Discrete element modeling of direct shear tests for a granular material

A succinct 3D discrete element model, with clumps to resemble the real shapes of granular materials, is developed. The quaternion method is introduced to transform the motion and force of a clump between local and global coordinates. The Hertz–Mindlin elastic contact force model, incorporated with the nonlinear normal viscous force and the Mohr–Coulomb friction law, is used to describe the interactions between particles. The proposed discrete element model is used to simulate direct shear tests of the irregular limestone rubbles. The simulation results of vertical displacements and shear stresses with a mixture of clumps are compared well with that of laboratory tests. The bulk friction coefficients are calculated and discussed under different contact friction coefficients and normal stresses. Copyright © 2009 John Wiley & Sons, Ltd.     

Discrete modeling of strain accumulation in granular soils under low amplitude cyclic loading

An advanced understanding of the strain accumulation phenomenon in granular soils subjected to low amplitude cyclic loading with relatively high frequency is needed to enhance the ability to predict the settlement of granular soils induced by vibrations. In the current study, the discrete element method is used to study this phenomenon. A loose and a medium dense sample composed of a relatively large number of spheres are considered. A series of stress controlled cyclic triaxial tests with different excitation amplitudes and frequencies is performed on these samples at different static stress states. The response of these samples at the macroscopic and microscopic scales is analyzed. The sample density, the cyclic stress amplitude and the static stress state importantly affect strain accumulation. However, the cyclic excitation frequency has a small effect on strain accumulation. At the microscopic scale, frictional sliding occurring at a few contacts continuously dissipates energy and the fraction of these contacts varies periodically during cyclic loading. The coordination number of these samples increases slightly as strain accumulates. However, the anisotropy remains almost constant during low amplitude cyclic excitation. A qualitatively good agreement between numerical and experimental results is found.     

Micromechanical modeling of particle breakage of granular materials in the framework of thermomechanics

The particle breakage of granular materials under compression is a phenomenon of great importance. In this paper, a micromechanically based model for the compression of crushable granular materials is developed in the framework of thermomechanics. Both the internal and dissipative energies in the model are derived using the micro–macro volume averaging approach to ensure that all parameters involved have concrete physical meanings. The particle breakage is quantified by the change of the maximum particle size, the size polydispersity and the fractal dimension of the gradation. Compared to other breakage models, there is a major difference that highlights the novelty of the proposed model: neither the ultimate particle size distribution, nor the evolution path of the gradation is predefined in the model. The initiation, evolution and the attenuation of the breakage can be determined by the maximum dissipation principle using thermomechanics and micromechanics. Finally, it is demonstrated that the proposed model can predict the stress dependence of the elastic bulk modulus, the size dependence of the yielding stress and the elastic–plastic-pseudoelastic phase transition of granular materials.

     

Modeling transport of arsenic through modified granular natural siderite filters for arsenic removal

Groundwater arsenic(As)contamination is a hot issue,which is severe health concern worldwide.Recently,many Fe-based adsorbents have been used for As removal from solutions.Modified granular natural siderite(MGNS),a special hybrid Fe(II)/Fe(III)system,had higher adsorption capacity for As(III)than As(V),but the feasibility of its application in treating high-As groundwater is still unclear.In combination with transport modeling,laboratory column studies and field pilot tests were performed to reveal both mechanisms and factors controlling As removal by MGNS-filled filters.Results show that weakly acid pH and discontinuous treatment enhanced As(Ⅲ)removal,with a throughput of 8700 bed volumes(BV)of 1.0 mg/L As(Ⅲ)water at breakthrough of 10 μg/L As at pH 6.Influent HCO_3~-inhibited As removal by the filters.Iron mineral species,SEM and XRD patterns of As-loading MGNS show that the important process contributing to high As(Ⅲ)removal was the mineral transformation from siderite to goethite in the filter.The homogeneous surface diffusion modeling(HSDM)shows that competition between As(III)and HCO_3~-with adsorption sites on MGNS was negligible.The inhibition of HCO_3~-on As(Ⅲ)removal was connected to inhibition of siderite dissolution and mineral transformation.Arsenic loadings were lower in field pilot tests than those in the laboratory experiments,showing that high concentrations of coexisting anions(especially HCO_3~-and SiO_4~(4-)),high pH,low EBCT,and low groundwater temperature decreased As removal.It was suggested that acidification and aeration of highAs groundwater and discontinuous treatment would improve the MGNS filter performance of As removal from real high-As groundwater.     

