Micromechanical Modelling of Granular Materials: Effect of Particle Size and Gradation

In this paper the effects of maximum particle size, particle gradation/sorting and fabric on bulk mechanical behaviour of granular materials such as coarse grained soils and rockfills are investigated" from micromechanical considerations starting from the grain scale level, using numerical" simulations based on Discrete Element Modelling (DEM). Hydrostatic compaction and biaxial tests on 2-dimensional assemblies of discs with varying particle sizes and gradations were modelled using DEM. An examination of the constitutive behaviour of granular media considering" the particulate nature of the medium has been attempted to explain the effect of particle size and gradation. Simulation results on perfectly parallel graded assemblies indicate that with increase in the size of the particles, a marginal increase (or no increase) in the angle of internal friction is observed during biaxial loading conditions. A change to a wider gradation (keeping the minimum grain size the same) results in a decrease in the angle of internal friction and an increase in volumetric strain to a considerable extent. Based on micromechanical force and fabric parameters, the basis for the physical behaviour was established. This helps in understanding the physics of parallel gradation techniques.     

含细粒砂土反常剪切行为的数值模拟研究

针对含细颗粒砂土的反常剪切行为,开展了双轴剪切试验的数值模拟,从宏细观角度分析了其反常剪切行为发生的内在机制。数值模拟结果表明,增加围压能提高含细颗粒砂土的抗剪切液化能力,该反常行为的根本原因在于围压上升使得粗细颗粒更有效地参与了力链传递,增加了颗粒间的接触,增强了土体的密实度。细颗粒在土骨架中的移动对砂土的液化起着至关重要的作用,而粗颗粒仅起次要作用。研究表明,细颗粒在剪切过程中会持续从有效土骨架中移出成为无效颗粒,而部分粗颗粒也因失去细颗粒的支撑作用会脱离土骨架,直至试样最终液化。细颗粒一般参与土骨架中的弱力链,而粗颗粒则一般参与强力链,导致细颗粒较粗颗粒更容易在土骨架中移动。     

刚性块体压入颗粒体系时的受力及力链演变

颗粒体系由大量离散颗粒组成,普遍存在于自然界中,比如砂土地基、泥石流及滑坡体等。外荷载通常沿着准直形的路径在体系内传递,形成区别于单个颗粒和整个体系的细观结构--力链,亦即颗粒物质具有典型的多尺度特征。采用颗粒离散元方法模拟刚性块体压入颗粒体系的过程,计算得到了刚性块体底部所受阻力与压入深度的幂率关系;给出力链的判断准则和搜索强力链程序,构建颗粒体系强力链网络,并分析了压入试验过程中力链的演变及其长度的分布规律。     

3D analysis of kinematic behavior of granular materials in triaxial testing using DEM with flexible membrane boundary

This paper describes the constitutive behavior and particle-scale kinematics of granular materials in three-dimensional (3D) axisymmetric triaxial testing using discrete element method (DEM). PFC3D code was used to run the DEM simulations using a flexible membrane boundary model consisting of spherical particles linked through flexible contact bonds. The overall deformation behavior of the specimen was then compared with the specimen with rigid boundary and experimental measurements. Computed tomography was used to track the evolution of particle translation and rotation within a laboratory triaxial specimen in 3D. The DEM model of the flexible membrane specimen successfully predicted the stress–strain behavior when compared with laboratory experiment results at different confining pressures. The DEM results showed that the rigid specimen applies a uniform deformation and leads to non-uniformities in the confining stress along the particle-boundary interface in the lateral direction. In contrast, the flexible specimen better replicates the uniformly applied confining stress of a laboratory triaxial experiment. The 3D DEM simulations of the specimen with flexible membrane overpredicted particle translation and rotation in all directions when compared to a laboratory triaxial specimen. The difference between the particle translation and rotation distributions of DEM specimens with rigid and flexible membrane is almost negligible. The DEM specimen with flexible membrane produces a better prediction of the macroscopic stress–strain behavior and deformation characteristics of granular materials in 3D DEM simulations when compared to a specimen with rigid membrane. Comparing macroscale response and particle-scale kinematics between triaxial simulation results of rigid versus flexible membrane demonstrated the significant influence of boundary effects on the constitutive behavior of granular materials.     

