Effect of Aspect Ratio on the Monotonic Shear Behaviour: Micromechanical Interpretations

The effect of aspect ratio on the mechanical behaviour and micromechanics of two different assemblies during drained triaxial shearing are reported in this paper. Discrete element simulations are done on two different sets of assemblies—first assembly consists of particles with aspect ratio 1.0 and second assembly consists of particles with aspect ratio 1.5. A log normal distribution of particle size is adopted for both the samples. The constitutive behaviour of the assemblies and the evolution of the microstructure of the samples under shearing are closely examined and is related to the aspect ratio of the particles constituting the assembly. The spherical harmonic distributions of contact forces and contact normals along with 3-D histograms are plotted to give quantitative information of the variation of these parameters as the loading progresses. The results indicate that as the aspect ratio increases, there is an increase in the maximum deviatoric stress at the macroscopic level. At the microscopic level, the values of the anisotropic coefficients which are representative of the microparameters also show an increase in the magnitude for the assembly with higher aspect ratio particles.     

Micromechanical parameters in bonded particle method for modelling of brittle material failure

Bonded particle modelling (BPM) is nowadays being extensively used for simulating brittle material failure. In BPM, material is modelled as a dense assemblage of particles (grains) connected together by contacts (cement). This sort of modelling seriously depends on the mechanical properties of particle and contact, which are named here as micro‐parameters. However, a definite calibration methodology to obtain micro‐parameters has not been so far established; and many have reported some serious problems. In this research, a calibration procedure to find a unique set of micro‐parameters is established. To attain this purpose, discrete element code of UDEC is used to perform BPM. This code can be conveniently developed by the user. The proposed BPM is composed of rigid polygonal particles interacting at their contact points. These contacts can undergo a certain amount of tension, and their shear resistance is provided by cohesion and friction angle. The results demonstrate that each material macro‐property (i.e. Young's modulus, Poisson's ratio, internal friction angel, internal cohesion, and tensile strength) is directly originated from and distinctly related to the contact properties (i.e. normal and shear stiffness, friction angel, cohesion, and tensile strength). Copyright © 2010 John Wiley & Sons, Ltd.     

Microscopic contact model of lunar regolith for high efficiency discrete element analyses

The grains of lunar regolith are characterized with rough surfaces, angular shapes and mutual adhesions due to short-range interactions. These features control the macroscopic mechanical behavior of lunar regolith but have not been completely captured by contact models in previous Discrete Element Method (DEM) analyses. In this paper, a simplified two-dimensional microscopic contact model is proposed for high efficiency DEM analyses of lunar regolith. The model consists of three components in the normal, tangential and rolling directions respectively, plus two new parameters. A shape parameter is used to control the rolling resistance ability at the contact area between two particles to capture the features of grain shape and interlocking. The second parameter, micro-separation, which denotes the nominal minimum distance between the molecules of the two contacting particles, is introduced to account for van der Waals force as the major component of the short-range interactions that contribute to the adhesion of regolith grains in lunar environment conditions. The novel model has been implemented in a two-dimensional DEM code for numerical simulations of biaxial compression tests on lunar regolith. The effects of interparticle friction, grain shape, lunar environment conditions and void ratio on the strength of lunar regolith were numerically investigated. The results show that soils in the simulated lunar environment exhibit greater strength and more apparent strain-softening and shear dilatancy than on the Earth. The proposed model can capture the main features of the mechanical behavior of lunar regolith (apparent cohesion and high peak friction angle) and a wide range of strength indices can be obtained by the contact model.     

A lattice type model for particulate media

In this paper, a lattice-type model to simulate the micro-mechanical behaviour of particulate/granular media is presented. In this numerical model, a particulate assembly is simulated as a lattice/truss. Nodes located at contacts between a particle and its neighbours are linked by bars to each other. Each particle is represented by a lattice within its microstructure and particle interact through load transfer at the nodes. Constraints are prescribed at the nodes to describe active, deactivated and reactivated contacts. When a particulate assembly develops into a mechanism (deformation with zero incremental load), further deformation is simulated through a framework that describes the kinematics of the particles (sliding, rolling and rotation of particles). This framework is formed by introducing nodes at the particle centroids and linking them with bars. Bars-linking particles with a non-sliding contact are assigned large stiffnesses relative to bars linking particles with a sliding contact. Numerical tests are conducted on two-dimensional assemblies of disks, arranged as very loose and very dense packing under simple shear loading conditions. The results concord with the results of numerical tests conducted using the discrete element method and with photoelastic experiments. Additionally, the model is applied to study the effects of initial imperfections caused by particles with low elastic modulus. Copyright © 1999 John Wiley & Sons, Ltd.     

