颗粒形状对粒状材料破碎演化规律及强度准则影响

为探讨颗粒形状对粒状材料的颗粒破碎演化规律及强度特征的影响,提出了一个新的粒状材料颗粒形状量化参数,设计了一种考虑三维颗粒形状的人工试样制备方法,随即进行了常规三轴压缩试验,并分析了颗粒破碎和强度特征,最终建立了一个二元介质强度准则,具体的研究成果为：建立颗粒形状量化参数——球形模量GM,在此基础上制备了5种不同形状的可破碎粒状材料三轴试样,并发现球形模量影响着粒状材料的三轴压缩强度特征;通过筛分确定试样的颗粒破碎情况,对试样的颗粒破碎演化规律和临界状态进行探讨,发现颗粒形状通过影响颗粒破碎规律而控制着宏观强度的非线性演化特征;以二元介质理论为基础,建立了考虑颗粒形状的可破碎粒状材料强度准则,并通过试验对其适用性进行了验证。     

脆性颗粒材料的动态多尺度模型研究

脆性颗粒材料的多尺度模型一般包含微观尺度的基本粒子、细观尺度的颗粒和宏观尺度的颗粒堆积体3个尺度。基于离散元方法（DEM）构建多尺度模型,并将该模型应用于动态加载。首先,对多尺度模型所涉及的两种接触模型和两种黏结模型的参数进行分析,详细讨论微细观模型参数与宏观材料常数之间的联系。然后,选用Hertz-Mindlin接触模型[1]和平行键黏结模型,建造石英砂的动态多尺度模型。通过选择合适的强度和局部阻尼参数发现,模型宏细观尺度上的动态压缩响应与对石英砂的相关试验结果吻合很好。利用多尺度模型和选定的参数,探讨与动态加载密切相关的局部阻尼机制对多尺度模型各个尺度上力学响应的影响。结果表明,阻尼越大则颗粒材料对波的衰减能力越强,但过高的阻尼会使团簇强度和模型的宏观压缩曲线都表现出异常的加载速度效应（后者实际是阻尼引起的微惯性效应）。另外,高阻尼会过度衰减颗粒破碎过程产生的应力波,从而阻碍颗粒破碎。最后,应用改进的动态多尺度模型,对脆性颗粒材料的动态破碎特性进行研究,发现该模型不但能给出与试验相吻合的颗粒级配曲线,还能揭示出颗粒破碎过程中微裂纹分布的空间不均匀性,即颗粒破碎过程中波的产生机制和衰减机制相互作用导致的微裂纹聚团分布的现象。     

Discrete element analysis of breakage of irregularly shaped railway ballast

In order to reduce the maintenance costs of ballasted railway track and improve passenger comfort, the railway ballast particle breakage and its effect on track settlement need to be better understood. The failure process of individual railway ballast loaded between flat platens is simulated using the discrete element method, considering its irregular shape with the incorporation of parallel bonds. The tensile strength, the stress of a survival probability of 37% of samples, is obtained and compared with laboratory results from published literature for the verification of DEM simulations. The evolution to failure of the particle is understood from the stress-strain curve and progressive failure modes. The internal breakage mechanisms are analysed by tracking the accumulation of bond breakage number and the contact force distributions.     

An enhanced constitutive model for crushable granular materials

Studies in the past have tried to reproduce the mechanical behaviour of granular materials by proposing constitutive relations based on a common assumption that model parameters and parameters describing the properties, including gradation of individual grains are inevitably linked. However successful these models have proved to be, they cannot account for the changes in granular assembly behaviour if the grains start to break during mechanical loading. This paper proposes to analyse the relation between grading change and the mechanical behaviour of granular assembly. A way to model the influence of grain breakage is to use a critical state‐based model. The influence of the amount of grain breakage during loading, depending on the individual grain strength and size distribution, can be introduced into constitutive relations by means of a new parameter that controls the evolution of critical state with changes in grain size distribution. Experimental data from a calcareous sand, a quartz sand, and a rockfill material were compared with numerical results and good‐quality simulations were obtained. The main consequences of grain breakage are increased compressibility and a gradual dilatancy disappearance in the granular material. The critical state concept is also enriched by considering its overall relation to the evolution of the granular material. Copyright © 2009 John Wiley & Sons, Ltd.     

