Three-dimensional Discrete Element Method Research Articles

Micromechanical Modeling of Cement-Treated Base Materials Considering Recycled Crushed Aggregate Morphology from Construction and Demolition Waste Using Three-Dimensional Discrete Element Method

Micromechanical Modeling of Cement-Treated Base Materials Considering Recycled Crushed Aggregate Morphology from Construction and Demolition Waste Using Three-Dimensional Discrete Element Method

Experimental and numerical study on the dynamic mode III fracture behaviors of rock using an axially notched flattened Brazilian disc in SHPB tests

The dynamic mode I and mode II fracture of rock have been widely investigated over the past decades. However, the lack of dynamic mode III fracture testing method and the rare understanding of mode III fracture mechanism of rock remain a significant knowledge gap in the realm of rock mechanics. In this work, an innovative axially notched flattened Brazilian disc (ANFBD) sample is proposed for the mode III fracture tests of rocks using the split Hopkinson pressure bar (SHPB). Firstly, the optimal geometrical dimension of the ANFBD sample for achieving true mode III fracture of rocks is comprehensively discussed using finite element method (FEM) analysis. Then, the reliability of ANFBD-SHPB method is experimentally verified through dynamic mode III fracture experiments on the Fangshan marble (FM). Laboratory experimental results show that the mode III fracture toughness (KIIId) values of FM are approximately 2.8 times of the mode I fracture toughness (KId) values at similar dynamic loading rates. Post-mortem examinations on the fracture surfaces show that the famous facet coarsening mechanism in mode III fracture is suppressed under high loading rates. Furthermore, insightful assessments regarding the inner progressive fracturing behaviors of the ANFBD sample are given by virtue of three-dimensional discrete element method (DEM) simulation. Moment tensor (MT) analysis indicates that the shear fracture mechanism mainly dominates the whole failure process of the ANFBD sample, while the tensile fracture mechanism slightly increases during the facet coarsening process. These results are of significant importance for revealing the failure mechanism of rock under dynamic mode III loading and give some beneficial implications for natural strike-slip fault structures.

Prediction of constrained modulus for granular soil using 3D discrete element method and convolutional neural networks

To efficiently predict the mechanical parameters of granular soil based on its random micro-structure, this study proposed a novel approach combining numerical simulation and machine learning algorithms. Initially, 3500 simulations of one-dimensional compression tests on coarse-grained sand using the three-dimensional (3D) discrete element method (DEM) were conducted to construct a database. In this process, the positions of the particles were randomly altered, and the particle assemblages changed. Interestingly, besides confirming the influence of particle size distribution parameters, the stress-strain curves differed despite an identical gradation size statistic when the particle position varied. Subsequently, the obtained data were partitioned into training, validation, and testing datasets at a 7:2:1 ratio. To convert the DEM model into a multi-dimensional matrix that computers can recognize, the 3D DEM models were first sliced to extract multi-layer two-dimensional (2D) cross-sectional data. Redundant information was then eliminated via gray processing, and the data were stacked to form a new 3D matrix representing the granular soil's fabric. Subsequently, utilizing the Python language and Pytorch framework, a 3D convolutional neural networks (CNNs) model was developed to establish the relationship between the constrained modulus obtained from DEM simulations and the soil's fabric. The mean squared error (MSE) function was utilized to assess the loss value during the training process. When the learning rate (LR) fell within the range of 10-5-10-1, and the batch sizes (BSs) were 4, 8, 16, 32, and 64, the loss value stabilized after 100 training epochs in the training and validation dataset. For BS = 32 and LR = 10-3, the loss reached a minimum. In the testing set, a comparative evaluation of the predicted constrained modulus from the 3D CNNs versus the simulated modulus obtained via DEM reveals a minimum mean absolute percentage error (MAPE) of 4.43% under the optimized condition, demonstrating the accuracy of this approach. Thus, by combining DEM and CNNs, the variation of soil's mechanical characteristics related to its random fabric would be efficiently evaluated by directly tracking the particle assemblages.

