Scaling granular material with polygonal particles in discrete element modeling

Despite advancements in computational resources, the discrete element method (DEM) still requires considerable computational time to solve detailed problems, especially when it comes to the large-scale models. In addition to the geometry scale of the problem, the particle shape has a dramatic effect on the computational cost of DEM. Therefore, many studies have been performed with simplified spherical particles or clumps. Particle scaling is an approach to increase the particle size to reduce the number of particles in the DEM. Although several particle scaling methods have been introduced, there are still some disagreements regarding their applicability to certain aspects of problems. In this study, the effect of particle scalping on the shear behavior of granular material is explored. Real granular particles were scanned and imported as polygonal particles in the direct shear test. The effect of particle size distribution, particle angularity, and the amount of scalping were investigated. The results show that particle scalping can simulate the correct shear behavior of the model with significant improvement in computational time. Also, the accuracy of the scalping method depends on the particle angularity and particle size range.     

Influence of particle shape on the microstructure evolution and the mechanical properties of granular materials

In order to study the influence of particle shape on the microstructure evolution and the mechanical properties of granular materials, a two-dimensional DEM analysis of samples with three particle shapes, including circular particles, triangular particles, and elongated particles, is proposed here to simulate the direct shear tests of coarse-grained soils. For the numerical test results, analyses are conducted in terms of particle rotations, fabric evolution, and average path length evolution. A modified Rowe's stress–dilatancy equation is also proposed and successfully fitted onto simulation data.     

Discrete element modeling of inherently anisotropic granular assemblies with polygonal particles

In the present article, we study the effect of inherent anisotropy, i.e., initial bedding angle of particles and associated voids on macroscopic mechanical behavior of granular materials, by numerical simulation of several biaxial compression tests using the discrete element method (DEM). Particle shape is considered to be irregular convex-polygonal. The effect of inherent anisotropy is investigated by following the evolution of mobilized shear strength and volume change during loading. As experimental tests have already shown, numerical simulations also indicate that initial anisotropic condition has a great influence on the strength and deformational behavior of granular assemblies. Comparison of simulations with tests using oval particles, shows that angularity influences both the mobilized shear strength and the volume change regime, which originates from the interlocking resistance between particles.     

Using a modified direct shear apparatus to explore gap and size effects on shear resistance of coarse-grained soil

This work used a modified direct shear apparatus, created newly by the authors, to explore effects of the gap between shear box halves and specimen size on the shear resistance of coarse-grained soil. The shear boxes of this apparatus were assembled from a series of steel structures capable of superimposition and nesting. Such characteristics facilitated variation of specimen size in both diameter and height. The new device can also maintain a constant gap during shearing. We performed a series of gap-effect and size-effect tests for two uniformly graded, coarse-grained soil samples. The test results showed that both the gap space and specimen size had significant influences on shear resistance of the coarse-grained soil. Further, analysis of variations in shear strength indices led to a reasonable gap dimension and specimen size of the two soil samples.     

非饱和黏性土抗剪强度的温度效应试验研究

为了系统地了解温度对黏性土工程性质的影响,本文采用南京地区三种不同矿物成分的黏性土,制成不同含水量和干密度的试样,在5~45℃条件下,开展了抗剪强度试验,获得了三种土的非饱和重塑试样的抗剪强度与温度的关系。试验结果表明:黏性土的黏聚力随温度升高呈线性变化; 亲水矿物含量较高的黏性土抗剪强度对温度变化较敏感,黏聚力随着温度的升高而降低,表现为强度的热软化现象; 亲水矿物含量较低的黏性土,当含水量较低(w≤17%)时,表现为强度的热硬化现象,当含水量较高(w≥22%)时,表现为强度的热软化现象,且干密度越高的试样,强度的温度效应越明显。论文还分析了非饱和黏性土抗剪强度的热硬化和热软化的内在机理。     

胶结砂砾石层面直剪试验及破坏行为细观研究

本文采用宏观试验和细观模拟相结合的方法研究胶结砂砾石层面在剪切过程中的破坏行为．首先进行了不同法向应力作用下的胶结砂砾石层面直剪试验,获得了不同的剪切面破坏特征：随着法向应力的不断增加,剪切破坏面凹凸起伏程度、骨料脱落现象越发明显．其次为了深入探究层面破坏现象,按照室内试验采用的骨料级配粒径建立细观颗粒数值模型,结合物理试验对模型进行参数标定,并进行数值模型的层面直剪模拟和细观分析．结果表明,数值模型可以再现宏观直剪试验层面破坏特征;法向应力越大,层面区域颗粒发生错动和翻转的数量越多;层面破坏方式为颗粒间的张拉和剪切混合破坏,裂隙均集中在层面位置,随着法向应力的增加,裂隙的集中区域逐渐由“面”向“带”转变．     

