state were elucidated through particle vortex-like flux formations, including contact rotations. The change in material stiffness was also investigated based on the evolution of strong and weak contact networks, together with the analysis of fabric anisotropy within the entire domain, including the high-mobility zone considered separately.

     

Modelling strain localization in granular materials using micropolar theory: numerical implementation and verification

Implementation and applications for a constitutive numerical model on F‐75 silica sand, course silica sand and two sizes of glass beads compressed under plane strain conditions are presented in this work. The numerical model is used to predict the stress versus axial strain and volumetric strain versus axial strain relationships of those materials; moreover, comparisons between measured and predicted shear band thickness and inclination angles are discussed and the numerical results compare well with the experimental measurements. The numerical model is found to respond to the changes in confining pressure and the initial relative density of a given granular material. The mean particle size is used as an internal length scale. Increasing the confining pressure and the initial density is found to decrease the shear band thickness and increase the inclination angle. The micropolar or Cosserat theory is found to be effective in capturing strain localization in granular materials. The finite element formulations and the solution method for the boundary value problem in the updated Lagrangian frame (UP) are discussed in the companion paper. Copyright © 2006 John Wiley & Sons, Ltd.     

Side resistance of drilled shafts in granular soils investigated by DEM

The paper presents a numerical study on the side resistance of a drilled shaft in granular materials. The numerical result is used to develop new design equations for the side resistance of drilled shafts in granular soils. The Discrete Element Method (DEM) is used to model a drilled shaft in granular material. The granular material is represented as assemblies of ellipsoidal particles. Nominal side resistance is represented as the product of a parameter (β) and vertical stress. The numerical result shows that the relationship between β and void ratio can be described by a hyperbolic function for a given vertical stress. DEM result is also compared with three design equations. Although these design equations capture the decrease of β with depth, deviation is observed between the DEM results and the design equations. Finally, new design equations based on state parameter are proposed.     

散粒体中锚杆间距的锚固效应研究

采用细观数值模拟方法研究散粒体的锚固效应,基于随机模拟技术生成三维多面体颗粒及其在空间中的分布,在随机散粒体不连续变形模型的基础上将砾石锚固试验进行数值实现,分析加锚散粒体材料的宏观与细观力学性能,研究加锚密度及其与颗粒粒径的关系对散粒体力学性质的影响,并探讨锚杆在散粒体材料中的作用机制。分别建立不同锚杆间距和不同颗粒粒径的数值试样,数值模拟结果表明：散粒体锚固数值试验能够较好地反映不同加锚散粒体结构的变形规律与锚固效应;散粒体材料的宏观特性与其细观组构的演化密切相关;锚杆加固散粒体的作用机制为加锚散粒体内形成压缩区,挤压加固作用提高了散粒体间的接触作用力,散粒体结构的整体性得到加强并能承受一定荷载;不考虑锚杆长度的情况下,当锚杆间距小于3倍的散粒体平均粒径时,锚杆能够有效地加固散粒体形成稳定结构。     

An approach to calculating large strain accumulation for discrete element simulations of granular media

For research on granular materials, establishing a method to calculate continuum strain from particle displacements is necessary for understanding the material behaviour at macro-level and developing continuum constitutive models. Existing methods are generally based on constructing a mesh or background grid to calculate strain from particle motions. These methods offer rigorous ways to measure strain for granular materials; however, they suffer from several problems such as mesh distortion and lacking grid-to-particle strain mapping procedure, which hinders their capability of calculating strain accumulation during large deformation processes of granular media. To address this issue, this study proposes a new strain calculation method for discrete element simulations of granular materials. This method describes a particle assembly as an equivalent continuum system of material points, each of which corresponds to a particle centre and represents a continuous region with its initial volume/area presumably equal to the volume/area of Voronoi cells generated in accordance with the particle assembly configuration. Smooth Particle Hydrodynamics (SPH) interpolation functions are then employed to calculate strain for these material points. This SPH-based method does not require any mesh or background grid for computation, leading to advantages in calculating strain accumulation under large deformation. Simulations of granular materials in both uniform and heterogeneous gradations were carried out, and strain results obtained by the proposed method indicate good agreements with analytical and numerical solutions. This demonstrates its potential for strain calculations in discrete element simulations of granular materials involving large deformations and/or large displacements.     