颗粒滚动-滑动转换机制及摩擦系数的试验研究

颗粒间的滑动、滚动摩擦对其微观、宏观动力特性有很大的影响。在颗粒流体动力学研究中,对颗粒介质的滑动摩擦已有深刻的认识,而对滚动摩擦及其与滑动摩擦间相互关系的研究还需进一步深入。滚动摩擦的影响因素较多,且作用机理复杂,至今没有形成统一的理论。通过颗粒滑动–滚动摩擦试验,分析了颗粒表面粗糙度和形状对颗粒摩擦力的影响,初步研究了颗粒滚动–滑动摩擦的转化机制。试验结果表明：颗粒在不同的粗糙度和不规则形态影响下表现出滑动或滚动的不同运动形式,并呈现出一定的转化特性。该试验还进一步测定了颗粒滑动、滚动摩擦系数,定性地分析了颗粒的表面粗糙度和几何形态对它们的影响。     

Macroscopic and microscopic behaviors of granular materials under proportional strain path: a DEM study

Under the proportional strain loading path, particle assemblies may exhibit various failure modes. Besides the strain localization, the diffuse failure may also occur under certain conditions. The diffuse failure mode corresponds to a homogeneous occurrence of failure with stress states strictly included within the plastic limit condition. This paper emphasizes the influences of the density degree and the rolling resistance under the strain path. A contact model considering rolling friction is adopted in a discrete element method analysis as an approximate means to account for the effects of particle shape. Mechanical responses indicate that loose assemblies without the rolling resistance are more vulnerable to static liquefaction. A sample with a smaller initial void ratio or larger rolling friction coefficient will reinforce the stability of the structure and reduce the likelihood of failure. For microscopic properties, the evolution of coordination numbers, contact forces, force chains and the anisotropies of the assemblies are explored and discussed. Rotational resistance helps increase the shear stress of the granular material, and the microscopic parameters indicate that the assembly has a strong anisotropy and a stable structure to resist the increasing loading.     

Biaxial test simulations using a packing of polygonal particles

The mechanical response of cohesionless granular materials under monotonic loading is studied by performing molecular dynamic simulations. The diversity of shapes of soil grains is modelled by using randomly generated convex polygons as granular particles. Results of the biaxial test obtained for dense and loose media show that samples achieve the same void ratio at large strains independent of their initial density state. This limit state resembles the so‐called critical state of soil mechanics, except for some stress fluctuations, which remain for large deformations. These fluctuations are studied at the micro‐mechanical level, by following the evolution of the co‐ordination number, force chains and the fraction of the sliding contacts of the sample. Copyright © 2007 John Wiley & Sons, Ltd.     

Accuracy of dynamic disk-based DDA with respect to a single sliding disk cluster

Disk clusters are developed to represent the shape of granular materials more precisely (compared to circular particles) and to minimise excessive rolling. Investigating the behaviour of dynamic disk-based discontinuous deformation analysis (DDA) with disk clusters is very important to evaluate the applicability of disk-based DDA to dynamic problems in geomechanics. In this paper, the accuracy of disk-based DDA under dynamic conditions is studied by a comprehensive sensitivity analysis. The results obtained by disk-based DDA are compared with the analytical solutions of a disk cluster on an incline subjected to gravitational force only, and three different accelerations of increasing complexity with sinusoidal input functions as well as gravitational load. In this research, the effects of time step size and interface friction angles on the results are studied. Overall, most of the error for both velocity and displacement occurs at the beginning of the solution. With increasing friction angle, the initial perturbation of the solution increases in the case of sliding under gravitational force only, and decreases in the case of sliding under dynamic loads. This study shows that disk-based DDA predicts accurately the velocities and displacements derived with respect to the frictional resistance offered by the inclines.     

基于抗转模型的颗粒材料宏−细观关系研究

接触模型的宏?细观参数标定是成功使用离散元方法的关键。在离散元的接触模型中线性接触模型与抗转线性接触模型均可用于模拟砂性土的力学行为,其中抗转线性接触模型在模拟密砂的剪胀性方面具备优势。采用抗转线性接触模型对室内密实砂土三轴试验进行了离散元模拟,验证了抗转线性接触模型的可靠性;进而系统分析了颗粒间摩擦系数、刚度比和抗转动系数等细观参数与砂土峰值内摩擦角、残余内摩擦角、峰值剪胀角等宏观参数的相关关系并进行了验证;揭示了偏应力作用下,细观参数对密实砂土试样内部剪切带宽度与倾角变化的影响规律,提出了考虑剪胀角的剪切带倾角经验公式。通过研究建立了抗转线性接触模型宏?细观参数的量化关系并给出了标定参数的具体流程图,提出了快速标定宏观参数的方法并应用实例进行了验证,为采用抗转线性接触模型精准模拟密实砂土的力学特性提供依据。     

