Two-dimensional Discrete Element Research Articles

Role of particle shape in sheared granular media: roundness and elongation

Particle shape is an intrinsic characteristic of soil particles that significantly influences mechanical responses. In this investigation, a meticulously calibrated and validated two-dimensional discrete element method (DEM) model of a biaxial shearing test was employed to simulate the shearing response of forty distinct particle shapes. The systematic evolution of particle roundness (R) and aspect ratio (AR) was achieved by utilizing idealized polygonal-shaped particles, aiming to comprehend their effects on the macro and micromechanical behaviors of granular materials. The results suggest that a reduction in R limits free rotations and enhances interlocking, thereby promoting relatively stable force transmission between particles and leading to a monotonic increase in shear strength. However, this effect diminishes as particles become more elongated. Conversely, a decrease in AR from 1.0 (increased elongation) constrains particle rotations, increases the coordination number, and enhances fabric anisotropy initially resulting in increased overall shear strength, reaching a maximum before exhibiting a decreasing trend, indicative of non-monotonic variation. For high elongations, notable fabric anisotropy impedes clear force transmission between particles thus facilitating interparticle sliding and overall strength diminishes. The extent to which AR impacts depends on the angularity feature of particles. Finally, a nonlinear equation has been proposed to predict the variation in critical state shear strength of granular samples, based on the R and AR values of the constituent particles.

Effect of Rate-Dependent Breakage on Strength and Deformation of Granular Sample—A DEM Study

The mechanical response of granular materials is influenced significantly by both the magnitude and strain rate. While traditionally considered rate-independent in the quasi-static regime, granular media can exhibit rate effects in certain instances. This research uses two-dimensional discrete element modelling (DEM) to investigate the rate effects in one-dimensional compression tests by comparing non-crushable with crushable granular samples. This study indicates that micromechanical properties such as particle breakage and contact force distributions are predominant factors in dictating the macroscopic responses of the material. The DEM simulations highlight differences in macroscopic changes between crushable and non-crushable samples, demonstrating a clear correlation between mechanical properties and underlying microstructural features. Notably, the distribution of contact forces varies with strain rates, influencing the degree of particle breakage and, consequently, the overall rate-dependent behaviour. Further, this study explores the impact of post-breakage contact creation and progressive force redistribution, which contributes to observable differences in macroscopic stress under varying loading rates, which is quantified using coordination number, particle velocity, and fabric tensor profiles at two loading rates.

Investigation of a secondary bonded pultrusion composite laminate containing a ply-drop, Part 2: A novel two-dimensional hybrid fracture discrete element for producing debond failure

This is the second of two papers in which a novel numerical method to predict the debond failure of a secondary bonded pultrusion laminate is presented. In Part 1 of this study, experimental work was described which is used here in the development, calibration and validation of the numerical model. The structure investigated in this work may be represented by a bonded composite laminate with external ply-drops (PDs).In this part of the study, a fully coupled mixed mode cohesive zone model is developed which relies upon a traction-separation relation and the virtual crack closure technique to obtain the mode mixity. These are used to develop a hybrid fracture discrete element (HFDE). Fracture toughness tests, as well as tests on PD specimens are used to calibrate the model. Based on these tests, run-arrest fracture criteria are defined. The model is validated by comparing test results for two other PD specimen types to those obtained with the HFDE and finite element analyses.

2D discrete element analysis of the footing above excavated circle in soil

The bearing capacity and settlements of surface foundations located on a soil slope are the important issues that have to be considered by geotechnical engineers for the design. The presence of an underground void beneath the footing can affect the foundation stability and can lead to serious structure damages. In this study, the results of two-dimensional (2D) discrete element (DE) and finite element (FE) analyses of a surface footing on a soil slope above a void are presented. To validate the numerical model results, the DE results obtained have been compared with experimental test presented in the previous study. After validation of the DE numerical model, parametric studies were carried out to evaluate the effect of important factors on the surface footing performance. The studied parameters include the horizontal spacing of the void axis relative to the slope edge (SH), the vertical spacing of the void crown relative to the footing base (SV), the horizontal spacing of the footing edge relative to the slope edge (De) and the void diameter (Dv). The effects of these parameters on the pressure-settlement curves and the contact force distributions in the soil slope are presented and discussed. The results showed that the footing bearing pressure increases with an increase of SH, SV and De but decreases when Dv increases. The behavior of a surface footing on a soil slope above a void significantly depends on the SV value.