Simulating shear behavior of a sandy soil under different soil conditions

Understanding of soil shear behavior is very important in the field of agricultural machinery and soil dynamics. In this study, a discrete element model was developed using a simulation tool, Particle Flow Code in Three Dimensions (PFC^3D). The model simulates direct shear tests of soil and predicts soil shear behavior, in terms of shear forces and displacements. To determine and calibrate model parameters (stiffness of particles, strength and stiffness of bond between particles), laboratory direct shear tests were conducted to examine effects of soil moisture content and bulk density on shear behaviors of a sandy soil. Three soil moisture levels (0.02%, 13.0%, and 21.5%) and four bulk density levels (0.99, 1.28, 1.36, and 1.50 Mg/m³) were used in the tests. The test results showed that in general drier and denser soil conditions produced higher shear forces. Based on the test results, the bond strengths of the model particles were determined from soil cohesion and internal friction angle. The model particle stiffness was calibrated based on the yield forces from the tests. The calibrated particle stiffness varied from 1.0 × 10³ to 8.2 × 10³ N/m, depending on soil moisture and density levels. The bond stiffness calibrated was 1.0 × 10⁷ Pa/m for all soil conditions.     

Determining a representative element volume for DEM simulations of samples with non-circular particles

Numerical studies on the number of particles or system size required to attain a representative element volume (REV) for discrete element method (DEM) simulations of granular materials have almost always considered samples with spherical or circular particles. This study considers how many particles are needed to attain a REV for 2D samples of 2-disc cluster particles where the particle aspect ratio (AR) was systematically varied. Dense and loose assemblies of particles were simulated. The minimum REV was assessed both by considering the repeatability of static packing characteristics and the shearing behaviour in biaxial compression tests, and by investigating the effect of sample size on the measured characteristics and observed shearing behaviour. The repeatability of the data considered generally improved with increasing sample size. The packing characteristics of the dense samples were more repeatable suggesting that the minimum REV reduces with increasing packing density. The minimum REV was observed to be sensitive to the characteristic measured. Although the overall responses of the samples during shear deformation were similar irrespective of the sample sizes, the smaller the sample size, the higher the fluctuations observed in the responses. Analysis of the coefficient of variation of the fluctuations around the critical state stress ratio can provide insight as to whether a REV is attained. The particle AR influences the effect of sample size on shearing characteristics and thus the minimum number of particles required to attain a REV; this can be explained by the influence of AR on the number of contacts within the samples.     

Discrete simulation and micromechanical analysis of two-dimensional saturated granular media

In this study, a novel approach to incorporate the pore water pressure in the discrete element method (DEM) to comprehensively model saturated granular media was developed. A numerical model was constructed based on the DEM by implanting additional routines in the basic DEM code; pore water pressure calculations were used with a two-dimensional (2D) model to simulate the undrained behavior of saturated granular media. This model coupled the interaction of solid particles and the pore fluid in saturated granular media. Finally, several 2D undrained shear tests were simulated. The test results showed that the model could predict the response of the saturated granular soil to shear loading. The effect of initial compaction was investigated. Biaxial tests on dense and loose specimens were conducted, and the effect of the initial density on the change in shear strength and the volume change of the system was investigated. The overall behavior of loose and dense specimens was phenomenologically similar to the real granular material. Constant volume tests were simulated, and the results were compared to those from the coupled model. Induced anisotropy was micromechanically investigated by studying the contact force orientation. The change in anisotropy depended on the modeling scheme. However, the overall responses of the media obtained using the coupled and constant volume methods were similar.     

Discrete simulation and micromechanical analysis of two-dimensional saturated granular media

In this study, a novel approach to incorporate the pore water pressure in the discrete element method （DEM） to comprehensively model saturated granular media was developed. A numerical model was constructed based on the DEM by implanting additional routines in the basic DEM code; pore water pressure calculations were used with a two-dimensional （2D） model to simulate the undrained behavior of satu- rated granular media. This model coupled the interaction of solid particles and the pore fluid in saturated granular media. Finally, several 2D undrained shear tests were simulated. The test results showed that the model could predict the response of the saturated granular soil to shear loading. The effect of initial compaction was investigated. Biaxial tests on dense and loose specimens were conducted, and the effect of the initial density on the change in shear strength and the volume change of the system was inves- tigated. The overall behavior of loose and dense specimens was phenomenologically similar to the real granular material. Constant volume tests were simulated, and the results were compared to those from the coupled model. Induced anisotropy was micromechanically investigated by studying the contact force orientation. The change in anisotropy depended on the modeling scheme. However, the overall responses of the media obtained usinz the couoled and constant volume methods were similar.     