Discrete element modeling of crushable sands considering realistic particle shape effect

This study proposed a novel approach for generating crushable agglomerates with realistic particle shapes in discrete element modeling (DEM). The morphologies of sand particles were obtained by X-ray micro-computed tomography scanning and image processing. Based on the particle surface reconstructed by spherical harmonic analysis, the crushable agglomerates with realistic particle shapes can be generated in DEM simulations. The results of single particle crushing tests showed that particle shapes significantly influence the fracture patterns and crushing strengths of sand particles. Furthermore, two one-dimensional compression tests were conducted to investigate the particle shape effect on micro- and macro-mechanical behaviors of crushable sands.     

Numerical modelling of fluid-induced soil erosion in granular filters using a coupled bonded particle lattice Boltzmann method

This paper presents a three-dimensional coupled bonded particle and lattice Boltzmann method (BPLBM) with an immersed moving boundary scheme for the fluid-solid interaction. It is then applied to investigate the erosion process of soil particles in granular filters placed within earth dams. The microscopic migration of soil particles can be clearly visualised as the movement of particles can be directly recorded. Three granular filters with different representative size ratios are simulated and the numerical results are seen to match the empirical criteria. In addition, the effect of the representative size ratio of granular filters, hydraulic loading and erosion time are discussed.     

Reliability assessment of granular filters in embankment dams

Empirical criteria have been used successfully to design filters of most embankment large dam projects throughout the world. However, these empirical rules are only applicable to a particular range of soils tested in laboratory and do not take into account the variability of the base material and filter particle sizes. In addition, it is widely accepted that the safety of fill dams is mainly dependent on the reliability of their filter performance. The work herein presented consists in a new general method for assessing the probability of fulfilling any empirical filter design criteria accounting for base and filter heterogeneity by means of first‐order reliability methods (FORM), so that reliability indexes and probabilities of fulfilling any particular criteria are obtained. This method will allow engineers to estimate the safety of existing filters in terms of probability of fulfilling their design criteria and might also be used as a decision tool on sampling needs and material size tolerances during construction. In addition, sensitivity analysis makes possible to analyse how reliabilities are influenced by different sources of input data. Finally, in case of a portfolio risk assessment, this method will allow engineers to compare the safety of several existing dams in order to prioritize safety investments and it is expected to be a very useful tool to evaluate probabilities of failure due to internal erosion. Copyright © 2006 John Wiley & Sons, Ltd.     

Influence of particle shape and angularity on the behaviour of granular materials: a numerical analysis

This paper analyses the influence of grain shape and angularity on the behaviour of granular materials from a two‐dimensional analysis by means of a discrete element method (Contact Dynamics). Different shapes of grains have been studied (circular, isotropic polygonal and elongated polygonal shapes) as well as different initial states (density) and directions of loading with respect to the initial fabric. Simulations of biaxial tests clearly show that the behaviour of samples with isotropic particles can be dissociated from that of samples with anisotropic particles. Indeed, for isotropic particles, angularity just tends to strengthen the behaviour of samples and slow down either local or global phenomena. One of the main results concerns the existence of a critical state for isotropic grains characterized by an angle of friction at the critical state, a critical void ratio and also a critical anisotropy. This critical state seems meaningless for elongated grains and the behaviour of samples generated with such particles is highly dependent on the direction of loading with respect to the initial fabric. The study of local variables related to fabric and particle orientation gives more information. In particular, the coincidence of the principal axes of the fabric tensor with those of the stress tensor is sudden for isotropic particles. On the contrary, this process is gradually initiated for elongated particles. Copyright © 2003 John Wiley & Sons, Ltd.     