黏土不排水条件下的应力路径损伤本构模型

黏土的变形主要受土颗粒之间的联结方式控制,将土颗粒之间的联结方式分为完善联结和滑动联结。在弹性变形阶段,颗粒之间的联结为完善联结,随着剪应力的增大,骨架中一部分完善联结逐渐变成滑动联结,这种转变即为损伤的演化。骨架的损伤和破坏遵循Mohr-Coulomb准则,在p-q平面中以应力点到初始损伤线和破坏线的相对距离表示损伤比,给出了一种描述骨架损伤和计算损伤演化的方法,进而提出了一种描述黏土在不排水条件下剪切变形的损伤本构模型。模型中的参数可根据常规三轴压缩试验确定,模型的形式简单,可适用于复杂的应力路径情况。对试验结果的拟合表明,该模型能较好地反映黏土在不排水条件下的剪切变形特征。     

考虑转动阻抗的粗粒土离散元模拟

转动阻抗被定义为作用颗粒接触上的一对对称力偶,用来抵抗颗粒之间的相互转动。将转动阻抗引入到离散元模拟中是对传统离散单元法的重要改进。开发出考虑颗粒转动阻抗的接触模型,并将其嵌入到PFC2D中,利用该模型进行粗粒土的双轴剪切数值模型试验,研究剪切过程中转动阻抗对粗粒土的宏细观力学性质的影响。结果显示,在宏观方面,颗粒转动阻抗对粗粒土的宏观力学行为（应力-应变及体应变-轴应变行为）有重要的影响,随着转动阻抗的增加,粗粒土的剪切强度和最大摩擦角随之增加,这与已有的研究结果一致,证明所建模型是可靠的;在微观方面,考察转动阻抗对粗粒土内部微观结构的影响发现,随着转动阻抗的增加,粗粒土的内部的接触数目减少,而粗粒土的剪切强度增加,表明转动阻抗能够提高粗粒土力链网络的稳定性,同时发现随着转动阻抗的增加,粗粒土的各向异性增加主要是强力链各向异性的增加,说明转动阻抗增强了强力链的传递力的能力以及抵抗力链屈曲破坏能力。数值模拟结果表明,增加颗粒转动阻抗,粗粒土出现组构与轴应变非共轴的现象。     

Bond rolling resistance and its effect on yielding of bonded granulates by DEM analyses

A discrete element modelling of bonded granulates and investigation on the bond effect on their behaviour are very important to geomechanics. This paper presents a two‐dimensional (2‐D) discrete element theory for bonded granulates with bond rolling resistance and provides a numerical investigation into the effect of bond rolling resistance on the yielding of bonded granulates. The model consists of mechanical contact models and equations governing the motion of bonded particles. The key point of the theory is that the assumption in the original bond contact model previously proposed by the authors (55th CSCE‐ASCE Conference, Hamilton, Ont., Canada, 2002; 313–320; J. Eng. Mech. (ASCE) 2005; 131 (11):1209–1213) that bonded particles are in contact at discrete points, is here replaced by a more reliable assumption that bonded particles are in contact over a width. By making the idealization that the bond contact width is continuously distributed with the normal/tangential basic elements (BE) (each BE is composed of spring, dashpot, bond, slider or divider), we establish a bond rolling contact model together with bond normal/tangential contact models, and also relate the governing equations to local equilibrium. Only one physical parameter β needs to be introduced in the theory in comparison to the original bond discrete element model. The model has been implemented into a 2‐D distinct element method code, NS2D. Using the NS2D, a total of 86 1‐D, constant stress ratio, and biaxial compressions tests have been carried out on the bonded granular samples of different densities, bonding strengths and rolling resistances. The numerical results show that: (i) the new theory predicts a larger internal friction angle, a larger yielding stress, more brittle behaviour and larger final broken contact ratio than the original bond model; (ii) the yielding stress increases nonlinearly with the increasing value of β, and (iii) the first‐yield curve (initiation of bond breakage), which define a zone of none bond breakage and which shape and size are affected by the material density, is amplified by the bond rolling resistance in analogous to that predicted by the original bond model. Copyright © 2006 John Wiley & Sons, Ltd.     

