Generation of a realistic 3D sand assembly using X‐ray micro‐computed tomography and spherical harmonic‐based principal component analysis

Three‐dimensional particle morphology is a significant problem in the discrete element modeling of granular sand. The major technical challenge is generating a realistic 3D sand assembly that is composed of a large number of random‐shaped particles containing essential morphological features of natural sands. Based on X‐ray micro‐computed tomography data collected from a series of image processing techniques, we used the spherical harmonics (SH) analysis to represent and reconstruct the multi‐scale features of real 3D particle morphologies. The SH analysis was extended to some highly complex particles with sharp corners and surface cavities. We then proposed a statistical approach for the generation of realistic particle assembly of a given type of sand based on the principle component analysis (PCA). The PCA aims to identify the major pattern of the coefficient matrix, which is made up of the SH coefficients of all the particles involved in the analysis. This approach takes into account the particle size effect on the variation of particle morphology, which is observed from the available results of micro‐computed tomography and QICPIC analyses of sand particle morphology. Using the aforementioned approach, two virtual sand samples were generated, whose statistics of morphological parameters were compared with those measured from real sand particles. The comparison shows that the proposed approach is capable of generating a realistic sand assembly that retains the major morphological features of the mother sand. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Study on the mechanical behavior of sands using 3D discrete element method with realistic particle models

Presented is a study on the geometrical characteristics of sand particles and the mechanical behavior of sand material under external loading. Based on computed tomography technique, a reconstruction method of granular particles was developed and used to build a database of 3D geometrical models for sand particles. The studied sand particles showed good regularities in morphological characteristics and thus were suitable to be used for the random generation of numerical samples. DEM tests using realistically shaped particles were proven to better simulate the mechanical behavior of the sample during elastoplastic loading stage, which was an issue for the simplified spherical particles. The generation, extension, and breakage of the force chains controlled the strain softening behavior of sands. Anisotropy analysis using the spherical harmonic series showed that the evolution of anisotropy directions and parameters corresponded well with the macroscopic mechanical behavior of the material. Pore volume computation based on Voronoi diagram was performed to illustrate the formation and evolution of localized shear zone. The mesoscopic analysis showed that particle shape significantly influences the mechanical behavior of sands and thus should be properly modeled in numerical simulations.

     

Influence of liquid bridges on the mechanical behaviour of polydisperse granular materials

We investigate a polydisperse granular material in which the particle interactions are governed by a capillary force law. The cohesion force for a grain‐pair with unequal diameters is expressed as an explicit function of the inter‐particle distance and the volume of the liquid bridge. This analytical relation is validated by experiments on a reference material. Then, it is completed by a rupture criterion and cast in the form of a force law that accounts for solid contact, capillary force and rupture characteristics of a grain‐pair. Finally, in order to evaluate the influence of capillary cohesion on the macroscopic behaviour, radial and axial compression tests on cylindrical assemblies of wet particles are simulated using a 3D distinct element method. Copyright © 2005 John Wiley & Sons, Ltd.     

Modeling the particle breakage of rockfill materials with the cohesive crack model

A practical combined finite–discrete element method was developed to simulate the breakage of irregularly shaped particles in granular geomaterials, e.g., rockfill. Using this method, each particle is discretized into a finite element mesh. The potential fracture paths are represented by pre-inserted cohesive interface elements (CIEs) with a progressive damage model. The Mohr–Coulomb model with a tension cut-off is employed as the damage initiation criterion to rupture the predominant failure mode occurs at the particle scale. Two series of biaxial tests were simulated for both the breakable and unbreakable particle assemblies. The two assemblies have identical configurations, with the exception that the former is inserted with CIEs and is breakable. The simulated stress–strain–dilation responses obtained for both assemblies are in agreement with experimental observations. We present a comprehensive study of the role of particle breakage on the mechanical behavior of rockfill materials at both the macroscopic and microscopic scales. The underlying mechanism of particle breakage can be explained by the force chain in the assemblies.     

Coupled bonded particle and lattice Boltzmann method for modelling fluid–solid interaction

This paper presents a two‐dimensional coupled bonded particle and lattice Boltzmann method (BPLBM) developed to simulate the fluid–solid interactions in geomechanics. In this new technique, the bonded particle model is employed to describe the inter‐particle movement and forces, and the bond between a pair of contacting particles is assumed to be broken when the tensile force or tangential force reaches a certain critical value. As a result the fracture process can be delineated based on the present model for the solid phase comprising particles, such as rocks and cohesive soils. In the meantime, the fluid phase is modelled by using the LBM, and the immersed moving boundary scheme is utilized to characterize the fluid–solid interactions. Based on the novel technique case studies have been conducted, which show that the coupled BPLBM enjoys substantially improved accuracy and enlarged range of applicability in characterizing the mechanics responses of the fluid–solid systems. Indeed such a new technique is promising for a wide range of application in soil erosion in Geotechnical Engineering, sand production phenomenon in Petroleum Engineering, fracture flow in Mining Engineering and fracture process in a variety of engineering disciplines. Copyright © 2016 John Wiley & Sons, Ltd.     

