Two-dimensional Discrete Element Model Research Articles

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.

Numerical Investigation of the Evolution Process of an Open-Pit Mine Landslide Using Discrete-Element Method

Because of the complexity of geological conditions and disturbance of external factors, the process of instability of open-pit landslides is very complicated. To illustrate this complex process, taking an open-pit coal mine landslide as an example, an accurate landslide geological section was established via detailed field investigation, remote sensing image interpretation, and field borehole data, in this study. A two-dimensional discrete-element model was established by the Fast CPU Matrix Computing of Discrete-Element Method (MatDEM, Version 1.60). The failure evolution of the landslide was investigated; then, the deformation behavior and dynamic characteristics of the landslide were systematically studied. The analyses of the failure process, velocity, displacement, and heat showed that the evolution of the landslide could be divided into the stages of initial deformation, accelerated deformation, and deceleration and stabilization. During the movement of the landslide, the gravitational potential energy of the landslide gradually converted into kinetic energy, heat, and elastic potential energy. The kinetic energy in the initial stage was small but rapidly increased and occupied the dominant position in the second stage. The kinetic energy gradually decreased and tended to be stable in the third stage. The final geometry and accumulation characteristics of the landslide obtained by numerical simulation were consistent with the corresponding field investigation and remote sensing interpretation. This work can provide a reference for the study of the evolution and prevention of open-pit mine landslides.

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.

In-situ and numerical investigation on dynamic response of asphalt pavement-low slag embankment system under traffic loading

In this study, the dynamic behaviors of the asphalt pavement-low slag embankment system were investigated by the in-situ standard truck driving test and a two-dimensional discrete element model under different cyclic harmonic moving loads by PFC5.02D. Roughly following the Stirling Exponential model, the dynamic responses rapidly decay during the load transfer within the slag embankment. In addition to a prominent energy absorption observed in the pavement structure, a hysteretic effect was also observed for the dynamic response of soils in deeper depths. To quantitatively evaluate the effect of the dynamic loading, the sensitive depth and influence depth were given by the attenuation levels of the dynamic impact. Because of the greater stiffness of slag material, stress concentration and greater influence depth were found for the case with a low slag embankment, and some suggestions were given accordingly.

Mechanical Properties and Failure Mechanism of the Weakly Cemented Overburden in Deep Mining

With increases in the mining depth and area in the Ordos coal field, the failure law of the super thick sandstone in the Zhidan group leads to frequent disasters, such as rock bursts and mine earthquakes, which have become a significant issue, restricting large-scale continuous mining. To adequately understand the movement mechanism of the super-thick and weakly cemented overburden, and to promote the large-scale mining of the coal resources under it, this study analyzes the physical and mechanical properties, along with the microstructural characteristics, of the weakly cemented overburden of the Yingpanhao Coal Mine through mechanics tests, scanning electron microscope tests (SEM) and hydrolysis experiments. A two-dimensional discrete element model of the survey region is then built to explore the temporal and spatial evolution laws of the overburden failure. The results show that, even though poorly cemented strata such as the Cretaceous Zhidan group sandstone and the Zhiluo group sandstone are weak in lithology, their unique mineral composition and microstructural characteristics give them a greater rigidity when their thickness reaches a certain value. The surface subsidence exhibits a sudden increase, and the dynamic disaster range of the overlying strata is wide when deep multi-face mining was carried out under the super-thick and weakly cemented overburden. The temporal and spatial evolution laws of the strata subsidence and influence boundary are closely related to their depth, and their relationships evolve into the Boltzmann function and Boltzmann–parabolic function, respectively. The failure mode of the super-thick and weakly cemented overburden is ‘beam–arch shell–half arch shell’, and the failure boundary exhibits arch fractures.

