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。     

An approach to calculating large strain accumulation for discrete element simulations of granular media

For research on granular materials, establishing a method to calculate continuum strain from particle displacements is necessary for understanding the material behaviour at macro-level and developing continuum constitutive models. Existing methods are generally based on constructing a mesh or background grid to calculate strain from particle motions. These methods offer rigorous ways to measure strain for granular materials; however, they suffer from several problems such as mesh distortion and lacking grid-to-particle strain mapping procedure, which hinders their capability of calculating strain accumulation during large deformation processes of granular media. To address this issue, this study proposes a new strain calculation method for discrete element simulations of granular materials. This method describes a particle assembly as an equivalent continuum system of material points, each of which corresponds to a particle centre and represents a continuous region with its initial volume/area presumably equal to the volume/area of Voronoi cells generated in accordance with the particle assembly configuration. Smooth Particle Hydrodynamics (SPH) interpolation functions are then employed to calculate strain for these material points. This SPH-based method does not require any mesh or background grid for computation, leading to advantages in calculating strain accumulation under large deformation. Simulations of granular materials in both uniform and heterogeneous gradations were carried out, and strain results obtained by the proposed method indicate good agreements with analytical and numerical solutions. This demonstrates its potential for strain calculations in discrete element simulations of granular materials involving large deformations and/or large displacements.     

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 granular materials with grain crushing and its application to a pyroclastic soil

A constitutive model for granular materials is developed within the framework of strain–hardening elastoplasticity, aiming at describing some of the macroscopic effects of the degradation processes associated with grain crushing. The central assumption of the paper is that, upon loading, the frictional properties of the material are modified as a consequence of the changes in grain size distribution. The effects of these irreversible microscopic processes are described macroscopically as accumulated plastic strain. Plastic strain drives the evolution of internal variables which model phenomenologically the changes of mechanical properties induced by grain crushing by controlling the geometry of the yield locus and the direction of plastic flow. An application of the model to Pozzolana Nera is presented. The stress–dilatancy relationship observed for this material is used as a guidance for the formulation of hardening laws. One of the salient features of the proposed model is its capability of reproducing the stress–dilatancy behaviour observed in Pozzolana Nera, for which the minimum value of dilatancy always follows the maximum stress ratio experienced by the material. Copyright © 2002 John Wiley & Sons, Ltd.     

A numerical investigation of the incremental behavior of crushable granular soils

The mechanical behavior of granular materials is characterized by strong nonlinearity and irreversibility. These properties have been differently described by a variety of constitutive models. To test any constitutive model, experimental data relative to the nature of the incremental stress–strain response of the material is desirable. However, this type of laboratory data is scarce because of being expensive and difficult to obtain. The discrete element method has been used several times as an alternative to obtain incremental responses of granular materials. Crushable grains add one extra source of irreversibility to granular materials. Crushability has been variously incorporated into different constitutive models. Again, it will be helpful to obtain incremental responses of crushable granular materials to test these models, but the experimental difficulties are increased. Making use of a recently introduced crushing model for discrete element simulation, this paper presents a new procedure to obtain incremental responses in discrete analogs of granular crushable materials. The parallel probe approach, previously used for uncrushable discrete analogs, is here extended to account for the presence of crushable grains. The contribution of grain crushing to the incremental irreversible strain is identified and separately measured. Robustness of the proposed method is examined in detail, paying particular attention to aspects such as dynamic instability or crushing localization. The proposed procedure is later applied to map incremental responses of a discrete analog of Fontainebleau sand on the triaxial plane. The effect of stress ratio and granular state on plastic flow characteristics is highlighted. Copyright © 2016 John Wiley & Sons, Ltd.     

