Modelling size effect on rock aggregates strength using a DEM bonded-cell model

Empirical evidence has shown that particle breakage affects the mechanical behaviour of granular materials. The source of this mechanism takes place at the particle scale, and the main consequence on the macromechanical behaviour is increasing compressibility. Due to the inverse correlation between particle size and particle crushing strength, coarse rockfill materials are particularly vulnerable to mechanical degradation due to particle breakage. However, such coarse materials do not fit in standard laboratory devices, and the alternative of large sample testing is usually unavailable or too expensive. Alternatively, recent works have proposed multi-scale approaches using the discrete element method (DEM) to carry out numerical testing of coarse crushable materials, although few studies have focused on size effects. This article presents the application of a DEM bonded-cell model to study particle size-strength correlation on angular rock aggregates. Each particle is modelled by a cluster of perfectly rigid polyhedral cells with Mohr–Coulomb contact law. Constant cell density within particles implies that the presence of potential fragmentation planes increases with size. Therefore, particle strength decreases with size. A comprehensive sensitivity analysis was carried out through 1477 particle crushing simulations in a given particle size. Based on published experimental data on calcareous rock aggregates, part of the simulations were used for calibration, and 97 additional simulations of a coarser size fraction were performed for validation. The results show a good agreement with the empirical data in terms of size effect and data scatter through Weibull statistics.

     

Effects of internal pores on the mechanical properties of marine calcareous sand particles

Calcareous sand is a typical problematic marine sediment because of its angular and porous particles. The effects of internal pores on the mechanical properties of calcareous sand particles have rarely been investigated. In this paper, the apparent morphology and internal structure of calcareous sand particles are determined by scanning electron microscopy and computed tomography tests, finding that the superficial pores connect inside and outside of the particles, forming a well-developed network of cavities and an internal porosity of up to 40%. The effects of particle morphology and internal porosity on the mechanical responses of particle were investigated by conducting photo-related compression test and 3D numerical simulations. Two failure modes are observed for the porous calcareous sand, i.e., compressive failure indicates that the particle skeleton is continually compressed and fragmented into small detritus without obvious splitting, and tensile failure indicates that the particles are broken into several fragments when the axial force clearly peaks. Calcareous sand particles with a high internal porosity or with small and dense pores often exhibit compressive failure, and vice versa. The particle strength is considerably reduced by increasing the internal porosity, but affected by pore size in nonlinear correlation. The crushing stress–strain points can be well fitted by an exponential curve, which is supplied for discussion.

     

Micromechanical inspection of incremental behaviour of crushable soils

In granular soils grain crushing reduces dilatancy and stress obliquity enhances crushability. These are well-supported specimen-scale experimental observations. In principle, those observations should reflect some peculiar micromechanism associated with crushing, but which is it? To answer that question the nature of crushing-induced particle-scale interactions is here investigated using an efficient DEM model of crushable soil. Microstructural measures such as the mechanical coordination number and fabric are examined while performing systematic stress probing on the triaxial plane. Numerical techniques such as parallel and the newly introduced sequential probing enable clear separation of the micromechanical mechanisms associated with crushing. Particle crushing is shown to reduce fabric anisotropy during incremental loading and to slow fabric change during continuous shearing. On the other hand, increased fabric anisotropy does take more particles closer to breakage. Shear-enhanced breakage appears then to be a natural consequence of shear-enhanced fabric anisotropy. The particle crushing model employed here makes crushing dependent only on particle and contact properties, without any pre-established influence of particle connectivity. That influence does not emerge, and it is shown how particle connectivity, per se, is not a good indicator of crushing likelihood.

     

Single-particle crushing strength under different relative humidity conditions

This paper presents a fundamental study on the effect of the relative humidity on the rockfill crushing strength. This aspect plays an important role in the mechanical behaviour of rockfill, and it is known that certain characteristics of the granular materials, such as compressibility and shear strength, depend on the confining stress, which is a function of the particles crushing. An increased interest has been observed regarding the effect of the relative humidity in the mechanical behaviour of rockfill. Unfortunately, limited research has been conducted until now regarding the study of individual particle crushing. Therefore, this paper thoroughly investigated particle crushing, by performing single-particle crushing tests on rockfill particles divided into four size ranges, under different relative humidity conditions. The experimental results reveal a considerable influence of the relative humidity in the studied rockfill particles, whose strength of the particles with the greatest dimensions in saturated conditions was reduced by half. Consistent macro-mechanical evidence demonstrates that particle’s size and relative humidity conditions depict the most important factors that influence particle crushing strength.