Failure Mechanism Analysis of Reinforced Foundation from Experimental and Numerical Simulations

Geogrid has been extensively used in engineering practice as a horizontal reinforcing material to improve the performance of foundations, embankments, and road base systems. This paper presented the results of laboratory static load tests on transparent soil foundations reinforced with biaxial polylactic acid geogrid and studied the reinforcement mechanism and foundation failure mode of the reinforced foundation. The different load settlement behaviour between reinforced foundations with different reinforcement layer numbers was studied by varying the number of geogrid layers. The deformation of reinforcements and foundation soil was recorded with an industrial camera. The strain of the reinforcements was monitored by Fiber Bragg Grating (FBG) sensors. In addition, a two-dimensional discrete element model was established based on the model tests to analyse the load transfer behaviour and deformation law of the reinforced foundation. The results indicated that geogrid can effectively improve the bearing capacity of the foundation. As the number of reinforcement layers increases, the improving effect is more significant. The reinforced soil can provide a stronger upward resistance than unreinforced soil by activating the tensile force of the geogrid. The simulation results present the load transfer behaviour and reinforcement mechanism of geogrid. With the increase of reinforcement layers, the position of the sliding surface moves downward, and the area of the sliding surface increases. Geogrid can limit soil displacement and delay the development of the sliding surface.

Coupled two-dimensional discrete element and multibody dynamic modeling for interaction of the soil and rough shaped rigid bodies

Coupled two-dimensional discrete element and multibody dynamic modeling for interaction of the soil and rough shaped rigid bodies

Modeling the orientation- and stress-dependent permeability of anisotropic rock with particle-based discrete element method

A novel physics-based numerical model is proposed to simulate the orientation and effective confining pressure dependent permeability of anisotropic rock . In the two-dimensional discrete element model, presence of anisotropy is explicitly represented by inserting a set of smooth joints. Based on the experimentally obtained effective stress law at sample scale, a physics-based relation is deduced to describe the reduction of pipe aperture upon the normal contact force at grain scale. Darcy test is conducted to validate the model by comparing the flow rate and pressure distributions with analytical solutions. Different parameters are assigned to represent the difference in flow capacity of rock matrix and beddings. Fluid flow tests performed on the isotropic model and anisotropic models with horizontal and vertical beddings reveal that the macro permeability decreases with increasing effective stress, following the same effective stress law. The initial aperture dominates the intrinsic permeability while the reduction of permeability is due to the closure of pipe aperture. Permeability anisotropy is caused by the different apertures assigned to the rock matrix and the bedding while the force sensitivity factors determine the stress-dependence of the permeability anisotropy. Simulations of the stress concentration and fluid dissipation around borehole confirm the capacity of the model in capturing the hydro-mechanical coupled responses of anisotropic rock formation. This study provides a fluid flow model for the exploration of mechanisms underlying the orientation and stress dependent permeability of anisotropic rocks and for the simulation of their engineering responses subjected to hydro-mechanical coupling.

Comparison of Dynamic Characteristics between Small and Super-Large Diameter Cross-River Twin Tunnels under Train Vibration

Train vibration from closely aligned adjacent tunnels could cause safety concerns, especially given the soaring size of the tunnel diameter. This paper established a two-dimensional discrete element model (DEM) of small (d = 6.2 m) and super-large (D = 15.2 m) diameter cross-river twin tunnels and discussed the dynamic characteristics of adjacent tunnels during the vibration of a train that runs through the tunnel at a speed of 120 km/h. Results in the D tunnel showed that the horizontal walls have the same horizontal displacement (DH) and the vertical walls have the same vertical displacement (DV). The stress state of the surroundings of the D tunnel is the decisive factor for DH, and the distance from the vibration point to the measurement point is the decisive factor for DV. Results in the comparison of the d and D tunnels showed that the D tunnel is more stable than the d tunnel with respect to two aspects: the time the tunnel reaches the equilibrium state and the vibration amplitude of the structure’s dynamic and static responses. The dynamic characteristic of the d and D tunnel is significantly different. This research is expected to guide the design and construction of large diameter twin tunnels.

Shear Deformation Behavior of a Double-Layer Asphalt Mixture Based on the Virtual Simulation of a Uniaxial Penetration Test.