Shear Resistance Evolution of Geogrid-Aggregate Interfaces under Direct Shear: Insights from 3D DEM Simulations

This paper presents a mesoscopic evaluation of the shear resistance evolution of geogrid-aggregate interfaces subjected to direct shear loading. A three-dimensional discrete element method (DEM) model was developed based on experimental data. The tensile response of geogrid were simulated through a series of calibration tests. Aggregate with complex particle shapes were simulated to accurately capture the interlocking effect among aggregates based on the real particle surface. The individual shear resistance components were quantified based on particle displacement field and contact distribution characteristics. The influences of aperture-aggregate size ratio and geogrid stiffness on the shear resistance components are discussed. The results indicate that the peak value of shear resistance component follows a descending order from frictional resistance of aggregate, to passive resistance of transverse rib, and to geogrid-aggregate interface frictional resistance. During the shear process, the frictional resistance of aggregate becomes active first, followed by the geogrid-aggregate interface frictional resistance, and then the development of passive resistance of transverse ribs starts with a certain lag. Optimizing the geogrid-aggregate size ratio and utilizing geogrids with higher rib stiffness could enhance the passive resistance of transverse ribs but would not significantly affect the geogrid-aggregate interface frictional resistance and frictional resistance of aggregate.

Collapse dynamics and deposition morphology of low-viscocohesive granular columns on a rough horizontal surface.

Using the three-dimensional discrete element method, we numerically investigate the collapse dynamics and deposition morphology of low-viscocohesive granular columns on a rough-horizontal plane by systematically varying a broad range of values of the initial column aspect ratio, cohesive stress, and liquid viscosity. The results show that the kinetic energy, half runout time, and runout distance increase with increasing the initial column aspect ratio but decrease with increasing the cohesive and viscous effects of the binding liquid, while the toe angle and deposit height decrease with increasing the aspect ratio and increase with increasing cohesive stress and liquid viscosity. Remarkably, by defining a dimensionless scaling number that incorporates the Bond number and initial column aspect ratio, this allows us to nicely describe the kinetic energy, half runout time, deposition height, runout distance, and toe angle. These unified descriptions may provide insights into the physical properties of the collapse dynamics and deposition morphology of low-viscocohesive granular columns, leading to good explanations of the complex properties of natural disaster events.

Fabric-based jamming phase diagram for frictional granular materials.

A jamming phase diagram maps the phase states of granular materials to their intensive properties such as shear stress and density (or packing fraction). We investigate how different phases in a jamming phase diagram of granular materials are related to their fabric structure via three-dimensional discrete element method simulations. Constant-volume quasi-static simple shear tests ensuring uniform shear strain field are conducted on bi-disperse spherical frictional particles. Specimens with different initial solid fractions are sheared until reaching steady state at a large shear strain (200%). The jamming threshold in terms of stress, non-rattler fraction, and coordination numbers (Z's) of different contact networks is discussed. The evolution of fabric anisotropy (F) of each contact network during shearing is also examined. By plotting the fabric data in the F-Z space, a unique critical fabric surface (CFS) becomes apparent across all specimens, irrespective of their initial phase states. Through the correlation of this CFS with fabric signals corresponding to jamming transitions, we introduce a novel jamming phase diagram in the fabric F-Z space, offering a convenient approach to distinguish the various phases of granular materials solely through the direct observation of geometrical arrangements of particles. This jamming phase diagram underscores the importance of the microstructure underlying the conventional jamming phenomenon and introduces a novel standpoint for interpreting the phase transitions of granular materials that have been exposed to processes such as compaction, shearing, and other complex loading histories.

