基于接触价键的颗粒材料微观临界状态

用颗粒离散元法,分别对二维圆形、椭圆形颗粒体进行了双轴压缩数值模拟。微观尺度的变形是基于孔隙胞元和其中的变形来计算的,而单个孔隙胞元的变形通过周围颗粒的相对运动来计算。针对该方法提出了以接触价键（每个孔隙胞元的边数）来表征颗粒材料微观临界状态的理论。为了定义临界接触价键的极限值,分别讨论了摩擦系数较大、较小时的两种情况。文中给出了微观几何织构（包括接触价键、孔隙胞元的形状、孔隙比）随压缩变形的演变过程,比较了不同颗粒形状、颗粒间摩擦系数以及颗粒体的固结压力对颗粒体的微观力学性能的影响。计算结果表明,颗粒材料的微观临界状态并不是可以唯一表征的,而是受围压、摩擦系数,颗粒形状等参数的共同影响。     

颗粒材料的微观临界状态理论模型

存在临界状态是颗粒材料的一个重要特性。基于孔隙胞元的颗粒离散元方法对二维颗粒体进行双轴加载数值试验,在详细分析数值模拟结果的基础上,从微观几何组构的角度揭示了临界状态的存在机制。基于剪胀性原理,提出了以接触价键表征的微观临界状态理论模型,得到了接触价键与塑性剪切应变的关系表达式,理论模型的结果和二维离散元数值模拟得到的结果吻合较好。通过比较不同情况下数值结果和理论模型中的参数,得到以下结论：表征微观临界状态的参数（临界接触价键和达到临界状态所需要的塑性剪切应变）依赖于颗粒体的微观特性,如颗粒形状、表面摩擦性质、颗粒体的围压和初始孔隙比。     

上海黏土压缩回弹变形的微观机理

黏土变形微观机理的研究过去多针对土体加载压缩开展,随着研究的深入,黏土卸载回弹变形的微观机理也逐步得到重视,但目前对此研究还很少。本文采用单向压缩及回弹试验、扫描电镜及压汞试验对上海黏土压缩及回弹变形过程中土体的微观特性及其变化进行了研究。研究结果表明,微观结构参数的变化能反映黏土的宏观变形特征。在加载过程中,随固结压力增加,土体孔隙体积减小,孔隙数量先增加再减小,孔隙平均形状系数的增加先急后缓,孔隙形态分维数先急剧减小后缓慢减小。在卸载过程中,随固结压力减小,孔隙数量增加,平均形状系数略有减小,孔隙形状分维数略有增加。加载压缩过程中,固结压力较小时中、小孔隙体积所占比例变化不大,而当固结压力较大时小孔隙所占比例显著增加、中孔隙所占比例明显减小。在卸载回弹过程中,各级固结压力下小孔隙都占绝对优势,但固结压力较大时中孔隙所占比例较大,而固结压力较小时中孔隙所占比例较小,黏土卸载回弹变形主要是小孔隙体积的少量增加。     

不同应力路径下K_0固结结构性黏土微观结构特征试验研究

研究结构性黏土在不同应力路径下的微观结构变化可深入了解K_0固结下结构性黏土结构性特性变化的内在机制。在对衡水地区天然黏土进行不同应力路径条件下三轴剪切试验的基础上,利用微观定量化技术,对比不同应力路径条件下土样的微观结构,从微观角度对结构性黏土的微观结构特征变化机制进行了解释。结果表明:在不同应力路径下土体的孔隙直径、颗粒和孔隙的定向排列变化较大,而颗粒和孔隙的形状特征变化较小。增大球应力使土颗粒变得密实,使孔隙压缩,土体体积减小;减小球应力使土颗粒变得松散,孔隙直径增大,土体体积膨胀。增大或减小偏应力对土体微观结构的影响相似,在土体结构破坏前使土骨架变形产生一定压缩,在土体结构破坏后使颗粒错动、翻滚并相互搭接,扩大了粒间孔隙,使土体出现剪胀。土颗粒形状的不规则性导致球应力和偏应力对体应变和剪应变的交叉影响。研究结果揭示了不同应力路径下结构性黏土应力-应变特性的微观机制。     