A spherical source distribution method for calculating acoustic radiation of elastic underwater structures

In this paper, a spherical source distribution method is established, and two kinds of spherical sound sources of symmetric and antisymmetric, distributed on a line inside the structure are proposed, in order to realize the vibro-acoustic calculation of three-dimensional elastic underwater structure. The spherical source distribution method has strong applicability and is suitable for the case where the shape of the structure is not axisymmetric. This method is a new method, and its fundamental formula is similar to the traditional acoustic boundary integral method, but it also has obvious differences. In numerical calculation, the traditional boundary element method is to divide the surface elements on the wet surface of the object, and transform the three-dimensional acoustic problem into the two-dimensional discrete element problem to solve. However, the spherical source distribution method, whose source points are only distributed on a straight line inside the object, transforms the three-dimensional acoustic problem into the quasi-one-dimensional discrete element problem, which makes the complexity and computation amount of the whole programming significantly reduced. In this paper, the fundamental principle of the spherical source distribution method, the calculation formula and the verification results of several numerical examples are discussed.

A fully coupled micro-hydromechanical (micro-HM) model for partially saturated soils based on DEM

A fully coupled micro-hydromechanical (micro-HM) model is developed for partially saturated soils in this study by integrating two-dimensional pore morphology (PM) approach and discrete element method (DEM). In the proposed model, the PM approach is employed to predict the tentative water distribution. The porous media marching cubes (PMMC) algorithm is adopted to evaluate the interphase interfaces and to further calculate the capillary forces. The combined effects of interparticle contact forces and the capillary forces on the motion of particles are handled by DEM. The developed model was then employed to conduct a series of numerical biaxial shear tests on a partially saturated soil with real particle shapes. The typical macroscopic responses such as stress–strain relationship, volume change, and saturation change can be well simulated by the micro-HM model. Based on the micro-HM model, a novel equation is proposed to directly evaluate the effective stress from the pore water distribution. The effective stress parameter and the suction contribution to effective stress calculated by the new equation well matches the experimental data, thus confirming the validity of the micro-HM model and the new equation of effective stress. The microscopic responses are then revealed and discussed through the proposed model.

Exploring the combined effect of particle shape and friction on cell structures in granular packings via LS-DEM modeling

To comprehensively understand and predict the macroscopic behavior of a granular system, one must consider not only the properties of individual particles but also the local structures. In this study, we prepare mechanically stable granular packings of super disks using the two-dimensional level set discrete element method (LS-DEM). We identify the cells, the irreducible loops enclosed by contacting particles, in the prepared granular packings and then analyze the statistics of these structures. We find the following. (1) The packing fraction or mean coordination number of studied systems exhibits a non-trivial dependency on particle shapes and inter-particle frictions, making it challenging to establish a direct correlation between them. (2) Using the cell-based description as a bridge, we can measure the packing behavior without considering the influence of particle shape and inter-particle friction. Specifically, the mean coordination number can be explicitly represented as a function of the mean cell order according to Euler’s topological relation. Upon the assumption that all cells are regular polygons, we can also approximately estimate the rattlers-free packing fraction via the mean cell order. (3) We have observed a nearly linear relationship between the mean cell order and rattler fraction. This enables us to determine the packing fraction as well.

