各向异性砂土宏微观特性三维离散元分析

各向异性对砂土强度和变形特性有显著的影响,为了研究各向异性砂土的宏微观特性,基于三维离散元法,对7个不同沉积角的试样进行了一系列的三轴模拟试验。利用"Clump"命令生成近似椭球形状颗粒,并且采用三维抗转动模型来模拟颗粒间的抗转动能力。离散元模拟结果与已知室内试验结果吻合很好。结果表明:随着沉积角的增大,偏应力和轴向应变的关系逐渐由应变软化向应变硬化发展。沉积角较小的试样剪胀性更强并且容易到达临界状态,颗粒组构–应力联合不变量(表征颗粒长轴组构张量和应力张量的相对角度)的值接近于-1,且颗粒长轴组构各向异性先增大后减小;然而对于沉积角较大的试样,在轴向应变50%处,仍不能达到临界状态,并且联合不变量的值大于-1,颗粒长轴组构各向异性先减小后不断增大。对于法向接触组构,组构主轴方向迅速向应力主轴方向偏转,组构各向异性的演化规律与偏应力随轴向应变的演化规律相似。     

Applicability of discrete element method with spherical and clumped particles for constitutive study of granular materials

Discrete element method(DEM)has been intensively used to study the constitutive behaviour of granular materials.However,to what extent a real granular material can be reproduced by virtual DEM simulations remains unclear.This study attempts to answer this question by comparing DEM simulations with typical features of experimental granular materials.Three groups of models with spherical and clumped particles are investigated from four perspectives:(i)deviatoric stress and volumetric behaviour;(ii)critical state behaviour;(iii)stress-dilatancy relationship;and(iv)the evolution of principal stress ratio against axial strain.The results demonstrate that DEM with spherical or clumped particles is capable of qualitatively describing macroscopic deviatoric stress responses,volumetric behaviour,and critical state behaviour observed in experiments for granular materials.On the other hand,some qualitative deviations between experiments and the investigated DEM simulations are also observed,in terms of the stress-dilatancy behaviour and principal stress ratio against axial strain,which are proven to be critical for constitutive modelling.The results demonstrate that DEM with spherical or clumped particles may not necessarily fully capture experimental features of granular materials even from a qualitative perspective.It is thus encouraged to thoroughly validate DEM with experiments when developing constitutive models based on DEM observations.     

Behaviour of Granular Materials in Relation to Their Fabric Dependencies

The roles of dilatancy and fabric on the behaviour of granular materials are both numerically and experimentally explored for the study of material instability and failure. This investigation has two basic ingredients: namely a stress dilatancy model with microstructural information embedded through a fabric tensor, and an experimental rendition of force transmission and structure in an assembly of 2-D photoelastic disks. In order to highlight material instability, model simulations of sand behaviour are carried out in axi-symmetric stress conditions along proportional strain paths with varying degrees of controlled dilation (or compaction) including isochoric deformations as a special case. It is shown that sand, otherwise stable under isochoric (undrained) conditions, can actually succumb to an instability or a liquefaction behaviour under other loading paths. This suggests that flow type of failures in soils may not be necessarily restricted to the classic saturated loose sand case in undrained conditions, but could manifest itself under other conditions as well.     

基于非线性接触本构的颗粒材料离散元数值模拟

在考虑颗粒间细观非线性接触关系的基础上,基于空隙胞元法,采用颗粒离散元法对二维颗粒体试样进行了平面应变数值模拟。颗粒间接触用广义弹簧单元表示,相邻颗粒接触点的塑性变形用非线性弹簧表示。在准静态、小变形条件下,研究了试样的微观织构变化和宏观力学行为。单个空隙胞元的变形通过周围颗粒的相对运动来计算,将离散系统中的变形与连续体中的相应变形联系起来,应用于颗粒离散元方法中平均应力的计算。文中给出了细观尺度上局部织构(通过空隙数,接触价键,配位数来表征)的变化过程,对比了不同情况下的应力–应变关系曲线,再现了试样的加卸载曲线。结果表明了颗粒介质之间的咬合作用对材料的宏观力学行为有比较明显的影响。     