考虑颗粒破碎影响的粗粒土本构模型

颗粒破碎直接改变了粗粒土本身结构,对粗粒土的剪胀、内摩擦角、峰值强度、渗透系数都会产生影响。为了能够准确地描述粗粒土的应力-应变关系,特别是高应力条件下出现显著颗粒破碎时的应力-应变关系,亟待建立考虑颗粒破碎的粗粒土本构模型。根据三轴试验数据,建立考虑颗粒破碎耗能的应力-应变关系,采用相关联流动法则导出考虑颗粒破碎的粗粒土本构模型。所建立的本构模型考虑了颗粒破碎对粗粒土剪胀、内摩擦角的影响。通过变异粒子群优化算法确定模型参数,拟合试验曲线。模型计算结果与试验曲线拟合较好,能够很好地描述粗粒土在不同围压下的体积剪胀、剪缩和应力硬化、软化现象。     

考虑颗粒破碎的冻结砂土非线性本构模型研究

颗粒破碎是粒状材料在高应力状态下的一种基本现象。为了研究冻结砂土中颗粒破碎对应力应变关系的影响,将冻结砂土视为复合颗粒材料,忽略冰的压融,考虑内摩擦角随应力状态的变化,构建一个适用于冻结砂土的考虑颗粒破碎的非线性本构模型。构建过程分为三步,首先是基于三轴剪切前后颗粒分析对冻结砂土颗粒破碎模式和产生机理进行探讨;其次是基于考虑颗粒破碎的能量平衡方程,对冻土在三轴剪切试验过程中的颗粒破碎耗能进行分析,结果表明颗粒破碎耗能随轴向应变呈双曲线变化趋势;最后应用考虑颗粒破碎的剪胀方程修正沈珠江三参数非线性模型中的体积切线模量ν_t,得到一个考虑颗粒破碎的非线性本构模型,模型参数可以通过单轴压缩试验和常规三轴试验确定。将原模型和修正后模型的计算结果与控制温度为-6℃,围压为1 MPa、4 MPa、6 MPa、8 MPa和10 MPa时冻结砂土的试验结果进行对比,结果表明该模型能够较好的模拟冻结砂土从低围压到高围压的应变软化特征与剪胀特征。      

单一粒径组颗粒材料破碎规律及破碎极限研究

岩土材料颗粒破碎演化规律是颗粒破碎过程复杂性的集中体现,对单一粒径组颗粒材料破碎规律的研究是进行多粒径组颗粒材料破碎规律的基础。从概率统计角度入手,先对前期研究中所提出的描述单一粒径组颗粒材料破碎规律的3个参数-破碎概率p、破碎状态参数a、b的演化规律进行了研究。通过对3组不同类型（不同试验材料、试验类型）的试验数据的研究,发现随着破碎的发展3个参数趋于定值,表明破碎极限的存在。基于上述研究,最后提出了计算单一粒径组颗粒材料破碎极限的方法,分别得到了3组试样的最终分形维数分别为2.3、2.34、2.28。     

A study on particle breakage behavior during pile penetration process using acoustic emission source location

Particle breakage is a common occurrence in granular systems when the external stress exceeds the individual particle strength.A large number of experimental evidences suggested that particle breakage may significantly influence the soil behavior.In the case of pile foundations,the subsoil below the pile tip experiences considerable high stress and consequently prone to break.Due to the lack of sufficient understanding on particle breakage mechanism,there is currently no consentaneous theoretical background for particle breakage analysis during the pile penetration process.This study aims to clarify the location of particle breakage and its evolving characteristics with the aid of acoustic emission(AE)source location method.The spatial distribution of AE hypocenters is interpreted to be associated with the mechanism of particle breakage.Results showed that the AE sources were not uniformly distributed,but concentrated within certain zones below the pile tip.This AE concentration zone was pushed downward with the advancing pile tip,and its distance from the real time pile tip position decreased after certain depth of pile penetration.The location of particle breakage interpreted from AE source location was verified with posttest excavations and the insights on the particle breakage evolution zone were further discussed.     