Discrete element analysis of the mechanical properties of deep-sea methane hydrate-bearing soils considering interparticle bond thickness

Due to increasing global energy demands, research is being conducted on the mechanical properties of methane hydrate-bearing soils (MHBSs), from which methane hydrate (MH) will be explored. This paper presents a numerical approach to study the mechanical properties of MHBSs. The relationship between the level of MH saturation and the interparticle bond thickness is first obtained by analyzing the scanning electron microscope images of MHBS samples, in which is the bridge connecting the micromechanical behavior captured by the DEM with the macroscopic properties of MHBSs. A simplified thermal-hydromechanical (THM) bond model that considers the different bond thicknesses is then proposed to describe the contact behavior between the soil particles and those incorporated into the discrete element method (DEM). Finally, a series of biaxial compression tests are carried out with different MH saturations under different effective confining pressures to analyze the mechanical properties of deep-sea MHBSs. The results of the DEM numerical simulation are also compared with the findings from triaxial compression tests. The results show that the macromechanical properties of deep-sea MHBSs can be qualitatively captured by the proposed DEM. The shear strength, cohesion, and volumetric contraction of deep-sea MHBSs increase with increasing MH saturation, although its influence on the internal friction angle is obscure. The shear strength and volumetric contraction increase with increasing effective confining pressure. The peak shear strength and the dilation of MHBSs increase as the critical bond thickness increases, while the residual deviator stress largely remains the same at a larger axial strain. With increasing the axial strain, the percentage of broken bonds increases, along with the expansion of the shear band.     

粗粒土离散元非球趋真颗粒模型

颗粒形状对粗粒土的物理力学特性有着显著的影响。离散元法广泛应用于粗粒土宏观物理力学特性的细观机理研究。为了考虑颗粒形状的影响,亟待发展计算高效的离散元非球趋真颗粒模型。本文基于X射线CT扫描技术并结合数字图像处理技术,对光滑和棱角性两类典型粗粒土(鹅卵石与碎石)进行三维重构,并提出了两类趋真颗粒模型,分别采用扩展超椭球模型和球多面体模型进行趋真逼近;开展了两类颗粒试样的3D打印和单轴压缩试验,分析了配位数和局部孔隙率分布等细观特性;基于离散元开源程序SudoDEM开展了两类试样的离散元模拟,并将模拟细观分析结果与物理试验进行了对比。结果表明,提出的两类趋真颗粒模型能够较好地对粗粒土颗粒进行离散元建模。     

Effect of particle breakage on the behavior of simulated angular particle assemblies

Many attempts have been made to find various relationships for different parameters and some kinds of constitutive models for studying the behavior of particulate media. All these models are based on concepts of continuous media. Using a numerical method such as discrete element method, one can figure out what is happening through a discontinuous media where soil particles play the main role in introducing the shear strength and deformation characteristics. The behavior of the media with breakable particles is studied in this paper and compared with that of the assembly with non-breakable particles. In this paper, the hyperbolic elastic model is investigated for the assembly of polygon shaped particles in two different test series. In addition, evolution of different macro parameters of the assembly such as volume strain, angle of friction, angle of dilatancy and elastic modulus is studied during the simulation tests both for non-breakable and breakable soil particles. At the end, a parametric study is performed on the effect of strength of particle breakage on the assembly behavior.     

Effect of particle polydispersity on micromechanical properties and energy dissipation in granular mixtures

A series of numerical tests was conducted to study the micromechanical properties and energy dissipation in polydisperse assemblies of spherical particles subjected to uniaxial compression. In general, distributed particle size assemblies with standard deviations ranging from 0% to 80% of the particle mean diameter were examined. The microscale analyses included the trace of the fabric tensor, magnitude and orien- tation of the contact forces, trace of stress, number of contacts and degree of mobilization of friction in contacts between particles. In polydisperse samples, the average coordination numbers were lower than in monodisperse assemblies, and the mobilization of friction was higher than in monodisperse assemblies due to the non-uniform spatial rearrangement of spheres in the samples and the smaller displacements of the particles. The effect of particle size heterogeneity on both the energy density and energy dissipation in systems was also investigated.     

Effect of particle polydispersity on micromechanical properties and energy dissipation in granular mixtures

A series of numerical tests was conducted to study the micromechanical properties and energy dissipation in polydisperse assemblies of spherical particles subjected to uniaxial compression. In general, distributed particle size assemblies with standard deviations ranging from 0% to 80% of the particle mean diameter were examined. The microscale analyses included the trace of the fabric tensor, magnitude and orientation of the contact forces, trace of stress, number of contacts and degree of mobilization of friction in contacts between particles. In polydisperse samples, the average coordination numbers were lower than in monodisperse assemblies, and the mobilization of friction was higher than in monodisperse assemblies due to the non-uniform spatial rearrangement of spheres in the samples and the smaller displacements of the particles. The effect of particle size heterogeneity on both the energy density and energy dissipation in systems was also investigated.     