Exploring the influence of interparticle friction on critical state behaviour using DEM

Understanding the extent to which discrete element method (DEM) simulations can capture the critical state characteristics of granular materials is important to legitimize the use of DEM in geomechanics. This paper documents a DEM study that considered the sensitivity of the critical state response characteristics to the coefficient of interparticle friction (μ) using samples with gradings that are representative of a real soil. Most of the features that are typically associated with sand behaviour at the critical state were seen to emerge from the DEM simulation data. An important deviation occurs when high μ values (μ ≥ 0.5) are used, as has been the case in a number of prior DEM studies. While there is a systematic variation in the critical state behaviour with μ for μ < 0.5, when μ ≥ 0.5, the behaviour at the critical state seems to be insensitive to further increases in μ. In contrast to observations of conventional soil response, when μ ≥ 0.5, the void ratio at the critical state initially increases with increasing mean effective stress (p′). Analysis of the DEM data and use of simple models of isolated force chains enabled some key observations. When ‘floating’ particles that do not transmit stress are eliminated from the void ratio calculation, the void ratio at the critical state decreases consistently with increasing p′. There is a transition from sliding to rolling behaviour at the contact points as μ increases. Beyond a limiting value of μ, further increases in μ do not increase the buckling resistance of individual strong force chains. Copyright © 2014 John Wiley & Sons, Ltd.     

基于B-DEM的颗粒聚合体应力计算和破碎路径模拟

结合边界元法和离散元法,提出一种可以进行计算颗粒内部应力和破碎路径的方法。该方法利用离散元法求解颗粒的相互作用和每个颗粒上的荷载。然后利用边界元法计算颗粒的应力分布,为了实现动态平衡,将颗粒的加速度视为恒定大小的体力。但体力导致边界积分方程中出现域积分,故采用直线积分法将域积分转化为边界积分,以保证边界元法降维的优势。为了提高边界元的计算效率,对于几何形状相似的颗粒,以其中一个颗粒作为模板颗粒,只需要计算模板颗粒在局部坐标系中的系数矩阵,其他相似颗粒可以通过局部和全局坐标系之间的映射获得。在得到应力后,基于Hoek-Brown准则来判断颗粒是否破碎。此外,将破坏路径简化为直线,并采用最小二乘法拟合得到破坏路径。     

Numerical study of inter‐particle bond failure by 3D discrete element method

The cohesive‐frictional nature of cementitious geomaterials raises great interest in the discrete element method (DEM) simulation of their mechanical behavior, where a proper bond failure criterion is usually required. In this paper, the failure of bond material between two spheres was investigated numerically using DEM that can easily reproduce the failure process of brittle material. In the DEM simulations, a bonded‐grain system (composed of two particles and bond material in between) was discretized as a cylindrical assembly of very fine particles connecting two large end spheres. Then, the bonded‐grain system was subjected to compression/tension, shear, rolling and torsion loadings and their combinations until overall failure (peak state) was reached. Bonded‐grain systems with various sizes were employed to investigate bond geometry effects. The numerical results show that the compression strength is highly affected by bond geometry, with the tensile strength being dependent to a lesser degree. The shear, rolling and torsion strengths are all normal force dependent; i.e., with an increase in the normal force, these strengths first increase at a declining rate and then start to decrease upon the normal force exceeding a critical value. The combined actions of shear force, rolling moment and torque lead to a spherical failure envelope in a normalized loading space. The fitted bond geometry factors and bond failure envelopes obtained numerically in this three‐dimensional study are qualitatively consistent with those in previous two‐dimensional experiments. The obtained bond failure criterion can be incorporated into a future bond contact model. Copyright © 2015 John Wiley & Sons, Ltd.     