DEM-based analysis of water inrush process of underground engineering face with intermittent joints in karst region


 
 
 
 Water inrush disaster of karst tunnel often lead to significant economic losses and serious casualties, which is an urgent engineering roadblock to be solved in the construction of tunnel in karst area. In this paper, three-dimensional discrete element method considering fluid-solid coupling effect and structural characteristics of water-mud resistant rock mass is adopted to systematically study the evolution law of displacement field and seepage field of intermittent joint type water-mud resistant rock mass of tunnel face and its water inrush critical characteristics during the process of sequential excavation of karst tunnel close to the frontal high-pressure water-rich karst cavity. The results show that: With the tunnel face gradually approaching the front-concealed high-pressure water-rich karst cavity, the stability of water-mud resistant rock mass is increasingly affected by high-pressure karst water, and karst water pressure gradually becomes the main control factor. The closer the tunnel face is to the front-concealed high-pressure water-rich karst cavity, the greater the extrusion displacement of karst tunnel face and its increase amplitude, the higher damage degree of water-mud resistant rock mass of face. With the advance of tunnel excavation, the intermittent cracks in the water-mud resistant rock mass of face gradually connect and form a stable hydraulic connection. The flow velocity and seepage pressure of karst water rise significantly at the moment of overall instability of face and the formation of water inrush channel, showing obvious precursor characteristics. The research achievements provide a reference for early warning and prevention and control of water inrush disaster of karst tunnel face.
 
 
 

The force and dynamic response of low-velocity projectile impact into 3D dense wet granular media

The presence of liquid bridges between particles in a wet granular media gives rise to capillary forces at the microscopic scale that dramatically alters the material's microstructure and macroscopic responses. Previous experimental studies show significant differences in the penetration depth of the projectile into assemblies of dry or wet particles. Still, there is a lack of fundamental understanding of the difference induced by the presence of liquid bridges in dynamic regimes. In this study, the contact model parameters of wet glass beads are calibrated employing the angle of repose tests and cylinder lifting tests, and a series of three-dimensional discrete element method simulations of spheres impact into wet granular packings are conducted. The dynamic characteristics of the projectile are obtained numerically and found to be in good agreement with the experimental data. The analyses indicate that the final penetration depth in the wet granular media is linearly related to the initial velocity and has a power function relationship with the impact energy. The generalized Poncelet law is suitable for wet granular materials, but the presence of liquid significantly affects the values of the parameters. There is a velocity “stagnation zone” at the initial stage of the wet granular impact, and the final penetration depth and the duration interaction time are smaller than that of the dry case. The difference can be attributed to the resistance evolution of the projectile exerted by particles and gives the parameter scaling law of the peak impact force. Further, a macro-micro transition technique is employed to characterize the velocity field, pressure field, and stress field inside the wet granular media and the spatial distribution is quantified based on stress theory.

Self-initiated static-dynamic state transition behavior and triggering mechanism of strain rockburst using three-dimensional discrete element method

The accurate understanding of rockburst mechanism poses a global challenge in the field of rock mechanics. Particularly for strain rockburst, achieving self-initiated static-dynamic state transition is a crucial step in the formation of catastrophic events. However, the state transition behavior and its impact on rockburst have not received sufficient attention, and are still poorly understood. Therefore, this study specifically focuses on the state transition behavior, aiming to investigate its abrupt transition process and formation mechanism, and triggering effects on rockburst. To facilitate the study, a novel burst rock-surrounding rock combined laboratory test model is proposed and its effectiveness is validated through experiment verification. Subsequently, corresponding numerical models are established using the three-dimensional (3D) discrete element method (DEM), enabling successful simulation of static brittle failure and rockbursts of varying intensities under quasi-static displacement loading conditions. Moreover, through secondary development, comprehensive recording of the mechanical and energy information pertaining to the combined specimen system and its subsystems is achieved. As a result of numerical investigation studies, the elastic rebound dynamic behavior of the surrounding rock was discovered and identified as the key factor triggering rockburst and controlling its intensity. The impact loading on the burst rock, induced by elastic rebound, directly initiates the dynamic processes of rockburst, serving as the direct cause. Additionally, the transient work and energy convergence towards the burst rock resulting from elastic rebound are recognized as the inherent cause of rockburst. Moreover, it has been observed that a larger extent of surrounding rock leads to a stronger elastic rebound, thereby directly contributing to a more intense rockburst. The findings can provide novel theoretical insights for the exploring of rockburst mechanism and the development of monitoring and prevention techniques.