This paper aims to clarify the shear deformation behavior of double-layer asphalt mixtures using the virtual uniaxial penetration test (UPT) with a discrete element method. For this purpose, asphalt mixtures with two different nominal maximum aggregate sizes were designed for the preparation of double-layer wheel tracking test specimens. Then, the cylindrical cores were prepared from the specimens and were cut for capturing the longitudinal profile images. These images were used to reconstruct a two-dimensional discrete element model (DEM) of the uniaxial penetration test specimen. The results indicate that the shear deformation behavior of the asphalt mixtures showed corresponding changes under the virtual loading. The tensile and compressive stress were distributed unevenly within the upper layer after the test, and both coarse aggregates and asphalt mortars bore a greater shear stress. Therefore, cracks were more likely to occur in the upper layer, leading to the failure of the specimens. This process enhanced the bonding between the asphalt mortars and the mineral aggregates. The aggregate particles in the upper layer moved more vertically, while those in the lower layer generally moved more laterally under the virtual loading. This behavior reveals the rutting mechanism of asphalt pavement.

Research on response of temperature change to pavement structure layer based on micromechanics

ABSTRACT The effect of temperature on the meso-mechanical properties of each structural layer of the pavement was studied in this paper. Fitting standard indoor uniaxial compression tests, meso-scale parameters of the material were obtained. With the mesoscopic parameters of each structural layer, a two-dimensional discrete element model of the pavement was constructed. This discrete element model of the road surface was coupled with the 2 DOF 1/4 vehicle model, and the unevenness of the road surface provided incentives for vehicles. At different temperatures, the meso-mechanical response of each structural layer of the road surface was solved under the action of vehicle loads. The movement of particles at different temperatures was analysed. The results show: compared with the finite element model, the vertical displacement produced by the discrete element model is 4.8% larger than the finite element model. That shows that the discrete element model data has certain credibility. The vertical displacement decreases as the depth of the structural layer increases and increases as the road surface temperature increases. And the vertical stress decreases as the depth of the structural layer increases, and increases as the road surface temperature increases. The horizontal stress of the upper layer is compressed, the horizontal stress of the lower layer is stretched, and the horizontal stress of the remaining structural layers does not change significantly. The horizontal stress decreases as the road surface temperature increases. The tangential stress of each structural layer is in anti-symmetric state, both tensile state and compressed state. Tangential stress decreases with increasing road surface temperature. The higher the temperature, the smaller the tangential stress. The effect of temperature on the velocity of particles in the early stage is greater than that in the late stage.

Discrete Element Analysis of Indirect Tensile Test Based on Image Processing with Annular Segmentation and Bimodal Threshold

Abstract The discrete element method (DEM) has recently been widely used to analyze the micromechanics behavior of asphalt mixtures. The objective of this study is to present a more accurate image-processing technique to perform an indirect tensile test of asphalt mixture. Cross-sectional images of the specimen were obtained by an X-ray computed tomography (CT) technique. These CT images were processed by annular segmentation combined with bimodal threshold. The image information was transformed to coordinate information by the user-defined program in Matrix Laboratory (MATLAB). Then, a two-dimensional discrete element model of the indirect tensile test specimen was reconstructed. The indirect tensile test was simulated by the DEM and verified in the laboratory. It was found that this image-processing technology could separate connected or overlapping aggregates and better avoid defects among the aggregates. During the simulation test, the distributed internal forces were gradually concentrated along the loading axis. Four-stage crack initially appeared directly under the loading area and quickly developed along the interface between the aggregate and mortar, mainly along the loading axis. In view of the consistency of the load–displacement curves and crack distribution characteristics in both the simulation and laboratory tests, this numerical method is able to simulate the indirect tensile test.