Discrete element modelling of deep penetration in granular soils

This paper presents a numerical study on deep penetration mechanisms in granular materials with the focus on the effect of soil–penetrometer interface friction. A two‐dimensional discrete element method has been used to carry out simulation of deep penetration tests on a granular ground that is under an amplified gravity with a K₀ lateral stress boundary. The numerical results show that the deep penetration makes the soil near the penetrometer move in a complex displacement path, undergo an evident loading and unloading process, and a rotation of principal stresses as large as 180°. In addition, the penetration leads to significant changes in displacement and velocity fields as well as the magnitude and direction of stresses. In general, during the whole penetration process, the granular ground undergoes several kinds of failure mechanisms in sequence, and the soil of large deformation may reach a stress state slightly over the strength envelope obtained from conventional compression tests. Soil–penetrometer interface friction has clear effects on the actual penetration mechanisms. Copyright © 2005 John Wiley & Sons, Ltd.     

Groundwater flow modeling and particle tracking for chemical transport in the southern Voltaian aquifers

Groundwater is the major source of water supply for most uses in the rural settlements in Ghana. A groundwater flow model was calibrated for some aquifers of the southern Voltaian sedimentary system under steady-state conditions. The objective was to determine estimates of the hydraulic conductivities of the different hydrostratigraphic units of the southern Voltaian, and the distribution of recharge from precipitation. Data on the stable isotopes of oxygen and hydrogen from the study area suggest that groundwater recharge in the area is from rainfall. The calibrated steady-state model suggests that aquifer hydraulic conductivities in the study area range from 1.19 to 6.3 m/day. Hydrostratigraphic unit specific hydraulic conductivities are discussed. The calibrated recharge ranges from 3.81e−05 m/day to 6.0e−04 m/day, which represents 0.9–6% of the precipitation in the form of rainfall. Six distinct flowpaths have been defined using particle tracking. The particle tracking simulation suggests travel times in the range of 380 to 5,199 years from recharge areas to discharge areas along the flowpaths identified. A contaminant dropped at the recharge areas in the central sections of the model area would travel at these rates along the flowpaths, assuming that advection is the dominant transport process. Inverse geochemical modeling indicates the dissolution of albite, K-feldspars and anorthite, respectively, along flowpaths I and IV. The inverse modeling along flowpaths I and IV suggest the dissolution of albite, K-feldspar and anorthite, respectively, at 1.085e−06, 3.16e−08 and 3.168e−07 mmol/year.     

Discrete numerical modelling of rockfill dams

The aim of this study is to obtain quantitative information on the behaviour of rockfill used in embankment dams, and particularly on the influence of block breakage on the displacement field, from a numerical analysis using the Distinct element method. A methodology is set up to define the resistance of the 2D particles so that the same probability of breaking blocks may be reproduced as in a 3D material. The model uses the discrete element code PFC^2D (Itasca Consulting Group Inc., PFC2D (Particle Flow Code in Two Dimensions), Version 3.0, 2002) and considers breakable clusters of 2D balls. The different parameters are determined from experimental data obtained from laboratory tests performed on rock blocks. The model is validated by comparing the results of the simulation of shearing tests with actual triaxial tests on rockfill material published in the literature. The numerical analysis of block crushing in an actual dam is proposed in the last part of this paper. Copyright © 2006 John Wiley & Sons, Ltd.     