Micromechanical analysis of failure propagation in frictional granular materials

The extent to which the evolution of instabilities and failure across multiple length scales can be reproduced with the aid of a bifurcation analysis is examined. We adopt an elastoplastic micropolar constitutive model, recently developed for dense cohesionless granular materials within the framework of thermomicromechanics. The internal variables and their evolution laws are conceived from a direct consideration of the dissipative mechanism of force chain buckling. The resulting constitutive law is cast entirely in terms of the particle scale properties. It thus presents a unique opportunity to test the potential of micromechanical continuum formulations to reproduce key stages in the deformation history: the development of material instabilities and failure following an initially homogeneous deformation. Progression of failure, initiating from frictional sliding and rolling at contacts, followed by the buckling of force chains, through to macroscopic strain softening and shear banding, is reproduced. Bifurcation point, marking the onset of shear banding, occurred shortly after the peak stress ratio. A wide range of material parameters was examined to show the effect of particle scale properties on the progression of failure. Model predictions on the thickness and angle of inclination of the shear band and the structural evolution inside the band, namely the latitudinal distribution of particle rotations and the angular distributions of contacts and the normal contact forces, are consistent with observations from numerical simulations and experiments. Copyright © 2009 John Wiley & Sons, Ltd.     

考虑颗粒棱角影响的直剪试验的离散元模拟

为了研究颗粒棱角对颗粒材料力学行为的影响,建立了具有不同棱角度的对称多面体颗粒,采用了一种简单并适合任意颗粒形状的接触本构模型,对三维离散元开源程序YADE进行了修改,研究了颗粒棱角度在模拟直剪试验中的影响以及接触力各向异性在剪切过程中的演化规律。研究结果表明,颗粒棱角度越小,颗粒间相互咬合自锁的作用越小,颗粒受剪更易转动,致使颗粒体系的剪切强度和剪胀性下降;竖向加载力越大,颗粒棱角度的影响越明显;法向接触力的各向异性在剪切过程中表现为先增后减最后趋向稳定的趋势;法向接触力的各向异性变化程度随颗粒棱角度的增大而增大。     

Three-dimensional discrete element method parallel computation of Cauchy stress distribution over granular materials

The paper presents Cauchy stress tensor computation over parallel grids of message passing interface (MPI) parallel three-dimensional (3D) discrete element method (DEM) simulations of granular materials, considering spherical and nonspherical particles. The stress tensor computation is studied for quasi-static and dynamic conditions, and its resulting symmetry or asymmetry is discussed within the context of classical continuum mechanics (CCM), granular materials mechanics (GMM), and micropolar continuum mechanics (MCM). The average Cauchy stress tensor computation follows Bagi's and Nicot's formulations and is verified within MPI parallel 3D DEM simulations involving dynamically adaptive compute grids. These grids allow calculation of temporal and spatial distributions of stress across granular materials under static and dynamic conditions. The vertical stress component in gravitationally deposited particle assemblies exhibits nonuniform spatial distributions under static equilibrium, and its zone of maximum value changes during the process of gravitational pluviation and collapse. These phenomena reveal a microstructural effect on stress distribution within granular materials that is attributed to their discrete particulate nature (particle size, shape, gradation, boundary conditions, etc).     

粗粒料多边形表征及二维FEM/DEM分析

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

A thermomicromechanical approach to multiscale continuum modeling of dense granular materials

A new method is proposed for the development of a class of elastoplastic thermomicromechanical constitutive laws for granular materials. The method engenders physical transparency in the constitutive formulation of multiscale phenomena from the particle to bulk. We demonstrate this approach for dense, cohesionless granular media under quasi-static loading conditions. The resulting constitutive law—expressed solely in terms of particle scale properties—is the first of its kind. Micromechanical relations for the internal variables, tied to nonaffine deformation, and their evolution laws, are derived from a structural mechanical analysis of a particular mesoscopic event: confined, elastoplastic buckling of a force chain. It is shown that the constitutive law can reproduce the defining behavior of strain-softening under dilatation in both the mesoscopic and macroscopic scales, and reliably predict the formation and evolution of shear bands. The thickness and angle of the shear band, the distribution of particle rotation and the evolution of the normal contact force anisotropy inside the band, are consistent with those observed in discrete element simulations and physical experiments.     