Evolution of induced fabric in a strain space multiple mechanism model for granular materials

The strain space multiple mechanism model idealizes the behavior of granular materials based on a multitude of virtual simple shear mechanisms oriented in arbitrary directions. Within this modeling framework, the virtual simple shear stress is defined as a quantity that depends on the contact distribution function as well as the normal and tangential components of inter‐particle contact forces, which evolve independently during the loading process. In other terms, the virtual simple shear stress is an intermediate quantity in the upscaling process from the microscopic level (characterized by the contact distribution and inter‐particle contact forces). The stress space fabric (i.e. the orientation distribution of the virtual simple shear stress) produces macroscopic stress through the tensorial average. Thus, the stress space fabric characterizes the fundamental and higher modes of anisotropy induced in granular materials. Comparing an induced fabric associated with the biaxial shear of plane granular assemblies obtained via a simulation using Discrete Element Method to the strain space multiple mechanism model suggests that the strain space multiple mechanism model has the capability to capture the essential features in the evolution of an induced fabric in granular materials. Copyright © 2012 John Wiley & Sons, Ltd.     

Equivalent continuum strain calculations based on 3D particle kinematic measurements of sand

Constitutive modeling of granular materials has been a subject of extensive research for many years. While the calculation of the Cauchy stress tensor using the discrete element method has been well established in the literature, the formulation and interpretation of the strain tensor are not as well documented. According to Bagi, 1 researchers mostly adopt well‐known continuum or discrete microstructural approaches to calculate strains within granular materials. However, neither of the 2 approaches can fully capture the behavior of granular materials. They are considered complementary to each other where each has its own strengths and limitations in solving granular‐mechanics problems. Zhang and Regueiro 2 proposed an equivalent continuum approach to calculating finite strain measures at the local level in granular materials subjected to large deformations. They used three‐dimensional discrete element method results to compare the proposed strains measures. This paper presents an experimental application of the Zhang and Regueiro 2 approach using three‐dimensional synchrotron microcomputed tomography images of a sheared Ottawa sand specimen. Invariant Eulerian finite strain measures were calculated for representative element volumes within the specimen. The spatial maps of Eulerian octahedral shear and volumetric strain were used to identify zones of intense shearing within the specimen and compared well with maps of incremental particle translation and rotation for the same specimen. The local Eulerian volumetric strain was compared to the global volumetric strains, which also can be considered as an averaging of all local Eulerian volumetric strains.     

Combined spheropolyhedral discrete element (DE)–finite element (FE) computational modeling of vertical plate loading on cohesionless soil

This paper presents a combined spheropolyhedral discrete element (DE)–finite element (FE) computational approach to simulating vertical plate loading on cohesionless soils such as gravels. The gravel particles are modeled as discrete elements, and the plate is modeled as a deformable FE continuum. The simulations provide a meaningful step toward better understanding how deformable bodies transmit loads to granular materials. The DE–FE contact algorithm is verified through comparison with an analytical solution for impact between two symmetric bars. A parametric study is conducted to ensure boundary effects are not significantly influencing the simulations. Numerical simulations are compared to experimental test results of lightweight deflectometer loading on a gravel base course with satisfactory agreement. Future developments of the approach intend to simulate wheel loading of military aircraft on unsurfaced airfields.     

A numerical study of particle motion and two‐phase interaction in aeolian sand transport using a coupled large eddy simulation – discrete element method

Wind‐blown sand movement, considered as a particle‐laden two‐phase flow, was simulated by a new numerical code developed in the present study. The discrete element method was employed to model the contact force between sand particles. Large eddy simulation was used to solve the turbulent atmospheric boundary layer. Motions of sand particles were traced in the Lagrangian frame. Within the near‐surface region of the atmospheric boundary layer, interparticle collisions will significantly alter the velocity of sand. The sand phase is quite dense in this region, and its feedback force on fluid motion cannot be ignored. By considering the interparticle collision and two‐phase interaction, four‐way coupling was achieved in the numerical code. Profiles of sand velocity from the simulations were in good agreement with experimental measurements. The mass flux shows an exponential decay and is comparable to reported experimental and field measurements. The turbulence intensities and shear stress of sand particles were estimated from particle root‐mean‐square velocities. Distributions of slip velocity and feedback force were analysed to reveal the interactions between sand particles and the continuous fluid phase.     