     

Quantification of particle crushing in consideration of grading evolution of granular soils in biaxial shearing: A probability‐based model

A probability‐based model is presented to estimate particle crushing and the associated grading evolution in granular soils during isotropic compression and prepeak shearing in biaxial tests. The model is based on probability density functions of interparticle and intraparticle stress (ie, particle normalized maximum shear stress and particle average maximum shear stress) derived from discrete element method simulations of biaxial tests. We find that the probability density functions of normalized maximum shear stress are dependent on the current sample grading, implying coupling effects between particle crushing and sample grading such that the particle crushing is affected by the current sample grading, and the grading change is also dependent on the current particle crushing extent. To incorporate these coupling effects into the model, particle crushing and grading change are calculated for each load increment, in which the crushing probability of a particle during any loading increment is denoted as the corresponding increment of probability of the internal maximum shear stress exceeding its maximum shear strength. The model shows qualitative agreement with published experimental data. The effects of the model parameters, including initial porosity, particle strength, initial grading, and crushing mode, on the calculated results are discussed and compared with previous studies. Finally, the strengths and limitations of the model are discussed.     

基于线性拟合的颗粒材料破碎状态表征

在荷载等因素作用下发生颗粒破碎是岩土材料的固有属性,选择合适的颗粒破碎状态表征指标是颗粒破碎问题研究中首先要解决的问题。基于颗粒破碎导致细颗粒含量增加,级配曲线抬升并趋向于分形的客观事实,提出了利用级配曲线的拟合直线的斜率和相关系数的变化规律描述颗粒破碎状态及其演化的新方法。在该基础上,提出了表征颗粒破碎状态的破碎分形指数及破碎分形相关性指数的概念,阐述了二者随颗粒破碎的发展规律。与试验结果对比表明,提出的状态指标与试验结果能够很好的吻合,颗粒破碎状态存在明确的对应关系,能够表征颗粒破碎难易程度及其发展趋势,为研究颗粒破碎问题提供了新思路。     

Discrete element modeling of crushable sands considering realistic particle shape effect

This study proposed a novel approach for generating crushable agglomerates with realistic particle shapes in discrete element modeling (DEM). The morphologies of sand particles were obtained by X-ray micro-computed tomography scanning and image processing. Based on the particle surface reconstructed by spherical harmonic analysis, the crushable agglomerates with realistic particle shapes can be generated in DEM simulations. The results of single particle crushing tests showed that particle shapes significantly influence the fracture patterns and crushing strengths of sand particles. Furthermore, two one-dimensional compression tests were conducted to investigate the particle shape effect on micro- and macro-mechanical behaviors of crushable sands.     

Discrete element modeling of the single-particle crushing test for ballast stones

In this paper, a discrete element modeling approach for the single-particle crushing test for irregularly shaped ballast stones is presented. Bonded spherical particles are used to represent test specimens. Parametric studies focusing on particle size, axial strain rate, particle aggregate size and number of bonds are performed. The selection criteria of these parameters are discussed from the perspective of railway engineering. The results indicate that the proposed modeling approach is reliable for simulating railway ballast stones and can thus be further used for simulations of ballast aggregations.     

Effect of microstructure on stress–strain and pore-pressure response of sabarmati sand under the influence of mica

ABSTRACT

Micaceous soil is believed to be detrimental for civil engineering constructions due to the effect of high compressibility, low compacted density and low shear strength. Individual mica particle has numerous intact mica flakes foliated over each other making it flexible upon loading and rebound upon unloading due to its low hardness and resilient nature. Hence, micaceous soils with mica content more than 10% are considered undesirable for highway pavements, embankments and railway track constructions. When platy mica particles are sufficiently numerous to interact with spherical sand particles, bridging and ordering phenomena are augmented within the soil mass creating unique sand-mica particle orientation (MS microstructure) unlike sand-sand particle orientation (PS microstructure). The current experimental research was conducted to evaluate the variation in stress–strain, pore pressure and effective stress path response of Sabarmati sand under the influence of mica (sand with 30% mica and pure sand) with MS and PS microstructure respectively. Effect of particle crushing on stress–strain and pore pressure response was also studied on Sabarmati sand with MS and PS microstructure. Distinctive macroscopic response was observed in Sabarmati sand with MS microstructure under the influence of mica as well as mica particle crushing.     