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.     

A constitutive model for coal-fouled ballast capturing the effects of particle degradation

Rail tracks undergo degradation owing to particle breakage and fouling of ballast by various fines including coal and subgrade soil. As the ballast becomes fouled, its strength and drainage capacity are compromised, sometimes resulting in differential settlement and reduced track stability. This paper demonstrates a continuum mechanics based framework to evaluate the detrimental effect of fines on the strength, deformation and degradation of coal-fouled ballast under monotonic loading. An elastoplastic constitutive model that considers the effect of fines content and energy consumption associated with particle breakage during shearing is presented. This multiphase constitutive model is developed within a critical state framework based on a kinematic-type yield locus and a modified stress-dilatancy approach. A general formulation for the rate of ballast breakage and coal particle breakage during triaxial shearing is presented and incorporated into the plastic flow rule to accurately predict the stress–strain response of coal-fouled ballast at various confining pressures. The behaviour of ballast at various levels of fouling is analysed and validated by experimental data.     

粗粒土的破碎耗能计算及影响因素

粗粒土的颗粒破碎直接改变了土体本身结构,对粗粒土的剪胀和内摩擦角都会产生影响。在土体剪切过程中,体积应力和剪切应力在体积应变和剪切应变上做功,这部分能量在剪切过程中转化为颗粒的弹性储能、颗粒间的摩擦耗能、颗粒剪胀时对外做功和颗粒破碎耗能4部分。准确计算剪切过程中粗粒土破碎耗能的目的是：从能量角度分析颗粒破碎对土体本构关系的影响,为建立考虑颗粒破碎的粗粒土本构关系创造条件。通过分析粗粒土的常规三轴试验数据,计算得到了剪切过程中的粗粒土破碎耗能。计算结果表明,常规三轴试验条件下粗粒土破碎耗能主要受固结应力、土体摩擦系数M等因素的影响。     

基于Cosserat连续体的颗粒破碎影响研究

颗粒破碎对颗粒材料宏观力学行为有重要影响。 结合Hardin的破碎经验公式,将表征破碎程度的破碎参量与Cosserat连续体的内部长度参数相关联,形成一个基于Cosserat连续体且能考虑颗粒破碎的弹塑性模型。数值算例主要考察了颗粒破碎对颗粒材料承载能力、塑性应变及局部化行为的影响,数值结果表明,颗粒破碎主要发生在剪切带内,颗粒破碎使得剪切带明显变窄且剪切带内外等效塑性应变梯度明显增大。     

岩石单颗粒压缩破碎的数值模拟分析

岩石颗粒破碎是影响粒状材料剪切强度和变形的最主要因素, 岩石颗粒破碎并不是想象的那么难, 像花岗岩颗粒有时在很小的压应力作用下就可以破碎。岩石单颗粒破碎的物理试验结果常常很离散, 完成大量单颗粒破碎的物理试验费时费力不现实, 采用离散单元法(Discrete element method, DEM)PFC软件模拟单颗粒压缩破碎试验, 既能克服单颗粒破碎物理试验的缺陷, 又能解决单颗粒破碎物理试验工作量大的难题, 是研究单颗粒破碎的理想选择。基于DEM的软件PFC2D, 将粒径为0.075～0.1245mm的基本粒子捆绑成不同粒径的单颗粒, 模拟岩石单颗粒压缩破碎试验, 观察颗粒破碎演化过程, 统计单颗粒破碎强度。计算单颗粒压缩破碎后颗粒分布的分维, 验证单颗粒破碎强度的分形模型和单颗粒破碎强度的尺寸效应。文中引用玄武岩单颗粒破碎试验结果, 与单颗粒破碎的离散单元模拟结果进行比较, 验证单颗粒破碎强度的尺寸效应和修正的Weibull理论的离散单元模拟结果。     

