A PACKING GENERATION SCHEME FOR THE GRANULAR ASSEMBLIES WITH PLANAR ELLIPTICAL PARTICLES

In this paper, a new generator algorithm and a computer program PG2D is introduced for 2D numerical simulation of packing configuration in a granular material composed of elliptical particles of different a/b aspect ratios. Each elliptical particle is approximated by four connected arcs. The centre co-ordinates and radius of each arc and co-ordinates of connecting points can be determined from the formulae derived by entering the major axis length, 2a, and the eccentricity. The domain to be filled with particles can be a polygon of any shape. Given the size of the packing domain, geometrical information and numbers of particles to be generated, the packing location of each particle and the co-ordinates of contact points along with contact normal rose diagram can be generated as outputs. Simulation results show that this new algorithm can provide quite a reasonable packing model in accordance with the initial input required for the analysis of the mechanics of granular material. This generation scheme has the potential to cover packing generation and behaviour analysis of 3D sphere or ellipsoidal shaped granular materials. © 1997 by John Wiley & Sons, Ltd.     

基于多因素椭圆堆叠的岩土细观建模方法

天然岩土体具有复杂的细观结构和组成特征,现有细观建模方法难以解决任意粒径、长短轴比、倾角以及平面分布特征的多因素岩土体细观建模问题。为此基于椭圆的4段圆弧等效,结合改进的分组波前堆叠法,实现了任意粒径、长短轴比、倾角以及平面分布的快速高体积率椭圆堆叠,并以此建立了与堆叠椭圆粒径、长短轴比、倾角以及平面分布一致的凸多边形结构。与现有的椭圆堆叠ALA法和圆盘堆叠ODR方法相比,提出的方法具有更高的椭圆堆叠体积率和堆叠效率,MATLAB环境下椭圆堆叠效率为500～600个/s。与现有仅能考虑颗粒粒径分布的岩土细观建模GBM法相比,提出的方法可以同时考虑颗粒的粒径、长轴、倾角,以及平面分布4个因素,快速生成任意粒径、长短轴比、倾角以及平面分布的颗粒堆积,并建立与椭圆分布一致的岩石细观结构。通过两个岩土体细观建模案例分析表明,所提方法可以提高岩土体模型的细观建模精度与生成效率。     

A packing generation scheme for the granular assemblies with 3D ellipsoidal particles

This paper introduces a new generator algorithm and computer program for 3-D numerical simulation of packing configuration in a granular assemblies composed of ellipsoidal particles of different a/b aspect ratios. Each ellipsoidal particle is approximated by the revolution of an ellipse, formed by four connected arcs, about the major axis passing through its centroid. The centroid co-ordinates, major axis direction and lengths of the major and minor axes are the essential data for the packing generation and associated contact detection. The domain to be filled with particles can be a polyhedron of any shape. The packing program was coded based on a newly proposed scheme which obeys the no interpenetration kinematics of solid bodies. New contact detection algorithms for any two ellipsoids in the packing space were developed. Though simple, these algorithms effectively determine the contact condition and contact point without solving the simultaneous equations of the two ellipsoidal surfaces. Each particle's packing location, contact-point co-ordinates, and three-dimensional graphs can be created using the packing domain given boundaries, along with numbers, and geometrical information of particles to be generated. Simulation results show that this new algorithm provides an effective packing model as a required initial input for analysing the mechanics of granular material. This generation scheme potentially can explore the complex 3-D behaviours of material composed of discrete particles. Copyright © 1999 John Wiley & Sons, Ltd.     