模型相似材料内部应变光纤量测应变传递

应用光纤传感技术测量模型相似材料内部应变,必须解决光纤与相似材料耦合的问题。传统的研究中普遍存在应变传递理论分析结果无法通过试验检验的问题。设计实现了一种基于光纤-胶体-相似材料3层应变传递结构的光纤Bragg光栅（FBG）相似材料一维传感器。通过对该传感器应变传递特性和标定方法的研究探索解决光纤与相似材料耦合性的问题。该传感器采用无涂覆层的光纤Bragg光栅作为传感元件,将光纤埋入相似材料应变试件内部直接测量轴向中心应变。通过应变传递理论分析、数值模拟以及全新设计的标定试验研究3种方法研究了该相似材料光栅传感器的应变传递特性。平均应变传递率结果显示3种方法所得到的数值非常接近,表明该传感器的光纤、胶体、相似材料具有良好的耦合性以及应变测量的准确性。该方法为解决模型相似材料内部三维应变测量提供了可行方案。     

控制应力路径散体材料真三轴试验强度特征的离散元模拟与细观机制分析

通过一系列真三轴离散元数值试验,模拟了不同应力路径下的等b试验中散体材料的强度特征。根据模拟结果详细地分析了三维应力条件下中主应力和应力路径对散体材料峰值强度的影响,研究了峰值摩擦角、峰值应力比的变化规律,并根据真应力的概念和组构张量的演化结果分析了散体材料的强度成因。研究表明,在不同类型的数值试验中峰值偏应力随b参数的变化规律不同,但采用初始围压归一化后的应力-应变曲线规律一致。峰值强度线的斜率只与b值有关而与应力路径无关,且随着b值的增加,峰值应力比qf /pf逐渐减小,数值模拟结果与室内试验结果吻合较好;随着应变的发展,数值试样的组构也随之发生变化,产生了明显的应力诱发各向异性;散体的强度为颗粒摩擦及材料各向异性共同作用的结果;理论上,组构比-应力比坐标系中破坏点位置仅取决于颗粒摩擦角 ,而数值模拟结果与理论值的差异源于颗粒间咬合和滚动摩擦的影响,其影响与颗粒表面摩擦系数有关,也受空间应力状态的影响。     

Compositional and morphological features of aragonite precipitated experimentally from seawater and biogenically by corals

The morphology and composition of abiogenic (synthetic) aragonites precipitated experimentally from seawater and the aragonite accreted by scleractinian corals were characterized at the micron and nano scale. The synthetic aragonites precipitated from supersaturated seawater solutions as spherulites, typically 20-100 μm in diameter, with aggregates of sub-micron granular materials occupying their centers and elongate (fibrous) needles radiating out to the edge. Using Sr isotope spikes, the formation of the central granular material was shown to be associated with high fluid pH and saturation state whereas needle growth occurred at lower pH and saturation state. The granular aggregates have significantly higher Mg/Ca and Ba/Ca ratios than the surrounding fibers.Two types of crystals are identified in the coral skeleton: aggregates of sub-micron granular material and bundles of elongate (fibrous) crystals that radiate out from the aggregates. The granular materials are found in “centers of calcification” and in fine bands that transect the fiber bundles. They have significantly higher Mg/Ca and Ba/Ca ratios than the surrounding fibers.The observed relationship between seawater saturation state and crystal morphology and composition in the synthetic aragonites was used as a framework to interpret observations of the coral skeleton. We propose that coral skeletal growth can be viewed as a cyclical process driven by changes in the saturation state of the coral’s calcifying fluids. When saturation state is high, granular crystals precipitate at the tips of the existing skeletal elements forming the centers of calcification. As the saturation state decreases, aragonitic fibres grow in bundles that radiate out from the centers of calcification.     

Numerical modelling of fluid flow in microscopic images of granular materials

A program for the simulation of two‐dimensional (2‐D) fluid flow at the microstructural level of a saturated anisotropic granular medium is presented. The program provides a numerical solution to the complete set of Navier–Stokes equations without a priori assumptions on the viscous or convection components. This is especially suited for the simulation of the flow of fluids with different density and viscosity values and for a wide range of granular material porosity. The analytical solution for fluid flow in a simple microstructure of porous medium is used to verify the computer program. Subsequently, the flow field is computed within microscopic images of granular material that differ in porosity, particle size and particle shape. The computed flow fields are shown to follow certain paths depending on air void size and connectivity. The permeability tensor coefficients are derived from the flow fields, and their values are shown to compare well with laboratory experimental data on glass beads, Ottawa sand and silica sands. The directional distribution of permeability is expressed in a functional form and its anisotropy is quantified. Permeability anisotropy is found to be more pronounced in the silica sand medium that consists of elongated particles. Copyright © 2001 John Wiley & Sons, Ltd.     

Discrete element simulation of geogrid-stabilised soil

A particle-based numerical simulation procedure is presented for the generation and calibration of geogrid-stabilised soil on the basis of experimental data. The paper describes how to simulate a biaxial geogrid depending on a specific particle and parallel bond model. Numerical and experimental pull-out tests have been performed to reproduce the pull-out force–strain behaviour of a biaxial geogrid specimen embedded in granular material under special consideration of the grain-size distribution, initial relative density, normal stress state as well as sample installation. Model analysis of soil mobilisation and geogrid deformation is presented to understand the significance of the interlocking effect as key mechanism for soil stabilisation. The procedure can be used for further investigations of the influence and effects of soil stabilisation depending on the significant properties of the interacting components (soils and geogrids).