石英砂砾破碎过程中粒径分布的分形行为研究

荷载作用下粒状土的颗粒破碎改变土的粒径分布,从而影响其力学特性。试验证据显示随着颗粒破碎的增加,任何初始分布的土粒都将趋向一种自相似的分形分布。为了揭示土的粒径分布的分形转变机制,利用侧限压缩试验研究高压应力下石英砂砾的粒径分布演化规律和颗粒破碎特性,基于分形模型和粒径分布实测数据研究破碎过程中粒径分布的分形行为。研究发现:颗粒破碎增长导致粒状土趋向分形分布的过程与颗粒破碎量密切相关,并可以通过增大的分形维数来描述。尽管石英砂砾的初始分布和粒径有所不同,分形维数大于2.2的粒径分布实测数据均展示了较为严格的自相似性,因而该数值可作为分形分布的分形维数下限值。研究还发现:相同破碎状态下Hardin相对破碎率小于Einav相对破碎率,但二者对应力和体应变的响应规律是一致的。颗粒破碎发展至粒径分布成为分形分布时,体应变与相对破碎率的比值将保持恒定,并且受初始分布的均匀性和颗粒大小的影响很小。这一特点可用于分形分布的识别,并意味着试验中如果粒径分布是分形的,则无须为了粒径分析而终止试验,只需测量到体应变就可估计相对破碎率。     

Numerical investigation of particle breakage as applied to mechanical crushing—Part I: Single-particle breakage

A numerical approach to particle breakage is applied using the Rock Failure Process Analysis code, RFPA^2D. The numerical tool is validated by simulating the Brazilian test with a two-dimensional disk sample. Then two irregularly shaped particles with an exact geometry and exact mechanical properties are numerically modelled to investigate their breakage behaviour under unconfined and confined loading conditions. The numerical results indicate that the dominant mode of failure is catastrophic splitting and progressive crushing, which mainly depends on the loading conditions with respect to confinement. The analysis of the load–displacement curves obtained from the simulations suggests a brittle-ductile transition between the two cases. The lateral constraint increases the initial stiffness and the maximum breakage strength of the particle. Most of the energy released during the failure process comes from the crushing of highly stressed areas, particularly, in the vicinity of the contact points where a crushed zone forms. It is also found that the particle shape governs the breakage strength in addition to the material properties themselves, and that the heterogeneity of the particles governs the fracture propagation paths.     

Particle breakage evolution of coral sand using triaxial compression tests

Particle breakage continuously changes the grading of granular materials and has a significant effect on their mechanical behaviors.Revealing the evolution pattern of particle breakage is valuable for development and validation of constitutive models for crushable materials.A series of parallel triaxial compression tests along the same loading paths but stopped at different axial strains were conducted on two coral sands with different particle sizes under drained and undrained conditions.The tested specimens were carefully sieved to investigate the intermediate accumulation of particle breakage during the loading process.The test results showed that under both drained and undrained conditions,particle breakage increases continuously with increasing axial strain but exhibits different accumulating patterns,and higher confining pressures lead to greater particle breakage.Based on the test results,the correlations between particle breakage and the stress state as well as the input energy were examined.The results demonstrated that either the stress state or input energy alone is inadequate for describing the intermediate process of particle breakage evolution.Then,based on experimental observation,a path-dependent model was proposed for particle breakage evolution,which was formulated in an incremental form and reasonably considers the effects of the past breakage history and current stress state on the breakage rate.The path-dependent model successfully reproduced the development of particle breakage during undrained triaxial compression using the parameters calibrated from the drained tests,preliminarily demonstrating its effectiveness for different stress paths.     

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.     

The Effect of Mode of Loading on Particle-Scale Damage

The effect of different modes of loading on particle characteristics of a silica sand is investigated. The particle characteristics were examined for samples taken to pre- and post- yield states in compression as well as after shearing to high strains. The change to particle characteristics such as surface roughness, shape and size due to loading were examined. The results show that although catastrophic particle breakage starts with the yielding of the material, changes to the particle surfaces at contacts, through minor damage to particle asperities by yielding or chipping, can impose some local changes even before reaching the yield stress. The study also confirmed the importance of the sample initial grading on defining the mode of particle interaction during compression.     