抗转动对颗粒材料组构特性的影响研究

颗粒材料大多由不规则形状的颗粒组成,如砂土、谷物等,抵抗转动是不规则形状颗粒的固有特性。已有研究表明,颗粒抗转动特性对其宏观力学特性有显著影响。因此,在颗粒材料的细观数值模拟中或采用非圆颗粒,或在圆颗粒离散元模拟中采用考虑抗转动的接触模型。采用有限元-离散元耦合方法（FDEM）和离散元方法（DEM）分别对椭球形状颗粒和具有抗转动能力的圆球颗粒进行三轴剪切数值模拟,指出了采用抗转动接触模型考虑颗粒形状影响的局限性,并基于颗粒的局部排布结构揭示了形状影响的细观来源。峰值内摩擦角和剪胀均随着转动摩擦系数和形状偏离圆球程度而单调增加,但颗粒形状对它们的影响呈现出明显的收敛趋势。细观组构分析也表明,虽然颗粒形状和转动摩擦都能显著增强组构各向异性,但是组构各向异性的演化模式有明显的区别。造成以上结果的差异在于其抵抗转动的影响机制不同。转动摩擦是通过限制颗粒转动,增强了颗粒间的稳定承载能力,而非圆颗粒是通过咬合作用形成稳定的局部排列结构。由于椭球颗粒腹部比端部能够传递更大的接触力,颗粒受剪切后发生转动,颗粒长轴倾向于正交大主应力方向,呈现交错排列,颗粒间相互锁定。     

基于物质点法的土体流动大变形过程数值模拟

土体滑坡作为一种自然地质灾害,受自然因素和人类活动的影响在我国时有发生,给周围居民的生命和财产安全带来了很大威胁,日益受到人们的广泛关注。滑坡防治也逐渐成为工程研究的热点之一。土体本质上是一种具有复杂组成结构的颗粒材料堆积体,通过对颗粒流动的模拟可以深入理解自然界中的土体流动现象,如滑坡、泥石流等,进而预测灾害破坏范围及改进相应工程防护措施。但由于土体流动是一个涉及大变形及大位移的复杂流动过程,传统的基于网格的有限元法（FEM）由于网格畸变,并不适合这类问题的研究。本文采用物质点法（MPM）模拟土体流动大变形问题。作为一种源于particle-in-cell（PIC）法的无网格法,兼具欧拉法和拉格朗日法的优点,因而,物质点法在处理大变形问题上具有独特的优势。目前,国内外利用物质点法模拟边坡滑动问题已有不少研究,但对相关参数进行敏感性分析的较少。本文基于物质点法模拟了黏性土体及无黏性土体流动大变形问题,并进行了参数敏感性分析,包括土体材料的内摩擦角、黏聚力、高宽比、底面坡度对土体滑动距离的影响规律。本文计算中采用Drucker-Prager（DP）弹塑性本构模型描述土的非线性特性。研究结果表明:（1）基于物质点法得到的土体的流动形态、滑动距离以及自然休止角等数值模拟结果均与文献中的实验结果基本吻合,验证了物质点法模拟土体大变形力学行为的精度及有效性;（2）随着内摩擦角、黏聚力的增大,滑动距离相应减小;（3）坡度对边坡稳定的影响是显著的,随着底面坡度的增大,滑动距离相应增大;（4）当土柱高宽比较小时,与滑动距离呈线性增长关系。其中,内摩擦角和黏聚力反映了土体的抗剪切性能,因此通过工程措施提高土体的抗剪能力可以降低土体滑坡带来的危害。研究结果为探索土体滑动破坏规律,降低滑动破坏范围提供了可靠的参考。     

On the stress-force-fabric equation in triaxial compressions: Some insights into the triaxial strength

The strength of granular materials during triaxial compression is investigated via a grain scale analysis in this paper. A 3D Discrete Element Method (DEM) program provides the triaxial strength data and helps to validate the micromechanical analysis. Some standard methods in statistics are employed first to quantitatively examine the assumptions made when deriving the stress-force-fabric (SFF) equation. After careful validation, a more concise format for the SFF equation is proposed for triaxial compressions. With this SFF equation, the strength is found to be jointly contributed by the magnitudes of the contact force anisotropy and fabric anisotropy. The influence of the initial void ratio, confining pressure and loading direction on the development of contact force anisotropy and fabric anisotropy is examined and presented. With similar techniques, the “force” term in the SFF equation is further decoupled, and an equation is obtained such that it explicitly links the contact force term with the friction coefficient between grains, a tensor defined as a statistic of the normal contact forces and a tensor defined as a statistic of the mobilisation status of contacts. Based on this equation, another equation regarding the stress ratio of granular assembly is obtained, and it clearly indicates two sources that contribute to the phenomenological friction nature of granular assembly. These two sources are caused by the contact force at the grain scale. The first is the anisotropy of the average normal contact forces, and the second is the mobilisation of contacts.     