A kinematic hardening constitutive model for sands: the multiaxial formulation

This paper explores the possibility of using well-accepted concepts—Mohr-Coulomb-like strength criterion, critical state, existence of a small strain elastic region, hyperbolic relationship for representing global plastic stress–strain behaviour, dependence of strength on state parameter and flow rules derived from the Cam-Clay Model—to represent the general multiaxial stress–strain behaviour of granular materials over the full range of void ratios and stress level (neglecting grain crushing). The result is a simple model based on bounding surface and kinematic hardening plasticity, which is based on a single set of constitutive parameters, namely two for the elastic behaviour plus eight for the plastic behaviour, which all have a clear and easily understandable physical meaning. In order to assist the convenience of the numerical implementation, the model is defined in a ‘normalized’ stress space in which the stress–strain behaviour does not undergo any strain softening and so certain potential numerical difficulties are avoided. In the first part the multiaxial formulation of the model is described in detail, using appropriate mixed invariants, which rationally combine stress history and stress. The model simulations are compared with some experimental results for tests on granular soils along stress paths lying outside the triaxial plane over a wide range of densities and mean stresses, using constitutive parameters calibrated using triaxial tests. Furthermore, the study is extended to the analysis of the effects induced by the different shapes of the yield and bounding surfaces, revealing the different role played by the size and the curvature of the bounding surface on the simulated behaviour of completely stress- and partly strain-driven tests. Copyright © 1999 John Wiley & Sons, Ltd.     

Cavity expansion analyses of crushable granular materials with state‐dependent dilatancy

Crushability is one of the important behaviors of granular materials particularly under high stress states, and affects both the deformability and strength of the materials that are in essence associated with state‐dependent dilatancy. In this presentation, first, a new critical state model is proposed to take into account the three different modes of compressive deformation of crushable granular materials, i.e. particle rearrangement, particle crushing and pseudo‐elastic deformation. Second, the governing equations for cavity expansion in crushable granulates are introduced, in which the state‐dependent dilatancy as well as the bounding surface plasticity model are used. Then, the procedure to obtain semi‐analytical solutions to cavity expansion in the material is described in detail, in which a commercial differential equation solver is employed. Finally, cavity expansion analyses are carried out on Toyoura sand, a well‐documented granular material, to demonstrate the effects of crushability and state‐dependent dilatancy. The study shows that particle crushing does occur at both high stress and critical states and affects the stress fields and the deformation behavior of the material surrounding the cavity in association with state‐dependent dilatancy. This leads to conclusion that particle crushing and state‐dependent dilatancy have to be taken into account when cavity expansion theory is used to interpret cone penetration tests and pressuremeter tests. Copyright © 2011 John Wiley & Sons, Ltd.     

Modeling of tensile strength on moist granular earth material at low water content

While most research has mainly focused on the volume change, flow, and shear strength of unsaturated earth materials, investigations of tensile strength of unsaturated earth materials especially granular materials have not received much attention except for cemented and clayey materials. Thus, direct tension experiments were carried out to quantify the actual magnitude of tensile strength induced by water in moist granular soil at especially low water contents (w<4%). The magnitudes of the measured tensile strength are significantly different from zero. A simple experimental tensile strength model is proposed. Practicing engineers can use this model for approximate estimation of the tensile strength of unsaturated granular soils without experiments and for precise design or analysis of most engineered facilities relying on the unsaturated granular soils in the vadose zone. The experimental data are also compared with a theoretical model developed for monosized spheres at low water contents, and its application for a real granular earth material having a variety of particles is discussed. The nonlinear behavior of the tensile strength for moist granular soil is appropriately simulated with a model.     

武汉东湖淤泥早强固化试验研究

利用传统淤泥主固化材料水泥与辅助固化材料粉煤灰和石膏,通过组合配比对武汉东湖疏浚淤泥分别进行固化,基于无侧限抗压强度试验和三轴剪切试验,确定不同材料组合及配比下淤泥固化强度和特点。试验研究表明：在疏浚淤泥固化过程中水泥占主导地位,对固化效果影响最为显著;粉煤灰起到的作用相当于降低了淤泥初始含水率,表现在固化淤泥早期强度的快速提高;石膏有利于固化淤泥早期强度的形成,其作用持续于整个淤泥固化过程。随着含水率的增大,单纯水泥固化淤泥试样的应力-应变关系曲线由应变软化逐渐过渡到应变硬化模式,围压对固化淤泥强度的影响程度也随着含水率的增大而逐渐减弱,辅助固化材料的添加使原单纯水泥固化淤泥的应变硬化型曲线变为应变软化模式。不同含水率东湖疏浚淤泥固化材料最佳配比为水泥掺入比20%,粉煤灰为3倍的水泥量,石膏为30%的水泥量,该研究成果有助于武汉东湖底泥的治理以及疏浚淤泥排放场地的地基处理和环境整治。     

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.