Discrete element modeling for predicting breakage behavior and fracture energy of a single particle in a jaw crusher

In the present study, Discrete Element Method (DEM) technique was applied to model the fracture behavior of a single spherical and cubic rock in a laboratory jaw crusher. The rocks studied were modeled as granular assemblies located between two jaws, and their fracture mechanism was studied. To verify the obtained results, the spherical and cubic specimens produced from Dokoohak Limestone and Dehbeed Granite were studied and the energy applied by the jaws was compared to those of the fracture energy estimated by the single particle breakage analysis. There is fairly good agreement between the energy acquired from the DEM model and the single particle fracture energy of the spherical rocks. It appears that DEM is a suitable method for predicting the crushing energy of the spherical rocks in the jaw crusher. The fracture behavior of the crushed rocks was examined and compared by the results obtained from the DEM model. The tensile mode of fracture occurring in the spherical rocks is well presented by the discrete element modeling. However, the DEM technique is not capable of modeling the delamination mode occurring in the cubic rocks.     

Discrete modeling of low-velocity penetration in sand

In this paper, a discrete particle method was evaluated and used in numerical simulations of low-velocity penetration in sand. Hemispherical, blunt, and ogival-nosed impactors were tested at striking velocities below 5 m/s. The tests were conducted in a dropped-object-rig where the resisting force from the sand was measured continuously during the experiments. This provided a basis for comparison for the simulations. The shapes of the force-penetration depth curves were different for the various impactors, but the ultimate penetration depths were similar in all tests that were done with the same impact velocity. Three-dimensional discrete particle simulations were generally capable of describing the behavior of the sand. However, the peak resisting force was underestimated, which led to a slight overestimation of the ultimate penetration depth. This discrete particle method has previously been evaluated at high impact velocities. The results presented in this study supplement past results and show that the method can also be used to describe the overall response of sand subjected to low-velocity penetration.     

A numerical representation of fracturing granular materials

This paper describes the computer algorithms used in a numerical simulation of the compression of an aggregate of crushable grains. It has been used in a model for the evolution of a granular medium under one-dimensional compression, in which the probability of fracture for individual particles is a function of applied stress, particle-size and co-ordination number. The information relating to the particles is represented in a compact way on the computer which allows the number of particles produced to become sufficiently large for satisfactory comparisons to be made with experimental data and which allows information, such as the positions and sizes of the particles, to be easily extracted. An algorithm based on the representation is used to locate neighbouring particles in a way which does not deteriorate unacceptably in terms of speed as the number of particles increases. © 1997 by John Wiley & Sons, Ltd.     

Role of particle crushing on particle kinematics and shear banding in granular materials

The paper provides an in-depth exploration of the role of particle crushing on particle kinematics and shear banding in sheared granular materials. As a two-dimensional approximation, a crushable granular material may be represented by an assembly of irregularly shaped polygons to include shape diversity of realistic granular materials. Particle assemblies are subjected to biaxial shearing under flexible boundary conditions. With increasing percentage of crushed particles, mesoscale deformation becomes increasingly unstable. Fragmented deformation patterns within the granular assemblies are unable to form stable and distinct shear bands. This is confirmed by the sparsity of large fluctuating velocities in highly crushable assemblies. Without generating distinct shear bands, deformation patterns and failure modes of a highly crushable assembly are similar to those of loose particle assemblies, which are regarded as diffuse deformation. High degrees of spatial association amongst the kinematical quantities confirm the key role that non-affine deformation and particle rotation play in the generation of shear bands. Therefore, particle kinematical quantities can be used to predict the onset and subsequent development of shear zones, which are generally marked by increased particle kinematic activity, such as intense particle rotation and high granular temperature. Our results indicate that shear band thickness increases, and its speed of development slows down, with increasing percentage of crushed particles. As particles crush, spatial force correlation becomes weaker, indicating a more diffuse nature of force transmission across particle contacts.     