基于微观力学的胶结岩土材料破损规律离散元模拟

采用离散元法（DEM）研究胶结岩土材料在不同加载条件下的结构破损规律。首先,基于微观力学理论,考虑胶结岩土材料颗粒间胶结特性,给出表征结构性损伤的破损参数式。该式具有微观物理意义,但不能直接用于建立宏观本构模型。其次,采用二维离散元源程序NS2D模拟等向压缩、等应力比压缩以及双轴压缩试验,分析破损参数在不同加载条件下随宏观力学变量（体积应变和剪应变）的演变规律。最后,根据模拟结果提出破损参数数学表达式,其为大主应变的函数。研究结果表明：胶结强度、应力比以及围压均在一定程度上影响了数值试样的结构破损规律。在等向压缩和等应力比压缩试验中,容易用函数式描述数值试样破损参数随体积应变或偏应变的演变规律;而在双轴压缩条件下,由于数值试样有剪胀特性,破损参数随体积应变的演变规律则不易描述。建议的破损参数数学表达式能够较好地描述数值试样在不同加载条件下结构破损规律。     

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。     

颗粒材料的剪胀模型

本文研究了颗粒材料的剪切变形机制,建立了颗粒体在变形过程中应力与组构量的相互关系,论证了产生剪胀的微观组构条件,推导出各向异性组构颗粒体剪胀方程。做了相应的单剪试验,理论结果与试验结果相当吻合,从而验证了理论模型的正确性。     

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。     

空心圆柱扭转仪定向剪切试验离散元模拟

为分析砂土在复杂应力条件下的剪切力学特性,采用商业离散元软件PFC3D对单粒组中密砂的空心扭剪试验进行了仿真模拟,分析了数值试样的应力-应变关系,研究了不同剪切方向下离散介质的强度、体积应变特性以及中主应力比对它们的影响,再现了力链在加载过程中的演化,并对剪切带的倾角做了深入分析。同时,从细观上看,以颗粒接触数和纯转动率变量为中心,观察了试样内部颗粒的运动状态,对比了不同剪切方向下剪切带内外颗粒接触数与纯转动位移的变化。最后,将数值试验结果与已有的室内试验结果进行了对比。此研究实现了复杂应力条件下空心扭剪试样的三维离散元模拟,加深了对空心扭剪试验过程和结果的理解和解释。     

饱和砂土液化后大变形机制的离散元细观分析

采用颗粒流软件模拟了饱和砂土在不排水条件下的循环剪切试验,研究了不同因素对液化的影响,并进一步分析了饱和砂土液化后宏观变形的基本规律。在此基础上,从孔隙分布角度解释了砂土液化后的大变形的细观物理机制。通过自编程序对颗粒排列和孔隙分布的演化过程进行定量描述,给出孔隙率标准差作为液化后体积收缩势的度量,并研究了孔隙率标准差与液化后大变形的关系。离散元细观数值模拟再现了室内试验中的宏观现象,证实了室内试验中饱和砂土液化后的有限剪切大变形是客观真实的材料响应。土体体积收缩势的累积所导致的孔隙均匀化以及土颗粒间自由空隙增大正是饱和砂土液化后循环剪应变逐渐增大的细观机制。孔隙率标准差作为孔隙均匀化的量化指标,与循环剪应变各周次幅值有良好的相关性。     

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.     

