岩石单颗粒压缩破碎试验研究

岩石颗粒结构复杂、形态不规则,很难用现有经典理论进行研究,分形理论可以从统计的角度研究颗粒破碎的强度。根据600颗大理岩单颗粒破碎试验,测量单颗粒破碎的应力与竖向应变关系曲线和破碎后的颗粒分布曲线,将颗粒破碎曲线按形态分为三种类型;根据颗粒破碎后的颗粒分布特性,建立了岩石颗粒破碎的分形模型,测得了大理岩颗粒破碎的分维D为2.48;根据颗粒破碎的分形模型,导出颗粒破碎强度的理论公式;将大理岩颗粒破碎强度的试验数据与理论公式预测结果进行比较,两者十分吻合,从而验证了颗粒破碎强度的分形理论。     

考虑破碎影响的颗粒材料亚塑性模型及应变局部化模拟

在基于2ndP-K应力率的亚塑性模型基础上,通过引入一个能够考虑颗粒破碎影响的孔隙比-平均压力临界状态方程,形成了一个能够模拟颗粒破碎影响的颗粒材料亚塑性模型,数值算例考查了颗粒破碎对应变局部化模式及位移-承载曲线的影响,结果表明,所建议模型具有模拟破碎对颗粒材料应变局部影响的良好性能。     

Micro-scale behavior of granular materials during cyclic loading

This study presents the micro-scale behavior of granular materials under biaxial cyclic loading for differ- ent confining pressures using the two-dimensional （2D） discrete element method （DEM）. Initially, 8450 ovals were generated in a rectangular frame without any overlap. Four dense samples having confining pressures of 15, 25, 50, and 100 kPa were prepared from the initially generated sparse sample. Numeri- cal simulations were performed under biaxial cyclic loading using these isotropically compressed dense samples. The numerical results depict stress-strain-dilatancy behavior that was similar to that observed in experimental studies. The relationship between the stress ratio and dilatancy rate is almost indepen- dent of confining pressures during loading but significantly dependent on the confining pressures during unloading. The evolution of the coordination number, effective coordination number and slip coordina- tion number depends on both the confining pressures and cyclic loading. The cyclic loading significantly affects the microtopology of the granular assembly. The contact fabric and the fabric-related anisotropy are reported, as well. A strong correlation between the stress ratio and the fabric related to contact normals is observed during cyclic loading, irrespective of confining pressures.     

椭球颗粒体系剪切过程中自由体积的分布与演化

颗粒材料是一种复杂的多体相互作用体系, 由大量离散的颗粒和其周围的自由体积组成. 虽然颗粒的自由体积与颗粒材料的力学性能和变形特征的相关性已得到证实, 但是由于表征上的困难, 目前对非球形颗粒体系的局部自由体积的认识还不够充分. 本文采用连续离散耦合分析方法进行了不同主轴长度的椭球颗粒试样的三轴剪切数值模拟, 基于Set Voronoi算法对剪切过程中的颗粒试样进行了Voronoi元胞分割, 分析了颗粒试验在剪切过程中自由体积的统计分布特性和演化规律, 研究了颗粒形态对自由体积的影响. 剪切过程中Voronoi元胞的各向异性逐渐增强, 且各项异性增强程度随颗粒非球度的增加而增大, 表明非球颗粒在剪切过程中经历更加强烈的重排列. 具有不同非球度的椭球颗粒体系的局部孔隙比均服从k?Γ分布, 且这个分布仅与颗粒体系的全局孔隙比相关, 不受颗粒形态和剪切状态的影响. 局部孔隙比的波动呈现非对称拉普拉斯分布, 非对称参数刻画了局部自由体积收缩和膨胀的博弈, 其与全局孔隙比呈线性关系.      