Effects of slope topography on rock avalanche mobility and deposition: A 2-D discrete element method investigation

The impact of rock avalanches is a major concern in mountain areas. However, fundamental understanding and reliable prediction of the depositional area of rock avalanches remains inadequate. Here, an idealized numerical study of granular materials flowing down a slope is carried out using two-dimensional (2-D) discrete element method simulations. The effects of the slope geometry on the mobility and deposit morphology of the granular flow are studied in detail. It is found that the granular flow mobility increases with the curvature radius of the circular ramp, leading to a longer runout distance, which is explained from the viewpoint of energy transfer and dissipation. The results are expected to enhance understanding of the travel and deposition mechanisms of rock avalanches and other related geophysical flows.

Quantification of the crack propagation and global failure mechanism of single- and multi-ring masonry arch bridges

This paper presents the development of a novel crack-based damage quantification method to assess the damage accumulation in masonry arch bridges subjected to externally applied loading. Initially, a damage index was proposed, considering the initiation and extension of tensile and sliding cracks. Then, the proposed damage indexing was adopted into a two-dimensional discrete element code of analysis to evaluate single and multi-ring masonry arch bridges. The numerical model was validated by comparing the computational outputs against the experimental results obtained from the literature. Following the validation, masonry arch bridge models were developed, featuring the four most representative bond configurations in arch barrels. Also, different bond properties were assigned to investigate their impact on the global failure characteristics of single- and multi-ring masonry arch bridges. From the analyses of results of the multi-ring masonry arch bridges investigated in this study, it was shown that the rapid growth of tensile cracks in radial joints and the occurrence of shear slippage in circumferential joints between adjacent rings were observed to be early signs for multi-ring bridges before the ultimate load reached. By analysing the correlation between the normalised damage index with the normalised load, damage accumulation in different masonry arch bridges were identified. This study offers a novel perspective on quantitively evaluating the damage accumulation and failure mechanism of masonry arch bridges and the findings may provide valuable insights into the assessment and management of existing masonry arch bridges.

Assessment of shear band evolution using discrete element modelling

PurposeThe objective of this paper is to quantitatively assess shear band evolution by using two-dimensional discrete element method (DEM).Design/methodology/approachThe DEM model was first calibrated by retrospectively modelling existing triaxial tests. A series of DEM analyses was then conducted with the focus on the particle rotation during loading. An approach based on particle rotation was developed to precisely identify the shear band region from the surrounding. In this approach, a threshold rotation angle ω0 was defined to distinguish the potential particles inside and outside the shear band and an index g(ω0) was introduced to assess the discrepancy between the rotation response inside and outside shear band. The most distinct shear band region can be determined by the ω0 corresponding to the peak g(ω0). By using the proposed approach, the shear band development of two computational cases with different typical localised failure patterns were successfully examined by quantitatively measuring the inclination angle and thickness of shear band, as well as the microscopic quantities.FindingsThe results show that the shear band formation is stress-dependent, transiting from conjugated double shear bands to single shear band with confining stress increasing. The shear band evolution of two typical localised failure modes exhibits opposite trends with increasing strain level, both in inclination angle and thickness. Shear band featured a larger volumetric dilatancy and a lower coordination number than the surrounding. The shear band also significantly disturbs the induced anisotropy of soil.Originality/valueThis paper proposed an approach to quantitatively assess shear band evolution based on the result of two-dimensional DEM modelling.

Study on generation and evolution of base voids in heavy-haul railway tunnels using particle flow method

