基于复杂网络的岩土颗粒材料分散性失稳先兆研究

岩土颗粒材料在达到Mohr-Coulomb塑性极限之前可能已经发生了没有明显局部损伤的全域准均匀破坏,即分散性失稳。近年来,网络科学工具在颗粒材料环境中的应用为研究其失稳破坏现象提供了有趣新颖的洞见。采用离散单元法对不同初始密实度的颗粒体系进行等体积应变加载路径的数值试验,发现初始状态越松散的颗粒体系越有可能发生分散性失稳;采用网络科学的理论和方法分析颗粒接触网络的拓扑结构特性和演化规律,发现颗粒材料分散性失稳的结构根源是颗粒接触网络完全崩塌。将颗粒体系划分为强、弱接触系统以构建强接触子网络、弱接触子网络和强−弱接触子网络,研究颗粒接触网络及其3个子网络的特征量演化,结果表明：当颗粒材料开始处于不稳定状态时,易受扰动的弱接触系统的部分接触先失效,导致强接触系统失去其稳定支撑作用而降低承载能力。随着加载的继续,系统通过非局部的自组织过程导致接触结构的全面崩塌,最终触发整体分散性失稳。因此,先于整体失稳的部分弱接触的失效,可视为颗粒材料分散性失稳的关键性临界征兆。     

Grain scale simulations of loose sedimentary beds: the example of grain-bed impacts in aeolian saltation

Sediment transport by wind is one of many processes of interest to the geomorphologist in which grain to grain contacts play an important role. In order to illustrate the modelling of collections of frictional, inelastic sedimentary grains with the particle dynamics method (PDM), we use the grain impact process in aeolian saltation as a specific example. In PDM, all the forces on each particle are evaluated at a sequence of small time-steps, and the Newtonian equations of motion are integrated forward in time. Interparticle forces at grain contacts are treated as springs with prescribed stiffness (normal force) and by a Coulomb friction law (tangential force); particle inelasticity is represented by spring damping. The granular splash resulting from saltation impacts is assessed for sensitivity to the choice of grain properties, and the integration time-step. We find that for the range of impact speeds and impactor masses relevant to aeolian settings, grain splashes are relatively insensitive to grain stiffness, grain inelasticity and grain friction, and that the pattern of ejection from the bed is largely controlled by bed microtopography. A large set of impact realizations involving a variety of impact points on a small set of target beds is used to collect the appropriate statistics for describing the stochastic splash process. The splash function representing these statistics is then available for use in calculations over longer time-scales, such as the evolution of the saltation curtain. The details given here will enable the interested reader to adapt PDM modelling to other types of clastic sedimentary systems.     

基于双胞元的颗粒材料应力-应变关系研究

基于细观力学,建立颗粒材料的宏观应力-应变与接触力、接触位移、枝矢量等细观量之间的关系。用改进的Voronoi-Delaunay法对颗粒材料进行几何和物理上划分,得到改进Bagi双胞元体系;以固体胞元为基础,运用牛顿第二定律和Gauss定理提出含有旋转矢量和重力的颗粒材料平均等效应力,避免了颗粒材料的准静态假设;在孔隙胞元区域内利用变形协调条件推导出含有孔隙面矢量等几何变量的颗粒材料平均等效应变。结合文献的二维颗粒材料宏观试验结果验证了双胞元平均等效应力-应变的正确性;在三维情形下,对比双胞元等效应变和最优拟合应变结果,同样验证了基于双胞元的颗粒材料应力-应变关系,因此,该颗粒材料应力-应变关系可以为数值模拟颗粒材料力学行为提供依据。     

颗粒接触力检测方法评述

颗粒物质是大量固体颗粒体系的集合体,其特性区别于普通固体和液体等物质的性质,颗粒物质基础力学问题的研究20年来一直是科学的前沿,从分析多尺度结构和相关物理机制的角度研究颗粒物质可能取得突破。首先介绍了微观尺度--亦即单颗粒尺度颗粒间接触力的检测方法,包括高精度电子天平称重法、显色灵敏复写纸压痕方法、光弹实验方法、荧光共聚焦显微镜法和磁共振弹性成像法等,根据检测过程中是否对颗粒带来影响划分为接触式检测和非接触式检测两大类,并对这些方法的工作原理、检测结果和优缺点进行了评述。我们指出接触式测量对颗粒体系带来了或多或少的干扰,特别是由于力链对局部力的变化反应极为敏感,轻微的变化足以使得力链结构发生很大变化,开展无干扰的光测实验是必然的发展趋势,而现阶段开展二维光弹性实验是很有意义的。最后介绍了作者正在进行的颗粒物质光弹力学实验的研究工作。     

