2D Discrete Element Method Simulations Research Articles

Simulation of the deformable lateral boundaries in biaxial test using DEM

Applying the discrete element method (DEM) in soil mechanics can provide abundant information at the particle-scale and facilitates illustration of the macro-mechanical behaviour of soils based on the inter-particle mechanisms. The triaxial test is one of the most common laboratory methods to study the macro-mechanical behaviour of particulate materials such as soil. However, many problems in geotechnical design can be assumed and simplified as a plane strain phenomenon. Therefore a biaxial test can be conducted to reproduce the macro-mechanical behaviour of soil, where the sample is enclosed by two horizontal rigid platens and a vertical latex membrane, which is a deformable continuous element and allows the enclosed specimen to deform freely while maintaining confining stress during loading. This paper presents an algorithm to represent physical and mechanical characteristics of latex membrane in the 2D DEM simulation of biaxial test using the PFC2D code. To investigate the impact of the lateral boundary conditions on the micro-macro mechanical behaviours of soil samples, two sets of DEM biaxial tests are conducted, i.e. with rigid and deformable lateral boundary conditions. The DEM modeling results indicate that the lateral boundary conditions have a significant effect on the micro-scale fabric properties, thickness and inclination of the shear band. The comparison between these two simulations also demonstrates that the lateral boundary conditions play a major role in the peak and post-peak stress-strain behaviours as well as the dilation and critical state behaviours of granular soils.

Investigation of Volumetric Block Proportion (VBP) Effect on Excavation-Induced Ground Response of Talus-like Rock Mass Based on DEM Simulations.

Due to the complexity of the talus-like rock mass with different values of volumetric block proportion (VPB), it is thus crucial to explore the VBP effect on the excavation-induced ground responses. We conduct a series of 2D DEM (discrete element method) simulations on a common circular tunnel excavation in the talus-like rock mass with different VBPs (0%, 15%, 50%, 85% and 100%). For each VBP, two support scenarios, i.e., unsupported and supported by a rigid lining, are considered. The micro characteristics of the excavation-induced ground responses, including the contact force, force chain, coordination number and shear-slip contact, and the stress distribution and ground settlement are elaborated in detail. Accordingly, three types of talus-like rock masses are identified as soil-, hybrid- and rock-types, corresponding to VBP = 0-15%, 50%, and 85-100%, respectively. It is found that the lining support is essential for maintaining the ground stability of a tunnel excavation in the soil- and hybrid-type talus-like rock masses while the backbones formed by rock blocks in the rock-type talus-like rock mass can provide a certain support for the surrounding ground. Our findings have important implications for optimizing the construction scheme of tunnel excavation in different types of talus-like rock masses.

Role of Particle Shape on Ground Responses to a Circular Tunnel Excavation in Sandy Soil: Consequences from DEM Simulations.

Due to the sensitivity of sandy soil’s mechanical behavior to the particle shape, it is thus of importance for interpreting the effect of particle shape on the ground response induced by tunnel excavation in sandy formations. We conducted a series of 2D DEM (discrete element method) simulations on a common circular tunnel excavation in sandy soil with variable-shaped particles, which are characterized as two descriptors, i.e., aspect ratio (AR) and convexity (C). The macroscopic responses and the microscopic characteristics of the sandy ground are elaborated in detail. The simulation results show obvious asymmetrical features of the excavated ground, which results from the ground heterogeneity caused by the irregular particle shape. In addition, we investigate the roles of AR and C on the ground response and find that reducing AR or increasing C will enlarge the ground settlement, i.e., the sandy ground deformation is more sensitive to the particles with more irregular shapes. However, elongated particles are beneficial for the generation of soil arching with stronger bearing capacity and thus reduce the soil pressure on the tunnel lining. Our findings have important implications for the safety assessment of the tunnel excavation, as well as other underground structure construction in sandy formations.

Loading rate dependence of granular cushion under rockfall impact and proposal of an analytical model for impact force estimation

The cushioning behaviour of granular materials, such as sand and gravel, has been studied for the rational design and performance evaluation of a rock shed intended for rockfall protection. The shape of the collision surface of a falling mass strongly affects the impact force waveform of the falling mass. However, the control factors for generating impact force waveform have not been fully clarified. Previous studies have shown that the maximum transmitted impact force acting on the top plate of a rock shed through a cushioning material depends not only on the maximum impact force acting on the falling mass but also on its duration. To accurately predict the maximum transmitted impact force acting on a structure, understanding the generation mechanism of the impact force waveform acting on the falling mass is necessary. These control factors were investigated through the two-dimensional (2D) discrete element method (DEM) analysis. It was shown that the mean principal stress of particles around a falling mass increased with the loading velocity of the falling mass. Based on this result, an analytical model for estimation the impact force waveform of the falling mass was proposed. The validity of the proposed method and the control factors estimated via simulations was confirmed by comparing the results obtained by the proposed method with 2D DEM simulation results and experimental results. This study contributes to the elucidation of the deformation mechanism of soil under high-speed loading and development of rational countermeasures considering the deformation behaviour of a sand cushion.