基于颗粒破碎特性的堆石材料级配演化模型

颗粒破碎会改变土体级配,进而影响其应力应变等力学行为。针对现有技术手段难以实时确定加载过程中颗粒破碎与级配变化的现状,依据天然岩石颗粒的破碎特性,建立了一个基于颗粒强度的级配演化模型。模型中应力参数采用增量加载法,可预测加载过程中的级配演化。由单粒强度试验确定颗粒破碎特性和模型参数,试验结果表明颗粒强度服从Weibull分布。筛分颗粒破碎后的碎片发现,粒径累计分布可用正态曲线拟合,且不同粒组的粒径累计分布相似。最后,模型计算结果与三轴试验数据的对比分析表明,模型可以较好地预测试样在加载过程中的级配变化。     

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.     

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。     

One-Dimensional Compression Behaviour of Uniformly Graded Sand Related to Single Particle Crushing Strength

In order to compare one-dimensional compression behaviour with the crushing strength characteristics of single particles, one-dimensional compression and single particle crushing tests were carried out on various granular materials with uniform gradings. The average characteristic tensile stress acting on a particle in a sample was calculated using a simplified approach. The one-dimensional compression yield stress was related to the particle size and this was also related to the single particle crushing strength. The decrease of the vertical yield stress with increasing initial void ratio can be explained by the increase in the particle characteristic stress as the void ratio increased and a corresponding decrease in co-ordination number. The single particle strengths were compared with the characteristic tensile stress for a particle embedded in the soil matrix. The logarithm of the characteristic tensile stress at maximum compression index for a particle embedded in a granular matrix could be related to the logarithm of the single particle strength multiplied by a proportional factor. The introduction of a factor was necessary because the calculated average characteristic tensile stress did not take into account the non-uniform distribution of inter-particle stresses. The ratio of the single particle strengths to the average characteristic tensile stress for a particle embedded in the soil matrix was considered to be an indicator of the non-uniform distribution. This ratio decreased and hence uniformity of inter-particle stress distribution increased with angularity and surface roughness.     

Investigation of the ultimate particle size distribution of a carbonate sand

A series of ring shear tests were conducted to investigate the ultimate particle size distribution of a carbonate sand. The tests were carried out under different stress levels, on three types of specimens: 1) uniformly graded specimens made of dry natural sand 2) remoulded specimens of the crushed sand after first shearing to large strains 3) specimens made of natural sand grains but with the same grading as in (2). The first series of tests on type (1), carried out to very large strains, led to apparently stable gradings, distinct for each stress level. Only limited additional particle breakage could be induced by remoulding the specimens after shearing (type (2)) and subjecting them to more shearing. Tests on specimens created at the apparently stable gradings (type (3)) but from the intact sand particles however led to significantly greater breakage. For the three types a stable, fractal grading was achieved. Analyses of the soil particles’ shape showed that the aspect ratio, sphericity and circularity reach a steady value at large strains, in parallel to reaching a stable grading. The mobilized angle of shearing resistance however was not significantly different in the different types of samples, suggesting the final grading dominates the behaviour.     

考虑细观单粒强度的堆石料破碎特性研究

颗粒破碎是影响堆石料力学性质的主要因素之一,但由于测试手段的限制,荷载作用过程中堆石的颗粒破碎难以实时度量,因而影响堆石料力学特性的深入研究。通过单粒强度试验,发现同一粒组的堆石料单粒强度较好地服从Weibull分布,而破碎后颗粒的粒径级配曲线基本服从分形分布。在此基础上,推求了堆石料三轴试验过程中级配的演化过程,给出了颗粒破碎的实时预测方法,与三轴试验结果比较,验证了本文方法的有效性。     

堆石料的颗粒破碎规律研究

粗颗粒土剪切过程中的颗粒破碎现象已被广泛认识,并且在试验和理论方面进行了大量研究。利用大型三轴仪开展了一系列不同级配、不同密度、不同围压条件下堆石料的排水剪切试验,并对试验前后的试样分别进行了颗粒分析,以探讨堆石料的颗粒破碎规律及其影响因素。试验结果表明:密度对颗粒破碎影响较小,而级配和围压的影响较大,围压越高则颗粒破碎越严重。对比试验前后的粒径分布曲线发现,颗粒破碎主要集中在粒径20 mm以上的颗粒范围内,粒径变化幅度随粒径的减小呈减小趋势。基于分形理论,建立了颗粒破碎分形维数与围压和颗粒级配之间的关系表达式,为进一步研究堆石料的强度、变形及剪胀特性提供依据。     