Suction and time effects in rockfill deformation

Ambient relative humidity controls the stress-strain-time behaviour of granular media exhibiting particle breakage. Breakage is the result of crack propagation inside loaded particles. The DEM model developed uses the results of subcritical crack propagation in brittle rock to predict breakage and the subsequent structural rearrangement. Two closed-form solutions at grain level, stress distribution under diametrically opposed forces and the mode I crack propagation velocity, were included in the DEM formulation. Crack propagation velocity depends explicitly on relative humidity. The resulting model incorporates comminution and splitting modes of particle breakage as well as arbitrary grain shapes by means of aggregation of spherical microparticles. The model was first validated against a large diameter suction-controlled oedometer test on hard limestone crushed gravel. Direct tests on contact properties (local stiffness and friction) helped to validate the model. The model was then used to predict the response of large diameter suction-controlled triaxial tests on gravels having different (uniform) initial sizes. Time delayed deformations and wetting-induced collapse deformations under maintained load are also a natural outcome of the model. They were shown to follow quite accurately the experimental results.     

A predictive deep learning framework for path-dependent mechanical behavior of granular materials

As we transition into an era of data generation and collection, empirical summaries in the classical continuum modeling of granular materials cannot take full advantage of the increasingly larger data sets. This work presents a data-driven model for modeling granular materials, with the material data being extracted from discrete element method (DEM) simulations. A long short-term memory (LSTM) network is then employed to learn the mechanical behaviors of granular materials from the material dataset. Particular emphasis is placed on three elements: modification of LSTM unit cell, phase space sampling, and material history parameterization. The LSTM unit cell is modified so that the initial hidden state can be specified as the initial states of granular materials. Massive DEM simulations are performed to consider the effects of particle size distribution, initial density, confining pressure, and loading path on the mechanical behaviors of granular materials. The history-dependency of the granular materials is well represented by the architecture of the LSTM network and internal variable-based history parameterization. We compare the model predictions against DEM simulations to assess the performance of the proposed data-driven model. The results demonstrate that the model can predict the material behaviors of granular materials with different microstructures and initial states and reproduce the material responses under complex nonmonotonic loading paths. This data-driven model exhibits good generalization ability and high prediction accuracy in various situations.

     

Study on the particle breakage of ballast based on a GPU accelerated discrete element method

Breakage of particles will have greatly influence on mechanical behavior of granular material(GM)under external loads,such as ballast,rockfill and sand.The discrete element method(DEM)is one of the most popular methods for simulating GM as each particle is represented on its own.To study breakage mechanism of particle breakage,a cohesive contact mode is developed based on the GPU accelerated DEM code-Blaze-DEM.A database of the 3D geometry model of rock blocks is established based on the 3D scanning method.And an agglomerate describing the rock block with a series of non-overlapping spherical particles is used to build the DEM numerical model of a railway ballast sample,which is used to the DEM oedometric test to study the particles’breakage characteristics of the sample under external load.Furthermore,to obtain the meso-mechanical parameters used in DEM,a black-analysis method is used based on the laboratory tests of the rock sample.Based on the DEM numerical tests,the particle breakage process and mechanisms of the railway ballast are studied.All results show that the developed code can better used for large scale simulation of the particle breakage analysis of granular material.     

Modelling size effect on rock aggregates strength using a DEM bonded-cell model

Empirical evidence has shown that particle breakage affects the mechanical behaviour of granular materials. The source of this mechanism takes place at the particle scale, and the main consequence on the macromechanical behaviour is increasing compressibility. Due to the inverse correlation between particle size and particle crushing strength, coarse rockfill materials are particularly vulnerable to mechanical degradation due to particle breakage. However, such coarse materials do not fit in standard laboratory devices, and the alternative of large sample testing is usually unavailable or too expensive. Alternatively, recent works have proposed multi-scale approaches using the discrete element method (DEM) to carry out numerical testing of coarse crushable materials, although few studies have focused on size effects. This article presents the application of a DEM bonded-cell model to study particle size-strength correlation on angular rock aggregates. Each particle is modelled by a cluster of perfectly rigid polyhedral cells with Mohr–Coulomb contact law. Constant cell density within particles implies that the presence of potential fragmentation planes increases with size. Therefore, particle strength decreases with size. A comprehensive sensitivity analysis was carried out through 1477 particle crushing simulations in a given particle size. Based on published experimental data on calcareous rock aggregates, part of the simulations were used for calibration, and 97 additional simulations of a coarser size fraction were performed for validation. The results show a good agreement with the empirical data in terms of size effect and data scatter through Weibull statistics.