颗粒接触力检测方法评述

颗粒物质是大量固体颗粒体系的集合体,其特性区别于普通固体和液体等物质的性质,颗粒物质基础力学问题的研究20年来一直是科学的前沿,从分析多尺度结构和相关物理机制的角度研究颗粒物质可能取得突破。首先介绍了微观尺度--亦即单颗粒尺度颗粒间接触力的检测方法,包括高精度电子天平称重法、显色灵敏复写纸压痕方法、光弹实验方法、荧光共聚焦显微镜法和磁共振弹性成像法等,根据检测过程中是否对颗粒带来影响划分为接触式检测和非接触式检测两大类,并对这些方法的工作原理、检测结果和优缺点进行了评述。我们指出接触式测量对颗粒体系带来了或多或少的干扰,特别是由于力链对局部力的变化反应极为敏感,轻微的变化足以使得力链结构发生很大变化,开展无干扰的光测实验是必然的发展趋势,而现阶段开展二维光弹性实验是很有意义的。最后介绍了作者正在进行的颗粒物质光弹力学实验的研究工作。     

颗粒体系中的骨架及力链网络

颗粒物质是大量离散的固体颗粒相互作用而组成的复杂体系,具有非连续和接触耗散等基本特征,其物理机制研究是近20年科学前沿之一。砂土就是典型的颗粒物质,土体中的有效应力是作用在土体骨架上的平均应力,土体变形主要来源于骨架上的颗粒位置,但对土体骨架并没有一个清晰的物理描述。近期颗粒物质力学研究认为,体系中颗粒相互接触形成的网络结构是外荷载传递路径的物理基础,可能就是土力学所指的骨架。同时还发现,较大的力通常沿着准直线的路径传递,人们常把传递较大力、与该准直线路径对应的若干颗粒组成的链状结构,称为强力链;弱力链则传递较小力。力链结构及其演变规律的描述是颗粒物质研究的核心之一。以单轴侧限压缩数值模拟为例,对比说明了土体颗粒骨架与力链结构的关系,明确提出强力链网络决定颗粒体系的宏观力学行为。     

Embedded beam element with interaction surface for lateral loading of piles

This paper presents a numerical formulation of a three dimensional embedded beam element for the modeling of piles, which incorporates an explicit interaction surface between soil and pile. The formulation is herein implemented for lateral loading of piles but is able to represent soil–pile interaction phenomena in a general manner for different types of loading conditions or ground movements. The model assumes perfect adherence between beam and soil along the interaction surface. The paper presents a comparison of the results obtained by means of the present formulation and by means of a previously formulated embedded pile element without interaction surface, as well as reference semi‐analytical solutions and a fully 3D finite element (FE) model. It is seen that the proposed embedded element provides a better convergence behavior than a previously formulated embedded element and is able to reproduce key features of a full 3D FE model. Copyright © 2015 John Wiley & Sons, Ltd.     

A note on the generation of periodic granular microstructures based on grain size distributions

This short communication discusses an algorithm suited for the generation of periodic microstructures of granular media. Its particular features are a user‐defined grain size distribution, a representative volume element which is intrinsically periodic ab initio and a user‐defined termination criterion, controlled by an increase of volume fraction. For low densities our particle packings resemble fluids or gases, while we aim to reach for rather dense particle packings, similar to granular solids. The generated microstructures can thus be readily incorporated into large multiscale simulations, e.g. on the integration point level of a finite element analysis of a particular sand or concrete. The individual grain size distribution of the granular medium is incorporated through the introduction of different growth rates governing the final particle size distribution. We briefly sketch the generation of the representative volume element within a serial event‐driven scheme and demonstrate how periodic boundary conditions are ensured throughout the representative volume element generation process. The potential of the suggested algorithm will be illustrated through the generation of two different periodic multi‐disperse microstructures. They are based on different given grain size distributions, one for a quartz sand with a low non‐uniformity index and one for concrete aggregates classified as A32 by the German standard norm DIN 1045 to have a rather large variation in grain size. Copyright © 2007 John Wiley & Sons, Ltd.     

