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。     

Particle breakage in triaxial shear of a coral sand

This paper presents a laboratory experimental study to comprehensively investigate the characteristics of particle breakage using numerous triaxial tests on a coral sand. Coral is a highly crushable granular material which fills the gaps between more crushable and less crushable granular materials. The monotonic tests and cyclic tests were terminated at the designated axial strains and the designated cyclic numbers, respectively. The grain size distributions were measured by sieve analyses of the specimens after the triaxial tests were performed. The relative breakage and relative fractal dimension were used to quantify the particle breakage. The cause of particle breakage that increased with increasing isotropic consolidation stress was shown to be isotropic stress. An almost linear increase in particle breakage in relative breakage was found as axial strain increased, whereas the increase in particle breakage in relative fractal dimension showed upward convexity. More particle breakage occurred in denser samples. During consolidation to the identical mean effective stress, the anisotropic stress state played a bigger role in particle breakage than the isotropic stress state, but during shearing particle breakage occurred more sharply in the triaxial tests with the isotropic consolidation to the higher confining pressure. In the cyclic shearing, the particle breakage in relative breakage and relative fractal dimension increased in upward convexity as the cyclic number increased, but in upward concavity with increasing axial strain. A hyperbolic model was proposed to correlate the relative fractal dimension with the relative breakage for use with both monotonic and cyclic tests. In the monotonic tests, a hyperbolic model was proposed to correlate the particle breakage in relative breakage and relative fractal dimension with the plastic work per unit volume. It is proposed that the loading-mode-induced (i.e., monotonic loading and cyclic loading) different mechanism of particle breakage meant that this model could not be applicable in the cyclic tests. The results suggested that the hyperbolic correlation of the particle breakage in relative fractal dimension and the plastic work per unit volume is the most reliable method of interpreting the energy consumption characteristics of particle breakage. This approach takes the fractal nature of soil into consideration. A microscopic view of particle breakage is also effective for observing the evolution of particle breakage.     

DEM analysis of energy dissipation in crushable soils

It is well known that particle crushing plays a critical role in the mechanical behavior of granular soils. Understanding energy dissipation under the influence of particle breakage is of key importance to the development of micromechanics-based constitutive models for sands. This paper reports the original results of the energy input/dissipation of an idealized crushable soil using 3D DEM simulations. Particle breakage is modeled as the disintegration of the synthetic agglomerate particles which are made up of parallel-bonded elementary spheres. A parametric study is performed to fully investigate the effects of initial specimen density and crushability on the energy allocation of the crushable soil.The simulation results show that the initial specimen density and the crushability strongly affect the energy allocation of the soil both at small and large strains. The major roles of particle breakage, which itself only dissipates a negligible amount of input energy, are to advance changes in the soil fabric and to promote the interparticle friction dissipation. Particularly, at small strains, particle breakage disrupts the strain energy buildup, and thus, reduces the mobilized shear strength and dilatancy of a granular soil. At large strains, where particle breakage is greatly reduced, steady energy dissipation by interparticle friction and mechanical damping is observed. Furthermore, it is found that shear bands develop in most dense crushable specimens at large strains, but they are only weakly correlated to the anisotropy of the accumulated friction dissipation.     

非饱和重塑与结构性黄土等向压缩试验离散元分析

为了研究非饱和重塑与结构性黄土在等向压缩条件下宏微观力学性质,进行了等向压缩室内试验的离散元数值分析。运用本团队提出的非饱和结构性黄土三维胶结接触模型,根据室内真三轴试验标定三维接触模型参数,进行了非饱和重塑与结构性黄土的等向压缩离散元模拟,并与室内试验结果进行了对比,在此基础上分析了其宏微观力学机理。结果表明:离散元模拟结果能较好的定性反映黄土的力学特征,非饱和黄土的孔隙比随平均应力先缓慢下降,后在屈服压力附近开始过渡到快速下降;胶结接触在达到某阈值平均应力时开始发生破坏;胶结开始发生大量破坏的阈值与压缩曲线上的结构屈服应力有很好的对应关系。     

不规则颗粒及其集合体三维离散元建模方法的改进

以土石混合体中的不规则块石和含石量为40%的土石混合体室内大三轴试样为例,研究了如何针对当前岩土材料建模方法的不足进行改进以建立尽可能真实的不规则颗粒及其集合体的三维离散元模型。为了模拟块石的真实形态特征,明确了块石几何模型建模方法的控制参数及其确定方法,建立了与真实块石球度相同、棱角度相似的三维半真实离散元模型。为了计算模型的体积以用于模型密度优化及颗粒集合体孔隙率的计算,提出了一种三维离散元模型虚拟切片技术,结合数字图像处理技术可快速准确计算块石三维半真实离散元模型的体积。为了使得土石混合体大三轴试样三维离散元模型的密实度与室内试样保持一致并兼顾建模效率,提出了基于拟振动压实法和分层复制法的土石混合体大三轴试样三维离散元建模方法。研究结果表明:所提出的不规则块石几何模型建模方法控制参数较少且可分别对球度和棱角度进行单独控制;当块石离散元模型填充球体数较少时,其体积与对应几何模型体积相差较大,不能直接采用对应几何模型的体积;所建立的土石混合体数值试样与室内试样的细观结构特征基本相同,即块石随机散布于土体基质中。     