Anisotropic swelling in black cotton soil

The influence of initial moisture content and the nature of granular material on the anisotropic swell behaviour in black cotton soil has been examined. It was observed that the amount and rate of swelling are guided by the initial particle orientation. For samples compacted with moisture below the optimum value, the variation in swelling trends in vertical and horizontal directions is a result of the particle arrangement, the pressure exerted by the air in the voids and also the subsequent expulsion of the same. In samples compacted with moisture content above the optimum, the initial dispersed state of the particles guides the anisotropy. The swelling in such samples is considerable in directions transverse to the particle orientation. At optimum moisture levels, because of the minimal differences in the particle arrangement for samples in vertical and horizontal directions, the swelling is similar in both cases and as such no anisotropic behaviour was noticed. Increasing presence of granular component in the soil reduces the rate of swelling, protracts the time for completion of swelling and also reduces the anisotropic behaviour. Reduction in the grain size of the granular material facilitates quick swelling. The variations in such samples for vertical and horizontal directions are explained on the basis of packing in the system and the constraints imposed by sand grains on osmotic swelling. Since similar variables exist in field conditions, the present study enables an understanding of their role in the anisotropic swell behaviour of black cotton soils.     

先期振动对筑坝材料变形特性的影响

通过大型振动三轴试验研究了先期振动荷载对高土石坝筑坝材料抵抗地震变形能力的影响,研究结果表明:经受过先期动应力作用的土石料,再次经受动应力作用时,其抵抗变形的能力明显提高,这是由于在初始动应力作用下,土石料颗粒破碎及试样内部重定向排列大部分已经完成,再次经受动应力作用时,土石料颗粒破碎的程度将降低,试样内部重定向排列的难度将加大,从而使得其变形量减小,抵抗变形的能力提高。抵抗变形的能力提高的幅值与土石料本身的性质、再次经受的动应力与先期动应力的比值,即先期动应力和再次经受的动应力大小有关。根据试验结果建立了先期振动对粗粒料变形能力影响的一般表达式,该表达式表明:先期振动对粗粒料抵抗变形能力的影响仅与k值有关,k反映了粗粒料对先期振动作用的敏感度,表示粗粒料经先期动应力作用后,在再次经受动应力作用时,粗粒料内部重定向排列和颗粒破碎的难易度,k值越小,粗粒料对先期振动的敏感性越大,反之则越小,k值大小与粗粒料本身的矿物组成有关,而与其自身的岩性、颗粒形状、级配、密度等没有关系。     

The role of particle breakage in the mechanics of a non-plastic silty sand

A detailed investigation was carried out on a silty sand from Bo?tanj, Slovenia, in order to identify the role that particle breakage plays in test interpretations and mechanics. The soil was tested up to a high pressure in the triaxial and oedometer apparatus. Unexpected for a silty sand, the basic patterns of behaviour, in terms of strength and stiffness, were found to be similar to those of many previously investigated clean sands, with unique and parallel Normal Compression and Critical State Lines at higher stress levels and a horizontal asymptote to the Critical State Line at lower stress levels. The stiffness was controlled primarily by the state of the soil relative to the location of these lines. Despite the better grading, there was still very significant particle breakage. However, the breakage was largely confined to the coarse fraction. The grading curves after various tests all showed convergence with the initial grading towards 1 μm, which may therefore represent the comminution limit. It is believed that it is the particle breakage that caused the behaviour to follow a simple Critical State type of framework and why transitional or non-convergent compression behaviour was not found.     

双轴压缩条件下散粒体的二维孔隙分布及演化规律研究

基于离散单元法建立了不同密实度的理想散粒体数值模型,通过Voronoi–Delaunay网格剖分建立离散域,采用基于边界点的椭圆拟合算法模拟散粒体中的孔隙,并进一步分析了在双轴压缩条件下散粒体孔隙的分布特征与演化规律,同时结合数值试样中单孔隙的变化过程,分析了散粒体变形的微细观力学机理。研究表明,散粒体二维孔隙表现出明显的双峰分布特征,在双轴压缩条件下,不同密实度散粒体的孔隙要素表现出明显不同的演化特征。总体说来,松散试样小孔隙比例增加,大孔隙比例减少,孔隙趋于均匀;而密实试样小孔隙比例减少,大孔隙比例增加。孔隙的排列方向与荷载主方向有关,初始密实度对其影响不大。双轴加载过程中长轴沿水平方向的细长孔隙首先崩溃,长轴沿轴向加载方向的孔隙存留下来并在散粒体变形过程中起主导作用,最终沿加载方向产生一个稳定的颗粒结构。单孔隙的发展过程显示,大孔隙上承担着较强的力链,双轴压缩过程中随着变形的发展,松散试样中接触力链较强的单个大孔隙逐渐分裂成为多个小孔隙,颗粒接触力链分布趋于均匀;而在密实试样中,随着变形发展小孔隙逐渐融合形成大孔隙。     