Modelling the tribocharging process in 2D and 3D

Many discrete element method (DEM) tribocharging models presented in the literature rely on ill-defined or poorly quantified charging parameters. This work presents a straightforward experimental method to quantify key parameters, namely the charge transfer limit, Γ, and the charging efficiency, κc. These parameters are then used in both 2D and 3D DEM simulations to evaluate the applicability of faster 2D models to tribocharge modelling. Both the 2D and 3D models are found to perform well against the experimental data for single-contact and single-particle, multi-contact systems. However, the 2D model fails to produce good agreement with experimental data for multi-contact, multi-particle systems. This approach for determining experimentally the parameters for the DEM tribocharging model is found to be effective and produces good agreement between simulated and experimental data. This method will improve and simplify the DEM modelling of triboelectric charging in dry material handling processes.

Efficient flexible boundary algorithms for DEM simulations of biaxial and triaxial tests

The accurate modeling of boundary conditions is important in simulations of the discrete element method (DEM) and can affect the numerical results significantly. In conventional triaxial compression (CTC) tests, the specimens are wrapped by flexible membranes allowing to deform freely. To accurately model the boundary conditions of CTC, new flexible boundary algorithms for 2D and 3D DEM simulations are proposed. The new algorithms are computationally efficient and easy to implement. Moreover, both horizontal and vertical component of confining pressure are considered in the 2D and 3D algorithms, which can ensure that the directions of confining pressure are always perpendicular to the specimen surfaces. Furthermore, the boundaries are continuous and closed in the new algorithms, which can prevent the escape of particles from the specimens. The effectiveness of the proposed algorithms is validated by biaxial and triaxial simulations of granular materials. The results show that the algorithms allow the boundaries to deform non-uniformly on the premise of maintaining high control accuracy of confining pressure. Meanwhile, the influences of different lateral boundary conditions on the numerical results are discussed. It is indicated that the flexible boundary is more appropriate for the models with large strain or significant localization than rigid boundary.

Modeling and estimation of hole-type flaws on cracking mechanism of SiC ceramics under uniaxial compression: A 2D DEM simulation

Ceramic materials usually contain a large number of hole-type flaws or defects with different characteristics. These flaws are closely related to the fracture failure of materials. Based on the discrete-element method (DEM), three different hole-type flaws were constructed by the super-ellipse equation for SiC ceramics in 2 dimensions. The relationship between the flaw with different characteristics and the failure of SiC ceramic specimens was studied. Further, the crack evolution and the two important parameters (distance from the tip of flaw d and the initiation angle α) to describe the crack initiation position were investigated. Lastly, the stress fields around the hole-type flaw were analyzed. The results show that with the increase of inclination angle of the flaws, the crack initiation position moves from the center position to the flaw tips and the crack initiation angle α increases. Moreover, when the aspect ratio is large and the inclination angle is small, the maximal-tensile stress region around the hole-type flaw is large. Moreover, as the inclination angle increases, the maximal-tensile-stress region moves clockwise around flaws. Finally, the critical dimension of the hole-type flaw affecting the material strength is discussed.

Strength anisotropy of granular material consisting of perfectly round particles

AbstractThe strength anisotropy of granular materials deposited under gravity has mostly been attributed to elongated particles' tendency to align long axes along the bedding plane direction. However, recent experiments on near‐spherical glass beads, for which preferred particle alignment is inapplicable, have exhibited surprisingly strong strength anisotropy. This study tests the hypothesis that certain amount of fabric anisotropy caused by the anisotropic stress during deposition under gravity can be locked in a circular‐particle deposit. Such locked‐in fabric anisotropy can withstand isotropic consolidation and leads to significant strength anisotropy. 2D discrete element method simulations of direct shear tests on circular‐particle deposits are conducted in this study, allowing for the monitoring of both stress and fabric. Simulations on both monodispersed and polydispersed circular‐particle samples generated under downward gravitational acceleration exhibit clear anisotropy in shear strength, thereby proving the hypothesis. When using contact normal‐based and void‐based fabric tensors to quantify fabric anisotropy in the material, we find that the intensity of anisotropy is discernible but low prior to shearing and is dependent on the consolidation process and the dispersity of the sample. The fact that samples with very low anisotropy intensity measurements still exhibit fairly strong strength anisotropy suggests that current typical contact normal‐based and void‐based second‐order fabric tensor formulations may not be very effective in reflecting the anisotropic peak shear strength of granular materials. Copyright © 2017 John Wiley & Sons, Ltd.