掘削卵砾石地层颗粒离散元模拟中的细观参数取值讨论

卵砾石地层被掘削时,其主要破坏模式并非一般的宏观整体剪切破坏,而是刀具切入卵砾石间的缝隙,将卵砾石颗粒剥离出原始地层,该过程较为契合颗粒离散元的物理力学假设。为确定掘削工况下的颗粒材料最优细观参数,对不同的颗粒接触法向刚度、接触刚度比、粒间摩擦系数、颗粒形状、颗粒尺寸等的颗粒材料开展了截割三维仿真试验,并分析研究了不同细观参数对掘削效果的影响。计算结果显示：颗粒接触法向刚度、接触刚度比的多种细观参数组合可以对应同一个宏观弹性模量值,接触刚度比大的细观参数组合的抗掘削能力更大。颗粒形状、粒间摩擦系数的多种细观参数组合可以对应同一个内摩擦角值,形状复杂的颗粒材料具有更大的抗掘削能力。在宏观参数相同的情况下,平均粒径更大的颗粒材料抗掘削能力更大。因此,利用颗粒离散元模拟掘削卵砾石地层问题时,除需保证虚拟颗粒材料的宏观整体剪切破坏响应与真实材料基本一致外,还需根据材料的抗掘削能力进一步标定细观参数,以获得更贴近实际情况的模拟效果。文章提出的方法可以为其他颗粒离散元掘削工况数值模拟中的参数标定提供参照依据。     

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.     

基于微形态理论的各向异性散体波动分析

基于散粒体微观力学理论,忽略颗粒转动引起的相对位移,考虑颗粒接触的组构各向异性,根据宏微观能量守恒推导得到了散体材料各向异性微形态本构关系,进而通过单位接触方向积分的递推公式推导出了各向异性本构张量表达式;在此基础上,根据哈密顿原理得到了各向异性散体材料的运动平衡方程和边界条件,从而求得了平面波在各向异性散粒体中的传播规律和频散关系,最后对波的频散关系和频率带隙进行了详细的参数分析。研究表明：该模型预测了散体中包含3类12种位移波：3种纵波、6种横波和3种平面内横向剪切波;横观各向同性条件下,接触各向异性参数a20越大,纵波和横波的频率越大,而平面内横向剪切波的频率越小;正交各向异性条件下,随着接触各向异性参数a22的增大,与2方向运动相关的横波频率增大,而与3方向运动相关的横波频率则减小;但a22的变化对纵波频率影响很小。材料各向异性程度对横波带宽影响不大,但对纵波带宽影响较大：a20的增大使得声?光学波间的带宽减小,而光学波间的带宽增大,当a20>0.84时,声?光学波间的带隙消失;但是a22的增大则使得声?光学波间的带宽增大,而光学波间的带宽减小。退化为各向同性模型后,预测3类波的频散曲线与其他各向同性模型的结果基本一致。     

离散单元法对粒状土的微观特性研究探讨

粒状土的微观结构和微观力学被认为是其宏观力学和体积特性的内在根本因素,近年来得到越来越多的关注和研究。离散单元法作为一种研究颗粒材料的数值模拟计算方法,比试验方法快捷、简便、经济,而且能够容易得到在实验室试验中很难或无法得到的更多重要的微观结构和微观力学的信息,近年来得到越来越多应用。本文介绍了离散单元法对土的微观特性研究的一些最新方法和进展,对数值建模中的一些重要方面如比重(质量)放大、树脂薄膜模拟等方面进行了阐述,对离散单元法在土的微观结构分析(如颗粒旋转、颗粒位移、中尺度孔隙率分布)的一些最新研究作了分析和介绍。分析表明,离散单元法是研究粒状土的微观特性的一个有力工具,可以对土的宏观特性从微观角度得到更好的解释和认识。     

A generalised D matrix for anisotropic elastic granular media

A matrix relating stress and elastic strain tensors for anisotropic particulate materials has been derived. The magnitude of the matrix depends on the state of the material anisotropy. Anisotropy in granular materials depends on strain because normal and tangential particle contact forces, as well as the spatial distribution of the contacts, vary with stress and strain. However, the rotation tensor and the strain tensor cannot be independent; they must satisfy certain constraints to meet the requirement for macroscopic stress tensor symmetry. These conditions and constraints lead to the derivation of the matrix presented in this article. The principal directions of the stress tensor and strain tensor are generally not coincident, and the values of deformation parameters, Young's modulus and Poisson's ratio, are direction dependent; these two aspects are also discussed in this paper. Whereas this matrix can be used in static numerical analyses for elastic problems, we note that this relationship can also be used as a basis upon which to derive a fully incremental stress–strain relationship for anisotropic granular materials in the plastic state, where the anisotropy is evolving with strain.     