Most existing freight railway tunnels have experienced basement cracking, damage, and even mud-pumping after a certain period of operation. For heavy-haul railway tunnels with high traffic densities, large capacities, and large axle loads, this situation will be more serious. This paper establishes a simplified model of a single-track heavy-haul railway tunnel using the two-dimensional particle discrete element method. The meso-evolution process of the concrete structure and surrounding rock void at the bottom of the tunnel is studied in the later stages of repeated loading by heavy-haul trains. The difference in the base void between waterless and water-saturated bases is compared. The cracks in the surrounding rock are first generated at the lowest position of the invert center, and run from the middle to the sides and from the top to the bottom. The terminal cracks return to the free surface, exhibiting a parabolic shape that opens upward. There are more cracks in the middle and fewer at the sides. The asynchronous deformation of the surrounding rock and the inverted arch is positively correlated with the number of cracks. The voiding process under water-saturated conditions is similar to that without water, but the depth and width over which the rock mass is crushed and the range of voiding increase exponentially in the water-saturated case, and the void appears earlier. It is anticipated that these research results will contribute to the structural design and operational safety of heavy-haul railway tunnels.

Discrete element modelling of the size-dependent mechanical behavior of Al2O3 ceramic under quasi-static uniaxial compression

The size-dependent mechanical behavior of Al2O3 ceramic under quasit-static uniaxial compression was simulated via two-dimensional discrete element method. The numerical sample of Al2O3 ceramic was established by adopting the linear parallel bond contact model, and the inherent defects was further generated by randomly removing a subset of elementary discs. The uniaxial compressive strength of Al2O3 ceramic samples with different sizes follows the Weibull distribution. With an increase in sample size, the magnitude of the uniaxial compressive strength decreases, while its variability increases. Additionally, with sample size increases, both the Young's modulus and Poisson's ratio decrease. Meanwhile, the variability in Young's modulus and Poisson's ratio is more pronounced in larger samples than in smaller ones. The progressive fracture process of Al2O3 ceramic sample can be categorized into four typical stages, namely linear-elastic stage, crack initiation stage, crack propagation stage and complete failure stage. The final fragment size distributions of Al2O3 ceramic samples of different sizes can be accurately described by the fractal model. Notably, smaller samples tend to exhibit a greater breakage extent compared to larger samples. Finally, a size-dependent statistical equation of uniaxial compressive strength of Al2O3 ceramic is proposed based on the numerical results and the inverse function of the Weibull distribution, which can provide a theoretical basis for the design and production of ceramic materials.

Novel hard rock breaking technique using ultra-high-frequency particle impact induced by ultrasonic vibration field

With the gradual increase in drilling and mining depth in geothermal, oil, and other fossil energy explorations, complex geological environments (especially hard strata) have forced researchers to develop high-efficiency rock-breaking techniques. Inspired by the dynamic impact theory and the particle jet technique, an ultrasonic vibration field-induced ultra-high-frequency particle impact rock-breaking (UPIRB) technique was proposed to solve these problems. After being subjected to ultrasonic vibration, the small-sized particles generate ultra-high frequency and high impact stress on the rock sample, which can significantly promote rock degradation and improve rock-breaking efficiency. A comparative study between UPIRB and traditional ultrasonic vibration rock-breaking (UVRB) techniques in terms of rock-breaking efficiency was conducted using a series of physical experiments and two-dimensional discrete element numerical simulations. The results showed that owing to the small contact area due to small size particles, UPIRB has incomparable advantages compared with traditional UVRB: its impact stress level is improved by more than ten times, the rock-breaking time is shortened from minutes (2–3 min) to seconds (2–4 s), and the rock-breaking efficiency is improved nearly ten-fold, overcoming the disadvantages of UVRB. This study proposed a novel and efficient rock-breaking technique for energy exploration engineering.

Micro-damage characteristics of cold recycled mixture under freeze–thaw cycles based on discrete-element modeling