Effects of particle shapes to achieve angle of repose and force displacement behaviour on granular assembly

Circular or spherical particles in Discrete Element Method (DEM) possess limitations on achieving desired angle of repose for some granular assemblies. However, by using various shapes/clumps of particles, the limitation posed by the circular or spherical particles on achieving angle of repose can be minimized. In this paper, 2D DEM simulation has been used to investigate the effect of particle shapes on (a) angle of repose, where the aim is to achieve the angle of repose of 35° observed in a laboratory scale sand pile experiment, and (b) force displacement behaviour of granular assembly. The simulated results show that the particle shapes have strong influence on the angle of repose but have a less effect on force displacement behaviour on the granular assembly.

Effect of Loading Rate on Sand Pile Failure: 2D DEM Simulation

Discrete element method (DEM) is a widely used simulation tool to model physical behaviour of granular materials. In this study 2D DEM simulation has been used to simulate the failure of a sand pile loaded at the crest. The model has been calibrated and validated using experimental force-displacement behaviour, angle of repose and particle velocity profile. The effects of numerical loading rates on simulation results have been investigated. The calibrated DEM model showed that the selection of loading rate is crucial in simulating particle assembly behaviour. In the quasi-static state a small change in loading rate does not change the force-displacement behaviour of the model. However, the system becomes unstable and force-displacement behaviour of the granular assembly diverges from the quasi-static state when the loading rate is higher than the quasi-static loading rate.

포천화강암의 결에 따른 간접인장강도 특성에 대한 실험 및 개별요소 수치해석

본 연구는 화강암에 존재하는 결 이방성이 간접인장강도에 미치는 영향을 평가하였다. 표준 간접인장시험 및 3개의 서로다른 중공 크기에 대한 중공 간접인장시험을 수행하였다. 2차원 개별요소 수치해석을 통해 간접인장시험에서의 파괴 과정 및 메커니즘을 고찰하였다. 간접인장강도는 화강암의 결에 따라 하드웨이, 그레인, 리프트 면의 순으로 감소하였다. 중공 간접인장강도는 일반 간접인장강도에 비해 2.5~6.4배 정도 크게 나타났으며, 중공 크기가 클수록 크게 나타났다. 중공 시편에 대한 간접인장 파괴 유형은 중공 크기 및 결과 하중방향 각도에 영향을 받는 것으로 나타났다. The purpose of this study is to investigate the influence of cleavages on indirect tensile strength (ITS) of the granite. Brazilian disc tests and ring tests with three different hole sizes were performed. 2D DEM (Discrete Element Method) simulation was employed to further understand the failure process during the tests and the mechanism behind. Results show that ITS decreases across hardway, grain and rift cleavage. Measured average ITS from ring tests is about 2.5 ~ 6.4 times of those measured from Brazilian disc tests, and it decreases with increasing ratio of diameters of inner hole and specimen. Failure pattern in ring tests is influenced by both hole size and relative positions of cleavages parallel and perpendicular to the loading direction.

Evolution of soil arching; 2D DEM simulations

A series of model tests were performed using a 2D multiple trapdoor system, similar to a 2D unreinforced piled embankment. Three soil arching evolution patterns were observed in the tests: the triangular expanding pattern, the tower-shaped evolution pattern, and the equal settlement pattern. The model tests were simulated using the discrete element method (DEM), and the micromechanical parameters were calibrated using the stress–strain curves from plane strain compression tests. Noncircular particle clumps were adopted to achieve a high frictional behavior of the sand. The calculated deformation and stress distribution well-matched the results of the model tests. The three evolution patterns were observed in the DEM simulations, and additional calculations were performed to specify the application conditions. The DEM simulations showed that the contact forces between the particles formed a strong force chain network enveloping the triangular and tower-shaped deformation regions. Another, much weaker, force chain within the deformation region supported the strong force chain outside.

Quantifying void fabric using a scan-line approach

The internal topology or fabric of granular materials including soil is known to influence their mechanical behaviour. Discrete element method (DEM) simulations, physical experiments using photo-elastic materials or Schneebli rods, and high resolution computed tomography scans can all give detailed particle-scale information for these materials. Data from these simulations and experiments can then be used to develop quantitative measures of the soil fabric. Considering DEM simulations in particular these measures of fabric have focussed on the particle and contact orientations; quantitative analysis of the topology of the void space is less common. This paper revisits a method for quantifying void fabric that was proposed by Oda et al. (1985) [1]. An approach for applying this method to 2D digital images of particle systems is outlined. The algorithm is then applied to analyse the results of a 2D DEM simulation of a biaxial compression test in which two complementary shear bands develop. This application highlights the viability of using digital image analysis to interpret DEM simulation data. The void anisotropy induced during shearing is significantly more pronounced in the shear bands. There is a clear link between the volumetric strain and the anisotropy, showing that the voids are becoming both larger and more elongated during shearing.