用于离散元分析的胶结材料三维微观接触模型

岩石、结构性土、含水合物深海沉积土(能源土)等岩土材料均可视为由颗粒骨架和粒间胶结物共同构成的胶结型材料。简单实用的微观粒间接触模型是采用离散元数值方法分析胶结体系宏微观力学特性的基础。针对有一定厚度的粒间胶结形式,将胶结物简化为存在于颗粒之间有一定厚度的短圆柱。通过对胶结物内部应力分布进行适当简化推导了三维粒间接触模型,包括法向、切向、弯曲和扭转四个方向的相互作用规律。最终所得模型结合了理论推导和既有室内胶结接触力学试验成果,考虑粒间胶结物的法向压碎过程,能描述切向、弯曲和扭转单独作用的破坏过程以及剪弯扭共同作用下的破坏准则。模型形式简单,易于引入离散元程序。     

A new probabilistic approach for predicting particle crushing in one-dimensional compression of granular soil

This paper presents a new probability-based method for the prediction of particle crushing in the one-dimensional compression of granular soil. The method is comprised of a joint-probability particle crushing criterion that takes into account the statistical particle-scale stress distribution information derived from the Discrete Element Method (DEM) simulations and Weibull׳s distribution of particle crushing strength. A normalized tensile stress index f and a diameter index I_d are introduced to quantify the statistical particle-scale data. The method is further implemented in DEM simulations and verified by comparing the simulation results with the experimental data of oedometer tests of sands.     

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。     

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。     

Experimental data of 3D printed granular material for verification of discrete element modeling simulation

Evaluating the verification of numerical simulation analysis results requires a benchmark for the real behavior of a material. The present report provides a set of experimental data as a benchmark for Discrete Element Method (DEM) analysis. The experiment consisted of the measurement of the particle characteristics and the angles of repose of artificial particles prepared by a 3D printer. The use of a printer is effective for reducing the errors in the particle modeling of the DEM analysis. The particle characteristics of the artificial particles were measured in terms of their size, frictional properties, coefficients of restitution, and elastic stiffness. Then, the angles of repose of the particles were tested under cubical and cylindrical conditions. In addition, the visualization inside samples in the repose state was carried out using X-ray CT analysis. Thus, in the resting state, the strain distribution inside the samples as well as the displacement levels and vectors could be obtained. This technical report is based on the activities of the TC105 domestic committee of the JGS.     

Comparison of undrained behaviors of granular media using fluid-coupled discrete element method and constant volume method

The fluid-coupled discrete element method (DEM) and the constant volume method as two types of discrete modeling methods for fundamental study of undrained responses of granular materials, have been discussed by many researchers. The fluid-coupled DEM, which couples the motions of discrete particles with pore fluid movements, is theoretically robust although it requires a large amount of computation time. As a substitution for the complex fluid-coupled DEM, the constant volume method simulates an undrained condition for a saturated granular material by simply preserving the total volume of a granular assembly without considering interactions between fluids and particles; hence, the validity of its results is questionable. In this paper, the undrained behaviors of granular assemblies simulated using the aforementioned two methods are compared. Based on a comparison of both macroscopic and microscopic responses given by the two methods, it is demonstrated that the constant volume method may reasonably simulate the responses of a loose saturated granular material with very coarse grains, which has a high permeability, and thus a rapid pore pressure equalization. However, it is ineffective in simulating the responses of a loose material with fine components due to its failure to capture the process of a slow dissipation of the excess pore pressure among the individual pores. With regard to the dense material adopted, similar behaviors at the early and intermediate shearing stages given by the two methods are displayed.     