Critical length of force chains and shear band thickness in dense granular materials

This paper investigates the existence of the critical force chain length and the buckling of unconfined grain columns in dense granular materials. Tests on assemblies of flat pentagon photoelastic particles were first carried out to demonstrate the maximum length of force chains. Then, the theoretical buckling analysis and distinct element method (DEM) simulations for grain columns composed of mono-sized elliptical particles were performed. The results revealed the existence of critical column length, which is generally affected by the particle shapes, the rotational resistance at particle contact points and the end constraints to the grain columns. The interparticle friction does not have explicit effect on the critical force chain length, but it has significant influence on the grain column’s curvature when collapse takes place. The thickness of shear band in granular soils can be determined as the critical length of grain columns by appropriately imposing the constraints on the boundaries, as confirmed by DEM simulations and experimental results.     

Micromechanical aspects of the shear strength of wet granular soils

This paper presents a micromechanical model for the analysis of wet granular soils at low saturation (below 30%). The discrete element method is employed to model the solid particles. The capillary water is assumed to be in a pendular state and thus exists in the form of liquid bridges at the particle‐to‐particle contacts. The resulting inter‐particle adhesion is accounted for using the toroidal approximation of the bridge. Hydraulic hysteresis is accounted for based on the possible mechanism of the formation and breakage of the liquid bridges during wetting and drying phases. Shear test computational simulations were conducted at different water contents under relatively low net normal stresses. The results of these simulations suggest that capillary‐induced attractive forces and hydraulic hysteresis play an important role in affecting the shear strength of the soil. These attractive forces produce a tensile stress that contributes to the apparent cohesion of the soil and increases its stiffness. During a drying phase, capillary‐induced tensile stresses, and hence shear strength, tend to be larger than those during a wetting phase. The proposed model appears to capture the macroscopic response of wet granular materials and revealed a number of salient micromechanical mechanisms and response patterns consistent with theoretical considerations. Copyright © 2008 John Wiley & Sons, Ltd.     

Simulations of realistic granular soils in oedometer tests using physics engine

Discrete element method (DEM) has become a preeminent numerical tool for investigating the mechanical behavior of granular soils. However, traditional DEM uses sphere clusters to approximate realistic particles, which is computationally demanding when simulating many particles. This paper demonstrates the potential of using a physics engine technique to simulate realistic particles. The physics engines are originally developed for video games for simulating physical and mechanical processes that occur in the real world to produce realistic game experiences. The simulation accuracy and efficiency of physics engines have been significantly improved in the last two decades allowing them to be used as a scientific tool in many disciplines. This paper introduces modeling methodologies of physics engine including realistic particle representation and the contact model. Then, oedometer tests are simulated using realistic particles scanned by X-ray computed tomography (X-ray CT). The simulation results agree well with experimental results. This paper demonstrates that physics engines can output contact parameters for geotechnical analysis and force chains for visualization.     

Numerical modelling of fluid flow in microscopic images of granular materials

A program for the simulation of two‐dimensional (2‐D) fluid flow at the microstructural level of a saturated anisotropic granular medium is presented. The program provides a numerical solution to the complete set of Navier–Stokes equations without a priori assumptions on the viscous or convection components. This is especially suited for the simulation of the flow of fluids with different density and viscosity values and for a wide range of granular material porosity. The analytical solution for fluid flow in a simple microstructure of porous medium is used to verify the computer program. Subsequently, the flow field is computed within microscopic images of granular material that differ in porosity, particle size and particle shape. The computed flow fields are shown to follow certain paths depending on air void size and connectivity. The permeability tensor coefficients are derived from the flow fields, and their values are shown to compare well with laboratory experimental data on glass beads, Ottawa sand and silica sands. The directional distribution of permeability is expressed in a functional form and its anisotropy is quantified. Permeability anisotropy is found to be more pronounced in the silica sand medium that consists of elongated particles. Copyright © 2001 John Wiley & Sons, Ltd.     

Macroscopic and microscopic behaviors of granular materials under proportional strain path: a DEM study

Under the proportional strain loading path, particle assemblies may exhibit various failure modes. Besides the strain localization, the diffuse failure may also occur under certain conditions. The diffuse failure mode corresponds to a homogeneous occurrence of failure with stress states strictly included within the plastic limit condition. This paper emphasizes the influences of the density degree and the rolling resistance under the strain path. A contact model considering rolling friction is adopted in a discrete element method analysis as an approximate means to account for the effects of particle shape. Mechanical responses indicate that loose assemblies without the rolling resistance are more vulnerable to static liquefaction. A sample with a smaller initial void ratio or larger rolling friction coefficient will reinforce the stability of the structure and reduce the likelihood of failure. For microscopic properties, the evolution of coordination numbers, contact forces, force chains and the anisotropies of the assemblies are explored and discussed. Rotational resistance helps increase the shear stress of the granular material, and the microscopic parameters indicate that the assembly has a strong anisotropy and a stable structure to resist the increasing loading.     

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.