     

颗粒体系中的骨架及力链网络

颗粒物质是大量离散的固体颗粒相互作用而组成的复杂体系,具有非连续和接触耗散等基本特征,其物理机制研究是近20年科学前沿之一。砂土就是典型的颗粒物质,土体中的有效应力是作用在土体骨架上的平均应力,土体变形主要来源于骨架上的颗粒位置,但对土体骨架并没有一个清晰的物理描述。近期颗粒物质力学研究认为,体系中颗粒相互接触形成的网络结构是外荷载传递路径的物理基础,可能就是土力学所指的骨架。同时还发现,较大的力通常沿着准直线的路径传递,人们常把传递较大力、与该准直线路径对应的若干颗粒组成的链状结构,称为强力链;弱力链则传递较小力。力链结构及其演变规律的描述是颗粒物质研究的核心之一。以单轴侧限压缩数值模拟为例,对比说明了土体颗粒骨架与力链结构的关系,明确提出强力链网络决定颗粒体系的宏观力学行为。     

Three-dimensional DEM investigation of critical state and dilatancy behaviors of granular materials

The critical state is significant to the mechanical behaviors of granular materials and the foundation of the constitutive relations. Using the discrete element method (DEM), the mechanical behaviors of granular materials can be investigated on both the macroscopic and microscopic levels. A series of DEM simulations under true triaxial conditions have been performed to explore the critical state and dilatancy behavior of granular materials, which show the qualitatively similar macroscopic responses as the experimental results. The critical void ratio and stress ratio under different stress paths are presented. A unique critical state line (CSL) is shown to indicate that the intermediate principal stress ratio does not influence the CSL. Within the framework of the unique critical state, the stress–dilatancy relation of DEM simulations is found to fulfill the state-dependent dilatancy equations. As a microscopic parameter to evaluate the static determinacy of the granular system, the redundancy ratio is defined and investigated. The results show that the critical state is very close to the statically determinate state. Other particle-level indexes, including the distribution of the contact forces and the anisotropies, are carefully investigated to analyze the microstructural evolution and the underlying mechanism. The microscopic analysis shows that both the contact orientations and contact forces influence the mechanical behaviors of granular materials.     

Revisiting the existence of an effective stress for wet granular soils with micromechanics

A possible effective stress variable for wet granular materials is numerically investigated based on an adapted discrete element method (DEM) model for an ideal three‐phase system. The DEM simulations consider granular materials made of nearly monodisperse spherical particles, in the pendular regime with the pore fluid mixture consisting of distinct water menisci bridging particle pairs. The contact force‐related stress contribution to the total stresses is isolated and tested as the effective stress candidate for dense or loose systems. It is first recalled that this contact stress tensor is indeed an adequate effective stress that describes stress limit states of wet samples with the same Mohr‐Coulomb criterion associated with their dry counterparts. As for constitutive relationships, it is demonstrated that the contact stress tensor used in conjunction with dry constitutive relations does describe the strains of wet samples during an initial strain regime but not beyond. Outside this so‐called quasi‐static strain regime, whose extent is much greater for dense than loose materials, dramatic changes in the contact network prevent macroscale contact stress‐strain relationships to apply in the same manner to dry and unsaturated conditions. The presented numerical results also reveal unexpected constitutive bifurcations for the loose material, related to stick‐slip macrobehavior.     

DEM investigations of internal erosion: Grain transport in the light of micromechanics

Internal erosion by suffusion can change dramatically the constitutive behavior of granular materials by modifying the fabric of granular materials. In this study, the effect of an internal fluid flow on granular materials is investigated at the material point scale using the numerical coupling between a discrete element method (DEM) and a pore-scale finite volume (PFV) coupling scheme. The influence of the stress state and the hydraulic loading (direction and intensity) on the occurrence of grain transport in dense widely graded granular samples is thus investigated and interpreted in terms of micromechanics. In particular, it is shown that grain transport is increased when the macroscopic flow direction is aligned with the privileged force chain orientation. The stress-induced microstructure modifications are shown to influence the transport distances by controlling the number of rattlers.