2D DEM analysis of the interactions between bio-inspired geo-probe and soil during inflation–deflation cycles

The cone penetration test and the standard penetration test are perhaps the most versatile techniques for investigating soil properties in-situ. Advancing the probe through the soil requires substantial downforce due to friction between the probe and the soil. Inspired by the ability of worms to conform their body to the most mechanically advantageous shape while tunneling, an innovative self-excavating geo-probe has been developed and deployed in a laboratory environment. Analogous to a worm’s ability to expand its body, a soft balloon mounted behind a rigid cone is inflated or deflated by applying pressure or vacuum periodically to alter the cone penetration resistance. Laboratory experiments have shown promising results that the new geo-probe can penetrate the soil more efficiently. However, the interactions at balloon–soil–cone interfaces are complex and not fully understood. This numerical study focuses on the behavior of the geo-probe during balloon inflation and deflation. A two-dimensional discrete element model is developed to provide particle-level insight into the micromechanics of the interactions between the geo-probe and the soil. A baseline simulation is first conducted to study the failure mechanisms of the bulk soil during inflation and deflation. Additionally, the contact forces at balloon–soil and soil–cone interfaces are analyzed to show the variation of penetration resistance. The displacement field, shear strain field, and contact force chains are numerically investigated to gain a fundamental understanding of the tool–soil interaction. Then, the effect of balloon locations and overburden stresses on the behavior of the probe are studied by performing sensitivity analyses. This study provides a numerical technique to study the tool–soil interactions that was inaccessible in laboratory test. Implementation of the simulation results enables extrapolation of bench-scale testing to a wider range of stresses and boundary conditions.

The Evolution of Grinding Mill Power Models

Mill power models have been used in a variety of ways in industrial practice since power directly equates to throughput and fineness of ground product. We first start with Hogg-Fuerstenau Power Model and show how this model successfully predicted the power draw of many grinding mills in several mining operations. Then, we show how this model was on the verge of being able to predict the influence of lifter design on power draw. Next, we describe the discrete element model and how it overcame the issues faced by the previous power model. Using a DEM software known as Millsoft, we show the influence of lifter design geometry on power draw and analyze the power draw of rubber lifters versus the steel lifters via several case studies. As years passed, the two-dimensional discrete element model imbedded in Millsoft is superseded by three-dimensional discrete element method. Due to the gigantic computational power of graphic processing units, new computational codes that can do the tumbling motion along the entire length of the mill has come about. Here, we show the predictive capability of Blaze-DEM for ball and SAG mills.

Discrete Element Analysis of Indirect Tensile Fatigue Test of Asphalt Mixture

In order to investigate the damage to microstructure and some other micromechanical responses during a fatigue test on asphalt mixture, Particle Flow Code (PFC) was used to reconstruct a two-dimensional discrete element model of asphalt mixture, based on computed tomography (CT) images and image-processing techniques. The indirect tensile fatigue test of asphalt mixture was simulated with this image-based microstructural model, and verified in the laboratory. It was found that there were four stages during the fatigue failure: no crack, crack initiation, crack developing, and interconnected crack. Cracks mainly developed between the aggregate and asphalt mortar, near the loading axis. The corresponding stages of failure, the developing trend and the distribution characteristics of the cracks matched well with those in the laboratory test. Furthermore, the trends of both the time-load curve and time-displacement curve from the simulation test were also consistent with those from the experimental test. In short, the distribution characteristics of cracks and internal forces of asphalt mixture show that it is feasible to simulate the fatigue performance of the asphalt mixture by a discrete element method (DEM).

Micromechanical analysis of cyclic and asymptotic behaviors of a granular backfill

The paper examines the mechanics and physics of granular material responses at the macroscopic and microscopic levels during both monotonic and cyclic loadings. A numerical analysis referring to a long retaining wall is conducted using a two-dimensional discrete element model representing a granular system with a free top surface. On one of the lateral boundaries referring to the retaining wall, both active and passive loadings were applied monotonically as well as cyclically. First, the development of sheared zones and classic failure wedges resulting from active and passive monotonic displacements are discussed with respect to Rankine’s and Roscoe’s solution angles. Then, a series of loading cycles were performed using slow small-amplitude displacements at different stress states chosen before the occurrence of failure along the passive monotonic stress response curve. Particular interest is focused on the ultimate asymptotic cyclic response of the granular system, the occurrence of a high-mobility (convective) zone and a detailed macroscopic and microscopic analysis. Finally, major kinematical features that are displayed during cyclic loading from different starting stresses to eventually reach the same asymptotic state were elucidated through particle vortex-like flux formations, including contact rotations. The change in material stiffness was also investigated based on the evolution of strong and weak contact networks, together with the analysis of fabric anisotropy within the entire domain, including the high-mobility zone considered separately.