ANALYTICAL MODEL OF PROGRESSIVE SLOPE FAILURE IN WASTE CONTAINMENT SYSTEMS

The potential for progressive failure in waste containment systems is an important design consideration. Many common interfaces between components in containment systems exhibit strain-softening behaviour; however, slopes are presently designed using limit equilibrium methods that do not account for these effects. An analytical model is developed to investigate the potential for progressive failure due to strain softening. Results are presented in a non-dimensional form relating the potential for strain softening to the slope geometry, the waste properties and the properties of the containment system interface. The potential for progressive failure increases as (i) the waste stiffness decreases relative to the initial stiffness of the interface resistance, (ii) the length of the slip surface increases and (iii) the rate of strain softening with displacement increases. Analysis of a case study slope failure indicates that the analytical approach produces results that are consistent with field observations and comparable to results from a more sophisticated, numerical analysis. Although simple, this analytical approach serves as a useful design guide to identify cases where it is unsafe to use the peak shear strength in a limit equilibrium analysis.     

Analysis of single rock blocks for general failure modes under conservative and non‐conservative forces

After describing the kinematics of a generic rigid block subjected to large rotations and displacements, the Udwadia's General Principle of Mechanics is applied to the dynamics of a rigid block with frictional constraints to show that the reaction forces and moments are indeterminate. Thus, the paper presents an incremental‐iterative algorithm for analysing general failure modes of rock blocks subject to generic forces, including non‐conservative forces such as water forces. Consistent stiffness matrices have been developed that fully exploit the quadratic convergence of the adopted Newton–Raphson iterative scheme. The algorithm takes into account large block displacements and rotations, which together with non‐conservative forces make the stiffness matrix non‐symmetric. Also included in the algorithm are in situ stress and fracture dilatancy, which introduces non‐symmetric rank‐one modifications to the stiffness matrix. Progressive failure is captured by the algorithm, which has proven capable of detecting numerically challenging failure modes, such as rotations about only one point. Failure modes may originate from a limit point or from dynamic instability (divergence or flutter); equilibrium paths emanating from bifurcation points are followed by the algorithm. The algorithm identifies both static and dynamic failure modes. The calculation of the factor of safety comes with no overhead. Examples show the equilibrium path of a rock block that undergoes slumping failure must first pass through a bifurcation point, unless the block is laterally constrained. Rock blocks subjected to water forces (or other non‐conservative forces) may undergo flutter failure before reaching a limit point. Copyright © 2007 John Wiley & Sons, Ltd.     

Role of particle crushing on particle kinematics and shear banding in granular materials

The paper provides an in-depth exploration of the role of particle crushing on particle kinematics and shear banding in sheared granular materials. As a two-dimensional approximation, a crushable granular material may be represented by an assembly of irregularly shaped polygons to include shape diversity of realistic granular materials. Particle assemblies are subjected to biaxial shearing under flexible boundary conditions. With increasing percentage of crushed particles, mesoscale deformation becomes increasingly unstable. Fragmented deformation patterns within the granular assemblies are unable to form stable and distinct shear bands. This is confirmed by the sparsity of large fluctuating velocities in highly crushable assemblies. Without generating distinct shear bands, deformation patterns and failure modes of a highly crushable assembly are similar to those of loose particle assemblies, which are regarded as diffuse deformation. High degrees of spatial association amongst the kinematical quantities confirm the key role that non-affine deformation and particle rotation play in the generation of shear bands. Therefore, particle kinematical quantities can be used to predict the onset and subsequent development of shear zones, which are generally marked by increased particle kinematic activity, such as intense particle rotation and high granular temperature. Our results indicate that shear band thickness increases, and its speed of development slows down, with increasing percentage of crushed particles. As particles crush, spatial force correlation becomes weaker, indicating a more diffuse nature of force transmission across particle contacts.     