散体颗粒介质变形局部化宏–细观机制研究

散体颗粒是自然界中广泛存在的一类特殊的介质,受内部组构影响,散体颗粒介质在外荷载作用下发生明显的变形局部化效应,这也是岩土力学领域一直研究的热点问题之一。然而目前对于其机制研究方面大都局限于细观统计参数的分析,忽视了宏观现象与细观机制的内在联系。本文以砂土颗粒介质为例,运用离散元法对其在直剪试验过程中的宏–细观力学特性及变形破坏机制进行系统分析,并取得一些有意义的认识。根据数值试验中试样在不同法向应力下剪应力比的发展,从颗粒运动角度探讨试样宏观抗摩擦特性变化趋势的细观机制;发现描述细观组构的各向异性参数及主方向与宏观上剪应力比的发展具有同步性,反映试样宏细观演化的统一性;通过对于颗粒旋转的统计分析,揭示颗粒间摩擦作用是维持细观力学结构相对稳定的重要因素;通过对力链网络的形态演化分析,发现试样大主应力方向与各向异性主方向一致,力链密集程度随剪切过程下降,试样孔隙度随之上升;提出不同法向应力下的2种主要力链结构的力学模型,通过稳定性分析与能量累积释放理论解释宏观力学参数波动情况的原因,揭示散体颗粒介质变形局部化和体应变剪胀的细观机制。     

Numerical study on liquefaction characteristics of granular materials under Rayleigh-wave strain conditions using 3D DEM

In liquefaction analyses, liquefaction is conventionally assumed to originate from the vertical propagation of shear waves. However, some field and theoretical evidence has demonstrated that the risk of liquefaction may be induced or increased by surface waves. In this study, the liquefaction characteristics of K₀-consolidated granular materials under Rayleigh-wave strain conditions, ideal deformation conditions under the assumption of constant volume, were investigated by the three-dimensional discrete element method (3D DEM). The results indicate that Rayleigh-wave strain conditions combine pure and simple shear modes. As the ratio of the shear strain amplitude to the normal strain amplitude (RSN) increases from 1 to +∞, granular materials tend to have a slower liquefaction rate and higher liquefaction resistance; however, the difference in the undrained responses is negligible when the RSN is less than 1. The distribution of the magnitude and orientation of the contact forces also varies with the RSN, while it is similar when the RSN is less than 1. The degradation of the skeleton structure and the evolution of the structural anisotropy accelerate the liquefaction of granular materials. Moreover, in situations with the same accumulated equivalent strain per cycle, the Rayleigh-wave strain condition with a low RSN value will make granular materials more vulnerable to liquefaction compared with Love- and SH-wave strain conditions.     

散粒介质三维应力-组构解析与破坏分析

基于散粒体宏-微观力学分析,首先提出了3类张量的概念,推导了散粒体三维应力-组构关系,接着给出了二维和轴对称条件下的应力-组构解析表达式,并采用双轴和三轴离散元（DEM）模拟结果对解析解进行了验证分析。最后基于应力-组构解析,采用“真应力”的概念分析了散粒体的强度问题。研究结果表明：散粒体中的应力分布受3类张量的共同影响,双轴与三轴的离散元模拟与解析关系较吻合。在略去了高阶项后,二维应力-组构关系式与Rothenburg等提出的表达式一致。进一步的分析表明：散粒材料强度受控于“真应力”,表观活动摩擦角的变化实质是颗粒摩擦和各向异性组构共同作用的结果。研究成果可以用于分析散粒体各向异性强度特征和本构关系。     

Strain localization analyses of idealized sands in biaxial tests by distinct element method

This paper presents a numerical investigation on the strain localization of an idealized sand in biaxial compression tests using the distinct element method (DEM). In addition to the dilatancy and material frictional angle, the principal stress field, and distributions of void ratio, particle velocity, and the averaged pure rotation rate (APR) in the DEM specimen are examined to illustrate the link between microscopic and macroscopic variables in the case of strain localization. The study shows that strain localization of the granular material in the tests proceeds with localizations of void ratio, strain and APR, and distortions of stress field and force chains. In addition, both thickness and inclination of the shear band change with the increasing of axial strain, with the former valued around 10–14 times of mean grain diameter and the later overall described by the Mohr-Coulomb theory.     