Impact of Rejuvenator-Modified Mastic on Asphalt Mixture Stiffness: Meso-Scale Discrete Element Method Approach

Encapsulated rejuvenators embedded in asphalt mixtures are a promising technology to extend the service life of asphalt pavements. However, their effects on the asphalt mixture’s performance still need to be properly understood. A recently developed three-dimensional discrete element method framework enables the evaluation of non-homogeneous distributions of the rejuvenator, closely resembling real conditions. This includes different scenarios involving capsule content and release efficiency. The presented numerical results show that the rejuvenator-to-mastic ratio and the number of rejuvenator-modified contacts influence the stiffness properties of asphalt mixtures. In cases where a homogeneous rejuvenator distribution is assumed, the three-dimensional DEM model predicts a significant reduction in the asphalt mixture’s stiffness that compromises the pavement’s performance. Simulations show that the diffusion effect needs to be considered for predicting the post-healed behavior of asphalt mixtures. For cases considering more suitable modified mastic amounts (less than 1.20 wt%), the effect on the asphalt mixture’s stiffness modulus is less pronounced, and the phase angle is not significantly affected. Additionally, the presented simulations suggest that the capsule content can be increased up to 0.75 wt%, and capsules with a release rate higher than 48% can be used without compromising the rheological performance of asphalt mixtures, possibly improving their self-healing properties. These numerical insights should be considered in future designs to achieve optimal post-healed behavior.

Numerical simulation of particle and bubble detachment process in turbulent flow environment using CFD-DEM

Three-dimensional discrete element method (DEM) models were developed to simulate particle-bubble interactions by utilizing the API function within the EDEM software platform. Geometric grids were constructed using FLUENT software to induce isotropic turbulence, and this turbulence environment was incorporated into the CFD-DEM framework. The simulations focused on the detachment of particles and bubbles, with particle sizes ranging from 0.10 to 0.30 mm, particle densities ranging from 1500 to 2500 kg/m³, and fixed bubble sizes of 1.00, 1.20, 1.60, and 2.00 mm. The detachment processes occurred within a turbulent flow field at distances of 1, 1.5, 2, and 3 mm from the grid. It is found that the particle-bubble bond required more capillary force to maintain attachment equilibrium as the particle density and size, bubble size, and flow field turbulence environment increased, the smaller the initial flow velocity to bring the bubble and particle to a critical desorption state, indicating the increase in all these factors were not conducive to attachment stability.

Microscopic analysis of the nonlinear stiffness of granular materials at small-to-medium strain

The nonlinear stiffness of dense and loose granular materials at small-to-medium strain is investigated using the three-dimensional discrete element method (DEM). The threshold strain of the nonlinear elasticity of granular materials, i.e., the Y2 surface in the kinematic yielding surface framework, is obtained from the simulated drained triaxial tests. The analytical stress-force-fabric relationship is used to quantitatively examine the evolution of fabric anisotropy. Results show that the after reaching Y2 surface, the contact normal anisotropy begins to increase from a steady low level, and evident slippage begins to occur at strong contacts. The threshold strains of the contact normal anisotropy and strong contact slippage increase linearly with the confining pressure, which is consistent with the threshold strain of the nonlinear elasticity of granular materials. The creation of new contacts and disruption of existing contacts during loading are investigated. A three-stage micromechanism of the observed nonlinear stiffness behavior is proposed.

Exploring the undrained behaviour of granular clumps after isotropic and Ko-consolidation paths using DEM

This paper investigates the undrained behaviour of granular clumps after isotropic and Ko-consolidation paths using a three-dimensional discrete element method (3D-DEM). Four randomly chosen clumped particles with a wide range of densification indexes, ID, and mean confining stresses, p' were considered. The specimens were sheared to the deviatoric strain, εq of 40 % to reach the critical state (CS) conditions. It was found from the results that a unique critical state line (CSL) was achieved, irrespective of consolidation paths. The micro-mechanical quantities such as the average coordination number (CN) and von Mises fabric in terms of the second invariant of deviatoric fabric, FvM, also reached CS values. Irrespective of the consolidation paths, unique relationships were found between e−log(p′)and CN−log(p′). The stress-fabric joint invariant, KF established a unique relationship with p′and e, which forms a relationship in the KF−p′−e space and the projection of this relationship in the e−log(p′) plane confirms the classical CSL. Moreover, the flow potential (uF), stress ratio at instability (ηIS), and average coordination number at instability (CNIS) showed no dependency on the consolidation paths, while a dependency was observed for the second-order deviator fabric, FvM.

