A probabilistic approach for computing water retention of particulate systems from statistics of grain size and tessellated pore network

The paper offers an analytical determination of the hydraulic properties of an unsaturated soil with reference to its retention curve, which describes the relationship between the volumetric water content and capillarity through matric suction. The analysis combines a particulate approach focused on the physics at the pore scale, including microstructural aspects, with a probabilistic approach where the void space and grain size are considered as random variables. In the end, the soil water characteristic curve of an unsaturated granular medium along a drying path can be derived analytically based on the sole information of particle size distribution. The analysis hinges on the tessellation of a wet granular system into an assemblage of tetrahedral unit cells revealing a pore network upon which capillary physics are computed with respect to pore throat invasion by a non-wetting fluid with evolving pendular capillary bridges. The crux of the paper is to pass from particle size probability distribution to a matching void space distribution to eventually reveal key information such as void cell and solid volume statistics. Making reasonable statistically based assumptions to render calculations tractable, the water retention curve can be readily constructed. Model predictions compare quite favourably with experimental data available for actual soils, especially in the high saturation range. Having a sound scientific basis, the model can be made amenable to address a variety of soils with a wider range of particle sizes.     

颗粒级配与孔隙比对粗粒土渗透系数的影响

颗粒级配、孔隙比是决定粗粒土渗透系数的关键因素。收集并整理得到93组粗粒土全级配（d10~d100）、孔隙比数据,采用遗传算法(genetic algorithm,GA)优化的BP(back propagation)神经网络分析和预测粗粒土渗透系数,通过平均影响值法和试验验证,评价各级配粒径对渗透系数的影响大小,探讨孔隙比对粗粒土渗透系数的影响。结果表明:d50为界限粒径,在其他粒径不变,若增大d50及以下粒径,渗透系数就增大,而增大d50以上粒径,渗透系数减小;d50及以下粒径的“细颗粒”对渗透系数的影响大于d50以上粒径的“粗颗粒”;按相对权重,d20、d80、d40属于高敏感度粒径,d10、d50、d100、d70为中敏感度粒径,d30、d90、d60为低敏感度粒径。孔隙比对渗透系数的影响大于任一特征粒径,渗透系数与孔隙比呈正相关关系;相同颗粒级配的粗粒土,随孔隙比变化可使渗透系数产生数量级跨越。采用GA-BP神经网络方法,由全级配和孔隙比能较好地预测粗粒土渗透系数。     

土体强度与变形尺度特性的理论与试验分析

土体是一种颗粒介质,其强度与变形特性具有显著的颗粒尺度效应。采用胞元土体模型和三轴抗剪试验分析了土体强度和变形的尺度效应特性。根据土体中不同尺度颗粒间相互作用表现出的聚集和摩擦效应,提出了“基体-增强颗粒”土体胞元模型,胞元体由基体和增强颗粒组成,其中基体由微小土颗粒集成,而增强颗粒为砂粒,宏观土体则简化为由许多胞元体构成的介质。引入广义球应变和广义等效应变,基于应变能导出了考虑颗粒尺度效应的应力-应变关系以及屈服应力计算公式;同时,针对增强颗粒不同粒径和体分比的土体进行一系列三轴不排水抗剪试验,给出了应力-应变和屈服应力尺度效应的测试结果。试验和理论计算结果均表明,土体强度和变形的尺度效应随增强颗粒的体分比增加以及粒径的减小而增强,由此反映出土体强度和变形显著的尺度效应;土体强度和变形尺度效应的理论预测结果与试验具有较好的一致性。     

Influence of initial density of cohesionless soil on evolution of passive earth pressure

This paper focuses on the influence of the initial void ratio on the evolution of the passive earth pressure and the formation of shear zones in a dry sand body behind a retaining wall. For the numerical simulation a rigid and very rough retaining wall undergoing a horizontal translation against the backfill is considered. The essential mechanical properties of cohesionless granular soil are described with a micro-polar hypoplastic model which takes into account stresses and couple stresses, pressure dependent limit void ratios and the mean grain size as a characteristic length. Numerical investigations are carried out with an initially medium dense and initially loose sand using a homogeneous and random distribution of the initial void ratio. The geometry of calculated shear zones is discussed and compared with a corresponding laboratory model test.     