A new model of edge-to-edge contact for three dimensional discontinuous deformation analysis

A robust contact theory can be regarded as key to three dimensional discontinuous deformation analyses (3D-DDA). Not only must this theory provide an efficient algorithm to judge the type and location of contacts but also it must be able to present comprehensive formulations for every kind of contact (open, sliding and locked contact). There are six types of contact in three dimensional discontinuous deformation analyses (vertex-to-vertex, vertex-to-edge, vertex-to-face, edge-to-edge, edge-to-face and face-to-face) that can be converted to vertex-to-face and edge-to-edge contacts. This paper presents a new model of edge-to-edge contact to three dimensional discontinuous deformation analyses (3D-DDA). This new model considers both kinds of edge-to-edge contact (cross-over and parallel edge-to-edge contact) and presents a criterion for inter-penetration. Sub matrices of normal and shear spring and friction force are derived by geometrical analysis and penalty method. This new model is implemented in a 3D-DDA computer programme, and the example results demonstrate the validity of the model.     

黏性土固结不排水剪切的滑动损伤模型研究

在工程荷载范围内,不计骨架颗粒的变形,骨架的变形实际是颗粒接触面变形的总和。当剪应力达到某个临界值时,黏性土骨架中有一部分颗粒接触面开始滑动,随着剪应力的增大,出现滑动的颗粒接触面的取向范围也会扩大。将这种颗粒接触面的滑动视为一种损伤。在损伤阶段,黏性土骨架中既有未滑动的接触面,也有已滑动的接触面,宏观剪切模量是这两种接触面的剪切模量的加权平均。在 平面中,根据应力圆与颗粒起始滑动包络线的相对位置,计算出已出现了滑动的颗粒接触面的取向范围,并定义该取向范围与其所能达到的最大值（由破坏时的应力圆计算）之比为骨架的损伤比。按损伤比进行加权平均得到骨架的整体剪切模量。模型中的参数完全可以根据常规三轴试验确定,模型的形式简单,可适用于复杂的应力路径。对试验结果的拟合表明,该模型能较好地反映黏性土在固结不排水条件下剪切变形的主要特征。     

沉积角对净砂宏微观力学特性影响的离散元分析

由颗粒定向排列导致的初始各向异性对净砂力学特性影响明显。为探究这一影响,首先采用自编的离散元软件生成4种不同沉积方向的椭圆颗粒净砂样,并分别对4种试样进行双轴压缩试验;其次,通过将离散元模拟结算与室内试验结果对比以验证该方法的可行性;最后,通过分析模拟结果研究沉积方向所产生的影响。结果表明：4种试样均出现应变软化及剪胀现象;随着沉积角? 的增加,试样具有由应变软化逐渐向应变硬化发展的趋势,试样的剪胀性逐渐减弱;在?=0°时试样取得最大峰值内摩擦角和最大残余内摩擦角,且随着? 的增大试样的峰值内摩擦角先降低然后基本不变,残余内摩擦角逐渐减小;颗粒排列初始优势方向基本与沉积方向平行,但随着轴向应变的增大,颗粒排列优势方向逐渐向平行于加载面方向旋转,接触点的优势方向由最初垂直于沉积方向逐渐向垂直于加载面方向旋转,且这两种旋转的改变幅度随着沉积角? 的增大而增大;而强接触力的优势方向始终垂直于试样的加载面。     

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.     

椭圆形颗粒堆积体模拟颗粒材料力学性能的离散元数值方法

针对离散元中圆形颗粒模拟出的内摩擦角小于真实砂土内摩擦角的缺陷,将已有NS2D离散元程序中的圆形颗粒参量改进为椭圆形颗粒参量,形成改进的NS2D程序。介绍了改进后NS2D程序的基本力学模型,详细推导了程序中椭圆颗粒间以及椭圆颗粒与墙之间接触点的力-位移关系。利用改进后的离散元程序分别模拟了恒定围压下长短轴比例分别为1.1:1、1.4:1,孔隙比均为0.19的椭圆颗粒堆积体的双轴试验,所得的内摩擦角在真实砂土的内摩擦角范围之内,且其应力特征与已有成果吻合良好,证明了改进后的NS2D离散元程序能够模拟分析真实砂土的力学性能