基于距离和局部Delaunay三角化控制的颗粒离散元模型填充方法研究

根据颗粒离散元Kelvin 接触力计算模型,分析了圆形颗粒体模拟材料力学特性应具备的条件,在此基础上提出了一种新颗粒模型构建方法。该方法首先在复杂模型域内随机生成种子,然后利用相切条件逐步扩展填充整个区域。填充过程中借助局部Delaunay三角化网格控制新颗粒的生成,采用复杂几何体距离控制颗粒与模型边界的相对位置,对靠近模型边界的颗粒进行容忍性优化填充,从而增加模型颗粒与边界的耦合性。同时对模型孔隙进行再填充,保证每个填充颗粒至少与3个颗粒相切,提高了模型内颗粒间的耦合性和模型的密度。最后采用任意多边形控制材料边界,将模型材料的设置简化为判断点是否在多边形内,简化了复杂模型材料属性的设置过程。结果表明：与膨胀颗粒生成法相比,该方法生成模型重叠量小、颗粒间及颗粒-边界相互耦合、填充率高。因此,颗粒黏结力破坏后不会造成飞溢现象,可适用于任意连通域模型的生成,能更好地实现复杂岩土细观介质变形破坏机制的模拟与研究。     

颗粒粒径对微生物固化砂土强度影响的试验研究

微生物固化技术（MICP）是岩土工程领域新兴起的一种不良地基处理技术,不同地基土体之间的颗粒粒径并不相同,其固化效果也可能存在一定差别。选用3种不同颗粒粒径范围的砂土进行微生物固化处理,并基于无侧限抗压强度试验、孔隙体积测量和洗酸处理,从宏观角度分析颗粒粒径对微生物固化效果的影响。结合扫描电镜测试,从细观角度对微生物固化机制进行了初探。研究结果表明,微生物固化砂土中碳酸钙晶体以颗粒簇形式堆积在砂土颗粒表面及颗粒间接触处,其尺寸随碳酸钙晶体堆叠程度的增加而增大;对于颗粒粒径较小的砂土,颗粒间孔隙较易被碳酸钙晶体填充密实,固化试样内有效碳酸钙晶体比例较大,“结构性”较强,无侧限抗压强度较高。     

Assessing the relative packing behaviour of Chandarpur and Khairagarh sandstones of Proterozoic Chhattisgarh Basin

The paper concerns mainly with properties of packing of the Proterozoic Chandarpur and Khairagarh sandstones of Chhattisgarh Basin. An attempt has been made to decipher the nature of boundary between Chandarpur Group and overlying Raipur Group on the basis of grain packing. For the purpose of study based on eight representative thin sections of Chandarpur and Khairagarh sandstones, measurements of grain size distribution, types of grain contacts, packing density (Pd), packing proximity (Pp) and linear regression analysis has been carried out. The relation of packing density with packing proximity of Khairagarh sandstone shows positive correlation coefficient (r) with linear regression equation (y) and no clear trend in packing proximity (Pp) vs grain size (Is) is observed whereas Chandarpur sandstone shows packing density increases and packing proximity decreases with linear regression equation (y) and correlation coefficient (r). Chandarpur grain size tends to increase with packing density (Pd) whereas packing proximity (Pp) increases but Khairagarh sandstone packing density (Pd) decrease with increase of grain size (Is) and packing proximity (Pp) tends to increase with decrease in grain size. Above study indicates that packing behaviour of Chandarpur sandstones and Khairagarh sandstones are entirely different.     

Three-dimensional random network model for thermal conductivity in particulate materials

This paper describes a three-dimensional random network model to evaluate the thermal conductivity of particulate materials. The model is applied to numerical assemblies of poly-dispersed spheres generated using the discrete element method (DEM). The grain size distribution of Ottawa 20–30 sand is modeled using a logistic function in the DEM assemblies to closely reproduce the gradation of physical specimens. The packing density and inter-particle contact areas controlled by confining stress are explored as variables to underscore the effects of micro- and macro-scales on the effective thermal conductivity in particulate materials. It is assumed that skeletal structure of 3D granular system consists of the web of particle bodies interconnected by thermal resistor at contacts. The inter-particle contact condition (e.g., the degree of particle separation or overlap) and the particle radii determine the thermal conductance between adjacent particles. The Gauss–Seidel method allows evaluation of the evolution of temperature variation in the linear system. Laboratory measurements of thermal conductivity of Ottawa 20–30 sand corroborate the calculated results using the proposed network model. The model is extended to explore the evolution of thermal conduction depending on the nucleation habits of secondary solid phase as an anomalous material in the pore space. The proposed network model highlights that the coordination number, packing density and the inter-particle contact condition are integrated together to dominate the heat transfer characteristics in particulate materials, and allows fundamental understanding of particle-scale mechanism in macro-scale manifestation.     