Effects of fines on the cyclic liquefaction behaviour in unsaturated,well-graded materials

The liquefaction of cargoes of metallic ores during maritime transportation is believed to have caused a number of ships to capsize during the past 30 years. To minimise the risk of liquefaction, shipping standards specify a transportable moisture limit (TML), which is the maximum moisture content for ore cargoes to be loaded onto a ship. However, the mechanics leading to the liquefaction of these cargoes is not well understood. This study uses an unsaturated soil mechanics perspective to understand the cyclic liquefaction behaviour of partially saturated materials, similar in grading to iron ore fines, a metallic ore that is known to liquefy during shipping transportation. Iron ore fines are transported at relatively low densities and have variable gradings containing a wide range of particle sizes and fines contents. Therefore, the effects of the degree of saturation and the fines content on the cyclic liquefaction behaviour of well-graded materials have been investigated by performing unsaturated, compression-only cyclic triaxial tests on samples prepared with four different gradings containing particle sizes from 9.5 mm to 2 μm with fines (<75 μm) contents of 18%, 28%, 40% and 60%. The trends in the data are discussed and used to develop a simple method that can conservatively estimate the number of cycles that samples with different degrees of saturation and fines contents are able to resist. The use of this method to describe the liquefaction behaviour of cargoes containing iron ore fines, in practice, is discussed.     

基于破碎能耗的粗颗粒料本构模型

现有的考虑颗粒破碎的本构模型主要是通过引入颗粒破碎率来反映颗粒破碎对材料力学性质的影响,由于颗粒破碎率只是粗颗粒料在受外荷作用下的一种外部表现,在测定的其它参数中实际上已经包含了颗粒破碎的影响,因此为反映颗粒破碎而引入颗粒破碎率的方法是不合适的。基于Ueng和Chen剪胀方程,通过分析三轴剪切试验过程中的能量平衡,提出了考虑颗粒破碎的剪胀方程及其参数确定方法。将Rowe剪胀方程和考虑颗粒破碎的剪胀方程分别引入Duncan E-非线性模型和沈珠江“南水”双曲服面模型,通过与三轴CD剪切试验成果的对比分析和工程实例的有限元数值分析,表明所提模型可较好地反映材料的剪胀特性。如采用弹塑性模型尚能反映颗粒破碎在增加变形的同时降低了材料的强度等特性,验证了所提模型的合理性和可靠性。与现有的考虑颗粒破碎的本构模型相比,所提模型具有试验工作量小、参数少和参数物理意义明确等优点,便于在工程中推广使用。     

模拟堆石料颗粒破碎对强度变形的影响

许多试验事实表明,极高压力下颗粒材料粒径极限分布并非 Hardin 所谓的以 0.074 mm 为截断粒径的均匀分布。通过拓展破碎概念提出了 Hardin 破碎指标修正定义,并用以区分剪切过程中破碎的暂时和永久终止状态。 开展了系列模拟 堆石料固结排水大型三轴试验,提出了系列非线性关系用以描述模拟堆石料的级配、破碎指标以及应力–应变–体变响应变化规律。分析表明：随着围压增加,特征粒径减小而级配指标增加,试样级配变化明显;随着围压增加,峰值（或临界）状态破碎指标增加,相应的应力比和内摩擦角则减小,两种状态下破碎指标与内摩擦角具有唯一对应关系;同一剪切过程中,破碎指标变化率、剪胀率和塑性剪切模量具有非同步变化关系,由此形成了颗粒破碎对于模拟堆石料应力变形影响的复杂性。     

Effects of particle size and confining pressure on breakage factor of rockfill materials using medium triaxial test

Rockfill dams are mostly constructed using blasted rockfill materials obtained by blasting rocks or alluvial rockfill materials collected from the riverbeds.Behaviors of rockfill materials and their characterization significantly depend on breakage factor observed during triaxial loading.In this paper,two modeled rockfill materials are investigated by using medium triaxial cell.Drained triaxial tests are conducted on various sizes of modeled rockfill materials used in the two dams,and test data are analyzed accordingly.Breakage factor of rockfill material is studied and the effects of particle size and confining pressure on breakage factor are investigated using medium triaxial cell as many researchers have already conducted investigation using large triaxial cell.