Strain localization analyses of idealized sands in biaxial tests by distinct element method

This paper presents a numerical investigation on the strain localization of an idealized sand in biaxial compression tests using the distinct element method (DEM). In addition to the dilatancy and material frictional angle, the principal stress field, and distributions of void ratio, particle velocity, and the averaged pure rotation rate (APR) in the DEM specimen are examined to illustrate the link between microscopic and macroscopic variables in the case of strain localization. The study shows that strain localization of the granular material in the tests proceeds with localizations of void ratio, strain and APR, and distortions of stress field and force chains. In addition, both thickness and inclination of the shear band change with the increasing of axial strain, with the former valued around 10–14 times of mean grain diameter and the later overall described by the Mohr-Coulomb theory.     

Modeling Granular Crushing in Ring Shear Tests: Experimental and Numerical Analyses

A fault consists of a zone of heavily fragmented granular rock (gouge), which is confined between two rough walls made of fractured rock. The granular gouge is the result of previous fracturing of the wall rock by the combined effect of compressive and shear stresses. Through time, the granular fault gouge will experience various episodes of further fragmentation (crushing) as a result of the mobilization by shear of the fault walls. The evolution of crushing in a simulated gouge material was studied using laboratory ring shear tests and DEM ring shear simulations. The laboratory ring shear tests were developed using sugar as a weak granular material. It was found that the residual friction coefficient of this material maintained a constant value regardless of the severe degradation of the particles. This degradation was induced by increasing the angular deformation or increasing the applied vertical stress. Moreover, it was found that the grain size distribution of the original uniform material evolved toward a fractal distribution of sizes. The results from the DEM simulations confirmed those from the laboratory tests and provided also a visualization of the evolution of crushing. Event though originally DEM does not consider particle breakage, this was allowed by replacing particles fulfilling a predefined tensile failure criterion with an equivalent group of smaller particles.     

Linking inherent anisotropy with liquefaction phenomena of granular materials by means of DEM analysis

The liquefaction phenomena of sands have been studied by many researchers to date. Laboratory element tests have revealed key factors that govern liquefaction phenomena, such as relative density, particle size distribution, and grain shape. However, challenges remain in quantifying inherent anisotropy and in evaluating its impact on liquefaction phenomena. This contribution explores the effect of inherent anisotropy on the mechanical response of granular materials using the discrete element method. Samples composed of spherical particles are prepared which have approximately the same void ratio and mean coordination number (CN), but varying degrees of inherent anisotropy in terms of contact normals. Their mechanical responses are compared under drained and undrained triaxial monotonic loading as well as under undrained cyclic loading. The simulation results reveal that cyclic instability followed by liquefaction can be observed for loose samples having a large degree of inherent anisotropy. Since a sample having initial anisotropy tends to deform more in its weaker direction, leading to lower liquefaction resistance, a sample having an isotropic fabric potentially exhibits the greatest liquefaction resistance. Moreover, the effective stress path during undrained cyclic loading is found to follow the instability and failure lines observed for static liquefaction under undrained monotonic loading. From a micromechanical perspective, the recovery of effective stress during liquefaction can be observed when a threshold CN develops along with the evolving induced anisotropy. Realising that the conventional index of the anisotropic degree (a) is not effective when the CN drops to almost zero during cyclic liquefaction, this contribution proposes an alternative index, effective anisotropy (a×CN), with which the evolution of induced anisotropy can be tracked effectively, and common upper and lower bounds can be defined for both undrained monotonic and cyclic loading tests.     

砂土的各向异性强度准则：原生各向异性

采用散粒材料的组构-应力微细观力学分析方法,在颗粒尺度上分析了砂土的原生各向异性强度特性。首先建立了砂土各向异性强度准则,若不考虑初始组构的变化,将蜕化为莫尔-库仑的原生各向异性强度准则,并可直接将现有的经典破坏准则推广到考虑砂土原生各向异性的情况,不需额外模型参数,方便于工程应用。接着基于三轴压缩与伸长试验破坏各向异性发展的不同,建立了考虑中主应力影响的简单破坏应力比-组构关系,建议了考虑组构演化的砂土原生各向异性强度准则,并考虑了砂土密实状态对其各向异性强度的影响。研究结果表明本文建立的原生各向异性强度准则,其物理机理比较明确,考虑了原生各向异性组构的演化,与真三轴试验结果吻合较好,有助于从微细观机理上分析砂土的原生各向异性强度特征。     

Effect of Dilatancy on Instability,Pre-Instability Strain Softening of Sand Along Proportional Strain Paths

The roles of dilatancy in granular materials are experimentally and numerically explored with regard to material instability and failure. Experimental results of sand corresponding to proportional strain paths show that either pre- or post-failure instability may take place, depending on the density and the imposed rate of volume change. Pre-instability strain softening is observed for both dense and very loose sand, however, strain softening is not a necessary condition for the occurrence of material instability. Both experimental results and constitutive modeling show that the difference between the forced rate of volume change and the inherent potential of dilation dominates the occurrence of strain softening and material instability. The dependency of inherent dilation on void ratio and stress level is a key factor in predicting the complicated stress responses of sand deforming along imposed strain paths.     