Discrete element modelling of cyclic behaviour of granular materials

Discrete Element Modeling (DEM) of cyclic behavior of granular material has been attempted to understand liquefaction behavior of sands. A series of cyclic biaxial tests in both undrained and drained conditions with constant stress and strain amplitudes were performed on assemblage of loose and dense systems. Tests are conducted on monodisperse (uniform) and polydisperse (well graded) samples. From this study, it has been shown that DEM can simulate the cyclic behavior of sands very satisfactorily. Characteristic features, i.e., occurrence of large plastic strains and changing over from contractile to dilative behavior beyond the phase transformation angle, anisotropy of reduced strength on the extension side etc are very well reflected in numerical simulations. Liquefaction of loose assemblage seems to be mainly due to continued and cumulative loss of co-ordination number under each cycle as there is a reversal of loading direction and hence a continuous reorientation of fabric. There is no cumulative loss of co-ordination number in dense states because the stress ratios are mostly higher than the phase transformation level where the fabric has reached a limiting orientation. Micro mechanical explanations to the macroscopic behavior of the disc assemblage under cyclic loading are presented in terms of the force and fabric anisotropy coefficients.     

Discrete modeling for natural objects

This paper presents a discrete technique specially designed for modeling the geometry and the properties of natural objects as those encountered in biology and geology. Contrary to classical Computer- Aided Design methods based on continuous (polynomial) functions, the proposed approach is based on a discretization of the objects close to the finite- element techniques used for solving differential equations. Each object is modeled as a set of interconnected nodes holding the geometry and the physical properties of the objects and the Discrete Smooth Interpolation method is used for fitting the geometry and the properties to complex data. Data are turned into linear constraints and some constraints related to typical information encountered in geology are presented.     

螺旋挤土桩下旋成孔过程的颗粒流数值模拟

卵砾石地层可压缩性低、抗剪强度大,水泥土搅拌桩工法在应用于卵砾石地层时存钻进困难、钻具磨损大等问题。为确定卵砾石地层条件下钻头形式的最优布置,基于离散元法(DEM),对不同切削叶片数量、切削叶片角度、截齿布置形式、钻头中心底部布置形式、机械压力工况下,搅拌桩机钻头钻进卵砾石地层的物理过程进行三维动态仿真模拟,并分析研究了不同钻头布置形式对钻进效果的影响。计算结果表明：钻头切削叶片数量的增加会提高钻进阻转矩,但是会增强钻头的定心能力。设置截齿的钻头钻进阻力矩并无明显提高,但钻进速度有一定程度的提高。钻头切削叶片角度的提高会增加钻进阻力矩,但过低或者过高的切削叶片角度均会降低钻进速度。适当提高钻进压力可提高钻进速度,但须考虑动力装置的功率及扭矩输出能力。三切削叶片、高切削叶片角度、设置三截齿的高效率钻头在应用于北京市某项目卵砾石地层时效果良好,文章提出的方法可以为其他工程的施工机械选型提供参照依据。

     

Hydro-micromechanical modeling of wave propagation in saturated granular crystals

Biot theory predicts wave velocities in a saturated granular medium using the pore geometry, viscosity, densities, and elastic moduli of the solid skeleton and pore fluid, neglecting the interaction between constituent particles and local flow, which becomes essential as the wavelength decreases. Here, a hydro-micromechanical model, for direct numerical simulations of wave propagation in saturated granular media, is implemented by two-way coupling the lattice Boltzmann method (LBM) and the discrete element method (DEM), which resolve the pore-scale hydrodynamics and intergranular behavior, respectively. The coupling scheme is benchmarked with the terminal velocity of a single sphere settling in a fluid. In order to mimic a small amplitude pressure wave entering a saturated granular medium, an oscillating pressure boundary on the fluid is implemented and benchmarked with the one-dimensional wave equation. The effects of input waveforms and frequencies on the dispersion relations in 3D saturated poroelastic media are investigated with granular face-centered-cubic crystals. Finally, the pressure and shear wave velocities predicted by the numerical model at various effective confining pressures are found to be in excellent agreement with Biot analytical solutions, including his prediction for slow compressional waves.