冲击载荷作用下颗粒材料动态力学响应的近场动力学模拟

颗粒材料在冲击载荷作用下的动态力学行为是学术界关注的热点问题. 新近问世的近场动力学(peridynamics)理论将材料视为由大量有限体积和有限质量的物质点组成,基于非连续性和非局部作用假定建模,建立空间积分形式的运动方程,自然适应于颗粒材料动态力学行为的描述与分析. 发展了描述颗粒间接触作用的物质点尺度的排斥力模型,考虑近场动力学方法中非局部长程力特征,改进了近场动力学中的初始微观弹脆性(prototype microelastic brittle, PMB) 模型的本构力函数,并消除了原PMB 模型中存在的“边界效应” 问题. 计算分析了冲击载荷作用下碳化钨陶瓷颗粒体系的动态力学响应,得到了不同冲击速度下颗粒体系的冲击波速,PD计算结果与试验结果高度一致;通过颗粒物质点尺度作用描述单颗粒尺度的接触作用,很好地再现了颗粒的转动与平动、颗粒挤压变形以及颗粒破碎等现象;刚性冲击板附近同时存在严重的颗粒破碎与轻微的颗粒损伤,远离冲击板的部分颗粒出现破损,且颗粒破碎主要是由颗粒间挤压、碰撞以及相对滑动剪切作用造成的. 研究结果表明,所发展的计算模型和分析方法能很好地反映颗粒材料动态力学行为,具有广泛的应用价值.      

Micromechanical study of elastic moduli of loose granular materials

In micromechanics of the elastic behaviour of granular materials, the macro-scale continuum elastic moduli are expressed in terms of micro-scale parameters, such as coordination number (the average number of contacts per particle) and interparticle contact stiffnesses in normal and tangential directions. It is well-known that mean-field theory gives inaccurate micromechanical predictions of the elastic moduli, especially for loose systems with low coordination number. Improved predictions of the moduli are obtained here for loose two-dimensional, isotropic assemblies. This is achieved by determining approximate displacement and rotation fields from the force and moment equilibrium conditions for small sub-assemblies of various sizes. It is assumed that the outer particles of these sub-assemblies move according to the mean field. From the particle displacement and rotation fields thus obtained, approximate elastic moduli are determined. The resulting predictions are compared with the true moduli, as determined from the discrete element method simulations for low coordination numbers and for various values of the tangential stiffness (at fixed value of the normal stiffness). Using this approach, accurate predictions of the moduli are obtained, especially when larger sub-assemblies are considered. As a step towards an analytical formulation of the present approach, it is investigated whether it is possible to replace the local contact stiffness matrices by a suitable average stiffness matrix. It is found that this generally leads to a deterioration of the accuracy of the predictions. Many micromechanical studies predict that the macroscopic bulk modulus is hardly influenced by the value of the tangential stiffness. It is shown here from the discrete element method simulations of hydrostatic compression that for loose systems, the bulk modulus strongly depends on the stiffness ratio for small stiffness ratios.     

Fracture of granular materials composed of arbitrary grain shapes: A new cohesive interaction model

Discrete Element Methods (DEM) are a useful tool to model the fracture of cohesive granular materials. For this kind of application, simple particle shapes (discs in 2D, spheres in 3D) are usually employed. However, dealing with more general particle shapes allows to account for the natural heterogeneity of grains inside real materials. We present a discrete model allowing to mimic cohesion between contacting or non-contacting particles whatever their shape in 2D and 3D. The cohesive interactions are made of cohesion points placed on interacting particles, with the aim of representing a cohesive phase lying between the grains. Contact situations are solved according to unilateral contact and Coulomb friction laws. In order to test the developed model, 2D uniaxial compression simulations are performed. Numerical results show the ability of the model to mimic the macroscopic behavior of an aggregate grain subject to axial compression, as well as fracture initiation and propagation. A study of the influence of model and sample parameters provides important information on the ability of the model to reproduce various behaviors.     