An analytical solution for geotextile-wrapped soil based on insights from DEM analysis

This paper presents a novel analytical solution for geotextile-wrapped soil based on a comprehensive numerical analysis conducted using the discrete element method (DEM). By examining the soil–geotextile interface friction, principal stress distribution, and stress–strain relations of the constituent soil and geotextile in the DEM analysis, a complete picture of the mechanical characterization of geotextile-wrapped soil under uniaxial compression is first provided. With these new insights, key assumptions are verified and developed for the proposed analytical solution. In the DEM analysis, a near-failure state line that predicts stress ratios relative to the maximums at failure with respect to deviatoric strain is uniquely identified; dilation rates are found to be related to stress ratios via a single linear correlation regardless of the tensile stiffness of the geotextile. From these new findings, the assumptions on the stress-state evolution and the stress–dilatancy relation are developed accordingly, and the wrapped granular soil can therefore be modeled as a Mohr–Coulomb elastoplastic solid with evolving stress ratio and dilation rate. The development of the proposed analytical model also demonstrates an innovative approach to take advantage of multiscale insights for the analytical modeling of complex geomaterials. The analytical model is validated with the DEM simulation results of geotextile-wrapped soil under uniaxial compression, considering a wide range of geotextile tensile stiffnesses. To further examine the predictive capacity of the analytical model, the stress–strain response under triaxial compression conditions is solved analytically, taking both different confining pressures and geotextile tensile stiffnesses into account. Good agreement is obtained between the analytical and DEM solutions, which suggests that the key assumptions developed in the uniaxial compression conditions also remain valid for triaxial compression conditions.     

Distinct element simulations of earthquake fault rupture through materials of varying density

Surface manifestations of earthquake fault rupture are strongly affected by the dilatant response of the soil deposit overlying the bedrock fault displacement. The granular material’s in-situ void ratio and effective confining stress affect its dilatancy, and hence, its stress-strain response and ductility. Distinct element method (DEM) assemblages of 3D, non-spherical particles are prepared with different void ratio distributions, and their dilatancy is characterized using direct shear test simulations. DEM simulations capture the response of sand in centrifuge experiments of earthquake fault rupture propagation. Macro-scale mechanisms of ground deformation and micro-scale mechanisms of shear band formation during dip-slip fault rupture propagation are analyzed through particle rotations, homogenized strains, frictional dissipation, and particle displacements. The brittle and ductile responses of granular media undergoing fault rupture are related to changes in the coordination numbers in each particle assemblage. The deformational characteristics of a metastable fabric in the loosest particle assemblages and a stable fabric in the densest particle assemblages are revealed through the accumulation of energy dissipated through friction. The normalized strong contact forces are also greater in magnitude in the loosest particle assemblages and greater in number in the densest assemblages.     

Experimental investigation of inter-particle contact evolution of sheared granular materials using X-ray micro-tomography

The inter-particle contact evolution of two sheared granular materials, i.e., a spherical glass bead (GB) specimen and an angular Leighton Buzzard Sand (LBS) specimen, is investigated non-destructively using X-ray micro-tomography. A miniature triaxial apparatus is developed for the testing with in-situ scanning. Full-field X-ray CT images of the two specimens are obtained at different shearing stages. A series of image processing and analysis techniques in combination with a particle-tracking approach is developed to detect the inter-particle contacts and to determine the contact gain, the contact loss, and the contact movement during each shear increment. It is found that the average coordination number (CN) experiences a strong change in the pre-peak shearing stage, and tends to reach a steady value after the peak. As the shear progresses, the average CN of the particles with different sizes follows the same trend as the overall average CN. Additionally, as the shear progresses, the branch vectors of the specimens, which, prior to shearing, are nearly isotropically distributed for the rounded GB and concentrated along the horizontal direction for the angular LBS, are found to show a directional preference towards the loading direction. The contact gain and the contact loss, which contribute to this directional preference, and the contact movement, which leads to the attenuation of the directional preference, are shown to be the two competing factors determining the evolution of the fabric anisotropy of granular materials. The higher degree of fabric anisotropy in the shear bands is shown to be mainly attributed to the higher percentages of contact gain and contact loss when compared to that of the entire samples.     