非饱和残积土的土-水特征曲线试验及模拟

土-水特征曲线是指基质吸力与含水率或饱和度的关系曲线。土-水特征及其相关数学模型可用于非饱和土性质如渗透系数和抗剪强度模型的建立。通常,土-水特征曲线仅有脱湿曲线。笔者详细讨论了初始含水率、干密度、竖向应力及干湿循环对脱湿曲线的影响。采用滤纸法测试了厦门地区残积土的土-水特征曲线(SWCC)及滞回环。结果表明,初始含水率对SWCC影响较小,最优含水率干侧试样SWCC的进气值小,滞回环小;湿侧试样的进气值大,滞回环大;最优含水率试样的滞回环居中。初始干密度对SWCC有显著影响,低干密度试样SWCC进气值小,脱湿速率快;高干密度试样SWCC进气值高,脱湿速率低。滞回环的大小随着初始干密度的减小而增大。不同竖向应力下SWCC变化较大。随着竖向应力的增加,进气值增大,脱湿速率减小,滞回环减小并趋于稳定。第1次干湿循环对SWCC影响最大,随着循环次数的增加,进气值减小,滞回环减小并趋于稳定。由于残积砂质黏性土SWCC的过渡区和残余区不易区分,残余含水率难以确定,因此,提出5种剔除残余含水率参数的修正SWCC模型,计算分析得出,修正Gardner模型最适合厦门地区残积土的SWCC建模。     

非等大球体的任意堆积

利用比重为1.80的分子筛材料球粒进行了等大球和不等大球的任意堆积,相当于水介质中天然颗粒的堆积。得出了不同堆积强度时等大球的堆积密度。不等大球的堆积在相当宽的范围内可视为等大球的堆积,粒径比的阈值为0.70,小球与大球直径之比小于该值时,堆积密度开始增大,通过实验得出了堆积密度随粒径比的变化曲线。实验结果对于了解沉积作用和沉积岩孔隙度等有重要意义。     

A computational procedure to assess the distribution of constriction sizes for an assembly of spheres

The effectiveness of filters to counteract internal erosion in earth structures is particularly related to their ability to capture fine particles moving under seepage flow through the porous material. More precisely, fine particles are likely to be trapped by the narrowest paths between pores: the constrictions. This paper proposes a methodology to compute the constriction size distribution of model granular filters taking into account the relative density of the material. The approach is based upon probabilistic methods which adopt stated simple geometric packing arrangements to represent the solid structure in the extreme density states. Two new models are proposed for the design of the constriction size distribution according to the type of filter grading: continuously graded or gap-graded materials. The models require the usual material characteristics: the grading curve, and the minimum and maximum void ratios for this material. Calibrated on the basis of statistical analyses over numerical assemblies of spheres generated by a discrete element method, the proposed new models constitute a promising tool to significantly improve the modeling of filtration processes in granular materials.     

基于梯度塑性本构理论的岩样侧向变形分析(II): 尺寸效应及弹性回跳

提出了利用不同尺寸试件的轴向应力-应变曲线得到轴向应力-侧向应变曲线的一种方法，并研究了结构尺寸对轴向应力-侧向应变曲线的影响。根据尺寸不同试件的轴向应力-轴向应变曲线的实验结果，并基于梯度塑性理论的解析解，在应变软化阶段，确定出了各种试件的剪切带条数。由此求出了不同宽度试样的轴向应力-侧向应变曲线。剪切带条数与试件宽度之比是决定轴向应力-侧向应变曲线特征的关键指标。若该比率为常量，则上述曲线不具有尺寸效应。当宽试件及窄试件在局部化启动后，在试件内部都出现一条剪切带时，随着试件宽度的增加，该曲线越陡，甚至出现回跳。上述方法也可用于分析轴向应力-环向应变曲线的尺寸效应问题。尺寸效应的原因是局部化，但局部化并非总引起尺寸效应。     