非均匀颗粒材料的类固-液相变行为及本构方程

以非均匀颗粒介质为研究对象,采用三维离散元方法对其在不同密集度和剪切速率下的动 力过程进行了数值模拟,分析了其在由瞬时接触的快速流动向持续接触的准静态流动的转变 过程及其行为特点. 通过对不同材料性质下相变过渡区内颗粒材料的宏观应力、接触时间数、 配位数、团聚颗粒数量、有效摩擦系数等参量的计算,更加全面地描述了非均匀颗粒材料在 类固-液相变过程中的基本特征. 基于以上数值计算结果,建立了一个适用于颗粒材料 类固态、类液态以及其相变过程的本构方程,并通过剪切室实验结果验证了它的合理性.     

含液颗粒材料液固耦合分析的离散颗粒模型及特征线SPH法

对含液颗粒材料流固耦合分析建议了一个基于离散颗粒模型与特征线SPH法的显式拉格朗日-欧拉无网格方案。在已有的用以模拟固体颗粒集合体的离散颗粒模型[1]基础上,将颗粒间间隙内的流体模型化为连续介质,对其提出并推导了基于特征线的SPH法。数值例题显示了所建议方案在模拟颗粒材料与间隙流相互作用的能力和性能以及间隙流体对颗粒结构承载能力及变形的影响。     

Micro-scale behavior of granular materials during cyclic loading

This study presents the micro-scale behavior of granular materials under biaxial cyclic loading for different confining pressures using the two-dimensional (2D) discrete element method (DEM). Initially, 8450 ovals were generated in a rectangular frame without any overlap. Four dense samples having confining pressures of 15, 25, 50, and 100 kPa were prepared from the initially generated sparse sample. Numerical simulations were performed under biaxial cyclic loading using these isotropically compressed dense samples. The numerical results depict stress–strain–dilatancy behavior that was similar to that observed in experimental studies. The relationship between the stress ratio and dilatancy rate is almost independent of confining pressures during loading but significantly dependent on the confining pressures during unloading. The evolution of the coordination number, effective coordination number and slip coordination number depends on both the confining pressures and cyclic loading. The cyclic loading significantly affects the microtopology of the granular assembly. The contact fabric and the fabric-related anisotropy are reported, as well. A strong correlation between the stress ratio and the fabric related to contact normals is observed during cyclic loading, irrespective of confining pressures.     

三维圆柱型颗粒堆坍塌问题的全相态数值模拟

静态颗粒堆在重力作用下的坍塌问题, 是认识和理解许多人为过程和自然现象的基础. 采用传统方法进行模拟存在单颗粒追踪数量大、宏观模拟流变特性明显和相态演变复杂等计算难点. 本文从颗粒介质表现出不同相态的物理机理出发, 对全相态概念进行了定义并进行了区域划分. 根据颗粒介质的应力-应变关系及体积分数的不同, 通过确定不同相态之间的耦合关系和转化准则, 将描述各相态的现有理论有效结合起来, 建立了描述颗粒介质经历全部相态的耦合模型理论. 采用光滑离散颗粒流体动力学方法和离散单元法相耦合的策略, 对颗粒介质物理模型求解, 实现了对不同长径比下的三维圆柱型颗粒堆坍塌过程的数值模拟. 计算结果与实验结果吻合较好, 同时与离散单元法相比, 计算量得到了控制. 不仅捕捉到了不同参数影响下颗粒堆坍塌后沉积的不同现象, 同时获得了不同条件参数对颗粒堆坍塌后铺展特性的影响规律, 为揭示工业和自然界中广泛存在的颗粒介质复杂运动机理提供有效的支撑.      

Discrete element modeling of inherently anisotropic granular assemblies with polygonal particles

In the present article, we study the effect of inherent anisotropy, i.e., initial bedding angle of particles and associated voids on macroscopic mechanical behavior of granular materials, by numerical simulation of several biaxial compression tests using the discrete element method (DEM). Particle shape is considered to be irregular convex-polygonal. The effect of inherent anisotropy is investigated by following the evolution of mobilized shear strength and volume change during loading. As experimental tests have already shown, numerical simulations also indicate that initial anisotropic condition has a great influence on the strength and deformational behavior of granular assemblies. Comparison of simulations with tests using oval particles, shows that angularity influences both the mobilized shear strength and the volume change regime, which originates from the interlocking resistance between particles.     