考虑颗粒破碎影响的粗粒土本构关系

粗粒土在较大的应力条件下容易产生颗粒破碎现象,而现有的大多数模型都没有考虑剪切过程中的颗粒破碎。模型将塑性功引入土体受力变形过程的能量方程中,推导得到土体流动法则。采用直线型屈服轨迹和非相关联流动法则,利用不排水应力路径计算得到硬化函数,建立了一个考虑颗粒破碎的粗粒土本构模型。对比分析表明：该模型对粗粒土在各种围压下的应力-应变和体应变计算结果与试验曲线吻合较好。     

考虑颗粒破碎的粗粒土剪胀性统一本构模型

粗粒土作为无黏性散粒状材料具有状态依赖特性,土体的剪切特性受密度和应力水平影响。易破碎是粗粒土的另一个特点,颗粒破碎影响粗粒土的剪胀、内摩擦角、峰值强度和渗透系数。为了能够准确地描述粗粒土的应力-应变关系,采用初始状态参量描述粗粒土的内部状态,根据三轴试验数据建立考虑颗粒破碎耗能的应力-应变关系,采用相关联流动法则推导考虑颗粒破碎的粗粒土剪胀性“统一本构模型”,并建立初始状态参量与模型参数之间的关系。所建立的统一本构模型既考虑了颗粒破碎对剪胀、内摩擦角的影响,又考虑了剪切特性对土体初始状态的依赖。采用变异粒子群算法拟合试验曲线,确定模型参数。模型计算结果能够很好地拟合试验曲线。采用同一组参数对假定的初始状态进行模拟计算,计算结果表明,模型能够模拟不同初始密度和应力水平下粗粒土变形的一般规律。     

Study on the particle breakage of ballast based on a GPU accelerated discrete element method

Breakage of particles will have greatly influence on mechanical behavior of granular material(GM)under external loads,such as ballast,rockfill and sand.The discrete element method(DEM)is one of the most popular methods for simulating GM as each particle is represented on its own.To study breakage mechanism of particle breakage,a cohesive contact mode is developed based on the GPU accelerated DEM code-Blaze-DEM.A database of the 3D geometry model of rock blocks is established based on the 3D scanning method.And an agglomerate describing the rock block with a series of non-overlapping spherical particles is used to build the DEM numerical model of a railway ballast sample,which is used to the DEM oedometric test to study the particles’breakage characteristics of the sample under external load.Furthermore,to obtain the meso-mechanical parameters used in DEM,a black-analysis method is used based on the laboratory tests of the rock sample.Based on the DEM numerical tests,the particle breakage process and mechanisms of the railway ballast are studied.All results show that the developed code can better used for large scale simulation of the particle breakage analysis of granular material.     

An elastoplastic constitutive model for frozen saline coarse sandy soil undergoing particle breakage

The mechanical property of frozen saline sandy soil is complicated due to its complex components and sensitivity to salt content and confining pressure. Thus, a series of triaxial compression tests were carried out on sandy samples with different Na₂SO₄ contents under different confining pressures to explore the effects of particle breakage, pressure melting, shear dilation and strain softening or hardening. The test results indicate that the stress–strain curves exhibit strain softening/hardening phenomena when the confining pressures are below or above 6 MPa, respectively. A shear dilation phenomenon was observed in the loading process. With increasing confining pressure, the strength firstly increases and then decreases. By taking into consideration the changes between the grain size distributions before and after triaxial compression tests, a failure strength line incorporating the influences of both particle breakage and pressure melting is proposed. In order to describe the deformation characteristics of frozen saline sandy soil, an elastoplastic incremental constitutive model is established based on the test results. The proposed model considers the plastic compressive, plastic shear and breakage mechanisms by adopting the non-associated flow rule. The breakage mechanism can be reflected by an index related to the initial, current and ultimate grain size distributions. The hardening parameters corresponding to compressive and shear mechanisms consider the influence of particle breakage. Then the effect of particle breakage on both the stress–strain and volumetric strain curves is analyzed. The calculated results fit well with the test results, indicating that the developed constitutive model can well describe the mechanical and deformation features of frozen saline sandy soil under various stress levels and stress paths. In addition, the strain softening/hardening, contraction, high dilation and particle breakage can be well captured.