Impact crushing of particle–particle compounds—experiment and simulation

Particle–particle compound consists of various sized particles with non-uniform properties, whose properties vary in large range depending upon applications, methods of manufacturing and ratio of its compositions. The different types of engineering agglomerates and building materials, like concrete, are some of the examples of particle compounds. Recycling of value material from building waste such as aggregates from concrete ball provides impetus to investigate particle–particle compounds.The liberation of aggregates is carried out by impact crushing in a large scale pneumatic cannon. Both experiments and Finite and Discrete Element simulations are adopted to study the cracking phenomena of aggregates. Also, the different aspects of crushing of particle–particle compounds at different velocities are discussed.     

多块体形状堆石体碾压颗粒破碎数值模拟

通过6种典型堆石块体的形状近似,分别采用两种接触本构模型建立了多块体形状堆石体离散元数值模型,研究堆石体在碾压荷载作用下的颗粒破碎过程,建立颗粒破碎的量化计算方法,分析碾压前、后堆石级配曲线的变化,讨论接触本构模型和颗粒形状对块体破碎的影响。模拟结果显示,碾压荷载下堆石颗粒以张拉破碎为主,随着碾压遍数的增加,局部开始出现剪切破碎;提出的颗粒破碎量化计算方法,在大粒径范围对粒径变化幅度预测偏大,但级配曲线整体趋势与实测结果比较吻合;相比较于接触连接模型,平行连接模型与现场碾压试验结果更接近。6种块体形状的数值结果显示,随着形状系数的增加,在其他条件不变的情况下颗粒破碎率逐渐降低,其中类长方形块体在碾压荷载作用下颗粒破碎最明显。相比较于纯圆颗粒或者单一非圆颗粒,采用的6种颗粒形状建立的堆石体振动碾压离散元模型,更接近现场实际情况。     

钙质粗粒料颗粒强度和压缩特性的试验研究

目前对钙质土压缩特性的研究主要集中在钙质细砂,而实际工程中广泛存在钙质粗粒料,因此对钙质粗粒料压缩特性开展研究具有重要意义。通过颗粒强度测定仪和全自动大型固结仪对钙质土进行了单颗粒破碎试验和一维压缩试验,研究了颗粒粒径和相对密度对钙质粗粒料的颗粒强度和压缩特性的影响。单颗粒试验结果表明,钙质砂单颗粒的特征应力随着颗粒相对密度的增大而增大;单颗粒的破碎强度具有明显的尺寸效应,可利用单颗粒的特征应力进行标准化,且服从Weibull分布。压缩试验结果表明,单一粒径试样破碎后的分形维数随颗粒粒径的增大而增大;试样的Hardin破碎率与塑性功的关系为幂函数关系;在本次试验条件下,单一粒径试样的屈服应力与单颗粒的特征应力存在近似线性关系。     

Study on the mechanical behavior of sands using 3D discrete element method with realistic particle models

Presented is a study on the geometrical characteristics of sand particles and the mechanical behavior of sand material under external loading. Based on computed tomography technique, a reconstruction method of granular particles was developed and used to build a database of 3D geometrical models for sand particles. The studied sand particles showed good regularities in morphological characteristics and thus were suitable to be used for the random generation of numerical samples. DEM tests using realistically shaped particles were proven to better simulate the mechanical behavior of the sample during elastoplastic loading stage, which was an issue for the simplified spherical particles. The generation, extension, and breakage of the force chains controlled the strain softening behavior of sands. Anisotropy analysis using the spherical harmonic series showed that the evolution of anisotropy directions and parameters corresponded well with the macroscopic mechanical behavior of the material. Pore volume computation based on Voronoi diagram was performed to illustrate the formation and evolution of localized shear zone. The mesoscopic analysis showed that particle shape significantly influences the mechanical behavior of sands and thus should be properly modeled in numerical simulations.