复杂区域四边形网格生成的一种改进方法

提出了一种改进的四边形网格生成算法。该法在行波法生成平面三角形网格的基础上，将一个三角形单元分解为三个四边形单元。经过优化处理，获得优良的计算域四边形网格。针对岩土工程结构问题，还提出了网格剖分中尖灭不连续面和锚杆及锚索的处理方案。地下洞室和边坡算例表明了这种方法的可行性和可靠性。     

微生物矿化作用对红黏土的影响研究

引入微生物矿化技术,利用其中巴氏芽孢杆菌的代谢产物对红黏土进行改性研究。对微生物矿化作用的红黏土试样开展常规物理指标试验,分析试样含水率、密度、比重、孔隙比和颗粒粒径的变化。利用三轴固结不排水剪切试验,测定土体的抗剪强度指标,并结合扫描电镜分析微生物矿化下红黏土的微观结构特征。结果表明:巴氏芽孢杆菌诱导碳酸钙沉淀胶结充填红黏土空隙作用明显,土样经过恒温养护10 d时的作用效果最佳,红黏土的物理性质朝着工程性质好的方向发展、抗剪强度有所增强。从SEM图像分析,红黏土试样中生成碳酸钙晶体填充胶结于土体孔隙,加强了土壤颗粒间的连接。      

基于SEM、NMR和X-CT的页岩储层孔隙结构综合研究

运用扫描电镜、核磁共振和计算机断层扫描3种孔隙结构研究方法对页岩进行了实验分析。研究结果表明：(1)扫描电镜对于页岩样品的局部观察能力较强,能够直观地反映页岩样品的微观孔隙类型和形态等信息,经氩离子抛光后还可观察到样品的有机质纳米级孔隙,但扫描电镜对样品的总体情况反映能力不够完善;(2)核磁共振受岩石骨架的影响小,可以更精确地测定页岩的孔隙度,进行孔隙大小分布、孔隙连通性和可动流体分析,得到样品的总体特征,但对样品细节的反映较欠缺;(3)CT扫描能够定量分析页岩组分,通过三维重构技术建立页岩样品孔隙和高密度物质分布状况的三维模型,从宏观角度反映孔隙的形态和空间配置特征,其主要不足在于三维重构时CT数阀值的选择对结果具有一定影响。综合运用3种方法,才能更准确地对页岩储层孔隙结构进行研究,以得到更加完善的储层孔隙结构资料。     

Haphazard Packing of Unequal Spheres

Haphazard packing of equal and unequal spheres can be performed for the spheres of molecular sieve material with a density of 1.80.The packing of such spheres in air is equivalent to that of nat-ural grains in water.Packing concentrations of equal spheres have been obtained for different pac-king intensities.Unequal spheres can be regarded as equal ones in a wide range of diameter ratios,so far as the packing concentration is concerned.A threshold of diameter ratio exists at 0.70,be-low which the packing concentration is expected to increase.The variation curves of concentration vs.diameter ratio were established in the experiment.The result will help us to understand the process of sedimentation and the concentration of voids in sedimentary rocks.     

An Algorithm for Generating Rock Fracture Patterns: Mathematical Analysis

A statistical, rule-based algorithm for generating fracture patterns similar to those observed in Limestone is presented. For each fracture set, initial seed points are randomly positioned within the modelled domain with the same density as the fractures observed in the field. An orientation is associated with each point by sampling from the distribution of orientations for the corresponding fracture set. Fractures are then allowed to grow from the seed points in both directions with this orientation until they meet other fractures whereupon they continue or terminate according to a fixed probability. A mathematical analysis of this method is presented for the case in which fractures within a set are assumed to be parallel. Approximations to the distribution of semi-trace lengths are derived which are shown to be in good agreement with simulation results. Fracture spacing distributions are also derived for this case.     

