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.     

DEM simulation of the behaviour of geogrid stabilised ballast fouled with coal

Geogrids are commonly used in railway construction for reinforcement and stabilisation. When railway ballast becomes fouled due to ballast breakage, infiltration of coal fines, dust and subgrade soil pumping, the reinforcement effect of geogrids decreases significantly. This paper presents results obtained from Discrete Element Method (DEM) to study the interface behaviour of coal-fouled ballast reinforced by geogrid subjected to direct shear testing. In this study, irregularly-shaped aggregates (ballast) were modelled by clumping together 10–20 spheres in appropriate sizes and positions. The geogrid was modelled by bonding a large number of small spheres together to form the desired grid geometry and apertures. Fouled ballast with 40% Void Contaminant Index (VCI) was modelled by injecting a predetermined number of miniature spheres into the voids of fresh ballast. A series of direct shear tests for fresh and fouled ballast reinforced by the geogrid subjected to normal shear stresses varying from 15 kPa to 75 kPa were then simulated in the DEM. The numerical results showed a good agreement the laboratory data, indicating that the DEM model is able to capture the behaviour of both fresh and coal-fouled ballast reinforced by the geogrid. The advantages of the proposed DEM model in terms of capturing the correct stress–displacement and volumetric behaviour of ballast, as well as the contact forces and strains developed in the geogrids are discussed.     

DEM investigation of the effect of intermediate principle stress on particle breakage of granular materials

This study investigates the influence of the intermediate principle stress on the particle breakage of granular materials. The crushable agglomerate method is applied to model soil particles and numerical true triaxial tests were carried out. The results show that particle breakage increases with increasing b value, the relationship of which follows an exponential function and agrees well with previous experimental results. More importantly, the study found that the relationship between particle breakage and total energy input is independent of the intermediate principle stress, which provides a good basis for the constitutive modeling of granular materials.     

DEM study on the effect of particle breakage on the macro- and micro-behavior of rockfill sheared along different stress paths

The behavior of crushable rockfill sheared along different stress paths is studied using the discrete element method. Rockfill particles are modeled as breakable agglomerates, and reasonable consistency is found between the predicted and experimental results. The simulation highlights the influence of agglomerate breakage on both the macro- and micro-behavior of the assembly. The evolution of both the number and mode of agglomerate breakage during shearing is significantly influenced by the confining pressure, deviator stress ratio, and loading direction. The relationship between the deviator stress ratio on the macro-scale and the deviator fabric on the micro-scale along different stress paths is explored.     

The effect of particle shape and hydrophobicity in flotation

The effect of particle shape on the flotation process has been investigated in laboratory experiments with monosized spherical ballotini and ground ballotini. The particles were treated by partial methylation with trimethylchlorosilane to achieve varying degrees of hydrophobicity. In flotation, the process of film thinning and liquid drainage is critical in the formation of stable bubble–particle attachments and this is affected by the particle shape and surface hydrophobicity. Flotation tests with different particle sizes were conducted in a modified batch Denver cell. Predictions from a computational fluid dynamic model of the flotation cell that incorporates fundamental aspects of bubble–particle attachment were compared with data from flotation tests. Contact angles of the particles were measured using a capillary rise technique to indicate surface hydrophobicity. Ground ballotini generally has higher flotation rates than spherical ballotini; the results are consistent with effects from faster film thinning and rupture at rough surfaces and are well correlated by the sphericity index.     

土工格栅加筋砂土中水平锚板抗拔特性试验研究

土工格栅加筋能够有效改善锚板的抗拔承载力,然而锚板在上拔过程中的破坏机制及其影响因素尚需进一步研究。针对砂土中水平锚板的抗拔特性,开展了多组锚板上拔试验,分析了砂土密实度、锚板埋深、土工格栅布设层数和位置等因素的影响,结合粒子图像测速（particle image velocimetry,简称PIV）技术探究了锚板周边土体的变形破坏机制。研究结果表明：单层接触式格栅加筋对锚板的抗拔承载力有明显的提升,且其对土体性能的改善优于非接触式格栅加筋情况,其原因与土工格栅变形量和上覆土体重力有关;当采用双层土工格栅加筋时,下层格栅可充分发挥限制土体侧向变形和均化应力分布的作用,上层格栅相对而言贡献不大;采用土工格栅加筋后,锚-土界面附近土体的变形模式发生了明显的变化,其破坏面相比未加筋前向内侧收敛,且剪应变分布更为均匀。     

DEM analysis of angular ballast breakage under cyclic loading

Railway ballast particles undergo significant amount of breakage under repeated train load. Breakage of ballast particles, especially highly angular fresh ones, causes an increase in settlement, contributing to track degradation. The quantitative analysis of the influence of breakage on the stress-strain properties of ballast can be performed either experimentally or numerically. Numerical modeling has the advantage of simulating ballast breakage subject to various types of loading and different boundary conditions for a range of material properties. In this paper, ballast breakage under cyclic loading is simulated using a 2D discrete element method (DEM) utilizing the software PFC^2D . A new subroutine is developed and incorporated in the PFC^2D analysis to study ballast breakage and to quantify breakage in relation to particle size distribution. The influence of confining pressure on both breakage and permanent deformation is also studied and compared with laboratory observations. The findings of this paper provide an insight into the true ballast behavior under cyclic loading and are expected to assist railway practitioners in developing suitable design criteria for track stability.     