Cold recycled mixture with bitumen emulsion (CRME) is an energy-saving and environmentally friendly material. However, the micro-scale damage characteristics under the coupling of water temperature are still unknown and need to be investigated. In this paper, based on the X-ray CT section, the two-dimensional discrete element method (DEM) was used to precise reconstruct the CRME under different freeze–thaw (F-T) cycles. Simultaneously, the fracture behavior, strength, and structural damage characteristics of CRME under F-T cycles were studied by DEM and digital image correlation technology. The results show that F-T cycle significantly damage the formation of strength force chain in CRME. After undergoing 20F-T cycles, the specimen exhibited tensile failure without any obvious crack penetration. The cracks required of the specimen after the F-T cycles to reach the peak load were less than the non-F-T. The stress–strain concentrations were reinforced, making the specimen more susceptible to unloading during the later stages of testing after F-T cycles. The repeated F-T cycles damaged the overall microstructure of the mixture, resulting in less noticeable tensile effects during the splitting test. Utilizing a precise DEM modeling method proved to be practical and effective in investigating the micro-damage characteristics of cold recycled mixture.

Optimal design in bionic wear-resistant structures by multiscale DEM simulation

To address the problems of long optimization times of bionic wear-resistant structures in discrete element simulation. We established two-dimensional homoscale discrete element simulation models for four biomimetic structures, along with their respective abrasive wear computational models. We then deliberated upon their wear behavior in relation to the structural morphology, contact constraints, contact force, and wear volume during the wear process. The study found that the shedding of brittle wear body surface abrasives had little effect on the substrate of the bionic structure. Based on the above findings, a multi-scale/cross-level study of the interaction between biological wear surface structure and abrasive was conducted. The findings evince that utilization of a multi-scale computational model ensures the precise examination of the mechanical response of a material to external forces, while also economizing computational time. Finally, the design of the conical bionic structure is optimized based on the multi-scale/cross-level computational model. The results show that the conical bionic structure has good wear resistance when the abrasive grain size is small and when the monomer spacing is not larger than the monomer width. The bionic structure/abrasive interaction multi-scale numerical simulation system established in this paper reduces the complexity of dynamic numerical simulation of wear behavior on the surface of wear- resistant organisms, improves the calculation efficiency, and provides an important research means and method for optimizing the design of bionic wear-resistant parts.

Cdem: A macOS program for discrete element modeling of tectonic structures

Abstract cdem is a macOS document-based application for two-dimensional discrete element modeling of tectonic structures and their associated deformation. Documents encapsulate simulations that can be run and explored simultaneously. A document contains three main views: (1) Set-up view, to define the assembly size, element properties, anisotropy, boundary conditions (type of faulting), overburden stress, erosion, and syn-tectonic sedimentation; (2) Summary view, which displays the details of the model after initialization; and (3) Results view, which displays the geometry of the model while it is running or after the run and allows exploring the model’s evolution in terms of geometry, displacement, strain, or stress. We illustrate the use of the program for assembly calibration and the modeling of contractional and extensional structures without and with syn-tectonic sedimentation. In all these cases, cdem produces realistic incremental and finite deformation. cdem is less powerful than its precursor cdem2D, but it can import and visualize cdem2D results, making the combined use of these two programs a robust suite for mechanically modeling tectonic structures.

DEM study on the effect of particle shape on the shear behaviour of granular materials

This study investigates the effects of particle convexity, sphericity and aspect ratio (AR) on the behaviour of sheared granular materials using two-dimensional discrete element method simulations. Isotropic, dense and loose assemblies with different particle shapes were prepared and subjected to drained shearing via biaxial compression until the critical state was reached. Macroscopic characteristics such as strength and dilatancy are presented. The factors underlying the macroscopic behaviour are then investigated by considering the coordination number, fabric anisotropy, particle moment, friction mobilisation at contacts and particle rotation. For the range of shapes considered here, the data indicate that the shear strength decreases as particle convexity and sphericity increases while the shear strength increases with increasing AR. The shear strength and convexity are weakly correlated, however a stronger correlation is observed between AR and strength. The volumetric strain at large strains tends to increase with increasing AR. There is a stronger correlation between the critical state strength and both the critical state coordination number and the critical state mechanical void ratio than there is between the critical state void ratio and the critical state strength. The contact fabric anisotropy, the magnitude of the moment transmitted by particles and the friction mobilised at the contacts are important factors underlying strength. The critical state strength increases as both the mean particle moment and the mean mobilised friction increased. Analysis of particle rotation provides insights into the response of the granular materials to shearing.