A Comparison of Two-Dimensional and Three-Dimensional Micromechanical Discrete Element Modeling of the Splitting Tests for Asphalt Mixtures

Simulation is an important approach for predicting the physical properties of asphalt mixtures. However, the simulation results are usually perfect because the model parameters or material properties were generally obtained by reverse modeling, and it is difficult to find the problems in simulation and distinguish superiority and inferiority of models by the results. Based on imaging and discrete element method (DEM), this study aims to compare two-dimensional (2D) and three-dimensional (3D) micromechanical modeling of the splitting tests for asphalt mixtures. The 2D and 3D microstructure-based discrete element models of a splitting test were established by a discrete element program called Particle Flow Code in Two/Three Dimensions (PFC2D/3D). The strengths and stresses at low temperatures were numerically simulated based on these models. The obtained results were compared, and then verified by an actual splitting test. Results reveal that the 3D discrete element simulations are more stable and more reliable than the 2D discrete element simulations.

Dynamic Behavior Analysis of High-Speed Railway Ballast under Moving Vehicle Loads Using Discrete Element Method

AbstractConsidering the real irregular shapes of ballast particles and complete track skeleton, a two-dimensional discrete element model is built to investigate the dynamic behavior of high-speed railway (HSR) ballasted track. Taking the moving wheel loads obtained from railway vehicle-track coupled dynamics simulation as the excitation inputs, the dynamic behavior of ballast particles in terms of contact force, stress, and vibration response are simulated using the discrete element model. Numerical results show that the ballast particles within the depth of 200 mm under sleepers would be most likely to carry a higher stress level when a vehicle passes by. Vibration amplitudes of ballast particles increase with the increase of vehicle speed, and the acceleration amplitudes rise sharply when the vehicle speed is higher than 200 km/h. Spectrum analyses indicate that the dominant frequencies of particle displacement and velocity are lower than 100 Hz, whereas the acceleration responses contain not only low-f...

Depth-independent cone penetration mechanism by a discrete element method (DEM)-based stress normalization approach

A two-dimensional discrete element model of driven piles in crushable sand was developed and validated against laboratory data. Numerical experiments were conducted to investigate the effects on the pile penetration behavior of initial sample porosity, particle crushability, initial stress state, ratio of pile diameter to median particle diameter, and ratio of model width to pile diameter. A new stress normalization method is adopted to synthesize the data at different driven depths from the simulations. The normalized vertical and horizontal stress fields surrounding the pile show an invariable pattern of stress distribution, suggesting a unique penetration mechanism independent of the penetration depth. The validity of the discrete element method (DEM) simulation results is verified by comparing the stress distributions to those observed from calibration chamber tests on model pile installation in sands.

Geosynthetics anchorage with wrap around: experimental and numerical studies

ABSTRACT: Geosynthetics are used as reinforcing elements in a wide variety of structures: reinforced slopes and walls; embankments on soft soils; piled embankment; reinforcement in the base layers of railroad and road constructions; reinforced foundation mattresses; bridging of sinkholes or reinforced abutments. In some cases, these reinforced structures require anchorage areas. Designing the required dimensions of this anchorage remains problematic. This paper focuses on the simple run-out and wrap around anchorages. Laboratory tests, performed with these two anchorage benches, consisted of the pull-out of three geotextiles (uniaxial or biaxial with different stiffness) anchored following various geometries in different kinds of soil. In order to confirm and to complete the experimental studies presented in these anchorage systems, a specific two-dimensional discrete-element model has been used. The soil was described by discrete elements and the geosynthetic behaviour was taken into account by the use of thin finite elements. The interface behaviour between the soil particles and the geosynthetic elements was considered at each contact point by using a Coulomb contact law. The numerical model reproduced the experimental campaign and the anchorage mechanisms reasonably. The load transfer between the geosynthetic and soil was visualised by the force and displacements distribution along the geosynthetic sheet. The numerical procedure could also be used to define the conditions of stability for reinforced slopes or walls.