     

考虑颗粒破碎效应的堆石料静动力本构模型

为合理反映颗粒破碎对堆石料力学特性的影响,基于试验结果分析,得出了堆石料在压缩和剪切作用下的颗粒破碎特性规律。通过引入压缩破碎和剪切破碎的相关参数,借鉴已有本构模型的合理定义,吸收临界状态理论和边界面理论的优点,发展了考虑颗粒破碎和状态相关的堆石料静动力统一弹塑性本构模型,并阐述了模型参数的确定方法。该模型不仅能够反映堆石料在静力荷载作用下的低压剪胀、高压剪缩、应变软化和硬化等特性,还能够反映在循环荷载作用下应力-应变的滞回特性和残余变形的累积效应。最后为验证模型的合理性,分别对堆石料的静力三轴和循环三轴试验进行了数值模拟预测,结果表明：模型预测与试验数据吻合良好,所提出的本构模型能够合理地描述颗粒破碎对堆石料静动力变形特性的影响。     

粗粒料颗粒破碎数值模拟研究

粗粒料在外力作用下存在明显的颗粒破碎特性,研究颗粒破碎过程是当前研究的热点问题之一。基于粗粒料单颗粒破碎机制,考虑单颗粒破碎强度与直径的变化规律,采用非线性接触H-Z模型和密度控制法建立了粗粒料颗粒破碎数值模型。开展粗粒料双轴剪切试验数值模拟研究,并与室内试验结果进行对比分析。研究表明：建立的粗粒料颗粒破碎数值模型能够较好地模拟粗粒料偏应力与轴向应变和体积应变与轴向应变的关系;数值模拟获得的粗粒料颗粒破碎率与室内试验结果基本一致;去除试样制备过程和固结过程引起的颗粒破碎,不同围压条件下的颗粒破碎率归一化后基本重合,且可以近似地采用双曲线函数进行拟合。颗粒破碎率随着围压的增大,逐渐增大,试验级配趋于Einav提出的颗粒破碎的最终级配（分维数等于2.6）     

3D finite element modeling of sand particle fracture based on in situ X‐Ray synchrotron imaging

Compressive loading of granular materials causes inter‐particle forces to develop and evolve into force chains that propagate through the granular body. At high‐applied compressive stresses, inter‐particle forces will be large enough to cause particle fracture, affecting the constitutive behavior of granular materials. The first step to modeling particle fracture within force chains in granular mass is to understand and model the fracture of a single particle using actual three‐dimensional (3D) particle shape. In this paper, the fracture mode of individual silica sand particles was captured using 3D x‐ray radiography and Synchrotron Micro‐computed Tomography (SMT) during in situ compression experiments. The SMT images were used to reconstruct particle surfaces through image processing techniques. Particle surface was then imported into Abaqus finite element (FE) software where the experimental loading setup was modeled using the extended finite element method (XFEM) where particle fracture was compared to experimental fracture mode viewed in radiograph images that were acquired during experimental loading. Load‐displacement relationships of the FE analysis were also compared with experimental measurements. 3D FE modeling of particle fracture offers an excellent tool to map stress distribution and monitors crack initiation and propagation within individual sand particles. Copyright © 2015 John Wiley & Sons, Ltd.