Micromechanical Modelling of Granular Materials: Effect of Particle Size and Gradation

In this paper the effects of maximum particle size, particle gradation/sorting and fabric on bulk mechanical behaviour of granular materials such as coarse grained soils and rockfills are investigated" from micromechanical considerations starting from the grain scale level, using numerical" simulations based on Discrete Element Modelling (DEM). Hydrostatic compaction and biaxial tests on 2-dimensional assemblies of discs with varying particle sizes and gradations were modelled using DEM. An examination of the constitutive behaviour of granular media considering" the particulate nature of the medium has been attempted to explain the effect of particle size and gradation. Simulation results on perfectly parallel graded assemblies indicate that with increase in the size of the particles, a marginal increase (or no increase) in the angle of internal friction is observed during biaxial loading conditions. A change to a wider gradation (keeping the minimum grain size the same) results in a decrease in the angle of internal friction and an increase in volumetric strain to a considerable extent. Based on micromechanical force and fabric parameters, the basis for the physical behaviour was established. This helps in understanding the physics of parallel gradation techniques.     

基于物理模型试验的碎屑流流态化运动特征分析

流态化运动是高速远程滑坡的主要运动形式,是揭示高速远程滑坡运动机理的重要基础。基于粒子图像测速（PIV）分析方法,采用物理模型试验对不同粒径组成条件下的颗粒流内部的速度分布、剪切变形及流态特征进行了研究,并对高速远程滑坡流态化运动特征进行了讨论分析。结果表明:碎屑流流态化运动特征与颗粒粒径呈显著的相关性,随着粒径的减小或细颗粒含量的增加,颗粒流底部相对于边界的滑动速度以及整体的运动速度均呈逐渐减小的趋势,颗粒流内部剪切变形程度增加,颗粒的运动形式由“滑动”向“流动”转变;当颗粒粒径较小或细颗粒含量较高时,颗粒流内部剪切速率增大的趋势在颗粒流底部更加显著,反映了粒径减小有助于促进颗粒流内部剪切向底部的集中;在同一颗粒流的不同运动阶段及不同纵向深度,其流态特征具有显著差别,颗粒流前缘及尾部主要呈惯性态,颗粒间以碰撞作用为主,而主体部分则主要呈密集态,颗粒间以摩擦接触作用为主;在颗粒流表面及底部,颗粒间相互作用方式主要是碰撞作用,中间部分则以摩擦作用为主;对于不同粒径的颗粒流,随着粒径的增大或粗颗粒含量的增加,颗粒流内部颗粒的碰撞作用加强,颗粒流整体趋于向惯性态转变。     

考虑粒组分类影响的最小孔隙比分布及模型验证

最小孔隙比是确定岩土体的密实程度与孔隙特征的有效物理指标,如何快速有效地确定岩土体的最小孔隙比,可为岩土体的固结与稳定提供可靠参数。多数估算细粗混合材料最小孔隙比的模型参数与细粗粒径比一一对应,导致估算困难。在分析尾矿粒度组成、沉积规律和固结稳定的基础上,以8种不同粗细粒径,7～9种不同细粒含量尾矿为试验对象,拟合得到不同粒组尾矿最小孔隙比分布模型参数的函数关系;基于混合尾矿颗粒的粒组特征,给出了确定参数幂函数关系的指数值。分别采用模型参数要求粒组范围内的其他6组岩土材料和非粒组范围内的3组岩土材料进行验证。结果表明,考虑粒组分类影响下的模型,参数简单,对不同材料的最小孔隙比估算准确率较高,给出的最小孔隙比的分布规律合理,可为岩土工程领域最小孔隙比估算提供可靠的计算方法。     