DISCRETE AND CONTINUUM MODELLING OF GRANULAR FLOW

This paper analyses three popular methods simulating granular flow at different time and length scales： discrete element method （DEM）, averaging method and viscous, elastic-plastic continuum model. The theoretical models of these methods and their applications to hopper flows are discussed. It is shown that DEM is an effective method to study the fundamentals of granular flow at a particle or microscopic scale. By use of the continuum approach, granular flow can also be described at a continuum or macroscopic scale. Macroscopic quantities such as velocity and stress can be obtained by use of such computational method as FEM. However, this approach depends on the constitutive relationship of materials and ignores the effect of microscopic structure of granular flow. The combined approach of DEM and averaging method can overcome this problem. The approach takes into account the discrete nature of granular materials and does not require any global assumption and thus allows a better understanding of the fundamental mechanisms of granular flow. However, it is difficult to adapt this approach to process modelling because of the limited number of particles which can be handled with the present computational capacity, and the difficulty in handling non-spherical particles. Further work is needed to develoo an aoorooriate aooroach to overcome these problems.     

Fabric and connectivity as field descriptors for deformations in granular media

Granular materials involve microphysics across the various scales giving rise to distinct behaviours of geomaterials, such as steady states, plastic limit states, non-associativity of plastic and yield flow, as well as instability of homogeneous deformations through strain localization. Incorporating such micro-scale characteristics is one of the biggest challenges in the constitutive modelling of granular materials, especially when micro-variables may be interdependent. With this motivation, we use two micro-variables such as coordination number and fabric anisotropy computed from tessellation of the granular material to describe its state at the macroscopic level. In order to capture functional dependencies between micro-variables, the correlation between coordination number and fabric anisotropy limits is herein formulated at the particle level rather than on an average sense. This is the essence of the proposed work which investigates the evolutions of coordination number distribution (connectivity) and anisotropy (contact normal) distribution curves with deformation history and their inter-dependencies through discrete element modelling in two dimensions. These results enter as probability distribution functions into homogenization expressions during upscaling to a continuum constitutive model using tessellation as an abstract representation of the granular system. The end product is a micro-mechanically inspired continuum model with both coordination number and fabric anisotropy as underlying micro-variables incorporated into a plasticity flow rule. The derived plastic potential bears striking resemblance to cam–clay or stress–dilatancy-type yield surfaces used in soil mechanics.     

A numerical analysis of the shear behavior of granular soil with fines

Shear behavior of granular soil with fines is investigated using the discrete element method(DEM) and particle arrangements and inter-particle contacts during shear are examined.The DEM simulation reveals that fine particles play a vital role in the overall response of granular soil to shearing.The occurrence of liquefaction and temporary reduction of strength is ascribed mainly to the loss of support from the fine particle contacts(S-S) and fine particle-to-large particle contacts(S-L) as a consequence of the removal of fine particles from the load-carrying skeleton.The dilative strain-hardening response following the strain-softening response is associated with the migration of fine particles back into the load-carrying skeleton,which is thought to enhance the stiffness of the soil skeleton.During shear,the unit normal vector of the large particle-to-large particle(L-L) contact has the strongest fabric anisotropy,and the S-S contact unit normal vector possesses the weakest anisotropy,suggesting that the large particles play a dominant role in carrying the shear load.It is also found that,during shear,fine particles are prone to rolling at contacts while the large particles are prone to sliding,mainly at the S-L and L-L contacts.     