     

考虑颗粒强度尺寸效应的原型堆石料破碎特性研究

高土石坝中,堆石体颗粒破碎是导致坝体变形的主要因素之一。但是由于原型坝料的颗粒尺寸较大,其破碎程度难以直接通过室内试验度量,因此通常要将原型级配缩尺为60 mm以下的小粒径级配堆石料,然后才能进行室内试验。而由于原型和试验级配差异较大,导致试验测得的参数往往和原型坝料实际参数有较大差异,因而影响了原型坝料力学特性的深入研究。这里提出了一种新的实时预测原型坝料破碎的方法。首先在颗粒尺度上,基于单粒强度的Weibull分布理论和颗粒分形破碎理论,阐述了原型堆石料级配演化的推求过程;然后通过单粒强度试验测得了相关参数,并与三轴试验测得的试样级配曲线对比,验证了参数选取的合理性;之后分析了颗粒强度离散程度对于原型坝料级配曲线形状的影响;最后,讨论了加载过程中原型级配和试验级配堆石体的相对破碎参量和受力状态的关系。     

颗粒破碎对钙质砂的应力-应变及强度影响研究

压力作用下颗粒发生破碎是引起砂土力学特性变化的重要因素之一, 对于钙质砂这种易破碎的材料更是如此。为进一步弄清颗粒破碎对钙质砂的应力-应变强度影响, 本文对钙质砂进行三轴固结排水剪切试验得到应力-应变曲线, 并筛分得到三轴试验前后钙质砂颗分曲线。通过引入Hardin定义的颗粒相对破碎率Br, 分析了相对密度、围压与颗粒破碎的关系及颗粒破碎对钙质砂应力-应变和抗剪强度的影响。结果表明:随围压的增大颗粒破碎增量逐渐减小, 直到破碎达到一个上限值, 此时围压和相对密度对颗粒破碎影响很小; 颗粒间的滑动标志着应力达到极限状态, 而颗粒破碎会阻碍应力达到极限状态, 在本实验中, 低围压时颗粒破碎少, 颗粒相对运动形式为滑移, 使应力-应变曲线为软化型, 高围压下颗粒破碎严重, 颗粒破碎在剪切过程中始终发生, 使应力-应变曲线呈应变硬化型; 颗粒破碎使体变从剪胀逐渐发展到剪缩, 且破碎越严重剪缩越严重; 在低围压下钙质砂强度主要由剪胀和咬合提供, 高围压下颗粒破碎严重, 剪胀消失, 咬合减小, 使峰值摩擦角减小, 抗剪强度降低。     

多尺度内聚颗粒模型破碎过程研究

岩石破碎过程涉及到多个变量（应力、应变和孔隙率等）变化和裂纹的产生、拓展和聚集,是研究岩石破碎机制的重要途径。为了克服现有研究中岩石颗粒模型未考虑岩石内部特征问题,针对岩石内部颗粒非均匀分布、聚集的特点,开展了岩石轴压破碎试验和岩石岩相分析试验,并在此基础上,构建符合真实岩石内部特征的多尺度内聚颗粒模型。根据离散元的颗粒黏结模型（BPM）理论,求解了多尺度内聚颗粒模型不同粒级颗粒间黏结键的力学关系,发现与二级颗粒形成的黏结键断裂判据为 ≥ 2 GPa,三级颗粒之间形成的黏结键断裂判据为 ≥ 6 GPa,并基于该判据建立了用于模拟颗粒模型破碎的演化模型。通过模拟轴压破碎试验,破碎演化模型可以从细观角度得到颗粒模型各颗粒间黏结键承受力的实时变化和岩石破碎过程中黏结键从外而内的断裂顺序;从宏观角度得到岩石内部裂纹呈V形从上表面两端延伸并相交于岩石中部。通过与岩石轴压破碎试验结果对比发现,模拟试验得到的岩石裂纹特征与岩石轴压破碎试验结果相似,验证模型的可靠性,实现了从细观和宏观角度分析岩石破碎过程。     