Investigation on the effects of asphalt mixes and their combinations on asphalt mix shear strength by 3D discrete element method

ABSTRACT This study investigated the effects of asphalt mixes and their combinations on the asphalt mix shear strength (SS) by a three-dimensional (3D) discrete element method (DEM). The uniaxial penetration test (UPT) for testing the asphalt mix SS was succinctly depicted. 3D micromechanical models used to predict the asphalt mix SS were built through X-ray computed tomography and discrete particle model implemented in particle flow code in three dimensions (PFC3D). The effects of asphalt mixes and their combinations on the SS were analysed on the basis of these models. Simulation results were proven against laboratory UPTs. As shown, the presented simulation results were in good agreement with the laboratory results, and the deviations between them were below approximately 6%, and most were less than 4%. The SS of high modulus asphalt mixes was greater than that of SBS-modified asphalt mixes and rubber-modified asphalt mixes. The asphalt mix SS increased with the increase in aggregate size, and it decreased with the rise in void content. The double-layer asphalt mix SS was more remarkably influenced by the bottom asphalt layer. The crumb rubber content also affected the rubber-modified the asphalt mix SS. The rubber-modified asphalt mix SS increased with the rise in crumb rubber content.

A study of particle flow in a ribbon reactor: Effect of ribbon configuration on mixing and heat transfer performance

The mixing and heat transfer of particles are two important operating units in the lithium-ion battery industry due to the cycling performance of the cathode is mainly dependent on the mixing and heat transfer performance of granular matter, such as needle coke and asphalt particles. In this work, simulations of the particle mixing and heat transfer process in a ribbon reactor were conducted based on the three-dimensional discrete element method (DEM). The stacking angle test, rotary drum, and thermal conductivity test were designed to obtain the DEM parameters. The trajectory of tracer particles, total velocity fluctuation, coordinate number, and relative standard deviation (RSD) were used to analyze the mixing and heat transfer process. It was found that particles in the ribbon reactor experience two types of movement. The first one is high-speed tangential movement, and the second one is low-speed recirculation movement in the vertical plane. Particles near the vessel wall and impeller shaft are first heated and a cold core is generated in the initial stage of heat transfer. Results obtained indicate that the mixing performance increases slightly with the increase of ribbon number. The mixing performance increases with the increase of velocity fluctuation and the decrease of coordination number, and the heat transfer can be improved by enhancing the mixing performance of granular matter. Increasing the ribbon width and ribbon pitch can improve the heat transfer performance, while the ribbon pitch has little influence on the mixing performance.

DEM study of the stress fields around the closed-ended displacement pile driven in sand

Three-dimensional discrete element method (DEM) is employed to model the published calibration chamber test of a closed-ended displacement pile driven in sand. To achieve large chamber-to-pile and pile-to-particle size ratios for unbiased predictions, a high-performance graphics processing unit-powered DEM code is utilised in conjunction with the axisymmetric assumption and particle refinement method. The DEM parameters are first calibrated against the drained triaxial compression test data on Fontainebleau sand. Then, the DEM modelling of pile driving demonstrates quantitative agreement with the experimental counterpart in terms of cone resistance, stress contours, and distributions.