Fractal analysis of the roughness and size distribution of granular materials

The roughness, i.e. general shape and surface irregularity, of particulate soil is an important characteristic that affects the mass behavior of the soil. Characterization of roughness has typically been limited to visual comparison of particles to standard charts, although other more quantitative methods such as Fourier analysis have also been used. Particle size distribution is another important mass-behavioral characteristic of granular soils, and similar to roughness, is defined within limited boundaries. Fractal geometry can be applied to irregular or fragmented patterns such as roughness and grain size distribution to provide quantifying and unique numerical values. This paper presents an evaluation of the applicability of fractal dimensioning techniques to the quantification of both physical particle roughness and grain size distribution of granular soil. The divider and the area-perimeter fractal dimensioning techniques are used to quantify roughness of planar profiles of individual sand grains. The characterization of the size distribution of granular material using fractal geometry is evaluated through Korcak's fragmentation theory. As shown herein, both the divider and the area-perimeter fractal dimensioning techniques are useful in characterizing soil particle roughness, and the results confirm the importance of differentiating between textural and structural aspects of roughness. Fractal geometry can also be used to quantify the size distribution of granular soils with relatively well-graded size distributions.     

The fractal micro mechanics of normal compression

The fundamental fractal micro mechanics of normal compression of granular materials is studied using DEM. This paper examines the emergence of a finite fractal bounded by two particle sizes as stress increases, and the evolution of various definitions of the ‘smallest particles’. It is revealed that if particles are categorised according to their coordination number, then the volume of all particles with 4 contacts or fewer is directly proportional to the void space. These particles are called ‘critical particles’ and are shown, for the first time, to explain quantitatively the voids reduction with increasing vertical stress.     

基于接触价键的颗粒材料微观临界状态

用颗粒离散元法,分别对二维圆形、椭圆形颗粒体进行了双轴压缩数值模拟。微观尺度的变形是基于孔隙胞元和其中的变形来计算的,而单个孔隙胞元的变形通过周围颗粒的相对运动来计算。针对该方法提出了以接触价键（每个孔隙胞元的边数）来表征颗粒材料微观临界状态的理论。为了定义临界接触价键的极限值,分别讨论了摩擦系数较大、较小时的两种情况。文中给出了微观几何织构（包括接触价键、孔隙胞元的形状、孔隙比）随压缩变形的演变过程,比较了不同颗粒形状、颗粒间摩擦系数以及颗粒体的固结压力对颗粒体的微观力学性能的影响。计算结果表明,颗粒材料的微观临界状态并不是可以唯一表征的,而是受围压、摩擦系数,颗粒形状等参数的共同影响。     

Small-Strain Shear Modulus and Damping Ratio of Sand-Rubber and Gravel-Rubber Mixtures

This study examines the small-strain dynamic properties of mixtures composed of sandy and gravelly soils with granulated tire rubber in terms of shear modulus (G_O), and damping ratio in shear (D_min). Torsional resonant column tests are performed on dry, dense specimens of soil-rubber mixtures in a range of soil to rubber particles size 5:1–1:10 and rubber content from 0 to 35% by mixture weight. The experimental results indicate that the response of the mixtures is significantly affected by the content of rubber and the relative size of rubber to soil particles. Concering the small-strain shear modulus, an equivalent void ratio is introduced that considers the volume of rubber particles as part of the total volume of voids. Based on a comprehensive set of test results a series of equations were developed that can be used to evaluate the shear modulus and damping ratio at small shear strain levels if the confining pressure, the content of rubber by mixture weight, the grain size of soil and rubber particles, and the dynamic and physical properties of the intact soil are known.     

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.     