MICP对钙质砂单颗粒的破碎行为影响研究

作为一种特殊的岩土介质材料,钙质砂具有在低压下易破碎的性质。微生物诱导方解石沉淀（MICP）技术得到了广泛的关注和认可,可用来改善钙质砂的破碎特性。文章从室内试验和离散元模拟两个角度分别对钙质砂颗粒MICP固化前后进行单颗粒压碎试验,通过Weibull分布和SEM扫描等探究了MICP对钙质砂颗粒破碎行为的影响。结果表明：离散元模拟得到的生存概率曲线及Weibull模量m值与试验结果均吻合较好,验证了该数值模型的有效性。与室内试验相比,数值模拟可以精确地反映颗粒的裂纹分布及破碎过程,且可以研究同一颗粒MICP固化前后的情形,弥补了室内实验的不足,但其取决于模型参数的选取;经过MICP固化后的钙质砂颗粒表面有明显的方解石结晶生成,颗粒表面及内孔隙分别得到一定程度的包裹和填充,导致颗粒破碎强度有明显的增强且离散性大大降低,破碎模式由“多峰型”向“单峰型”转变,局部裂纹减少,多以表面磨损和直接产生贯穿裂纹为主。     

钙质砂破碎过程及其微观机制试验研究

为了掌握南海钙质砂压缩变形特征及其微观机制,对3种不同粒组(S1:1.43~2mm、S2:0.5~1mm、S3:0.5~2mm)的钙质砂进行100~3200kPa压力范围的压缩试验,利用自制的砂土微观结构提取装置和图像处理软件(PCAS)获得并分析了钙质砂压缩过程中微观结构。结果表明:(1)钙质砂的大小、形状和级配对颗粒的破碎具有显著影响,当压力较低时(＜800kPa),粒径较大的S1组以砂颗粒棱角破碎为主;粒径较小的S2组没有明显破裂,相对规则的颗粒形态使S2粒组在该压力范围内主要因颗粒的滚动与重分布导致压缩;级配良好的S3组除部分低宽度断肢状颗粒外其余大小、形态颗粒无明显破裂。(2)当压力较大时(＞800kPa),S1组钙质砂逐渐转向以颗粒的整体破坏为主的破碎形式;S2、S3两组试样随着密实度的提高,砂颗粒的破坏以整体破碎为主。基于对破碎过程中试样微观结构变化的提取与分析,总结并提出了控制钙质砂颗粒破碎的4种接触模式:点-线接触、线-面接触、面-面接触和复合接触,可用于判断不同条件下的颗粒破碎形式。最后,讨论了钙质砂在破碎过程中颗粒几何参数的变化。     

岩石颗粒破碎的尺寸效应

固体颗粒破碎强度的尺寸效应是一种普遍存在的现象,冰块、岩石颗粒、陶瓷和混凝土块等的破碎强度都表现出随颗粒直径增加而减小的现象,分形模型为解释固体颗粒破碎强度的尺寸效应提供了可行的方法。本文采用Steacy和Sammis分形模型模拟了岩石颗粒压碎特征,分析岩石颗粒破碎后的颗粒分布规律,给出颗粒破碎分维的确定方法,建立颗粒压碎强度与粒径的理论关系,颗粒破碎强度与颗粒粒径的关系用分维D表示为fdD-3。已有的颗粒破碎分布的数据表明,岩石颗粒破碎的分维大约为2.50～2.60,颗粒破碎强度符合用分维表示的尺寸效应。     

A non-linear numerical model for soil mechanics

A new computer program (CONBAL-2) is developed for 2D numerical simulations of granular soil by random arrays of spheres. CONBAL-2 uses the discrete-element method and is based on 3D program TRUBAL, previously presented by Cundall. As in TRUBAL, the new program models a random array of elastic spheres in a periodic space. The main modification of TRUBAL is the implementation by the authors of a rigorous solution for the force–displacement relation at the interparticle contacts. This force-displacement relation is a function of the elastic constants, friction coefficient and sizes of the spheres, with the properties of quartz used to simulate sand. Other specific features of CONBAL-2 include its 2D character, the lack of particle rotation and its capability to simulate shear loading on any plane. Simulated laboratory test results are presented using CONBAL-2 and several random arrays of 531 spheres having two particle sizes. These simulations include monotonic loading drained and undrained (constant volume) ‘triaxial’ experiments, as well as a cyclic-loading, constant-volume ‘torsional shear’ test. The stress–strain curves, effective stress paths, volume changes, as well as the ‘pore water pressure’ build-up behaviour obtained in the simulations compare favourably—qualitatively and in some aspects quantitatively—with similar laboratory results on sands. However, the simulated soil is somewhat stiffer and stronger due to the perfectly rounded particles, limited range of grain sizes, lack of particle rotation and 2D character of the model.