Study on the particle breakage of ballast based on a GPU accelerated discrete element method

Breakage of particles will have greatly influence on mechanical behavior of granular material(GM)under external loads,such as ballast,rockfill and sand.The discrete element method(DEM)is one of the most popular methods for simulating GM as each particle is represented on its own.To study breakage mechanism of particle breakage,a cohesive contact mode is developed based on the GPU accelerated DEM code-Blaze-DEM.A database of the 3D geometry model of rock blocks is established based on the 3D scanning method.And an agglomerate describing the rock block with a series of non-overlapping spherical particles is used to build the DEM numerical model of a railway ballast sample,which is used to the DEM oedometric test to study the particles’breakage characteristics of the sample under external load.Furthermore,to obtain the meso-mechanical parameters used in DEM,a black-analysis method is used based on the laboratory tests of the rock sample.Based on the DEM numerical tests,the particle breakage process and mechanisms of the railway ballast are studied.All results show that the developed code can better used for large scale simulation of the particle breakage analysis of granular material.     

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.     

Overview of continuum and particle dynamics methods for mechanical modeling of contractional geologic structures

Mechanically-based numerical modeling is a powerful tool for investigating fundamental processes associated with the formation and evolution of both large and small-scale geologic structures. Such methods are complementary with traditional geometrically-based cross-section analysis tools, as they enable mechanical validation of geometric interpretations. A variety of numerical methods are now widely used, and readily accessible to both expert and novice. We provide an overview of the two main classes of methods used for geologic studies: continuum methods (finite element, finite difference, boundary element), which divide the model into elements to calculate a system of equations to solve for both stress and strain behavior; and particle dynamics methods, which rely on the interactions between discrete particles to define the aggregate behavior of the system. The complex constitutive behaviors, large displacements, and prevalence of discontinuities in geologic systems, pose unique challenges for the modeler. The two classes of methods address these issues differently; e.g., continuum methods allow the user to input prescribed constitutive laws for the modeled materials, whereas the constitutive behavior ‘emerges’ from particle dynamics methods. Sample rheologies, case studies and comparative models are presented to demonstrate the methodologies and opportunities for future modelers.     

考虑颗粒棱角影响的直剪试验的离散元模拟

为了研究颗粒棱角对颗粒材料力学行为的影响,建立了具有不同棱角度的对称多面体颗粒,采用了一种简单并适合任意颗粒形状的接触本构模型,对三维离散元开源程序YADE进行了修改,研究了颗粒棱角度在模拟直剪试验中的影响以及接触力各向异性在剪切过程中的演化规律。研究结果表明,颗粒棱角度越小,颗粒间相互咬合自锁的作用越小,颗粒受剪更易转动,致使颗粒体系的剪切强度和剪胀性下降;竖向加载力越大,颗粒棱角度的影响越明显;法向接触力的各向异性在剪切过程中表现为先增后减最后趋向稳定的趋势;法向接触力的各向异性变化程度随颗粒棱角度的增大而增大。     

Discrete element modeling for the study of the effect of soft inclusions on the behavior of soil mix material

The influence of soil inclusions on the mechanical behavior of deep soil mix material was studied by discrete element simulations in combination with some laboratory tests. The innovative aspect of the simulations was that individual fracturing in the heterogeneous material was modeled. It was observed that the reduction of strength and stiffness did not correspond to the weighted average of the UCS and Young’s modulus, taking into account the volumes of the strong and weak material. The actual reduction was considerably larger, e.g., on average the strength was reduced by 13% and 50% for 1% and 10% of inclusions, respectively. Moreover, other parameters, such as the shape, number, and relative position of inclusions, also have an important influence on the strength and stiffness. First, sharp-ended inclusions have a more negative impact on the strength and stiffness than rounded inclusions. Second, one large inclusion reduces strength and stiffness more than three smaller inclusions with the same shape and accounting for the same total volume percentage. Finally, diagonally-located and more-concentrated inclusions have a more negative impact on the mechanical behavior than vertically-aligned and widely-spread inclusions. The results of the numerical simulations showed good agreement with the results of laboratory tests with regard to the effect on strength and stiffness as well as the observed fracture patterns.     