Effect of grain crushing on shear localization in granular bodies during plane strain compression

This article deals with the effect of grain crushing on shear localization in granular materials during plane strain monotonic compression tests under constant lateral pressure. The grain diameter and the initial void ratio were stochastically distributed using a spatial correlation. To describe the mechanical behavior of cohesionless granular materials during a monotonic deformation path in plane strain compression, we used a micropolar hypoplastic constitutive model that is able to describe the salient properties of granular bodies including shear localization. The model was extended by introducing changes to the grain diameter with varying pressure using formulae from breakage mechanics proposed for crushable granulates. The initial void ratios and grain diameters took the form of correlated random spatial fields described by both symmetric and nonsymmetric random distributions using a homogeneous correlation function. The field realizations were generated with the help of an original conditional rejection method. A few representative samples of the random fields selected from the generated set were taken into account in numerical calculations. Copyright © 2011 John Wiley & Sons, Ltd.     

Rapid estimation of maximum and minimum void ratios of granular soils

Maximum and minimum void ratios (e_max and e_min) of granular soils are commonly used as indicators of many engineering properties. However, few methods, apart from laboratory tests, are available to provide a rapid estimation of both e_max and e_min. In this study, we present a theoretical model to map the densest and the loosest packing configurations of granular soils onto the void space. A corresponding numerical procedure that can predict both e_max and e_min of granular soils with arbitrary grain size distributions is proposed. The capacity of the proposed method is evaluated by predicting the maximum and minimum void ratios of medium to fine mixed graded sands with different contents of fines. The influence of the grain size distribution, characterized quantitatively by uniformity parameter and the fractal dimension, on e_max and e_min is discussed using the proposed method. Moreover, application of this method in understanding the controlling mechanism for the void ratio change during grain crushing is presented.

     

长江口盐沼滩面发育对有机碳深度分布的制约

通过对长江口崇明东滩高潮滩、中潮滩以及光滩柱状样的有机碳含量与碳稳定同位素组成（δ13C）、粒度组成等的测定，研究盐沼有机碳深度分布特征与形成机制。结果表明，盐沼土壤颗粒有机碳（POC）主要赋存于粒径小于0.016 mm的颗粒中，POC含量对粒径在0.002~0.004 mm区间的颗粒含量变化最敏感，说明盐沼POC主要来自长江径流悬移质，这与有机碳稳定同位素结果一致。土壤POC含量与不同粒径区间颗粒含量相关关系表明，高潮滩与中潮滩柱样的泥沙级配较为接近；光滩柱样POC含量与不同粒径区间颗粒含量相关关系特征与高、中潮滩柱样的基本类似，主要不同表现在粒径大于0.016 mm的粗颗粒，这很可能受控于盐沼不同高程部位动力沉积过程。盐沼植被对高、中潮滩柱样POC的贡献相当可观，个别层段高达55.6%；植被对土壤POC的贡献受到滩面过程的明显制约。滩面动力沉积过程形成盐沼垂向上独特的沙、泥纹层构造，其优良的封堵效能显著影响土壤有机碳的垂向分布。盐沼滩面动力沉积过程是塑造有机碳深度分布特征的关键因素。     

颗粒材料底面动摩擦系数特征研究

离散态颗粒物质具有明显不同于普通固体的界面摩擦特性,而摩擦系数是界面摩擦特性的主要表征参数之一。通过倾斜仪开展不同级配条件下颗粒材料的滑动摩擦试验,基于视频图像解析以及函数拟合方法,建立滑动位移与滑动时间的最佳函数拟合关系,分析滑动过程的加速度并推算底面动摩擦系数,研究颗粒粒径、质量配比等级配因素对颗粒材料底面动摩擦系数的影响。研究结果表明:(1)各级配颗粒材料的平均底面动摩擦系数随着运动时间的增加均呈线性减小趋势;(2)对于单粒径材料,与粗颗粒相比,细颗粒具有较大的底面动摩擦系数;(3)对于双粒径材料,随着细颗粒含量的增加,颗粒材料的平均底面动摩擦系数先急剧降低至最小值(细颗粒含量≤40%),后急剧增加(细颗粒含量40% ~60%),最终增加趋势明显变缓(细颗粒含量≥60%)。     

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.     