基于PFC~(3D)的砂土直剪模拟及宏细观分析

为能更好地分析砂土在剪切过程中的体积变化及力学行为,通过PFC~(3D)颗粒流程序,按照室内实际级配建立数值试样,进行了不同垂直压力下的砂土直剪试验模拟,并将模拟结果与室内试验结果进行了对比;研究了砂土在剪切过程中的体积变化,并用两种方法分析了砂土剪切带的演变过程;从细观角度对试样颗粒的速度场及力链网络的发展变化进行了分析研究。结果表明,数值模拟结果与室内试验结果基本一致,砂土的体积变化表现为先剪缩后剪胀,剪胀量与垂直压力成反比;剪切带厚度约为11～12倍d_(50),在剪切带内颗粒的位移和欧拉角变化较大;试样内部强力链的演变较为明显,力链网络对外荷载变化的敏感性很高;剪切过程中上盒颗粒速度场方向的变化能够较好地解释砂土产生的剪胀现象。     

THE VARIATIONS OF PHYSICAL AND MECHANICAL PROPERTIES OF REMODELING AND UNDISTURBED EXPANSIVE ROCKS OF DIFFERENT PARTICLE SIZES 1)

以南宁盆地膨胀岩为研究对象,通过室内试验测定原状样与不同颗粒粒径重塑样的膨胀力、抗剪强度及热特性,研究其性质差异。结果表明：重塑后不同粒径范围膨胀岩土样的无荷膨胀率较原状样明显升高,而主应力差峰值、抗剪强度和热物理指标较原状样均有降低。因此,应选择合适粒径范围的土颗粒重塑代替原状样进行室内试验：无荷膨胀率和膨胀力试验应选择粒径范围1 mm≤d<2 mm的土颗粒;三轴试验和热物理指标测试应尽量选择粒径较小的土颗粒。     

固化滨海盐渍土路用性能的室内试验与现场测试

渤海湾西海岸带地区的路堤多为填方型式,且以滨海盐渍土为主要填料。以滨海盐渍土填筑路堤,须解决土的盐胀、溶陷和吸湿软化带来的强度下降和稳定性降低问题,以进行土的改性或固化处理。为降低工程费用,固化材料应以常规的无机材料为主,辅助少量的高分子材料。为研究滨海盐渍土填筑路堤的力学性能,完成了石灰固化土和石灰+SH固土剂固化土的无侧限抗压强度、劈裂法抗拉强度、三轴抗剪强度和加州承载比等室内试验,同期还进行了固化土的现场碾压试验,检测了碾压固化土的压实度、平整度、回弹弯沉、加州承载比和回弹模量等指标。试验与研究结果显示:(1)石灰固化土和石灰+SH固土剂固化土均满足填筑路堤的强度和变形指标要求,后者的力学性能优于前者; (2)SH固土剂干燥后的胶膜包裹了土颗粒,且在颗粒间形成了抗水的胶结联结,胶丝在土的孔隙内形成了絮状联结网。胶膜和胶丝网共同作用,提高了固化土的强度、抗变形能力和水稳性; (3)2种固化土的现场碾压试验效果都很好,碾压固化土的现场测试结果与固化土的室内试验结果相一致。石灰+SH固土剂固化土的碾压性能和力学指标均满足"公路路基设计规范"的要求,效果良好,这种固化方法适宜在滨海盐渍土地区推广使用。     

Effect of the Interfacial Stress Distribution on the Material Interfacial Shear Strength Measurement

An integrated experimental and numerical analysis is carried out to study the interfacial shear strength of bonded materials. Two types of shear tests, namely the Iosipescu shear test, and the short-beam shear test are employed to understand the effect of interfacial stress on the interfacial shear strength measurements. The measured average shear strengths are very close, even though the interfacial shear stress distributions of these two kinds of specimens are very different. Therefore, we conclude that the interfacial stress distribution has the least effect on the interfacial strength measurement if the interfacial shear stress is non-singular.     

柱状节理玄武岩体抗剪强度参数尺寸效应研究

结合柱状节理玄武岩块室内直剪试验和现场大尺度直剪试验所取得不同尺度岩块的抗剪参数试验成果,进行异计拟合回归分析得到柱状节理玄武岩体抗剪强度参数内聚力c和内摩擦系数f的尺寸效应经验表达式,认为抗剪强度参数与试样尺寸间近似呈幂函数形式。抗剪强度参数的表征单元体积研究表明,内聚力对试样的尺寸更为敏感。