Study of Strain-rate Effect in Two-dimensional Biaxial Test on Granular Material using Discrete Element Method

Numerical study to investigate the effect of various strain rates on global friction angle in the sand has been performed. Granular material behavior is influenced by several factors, among others: pack configuration, grain macro and micro roughness, confinement pressure, loading rate, etc. Sand is a granular material composed of discrete particles that the most refined microscopic techniques are needed to study its mechanical properties. In Indonesia, research related to the Discrete Element Method is still very limited. The two-dimensional discrete element method is capable to calculate the motion and interparticle contacts of large number of small particles, and each particle is modeled as a rigid circular element. The study started with the validation of the DEM model using YADE. Particles with a local friction angle of 35° are arranged in a closed rectangular box (frictionless wall). The number of particles used in this model validation simulation is 1000 sphere-type particles with monodisperse particle gradations. The simulation was done by a drained biaxial test with confinement stress of 100 kPa, thereafter varying strain rate are applied. Based on the deviatoric stress–axial strain curve from YADE, the result can be depicted on the Mohr circle to obtain the value of the global friction angle. It is found that the different value of strain rate affects its global friction angle. Increasing the value of the strain rate can increase the material global friction angle, which increases the strain rate from 1% to 5%, 10%, 25%, and 50% will increase its global friction angle by 5%, 5%, 14%, and 18%, respectively.

Shield Attitude Adjustment Induced by Slurry Pressure Balance (SPB) Shield Tunneling Considering the Effects of Overbreak Cutter: A Numerical Simulation by DEM and Engineering Application

Based on a cross-river tunnel of Wuhan Metro Line 8, we present a two-dimensional discrete element model for shield attitude adjustment considering the effect of overbreak cutters. The shield shell mechanics under the influence of over-excavation rate, over-excavation orientations, and overburden load are simulated, and the tunneling mechanics law and the ultimate range during the adjustment of the shield attitude are investigated. The simulation results indicate the following: (1) The greater the over-excavation rate, the smaller the force exerted by the soil layer in the negative direction of the shield movement; therefore, increasing the over-excavation rate is helpful in expanding the range of shield attitude adjustment. (2) The shield is stressed symmetrically while conducting positive and negative horizontal adjustments in the soil layer, which has a symmetrical distribution, but vertical upward adjustment is more difficult than vertical downward adjustment. (3) With the increase in overburden load, the space of the shield attitude adjustment is gradually reduced at the same over-excavation rate. A good engineering application was achieved in this project using the simulation model. It is recommended to use the attitude adjustment method by controlling the tunneling parameters. In difficult situations such as high overlying loads, the over-excavation cutter can be used to assist in adjusting the shield attitude.

Understanding of penetrating resistance on an inclined plate to cohesive soil using two-dimensional discrete element method

In order to know the effect of varied grousers on the reaction of soil, the reaction of soil by a plate at different angles of inclination using the two-dimensional discrete element method (DEM) has been investigated. Either the simulation or the experiment, a flat iron plate with 5 × 77 × 100 (mm) was used, and the inclination angle between the plate and the soil surface ranged from 0 to 60 degrees with 15-degree intervals. According to the result, the cohesive soil model introduced in the 2D DEM could successfully replicate the experimental results considering the effects of different inclination angles of the plate and the values of the root mean square error between the simulation and the experiment were found as 6.62, 36.60, 58.63, 60.84, and 66.25 N for inclination angles from 0 to 60 degrees in the horizontal direction. Moreover, the RMSE values of 127.91, 216.06, 75.88, 110.40, and 25.49 N were obtained for the vertical direction. Overall, a minimal discrepancy was observed between the results of DEM simulation and those of experiments in the vertical component of reaction force when the inclination angle of the plate was increased.