     

基于颗粒破碎的粗粒土剪切强度的模拟分析

颗粒破碎在岩土工程领域是很常见的现象,土工试验中无法显示颗粒破碎过程及其影响,本文采用离散单元软件PFC2D模拟了考虑颗粒破碎影响的粗粒土的直剪试验,给出了考虑颗粒破碎的粗粒土直剪试验的模拟方法,分析粗粒土的剪应力-剪切位移关系、剪胀和剪切强度等宏观力学行为,探讨基本颗粒间黏聚力、单颗粒孔隙率和粗粒土试样的孔隙率对剪切强度的影响。结果表明:颗粒破碎对剪切强度的破碎准则有影响,颗粒不破碎试样的剪切强度符合Mohr-Coulomb准则;颗粒破碎试样的强度包络线是幂函数关系。     

Notes on the effect of grain crushing on the granular soil behaviour

Two granular materials — alluvial quartzy Zbraslav sand and granular silica gel — were tested with the intention to demonstrate the effect of grain crushing. Stepwise transformation of the compression curve produced by progressive grain crushing was observed. Due to grain crushing, shear strength envelope became nonlinear, and the behaviour was no more physically isomorphous. The shear stress–strain diagrams acquire a typical wavy (garland-like) form, induced by periodic softening and hardening of the soil response. The intensity of grain crushing depends (in addition to stress level, grain resistance and time) on the shear path. In the crushing phase, initial porosity and angularity play a secondary role. Many other behavioural features common with granular soils (like increase in dilatancy with density and grain size) are suppressed. Grain crushing thus produces a qualitatively different feature of geomaterial behaviour with grave practical consequences (dense sand, e.g. starts to behave like loose).     

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。     

Fast shear behavior of granular materials in ring-shear tests and implications for rapid landslides

The high mobility of rapid landslides is one of the most important subjects of both theoretical and practical interest to engineers and scientists. The idea that ultralow resistance could explain the high mobility inspires researchers to examine the shear behavior of granular materials under a wide range of conditions, but the response of granular materials to fast loading rates is largely unknown. The motivation for this study was to examine several fundamental issues of particle properties and mechanical conditions on the fast shear behavior of granular materials. Two granular materials were studied in the oven-dried state and were sheared by employing a ring-shear apparatus. Results indicated that angular particles (silica sand) had higher shear strength parameters than spherical particles (glass beads). In addition, the dilative process was observed during shearing, which depended on normal stress and particle shape. A slightly negative shear-rate effect on shear strength was observed for both granular materials under a certain range of shear rates. Furthermore, cumulative shear displacement had a significant effect on the degree of particle crushing. Fast ring-shear tests also revealed that shear rate had a slightly negative effect on particle crushing. Based on these experimental results, the possible applications of dynamic grain fragmentation theory to assess the high mobility of rapid landsliding phenomena were discussed. It was indicated that the magnitude and release rate of elastic strain energy generated by grain fragmentation played important roles on the dynamic process of landslide mobility.     

DEM modelling of cone penetration tests in a double-porosity crushable granular material

A three-dimensional discrete element model is used to investigate the effect of grain crushing on the tip resistance measured by cone penetration tests (CPT) in calibration chambers. To do that a discrete analogue of pumice sand, a very crushable microporous granular material, is created. The particles of the discrete model are endowed with size-dependent internal porosity and crushing resistance. A simplified Hertz–Mindlin elasto-frictional model is used for contact interaction. The model has 6 material parameters that are calibrated using one oedometer test and analogies with similar geomaterials. The calibration is validated reproducing other element tests. To fill a calibration chamber capable of containing a realistic sized CPT the discrete analogue is up-scaled by a factor of 25. CPT is then performed at two different densities and three different confinement pressures. Cone tip resistance in the crushable material is practically insensitive to initial density, as had been observed in previous physical experiments. The same CPT series is repeated but now particle crushing is disabled. The ratios of cone tip resistance between the two types of simulation are in good agreement with previous experimental comparisons of hard and crushable soils. Microscale exploration of the models indicates that crushing disrupts the buttressing effect of chamber walls on the cone.     