State of the art modeling of soil–tillage interaction using discrete element method

Soil–tillage interaction presents a continuous challenge for researchers, developers and manufacturers. However, modeling soil–tillage interaction is a complex process due to the following: the spatial variability of the soil media; the nonlinearity of soil material; and the contact phenomenon and flow that occur at the interface zone between the soil and the tillage tool. The need for a sound modeling technique for soil–tillage interaction is the motivation for the present work. The discrete element method (DEM) seems to be a promising approach for constructing a high-fidelity model to describe the soil–tillage interaction and may serve as a predictive simulation tool in the process of designing the tillage shape. The paper will explain, in general, the method and provide comprehensive state of the art studies of soil–tillage interaction based on 2D and 3D DEM simulations. The limitations and advantages of the method are demonstrated. The potential of the DEM to serve as an engineering tool for an optimization of soil–tillage interaction is presented by several case studies. Finally, future considerations and recommendations of improving the use of the DEM techniques are presented.

Multiscale investigation of shear bands in sand: Physical and numerical experiments

AbstractIn many geotechnical systems, it is not uncommon to observe failure in zones of high localized strain called shear bands. The existing models predict the existence and the extent of these localizations, but provide little insight into the micromechanics within the shear bands. This research captures and compares the variation in microstructure both inside and outside of shear bands that formed in physical laboratory plane strain and companion numerical two‐dimensional discrete element method (DEM) biaxial compression experiments. Unsheared and sheared laboratory specimens of Ottawa 20–30 sand of varying dilatancy were solidified using a two‐stage resin impregnation procedure. The solidified specimens were sectioned and the resulting surfaces were prepared for microstructure observation using optical bright‐field microscopy and stereological analysis. Statistical properties of microstructural parameters for sub‐regions in a grid pattern and along predefined inclined zones were determined. Similar measurements were performed on 2D DEM simulation specimens at varying strain levels to characterize the evolution of microstructure with increasing strain. The results showed how differences evolved in the mean, standard deviation, and entropy of void distributions with increasing global strain levels. The results indicate how disorder increases and that the material within the shear band does not adhere to the classical concept of critical state, but reaches a terminal void ratio that is largely a function of initial void ratio. Furthermore, there appears to be a transition zone between the far field and the fully formed shear block, as opposed to an abrupt delineation as is traditionally inferred. Copyright © 2010 John Wiley & Sons, Ltd.

An efficient method for packing polygonal domains with disks for 2D discrete element simulation

The discrete element method (DEM) is frequently used in numerical simulation of the behaviour of discontinuum often encountered in granular flow, soil or rock mechanics or powder compaction. The DEM requires an assemblage of elements that need to fill the domain geometry. Generation of such arrangement of elements, such as disks in 2D DEM simulation is not a trivial task. The available methods to create the arrangements of disks can either take considerable time, have limited control over the final outcome of the disk generation or exhibit difficulty in generating a tight arrangement of disk with varying radii. This paper presents an algorithm employing principles of computational geometry to efficiently generate a tight packing of disks while addressing the common problems of disk generation. The algorithm’s performance is linear with respect to time and scales well. As a demonstration of the algorithm’s capabilities, a DEM model of an ore pass is presented.

Effective simulation of flexible lateral boundaries in two- and three-dimensional DEM simulations

Discrete element method (DEM) models to simulate laboratory element tests play an important role in advancing our understanding of the mechanics of granular material response, including bonded or cemented, particulate materials. Comparisons of the macro-scale response observed in a real physical test and a “virtual” DEM-simulated test can calibrate or validate DEM models. The detailed, particle scale information provided in the DEM simulation can then be used to develop our understanding of the material behaviour. It is important to accurately model the physical test boundary conditions in these DEM simulations. This paper specifically considers triaxial tests as these tests are commonly used in soil mechanics. In a triaxial test, the test specimen of granular material is enclosed within a flexible latex membrane that allows the material to deform freely during testing, while maintaining a specified stress condition. Triaxial tests can only be realistically simulated in 3D DEM codes, however analogue, 2D, biaxial DEM simulations are also often considered as it is easier to visualize particle interactions in two dimensions. This paper describes algorithms to simulate the lateral boundary conditions imposed by the latex membrane used in physical triaxial tests in both 2D and 3D DEM simulations. The importance of carefully considering the lateral boundary conditions in DEM simulations is illustrated by considering a 2D biaxial test on a specimen of frictional unbonded disks and a 3D triaxial test on a bonded (cemented) specimen of spheres. The comparisons indicate that the lateral boundary conditions have a more significant influence on the local, particle-scale response in comparison with the overall macro-scale observations.