Discrete element modelling of thermal penetration test with heating and cooling

A three-dimensional discrete element method (DEM) is employed to simulate thermal penetration tests with heating and cooling. This study investigates the mechanical behavior of soil particles during penetration, and examines the effects of temperature boundary condition, overburden load, and heating duration on the heat transfer mechanisms of the probe-soil system. Simulation results of penetration indicate that larger overburden load causes an increase in tip resistance (qc), sleeve friction (fs), and the isotropy of particles, whereas less influence is found on the distributions of penetration-induced displacement. Despite of the negligible effects of various temperature boundary conditions, the thermal responses of DEM model show that both the peak temperature of the probe heating module and the cooling rate of soil increase with the overburden load, while the probe insulation section shows a decreasing trend. The heat concentrates around the vicinity of the cone tip and probe shaft, and the high temperature area gradually expands with longer heating duration. Additionally, thermo-coupling analysis illustrates that the heat transfer process has a milder effect on the mechanical properties of granular soils. The numerical results are then validated against laboratory model chamber tests under comparable conditions, showing acceptable agreements.

Discrete-element method simulations of the seismic response of tunnels in deep granular deposit

The seismic response of tunnels constructed in a deposit of granular soil of depth greater than 20 m is examined in this paper. Three-dimensional discrete-element method (DEM) simulations were used to model the soil assembly and the tunnel lining. Soil particles were simulated as rigid spherical particles that are allowed to overlap at the contact points. The tunnel lining was modeled as a flexible system using a collection of particles that were glued together using cementitious bonds to mimic the physical properties of an actual tunnel. Free-field boundaries were utilized at the model’s lateral sides to prevent the propagating wave’s reflections back to the domain and enforce the free-field motion. The DEM computational framework was validated using published centrifuge test results. DEM simulation results reveal good agreement with the experimental centrifuge test results when subjected to the same input motion. Further simulations were carried out to investigate the seismic response of the system under different input motion characteristics. The dynamic earth pressure was monitored at certain points on the tunnel lining. It was found that the dynamic earth pressure and tunnel lining forces increased during seismic excitation and the final residual values were, in most cases, considerably larger than the initial static values. The results also showed that the maximum amplification factor, ground settlement and tunnel lining internal forces occurred close to the resonant frequency of the system.

The Modelling of Rock Fragmentation Mechanisms by Carbide Buttons Using the 3D Discrete Element Method

Button cutters are commonly used in hard rock drilling because the inserted carbide buttons provide exceptional wear resistance, impact resistance, and high strength in challenging geological formations. One of the most pressing issues in designing a button cutter is to study the rock breaking mechanisms of carbide buttons. In this study, the three-dimensional discrete element method (DEM) was employed to investigate the rock breaking mechanism and cutting performance of five widely used carbide buttons, i.e., spherical, saddle, wedge, conical, and parabolic buttons. The simulation results were compared with laboratory tests to reveal the rock indentation process. The crack propagation pattern, energy dissipation, and damage evolution associated with the force–penetration depth curve were investigated. Tensile damage was the primary determinant for crack propagation and coalescence. By systematically exploring the penetration index, specific energy, and crack propagation characteristics, the conical button had a high rock breaking efficiency when the penetration depth was low, and the saddle button had a high rock breaking efficiency when the penetration depth was high. The findings can provide references for the design of a button cutter.

Macro-micro mechanical study of principal stress rotation in granular materials using DEM simulations of hollow cylinder test

The dependency of sand behavior anisotropy on microstructure reveals the importance of macro-micro mechanical analysis of the principal stresses rotation effect on the strength-deformation response of granular material. In this study multi-scale analysis of the granular material's behavior using three-dimensional discrete element method simulations of the hollow cylinder test was presented. The effect of principal stresses rotation (α) on the macro-mechanical behavior of the soil was investigated from the micro-mechanical anisotropy aspect. It was observed that principal stress rotation affects the anisotropy coefficient and directional distribution of all micro-parameters which can change the soil's behavior according to loading conditions. The stress-force-fabric relationship was used to analyze the microstructure's stress state based on micro-parameters anisotropy coefficients. In addition to the good agreement between stress-force-fabric and general stress tensors, the decreasing trend of the maximum deviator stress and internal friction coefficient angle with increasing α can be observed for both stress tensors.