堆石料单粒强度尺寸效应的颗粒流模拟方法研究

围绕堆石料单粒强度尺寸效应的颗粒流模拟方法展开研究。首先,基于FISH二次开发建立了堆石料的随机不规则单粒模型,充分考虑堆石料的形状特征和破碎现象;然后,建立了堆石料单粒强度尺寸效应的等效模拟方法,以单粒强度随其粒径的变化规律为基础,推导了堆石料模型中细观黏结强度与堆石料等效粒径的负指数经验公式;其次,基于建立的数值模型对堆石料的室内单粒压缩试验进行仿真模拟,验证数值模型的正确性和合理性,并对较大粒径堆石料的单粒强度进行模拟预测,突出数值试验的优势;最后,基于建立的数值模型对相同粒径不同形状特征堆石料的单粒强度分布特征进行模拟研究。研究结果表明：（1）堆石料内部缺陷含量和尺寸随粒径增加对其单粒强度所产生的尺寸效应,可通过堆石料模型中细观强度参数随粒径折减进行等效模拟;（2）形状特征对堆石料的破裂机制具有重要影响,方形颗粒为压剪破裂,单粒强度较高,而随机不规则颗粒和圆形颗粒为拉剪或劈裂,单粒强度相对较低;（3）拉剪或劈裂条件下,堆石料形状越不规则,其单粒强度的离散程度越高,反之则离散程度越低。相关研究成果可为进一步研究荷载作用下堆石体内各粒径段堆石料的破碎量奠定基础,从而更加真实地反映堆石体的级配演化规律。     

California Bearing Ratio and Brazilian Tensile Strength of Mine Overburden–Fly Ash–Lime Mixtures for Mine Haul Road Construction

The production and utilization of coal is based on well-proven and widely used technologies. Fly ash, a coal combustion byproduct, has potential to produce a composite material with controlled and superior properties. The major challenges with the production of fly ash are in its huge land coverage, adverse impact on environment etc. It puts pressure on the available land particularly in a densely populated country like India. In India the ash utilization percentage has not been very encouraging in spite of many attempts. Stabilization of fly ash is one of the methods to transfer the waste material into a safe construction material. This investigation is a step in that direction. This paper presents the results of an investigation on compressive strength and bearing ratio characteristics of surface coal mine overburden material and fly ash mixes stabilized with lime for coal mine haul road construction. Tests were performed with different percentages of lime (2, 3, 6 and 9%). The effects of lime content and curing period on the bearing ratio and tensile strength characteristics of the stabilized overburden and fly ash mixes are highlighted. Unconfined compressive strength test results cured for 7, 28 and 56 days are presented to develop correlation between different tensile strengths and unconfined compressive strength. Empirical models are developed to estimate bearing ratio and tensile strength of mine overburden–fly ash–quick lime mixtures from unconfined compressive strength test results.     

珊瑚颗粒力学特性应变率效应试验研究

珊瑚单颗粒破碎特性与珊瑚砂高压缩性、剪缩性及良好蠕变性等宏观力学行为密切相关。珊瑚颗粒的应变率效应对于不同形式荷载作用下珊瑚砂强度与变形特性研究具有重要意义。对约300颗珊瑚颗粒进行0.1～50 mm/min位移速率下的单颗粒破碎试验,探讨加载应变速率对颗粒破碎强度、破碎模式、破碎能量及破碎分形的影响。结果表明,珊瑚颗粒破碎强度服从Weibull分布规律,且特征破碎强度随应变率的提高非线性增大;随着加载速率的增大,颗粒主劈裂破坏往往先于棱角的局部碎裂和表面研磨,相应的荷载?位移曲线呈现出由峰前“多峰”向峰后“多峰”现象转变;珊瑚颗粒破碎能量密度和破碎分形维数同样具有明显的应变率效应,且均与对数应变率呈线性正相关关系,表征能量耗散和破碎程度均随加载应变率的增大而增大。     

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。     

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。