锚杆挡土墙可靠度分析与计算方法

提出了锚杆挡墙中肋柱锚杆体系的串-并联模型。将肋柱视为连续梁,锚杆视为弹性支座,引入锚杆与锚固段周围岩土体的复合刚度系数,用位移法导出了各根锚杆所受荷载的统一计算公式。考虑各功能函数之间的相关性,运用系统可靠性理论,提出了单根锚杆3种破坏模式的串联系统与多根锚杆并联系统的体系可靠度计算方法,并编制了计算程序。对一工程实例进行计算,并对计算结果进行了分析,发现单根锚杆的3种失效模式并非相互独立,每种失效模式对锚杆可靠度的影响也不一样,而3根锚杆并联系统的失效概率近似等于在其他锚杆均未破坏的条件下每根锚杆单独失效概率之和。     

颗粒大小对颗粒材料力学行为影响初探

利用一种特殊颗粒材料-玻璃珠进行了一系列室内直剪试验,研究颗粒大小对颗粒材料力学行为的影响。试验一共考虑了3条近乎平行的级配曲线和4种颗粒摩擦情况：干燥状态、水浸润状态、水淹没状态和油浸润状态。试验结果表明,颗粒大小对颗粒材料的力学行为有显著影响,剪胀性随着粒径的增大而增强。为考虑颗粒大小对剪胀性的影响,提出了一种新的剪胀关系式。在该剪胀关系式中,剪胀系数为依赖于颗粒大小和颗粒摩擦等颗粒基本性质的变量。试验研究同时表明临界状态摩擦角随着颗粒大小的增加而增加。此外,从颗粒细观运动的角度提出了颗粒滑动的功能模型,推导出了功能方程,并以此揭示了颗粒大小对临界状态摩擦角影响的细观机制。     

A generalized constitutive relation for a randomly packed particle assembly

A generalized stress-strain relationship is derived for a randomly packed particle assembly taking into account the effect of particle rotation. A second-order polynomial function is assumed for the field of particle displacement. From the principle of virtual work, stress measures for a granular solid are expressed in terms of contact forces, contact moments, and geometric measures for the particle structure. An explicit stress-strain relationship is derived for isotropic packing with equal-sized particles. Examples of a representative element under torsion and bending are given to demonstrate the applicability of the presently derived higher-order stress-strain relationship.     

竖向荷载下刚性板桩筏基础分析方法

根据群桩中桩侧摩阻力分布规律,在桩筏基础中基于弹性理论中的变形协调关系、桩体物理方程和力的平衡关系,推导了竖向荷载作用下桩筏基础的荷载和位移之间的刚度矩阵,从而提出了一种刚性板下桩筏基础的分析方法。刚性板桩筏基础分析中考虑了4种相互作用,分别为桩-土-桩、桩-土-板、板-土-桩和板-土-板相互作用。基础中各桩可具有不同的桩长、桩半径和刚度等特性。应用该方法不需要划分桩-土体单元,分析中的计算矩阵仅与基础中桩数和筏板下土节点数量相关而与其他变量无关,分析过程简洁通用。通过与各种分析方法的比较验证,证明该方法是合理可行的。     

On the role of particle breakage in the shear failure behavior of granular soils by DEM

This article presents a fundamental study on the role of particle breakage on the shear behavior of granular soils using the three‐dimensional (3‐D) discrete element method. The effects of particle breakage on the stress ratio, volumetric strain, plastic deformation, and shear failure behavior of dense crushable specimens undergoing plane strain shearing conditions are thoroughly investigated through a variety of micromechanical analyses and mechanism demonstrations. The simulation of a granular specimen is based on the effective modeling of realistic fracture behavior of single soil particles, which is demonstrated by the qualitative agreement between the results from platen compression simulations and those from physical laboratory tests. The simulation results show that the major effects of particle breakage include the reduction of volumetric dilation and peak stress ratio and more importantly the plastic deformation mechanisms and the shear failure modes vary as a function of soil crushability. Consistent macro‐ and micromechanical evidence demonstrates that shear banding and massive volumetric contraction depict the two end failure modes of a dense specimen, which is dominated by particle rearrangement–induced dilation and particle crushing–induced compression, respectively, with a more general case being the combination and competition of the two failure modes in the medium range of soil crushability and confining stress. However, it is further shown that a highly crushable specimen will eventually develop a shear band at a large strain because of the continuous decay of particle breakage. Copyright © 2011 John Wiley & Sons, Ltd.     

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。     

Analysis of Rigid Short Caisson with Granular Core Incorporating Nonlinear Interface and Base Responses

It is difficult to construct a conventional shallow foundation in alluvial lowlands because of soft soils and high ground water table. A rigid short caisson foundation with granular core is being proposed for alluvial lowlands. The proposed foundation is analyzed using non-linear hyperbolic stress–displacement responses of homogeneous alluvial deposits. Extensive parametric studies are carried out to study the effects of length ratio (L/d₀), diameter ratio (d/d₀) of granular core with respect to casing, relative stiffness of shaft (α_τ), relative casing base stiffness (α_b), and friction angle of granular material (ϕ_gp) on the load sharing and the settlement of the proposed foundation.