Effects of periodic fluctuations of micro‐polar boundary conditions on shear localizations in granular soil–structure interaction

In this work, the interface behavior between an infinite extended narrow granular layer and a rough surface of rigid body is investigated numerically, using finite element method in the updated Lagrangian (UL) frame. In this regard, the elasto‐plastic micro‐polar (Cosserat) continuum approach is employed to remove the limitations caused by strain‐softening of materials in the classical continuum. The mechanical properties of cohesionless granular soil are described with Lade's model enhanced by polar terms, including Cosserat rotations, curvatures, and couple stresses. Furthermore, the mean grain diameter as the internal length is incorporated into the constitutive relations accordingly. Here, the evolution and location of shear band, within the granular layer in contact with the rigid body, are mainly focused. In this regard, particular attention is paid to the effects of homogeneous distribution and periodic fluctuation of micro‐polar boundary conditions, prescribed along the interface. Correspondingly, the effects of pressure level, mean grain diameter, and stratified soil are also considered. The finite element results demonstrate that the location and evolution of shear band in the granular soil layer are strongly affected by the non‐uniform micro‐polar boundary conditions, prescribed along the interface. It is found that the shear band is located closer to the boundary with less restriction of grain rotations. Furthermore, the predicted thickness of shear band is larger for higher rotation resistance of soil grains along the interface, larger mean grain diameter, and higher vertical pressure. Regarding the stratified soil, comprising a thin layer with slightly different initial void ratio, the shear band moves towards the layer with initially higher void ratio. Copyright © 2011 John Wiley & Sons, Ltd.     

Deterministic and statistical size effect during shearing of granular layer within a micro‐polar hypoplasticity

The paper deals with numerical investigations of a deterministic and statistical size effect in granular bodies during quasi‐static shearing of an infinite layer under plane strain conditions, free dilatancy and constant pressure. For a simulation of the mechanical behaviour of a cohesionless granular material during a monotonous deformation path, a micro‐polar hypoplastic constitutive relation was used which takes into account particle rotations, curvatures, non‐symmetric stresses, couple stresses and the mean grain diameter as a characteristic length. The proposed model captures the essential mechanical features of granular bodies in a wide range of densities and pressures with a single set of constants. In the paper, a deterministic and statistical size effect is analysed. The deterministic calculations were carried out with an uniform distribution of the initial void ratio for four different heights of the granular layer: 5, 50, 500 and 2000 mm. To investigate the statistical size effect, the Monte Carlo method was applied. The random distribution of the initial void ratio was assumed to be spatially correlated. Truncated Gaussian random fields were generated in a granular layer using an original conditional rejection method. The sufficient number of samples was determined by analysing the convergence of the outcomes. In order to reduce the number of realizations without losing the accuracy of the calculations, stratified and Latin hypercube methods were applied. A parametric analysis of these methods was also presented. Some general conclusions were formulated. Copyright © 2007 John Wiley & Sons, Ltd.     

Mechanical trapping of fine particles in a medium of mono‐sized randomly packed spheres

Mechanical trapping (or straining) of fine particles is a key mechanism in many filtration systems. For example, the performance of rapid sand filters depends in part on mechanical trapping of larger fine particles, while relying on adsorptive processes to trap very small fine particles and microbes. The ability to trap these particles is directly related to the construction of the packed bed used for filtration in this system. Thus, the ability to model the effect of the inner structure of the packed bed can lead to more efficient design for improved filtration. Because of its significant efficiency, gravitational sphere packing is employed in this work to simulate a bed of mono‐sized randomly packed spheres. The simulated bed provides a way to visualize the pore network and estimate the pore size distribution associated with the void space between particles. Furthermore, by subsequently introducing fine particles into the bed, we evaluate the mass‐rate of fine particles passing through and possibly saturating the packed bed. Results show that fine particles between 15% and 25% of the coarse particle size can be physically strained within the randomly packed bed. These results differ significantly from the results obtained assuming a periodically spaced bed. The technique therefore provides an efficient yet accurate alternative for understanding how fine particles pass through a coarse particulate medium. Copyright © 2014 John Wiley & Sons, Ltd.