劈裂砂岩有、无砂粒填充条件下的多因素对渗流量影响对比分析

采用宜昌劈裂砂岩,在有、无砂岩填充条件下,分别从轴压、围压、劈裂面面积、凹凸高差、迹线长度、劈裂面2D投影面积、进出口长度、结构面粗糙度对渗流量的影响规律进行了对比分析。研究结果表明：有、无砂粒填充下轴压与渗流量均呈线性递增关系;无填充时围压与渗流量呈对数递减关系,有充填时围压与渗流量呈线性关系;无充填时渗流量与流面积呈三次函数关系,而充填后过流面积对渗流量几乎无影响;凹凸高差、2D面积与渗流量的关系也有相似规律,分析认为,这主要是砂粒充填后带来的过流通道要远大于上述三因素对过流通道的改变;无充填时,渗流量随迹线长度线性递减,有填充时该规律被淹没;无论有、无填充,渗流量与过流面粗糙度系数在一定范围内均呈现二次函数关系。这些规律能指导渗流测量时各因素的优先次序,可有效减少对次要影响因素的测量工作,同时可对渗流的数值模拟提供参考。     

A probabilistic permeability model and the pore size density function

Mathematical interpretation of the pore size disribution (PSD) data as measured by mercury intrusion porosimetry was revealed in detail. The PSD data were commonly presented as cumulative intruded volume per gram of specimen versus pore size. In this paper, however, they were expressed in a dimensionless term for convenient mathematical operations. The pore size density function was deduced from the PSD data using the finite difference approximation and curve-fitting technique. For the prediction of permeability, first the published correlations between permeability and pore geometry were critically reviewed. A probabilistic permeability model based on the pore size density function was then developed, which can be thought of as a generalization of Childs and Collis-George's model. Predictions of permeability of the compacted soils studied using the developed model were very good for a wide range of permeabilities.     

Gravity anomaly modeling of sedimentary basins by means of multiple structures and exponential density contrast-depth variations: A space domain approach

An automatic modeling scheme is developed in the space domain to interpret the gravity anomalies of sedimentary basins, among which the density contrast decreases exponentially with depth. Forward modeling is realized in the space domain using a combination of both analytical and numerical approaches. A collage of vertical prisms having equal widths, whose depths are to be estimated, describes the geometry of a sedimentary basin. Initial depths of a sedimentary basin are predicted using the Bouguer slab formula and subsequently updated, iteratively, based on the differences between the observed and theoretical gravity anomalies until the modeled gravity anomalies mimic the observed ones. The validity and applicability of the method is demonstrated with a synthetic and two real field gravity anomalies, one each over the Chintalpudi sub-basin in India and the other over the San Jacinto graben, California. In case of synthetic example, the assumed structure resembles a typical intracratonic rift basin formed by normal block faulting and filled with thick section of sediments. The proposed modeling technique yielded information that is consistent with the assumed parameters in the case of synthetic structure and with the available/drilling depths in case of field examples.     

Population balance in confined comminution using a physically based probabilistic approach for polydisperse granular materials

A novel, simplified approach is presented in order to compute variations of grading in granular assemblies during confined comminution under quasi‐static compression. The method is based on a population balance equation and requires a breakage probability, considered here as a probabilistic phenomenon that takes into account the particle strength and the loading condition of individual grains. Under basic assumptions, a simple breakage probability can be defined in order to get a valuable result for engineering applications and powder technology. The size effect in the strength of individual particles is introduced according to Weibull's theory. The particle loading and the cushioning effect in the granular packing are accounted for by considering the orientations of the contact forces obtained from 3D discrete element method simulations of highly polydisperse materials. The method proposed could have a value for engineering purposes in powder technology and geomechanics and gives a general framework for further research developments based on population balance. Copyright © 2016 John Wiley & Sons, Ltd.