弹塑性颗粒物质准静态变形的细观力学行为

本文介绍了对由弹塑性圆球组成的粒度多分散系统进行的轴向准静态加载和卸载的数值模拟成果。首先介绍了基于理论接触力学导出的颗粒弹塑性接触模型,进而阐明了基于颗粒离散元法对颗粒物质准静态变形模拟的基本方法。研究发现:弹塑性球颗粒系统在加载时其轴向刚度对颗粒间产生的塑性变形量及颗粒间的摩擦均很敏感。然而,颗粒间的摩擦对轴向加载时系统产生的水平应力没有很强的影响。数值模拟还提供了颗粒量级上的微力学内部变量的信息。这里引入并介绍了结构异性张量、滑动接触比率以及平均配位数。通过对这些参数的研究表明:在卸载的全过程中,颗粒间相对滑移出现,相互作用的颗粒数减少,系统内部结构产生不可恢复变形。因此,尽管在卸载应力应变曲线的初始段约为线性,但这并不意味着颗粒系统的响应如传统连续力学中假定的那样为弹性。     

基于颗粒离散单元法的获取任意相对密实度下级配颗粒堆积体的数值方法

土体的密实程度对土体的工程性质影响很大。获得给定相对密实度下的初始颗粒堆积体,是利用离散单元法进行土体细观力学分析的重要前提。基于离散单元法,首先获得颗粒在自重作用下稳定后的最松散堆积体。其次提出采用减小压实过程中颗粒间摩擦系数的拟振动压实法来模拟现实中的振动压实作用,并验证了其可行性。当压实过程中颗粒间摩擦系数为0时获得最密实堆积体。研究了拟振动压实过程中颗粒间摩擦系数与压实稳定后的堆积体孔隙率的关系。最后根据该关系可估算出获得任意给定相对密实度堆积体所需的压实过程中颗粒间的摩擦系数。研究结果表明:颗粒的配位数与粒径近似满足指数关系;通过减小压实过程中颗粒间的摩擦系数能较好的模拟振动压实效果;压实过程中颗粒间的摩擦系数与堆积体孔隙率满足负指数关系;该方法可获得任意相对密实度下的颗粒堆积体,可以为土体细观力学的数值模拟提供初始颗粒堆积结构。     

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.     

A bounding surface plasticity model for highly crushable granular materials

A bounding surface plasticity model is presented for crushable rockfills in the framework of the critical state soil mechanics which includes translation of the critical state line due to particle crushing. A translating limiting isotropic compression line is also introduced and incorporated in the model to describe the position and evolution of the bounding surface. A particle breakage index is introduced as a function of stress invariants which controls the translation of the critical state and limiting isotropic compression lines. The performance of the model is demonstrated using the results of experimental tests on different types of rockfill materials conducted under both monotonic and cyclic loading conditions. The study shows the capability of the model in capturing the characteristic features of the behavior of rockfill and other crushable materials such as ballast and coarse gravel under both conventional and complex loading paths.     

3种胶结岩土材料本构模型中破损规律的离散元验证

采用离散元法（DEM）对胶结岩土材料本构模型中的破损规律进行验证。首先,根据胶结颗粒间胶结特性,建立适用于胶结颗粒的微观理论;其次,基于该微观理论,给出3种经典胶结岩土材料本构模型破损参数的微观解释;最后,对数值试样进行等向压缩、等应力比压缩及双轴压缩试验的离散元数值模拟,并对比验证数值试样破损规律的模拟结果与本构模型的预测结果。结果表明：采用DEM对胶结岩土材料本构模型的破损规律进行验证是可行的。3种加载条件下,扰动状态模型假定的破损规律同模拟结果均较为一致;Nova模型在双轴压缩试验条件下的预测结果同模拟结果存在很大差异;而上负荷面剑桥模型假设的破损参数则不能很好描述上述加载条件下数值试样的破损规律。     

煤矸石压缩试验的颗粒流模拟

 根据煤矸石颗粒材料的特点,采用三维颗粒流方法PFC3D的接触连接本构模型模拟煤矸石的压缩特性,再现其复杂的非线性本构关系。设计单一级配和泰波理论级配方案,并用Fish语言生成级配颗粒模型。对煤矸石的三轴压缩试验过程进行数值模拟,比较不同围压下的应力–应变曲线、体积应变曲线和微裂纹发展曲线,从细观角度验证不同级配煤矸石试样的强度及变形规律。研究结果显示,优化的级配方案能提高矸石的峰值强度,降低其压缩量,这对优化矸石充填的级配设计有一定的参考价值。     

Induced fabric anisotropy of granular materials in biaxial tests along imposed strain paths

In granular materials, loading on an initially isotopic assembly usually induces particle rearrangement, and this is referred to as the induced anisotropy of fabric. A series of biaxial tests are conducted along various strain paths using DEM to investigate the evolution of the induced anisotropy. The evolution of both the overall contact network and the sub-networks (the strong and weak) are examined separately. Results of DEM simulations indicate that the evolution of the fabric deviator in the overall contact network can be described as a power function of the stress ratio prior to the peak stress ratio that depends on the imposed dilation rate. A unique fabric-stress relation is obtained for the strong sub-network, which is independent of the strain path, the initial porosity and the confining pressure. Moreover, deformation instability is observed only along dilatant strain paths, which can be related to the degradation or even collapse of a weak sub-network, even though the strong sub-network dominates the strength of the granular assembly.