Side resistance of drilled shafts in granular soils investigated by DEM

The paper presents a numerical study on the side resistance of a drilled shaft in granular materials. The numerical result is used to develop new design equations for the side resistance of drilled shafts in granular soils. The Discrete Element Method (DEM) is used to model a drilled shaft in granular material. The granular material is represented as assemblies of ellipsoidal particles. Nominal side resistance is represented as the product of a parameter (β) and vertical stress. The numerical result shows that the relationship between β and void ratio can be described by a hyperbolic function for a given vertical stress. DEM result is also compared with three design equations. Although these design equations capture the decrease of β with depth, deviation is observed between the DEM results and the design equations. Finally, new design equations based on state parameter are proposed.     

砂土颗粒形状量化及其对力学指标的影响分析

砂作为一种特殊的散体材料,其宏观物理力学性质,如密实度、剪切特性（临界状态角,剪胀角）、压缩性及颗粒破碎特征等均受到颗粒形状的影响,目前为止,对于砂粒土颗粒形状的量化工作,未到达成熟阶段。试验采用普通光学显微镜获取3种不同砂颗粒及一种相似材料（玻璃球）数字图像,利用ImageJ图形软件对其进行黑白二值化处理,获取颗粒形状轮廓边界;从3个层次定义颗粒形状参数,并利用java语言编制形状量化插件程序,计算砂粒各形状参数值,最后通过相对密度试验、直剪试验测试不同砂样的极限孔隙比、剪切强度指标。试验结果表明：整体轮廓系数、球形度、棱角度3项形状参数可作为不同砂粒形状鉴别和量化的关键参数,且与剪胀角、临界状态摩擦角均具有良好的相关性,试验提供了一种量化砂颗粒形状的有效方法,并可将得到的关键量化参数应用到宏观力学性质分析与数值模拟工作中     

Improvements for the smooth joint contact model of the particle flow code and its applications

This paper deals with two shortcomings of the smooth-joint contact model (SJCM) used in the particle flow code (PFC). The first shortcoming is the increase of the shear strength of the joint when the shear displacement of the joint exceeds a specific value that is related to the particle size. This problem is named as the interlocking problem, which is caused by the interlocking particles. It occurs due to a shortcoming of the updating procedure in the PFC software related to the contact conditions of the particles that lie around the intended joint plane during high shear displacements. This problem also increases the dilation angle and creates unwanted fractures around the intended joint plane. To solve this problem two new approaches are proposed in this paper: (1) joint plane checking (JPC) approach and (2) joint sides checking (JSC) approach. These approaches and the regular approach are used to model: (a) the direct shear test using the PFC^2D and PFC^3D, (b) the biaxial test on a sample having a persistent joint with a dip angle varying from 0° to 90° at an interval of 15° using the PFC^2D and (c) the polyaxial test on two samples, one of them having a joint with a dip direction of 0° and the dip angle varying from 0° to 90° at an interval of 15°, and the other sample having a joint with a dip angle of 60° and the dip direction varying from 0° to 90° at an interval of 15° using the PFC^3D. All numerical results show that the JPC and JSC approaches can solve the interlocking problem. Also, they proved to be more consistent with the theory compared to the regular approach. However, the JPC approach leads to a slightly softer joint. Therefore, the JSC approach is suggested for jointed rock modeling using the PFC. The other shortcoming of the SJCM dealt within this paper is its inability to capture the non-linear behavior of the joint closure varying with the joint normal stress. This problem is solved in this paper by proposing a new modified smooth-joint contact model (MSJCM). MSJCM uses a linear relation between the joint normal stiffness and the normal contact stress to model the non-linear relation between the joint normal deformation and the joint normal stress observed in the compression joint normal stiffness test. A good agreement obtained between the results from the experimental test and the numerical modeling of the compression joint normal test shows the accuracy of this new model.     

加筋材料动态松弛有限元模型的建立及应用

为分析加筋材料的抗弯刚度对加筋性能的影响,加筋材料采用梁单元形式。基于动态松弛法,通过定义梁单元的刚度矩阵,求解内力矢量,随后定义虚拟质量密度而建立总质量矩阵,将加筋材料的梁单元有限元模型嵌入到已有的动态松弛法求解程序中。通过对简支梁的简单加载模拟验证了该梁单元模型的准确性能。随后,将该有限元模型与已有的动态松弛法计算程序结合（含砂土本构及弱面单元模型）,对加筋砂土地基室内模型试验进行了数值模拟。将梁单元的模拟结果与杆单元（梁单元的特例）模拟结果进行了比较,并分别探讨了抗拉刚度和抗弯刚度对加筋砂土地基承载性能的影响。结果表明：抗拉刚度对承载能力的影响较小;抗弯刚度对承载力的影响程度与加筋材料的布置形式有关,特别是当加筋砂土中出现剪切带以后,其影响逐渐增大。因此,在分析加筋砂土结构的增强机制时,建议采用梁单元（具有一定的抗弯刚度）对加筋材料进行模拟。