基于离散元法的真三轴应力状态下砂土破碎行为研究

基于可破碎三维离散颗粒模型模拟了一系列常规三轴试验与真三轴试验,研究了砂土在真三轴应力状态下的破碎行为。数值调查主要关注试样的应力应变特性、级配及相对破碎率的演化。随着围压增大,颗粒破碎率增大,试样应变软化特性和剪胀性逐渐减弱,而超过临界高围压后,由于固结中颗粒大量破碎,试样剪胀性反而增强。真三轴试验中,试样偏应力比峰值均随中主应力参数b值增大而减小。由于破碎随b值增加而明显增大,试样剪胀性随b值增大而逐渐减弱。试样内摩擦角φ随围压增大而减小,其演化关系基本满足对数关系;内摩擦角随b值增大先增大后减小,Lade-Duncan准则较为适合描述其变化规律。此外,试样相对破碎率增大的速率随围压和轴向应变增大而逐渐降低,暗示试样最优终极级配的存在,且相对破碎率与试验输入能量之间存在唯一的双曲线关系。     

Isotropic compression behavior of granular assembly with non-spherical particles by X-ray micro-computed tomography and discrete element modeling

The particle morphological properties, such as sphericity, concavity and convexity, of a granular assembly significantly affect its macroscopic and microscopic compressive behaviors under isotropic loading condition. However, limited studies on investigating the microscopic behavior of the granular assembly with real particle shapes under isotropic compression were reported. In this study, X-ray computed tomography(μCT) and discrete element modeling(DEM) were utilized to investigate isotropic compression behavior of the granular assembly with regard to the particle morphological properties,such as particle sphericity, concavity and interparticle frictions. The μCT was first used to extract the particle morphological parameters and then the DEM was utilized to numerically investigate the influences of the particle morphological properties on the isotropic compression behavior. The image reconstruction from μCT images indicated that the presented particle quantification algorithm was robust, and the presented microscopic analysis via the DEM simulation demonstrated that the particle surface concavity significantly affected the isotropic compression behavior. The observations of the particle connectivity and local void ratio distribution also provided insights into the granular assembly under isotropic compression. Results found that the particle concavity and interparticle friction influenced the most of the isotropic compression behavior of the granular assemblies.     

砂土直剪力学性状的非圆颗粒模拟与宏细观机理研究

基于PFC2D非圆颗粒单元的二次开发,对砂土直剪力学过程进行了非圆颗粒仿真模拟,分析了数值试样的应力–剪胀关系并与实际砂土进行对比,探讨了颗粒位移与颗粒旋转特征及其与剪切带演化的内在关联,研究了主应力与主应变增量的非共轴效应,揭示了细观组构各向异性的演化规律及其与宏观剪切强度之间的宏细观关联。研究结果表明,数值试验能够较好的模拟实际砂土的应力–剪胀关系和剪切过程主应力与主应变增量的非共轴效应;剪切带的演化与颗粒位移和颗粒旋转密切相关,颗粒形状影响剪切带的厚度;试样宏观的剪切强度主要受控于粒间法向接触力的分布及其各向异性演化;整个加荷过程中,剪切带内大主应力的偏转方向与法向接触力各向异性的主方向保持了良好的一致性。     

砂土在小应变下考虑应力路径影响的本构模型的试验研究

以标准砂为试样,利用GDS数字控制应力路径三轴仪进行了K0初始应力条件下8条特殊应力路径试验。在小应变区域内,通过刻画在应力空间的等应变应力线的变化规律,推导了可以考虑任意应力路径和应力路径方向变化的杨氏模量计算方法,并对泊松比进行了研究,建立了砂土在小应变区域内可以考虑复杂应力条件的本构模型。模型可以反映小应变时砂土的高模量、非线性以及模量急剧变化等主要特征;也可以模拟一般模型所不能考虑的应力路径方向变化引起的模量变化。