基于水平集-离散元方法的球谐函数颗粒材料缓冲性能分析

在自然环境与工业领域中,颗粒材料是一种常见的缓冲材料,其中大量形态各异的非球形颗粒表现出复杂的力学特性并应用于不同工程领域。本文采用球谐函数构造不同球面度和表面凹凸特性的非规则颗粒,通过水平集方法计算球谐函数颗粒间的接触点和碰撞力,并对冲击过程中球形和凹形颗粒的缓冲性能进行离散元分析。数值结果表明,颗粒床厚度、冲击速度和颗粒形状显著影响球谐函数颗粒材料的缓冲性能。颗粒床底部的冲击力峰值随着颗粒床厚度和表面凹凸性的增加而降低,同时冲击力峰值随着冲击速度和颗粒球面度的增加而增加。与球形颗粒相比,球谐函数颗粒具有凹凸表面和多接触点特性,这有利于冲击荷载向四周扩展并提高凹形颗粒的缓冲效果。     

Numerical simulation study on particle breakage behavior of granular materials in confined compression tests

In order to study the fragmentation law, the confined compression experiment of granular assemblies has been conducted to explore the particle breakage characteristic by DEM approach in this work. It is shown that contact and contact force during the loading process gradually transform from anisotropy to isotropy. Meanwhile, two particle failure modes caused by different contact force states are analyzed, which are single-through-crack failure and multi-short-crack failure. Considering the vertical distribution of the number of cracks and the four characteristic stress distributions (the stress related to the maximum contact force, the major principal stress, the deviatoric stress and the mean stress), it is pointed out that the stress based on the maximum contact force and the major principal stress can reflect the distribution of cracks accurately. In addition, the size effect of particle crushing indicates that small size particles are prone to break. The lateral pressure coefficient of four size particles during the loading process is analyzed to explain the reason for the size effect of particle breakage.     

Micromechanical study of elastic moduli of three-dimensional granular assemblies

In micromechanics of granular materials, relationships are investigated between micro-scale characteristics of particles and contacts and macro-scale continuum characteristics. For three-dimensional isotropic assemblies the macro-scale elastic characteristics are described by the bulk and the shear modulus, which depend on the micro-scale characteristics of the coordination number (i.e. the average number of contacts per particle) and the interparticle contact stiffnesses in directions normal and tangential to the contact.     

Superquadric DEM-SPH coupling method for interaction between non-spherical granular materials and fluids

The research on the coupling method of non-spherical granular materials and fluids aims to predict the particle–fluid interaction in this study. A coupling method based on superquadric elements is developed to describe the interaction between non-spherical solid particles and fluids. The discrete element method (DEM) and the smoothed particle hydrodynamics (SPH) are adopted to simulate granular materials and fluids. The repulsive force model is adopted to calculate the coupling force and then a contact detection method is established for the interaction between the superquadric element and the fluid particle. The contact detection method captures the shape of superquadric element and calculates the distance from the fluid particle to the surface of superquadric element. Simulation cases focusing on the coupling force model, energy transfer, and large-scale calculations have been implemented to verify the validity of the proposed coupling method. The coupling force model accurately represents the water entry process of a spherical solid particle, and reasonably reflects the difference of solid particles with different shapes. In the water entry process of multiple solid particles, the total energy of the water entry process of multiple solid particles tends to be stable. The collapse process of the partially submerged granular column is simulated and analyzed under different parameters. Therefore, this coupling method is suitable to simulate fluid–particle systems containing solid particles with multiple shapes.     

On the degradation of granular materials due to internal erosion

A new state-based elasto-plastic constitutive relationship along with the discrete element model is established to estimate the degradation of granular materials due to internal erosion.Four essential effects of internal erosion such as the force network damage and relaxation are proposed and then incorporated into the constitutive relationship to formulate internal erosion impacts on the mechanical behavior of granular materials.Most manifestations in the degradation of granular materials,such as reduction of peak strength and dilatancy are predicted by the modified constitutive relationship in good agreement with the discrete element method(DEM)simulation.In particular,the sudden reduction of stress for conspicuous mass erosion in a high stress state is captured by force network damage and the relaxation mechanism.It is concluded that the new modified constitutive relationship is a potential theory to describe the degradation of granular materials due to internal erosion and would be very useful,for instance,in the prediction and assessment of piping disaster risk during the flood season.