Fabric evolution within shear bands of granular materials and its relation to critical state theory

In an effort to study the relation of fabrics to the critical states of granular aggregates, the discrete element method (DEM) is used to investigate the evolution of fabrics of virtual granular materials consisting of 2D elongated particles. Specimens with a great variety of initial fabrics in terms of void ratios, preferred particle orientations, and intensities of fabric anisotropy were fabricated and tested with direct shear and biaxial compression tests. During loading of a typical specimen, deformation naturally localizes within shear bands while the remaining of the sample stops deforming. Thus, studying the evolution of fabric requires performing continuous local fabric measurements inside these bands, a suitable task for the proposed DEM methodology. It is found that a common ultimate/critical state is eventually reached by all specimens regardless of their initial states. The ultimate/critical state is characterized by a critical void ratio e which depends on the mean stress p, while the other critical state fabric variables related to particle orientations are largely independent of p. These findings confirm the uniqueness of the critical state line in the e ? p space, and show that the critical state itself is necessarily anisotropic. Additional findings include the following: (1) shear bands are highly heterogeneous and critical states exist only in a statistical sense; (2) critical states can only be reached at very large local shear deformations, which are not always obtained by biaxial compression tests (both physical and numerical); (3) the fabric evolution processes are very complex and highly dependent on the initial fabrics. Copyright © 2010 John Wiley & Sons, Ltd.     

DEM study of fabric features governing undrained post-liquefaction shear deformation of sand

In an effort to study undrained post-liquefaction shear deformation of sand, the discrete element method (DEM) is adopted to conduct undrained cyclic biaxial compression simulations on granular assemblies consisting of 2D circular particles. The simulations are able to successfully reproduce the generation and eventual saturation of shear strain through the series of liquefaction states that the material experiences during cyclic loading after the initial liquefaction. DEM simulations with different deviatoric stress amplitudes and initial mean effective stresses on samples with different void ratios and loading histories are carried out to investigate the relationship between various mechanics- or fabric-related variables and post-liquefaction shear strain development. It is found that well-known metrics such as deviatoric stress amplitude, initial mean effective stress, void ratio, contact normal fabric anisotropy intensity, and coordination number, are not adequately correlated to the observed shear strain development and, therefore, could not possibly be used for its prediction. A new fabric entity, namely the Mean Neighboring Particle Distance (MNPD), is introduced to reflect the space arrangement of particles. It is found that the MNPD has an extremely strong and definitive relationship with the post-liquefaction shear strain development, showing MNPD’s potential role as a parameter governing post-liquefaction behavior of sand.     

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.     

Non‐coaxiality and stress–dilatancy rule in granular materials: FE investigation within micro‐polar hypoplasticity

This paper deals with FE investigations of shear localization in dilatant granular bodies. The calculations were carried out with a hypoplastic constitutive law enhanced by micro‐polar terms to properly model the shear zone evolution. The behaviour of an initially medium dense sand specimen with very smooth and very rough horizontal boundaries was analyzed during a plane strain compression test. A stochastic distribution of the initial void ratio was assumed to be spatially correlated. Attention was focused on the non‐coaxiality of the directions of the principal strain increments and principal stresses in the shear zone and on the stress–dilatancy rule. Copyright © 2008 John Wiley & Sons, Ltd.     

Micromechanical investigation of the particle size effect on the shear strength of uncrushable granular materials

Particle size strongly influences the shear strength of granular materials. However, previous studies of the particle size effect have focused mainly on the macroscopic behavior of granular materials, neglecting the associated micro-mechanism. In this study, the effect of particle size on the shear strength of uncrushable granular materials in biaxial testing is investigated using the discrete element method (DEM). First, a comprehensive calibration against experimental results is conducted to obtain the DEM parameters for two types of quartz sand. Then, a series of biaxial tests are simulated on sands with parallel particle size distributions to investigate the effect of particle size on macro- and microscopic behaviors. Finally, by adopting the rolling resistance method and the clump method, irregular-shaped particles are simulated to investigate how the particle size effect will be influenced by the particle shape. Simulation results demonstrate that (1) the peak shear strength increases with particle size, whereas the residual shear strength is independent of particle size; (2) the thickness of the shear band increases with the particle size, but its ratio decreases with particle size; (3) the particle size effect can be explained by the increase of friction utilization ratio with particle size; and (4) the particle size effect is more significant in granular materials that consist of particles with higher angularity.