Two-dimensional Discrete Element Model Research Articles

Influence of mobile shale on thrust faults: Insights from discrete element simulations

We study the effects of sedimentary loading of a mobile shale substrate, using two-dimensional discrete element modeling. We develop an updip extensional zone connected at depth to a downdip contractional zone, allowing us to study the formation of gravity-driven fold and thrust belts, and the evolution of decollements within this system. We compare our models to the Niger Delta type locale for shale tectonics. In general, most seismic interpretations of the Niger Delta include decollement(s) at the top of the mobile shale unit, but exact locations vary depending on area of investigation. Our models, particularly ones with mobile shale thicker than 2 km (1.2 mi), show more diffuse decollements, spanning the width of the mobile shale unit, which propagate out in front of the syntectonic sediment wedge and connect normal faults in the extensional zone with toe thrusts in the contractional zone. We also look at the distributions of stress and strain within our models, plotting the distributions of (maximum principal stress) and relating that to the vergence of thrust faults developed in our models. We quantify the amount of strain in different sections of the models, showing that extension is much greater than compression in the fold and thrust belt(s) alone, and that compression is distributed throughout the model, including in front of the fold and thrust belt.

Displacement Fields of Sedimentary Layers Controlled by Fault Parameters: The Discrete Element Method of Controlling Basement Motions by Dislocation Solutions

In the two-dimensional discrete element modeling of displacement of sedimentary layers caused by faulting within the basement, we attempted to move a rigid basement as if it were an elastic basement by controlling its motion through application of dislocation solutions. An advantage of our modeling procedure is that we can discuss displacement fields of sedimentary layers in connection with fault parameters. We simulated displacement fields of the sedimentary layers by means of our modeling procedure and found that our simulated fields are different from the fields obtained in rigid basement models and are dependent on the selected fault parameters.

Revisiting rolling and sliding in two-dimensional discrete element models

It has long been recognized that the rotation of single particles plays a very important role in simulations of granular flow using the discrete element method (DEM). Many researchers have also pointed out that the effect of rolling resistance at the contact points should be taken into account in DEM simulations. However, even for the simplest case involving two-dimensional circular particles, there is no agreement on the best way to define rolling and sliding, and different definitions and calculations of rolling and sliding have been proposed. It has even been suggested that a unique rolling and sliding definition is not possible. In this paper we assess results from previous studies on rolling and sliding in discrete element models and find that some researchers have overlooked the effect of particles of different sizes. After considering the particle radius in the derivation of rolling velocity, all results reach the same outcome: a unique solution. We also present a clear and simple derivation and validate our result using cases of rolling. Such a decomposition of relative motion is objective, or independent of the reference frame in which the relative motion is measured.

Discrete element modelling on creep behaviour of PI/SiO2 composite

In this paper, a two-dimensional discrete element model (DEM) was adopted to predict the creep behaviour of polymer matrix particle reinforced composite PI/SiO2. The polymer matrix was simulated by regularly and closely compacted disks which were bonded together with viscoelastic Burger’s model. The parameters of the Burger’s bond model were derived based on their macroscale material properties. The elastic filler particles with different contents randomly distributed in the models and bonded with the neighbouring matrix disks. Tensile tests of the PI/SiO2 composite with different SiO2 contents under constant loading were performed based on the developed DEM models. The creep strain curves were presented and compared with finite element method (FEM) results. The favourable agreement between the DEM results and the FEM results indicate that the viscoelastic DEM model developed in this study is very capable of simulating constitutive behaviour of PI/SiO2 composites.

PFC’s Application on the Dynamic Response Analysis of High Speed Railway Ballastless Subgrade

The biaxial test on ballastless track subgrade material of surface layer and bottom layer of subgrade was established using the particle flow code(PFC). Based on the micro parameter gotten from the biaxial test, a two-dimensional discrete element model of slab Ballastless Track subgrade is modeled. The dynamic response under dynamic load was calculated. A comparison of simulation results and the field measured data shows goodness of fit which provides a new way of simulation on dynamic response of high speed railway subgrade.

Estimation of Fracture Stiffness, In Situ Stresses, and Elastic Parameters of Naturally Fractured Geothermal Reservoirs

AbstractKnowledge of fracture stiffness, in situ stresses, and elastic parameters is essential to the development of efficient well patterns and enhanced geothermal systems. In this paper, an artificial neural network (ANN)–genetic algorithm (GA)-based displacement back analysis is presented for estimation of these parameters. Firstly, the ANN model is developed to map the nonlinear relationship between the fracture stiffness, in situ stresses, elastic parameters, and borehole displacements. A two-dimensional discrete element model is used to conduct borehole stability analysis and provide training samples for the ANN model. The GA is used to estimate the fracture stiffness (kn, Ks), horizontal in situ stresses (σH, σh), and elastic parameters (E, v) based on the objective function that is established by combining the ANN model with monitoring displacements. Preliminary results of a numerical experiment show that the ANN-GA-based displacement back analysis method can effectively estimate the fracture stif...

Numerical study of variation in Biot's coefficient with respect to microstructure of rocks

Abstract Biot's coefficient, which is the key parameter of poroelasticity, strongly depends on the microstructure of the porous medium. Due to the complexity to conduct effective experiments at the microscale, there are very limited experimental data available, which document the influence of microstructure on Biot's coefficient. Therefore, numerical method was used in this paper to specify the influences of microstructural parameters on Biot's coefficient. Two-dimensional discrete element models with simplified microstructural geometries have been constructed with the purpose of obtaining a quantitative description of the influences of internal cavities (pores, fractures etc.) on the macroscopic deformability. Based on the numerical results some observations were revealed: 1) the Biot's coefficient is strongly dependent on the internal microstructure of the rock, and different porous media with the same composition of constituents may exhibit quite different poroelastic behavior due to their different microstructures; 2) the cracks, rather than the pores seem to have the dominant effect on Biot's coefficient; 3) the distribution of cracks and pores influences the Biot's coefficient and creates anisotropy. Two phenomenological equations were established by using the generalized mixture rule to describe the relationship between Biot's coefficient and rock microstructures, which give more accuracy results than the existing empirical equations.

Use of a two-dimensional discrete-element line-sink model to gain insight into tunnelling-induced deformations

A two-dimensional discrete-element model (DEM) is shown to provide useful information regarding the kinematics of ground deformation in response to tunnelling. Tunnel excavation and construction is a highly complex process and the line-sink model approach used in previous analytical studies provides a simple means to simulate the excavation process. A virtual sand box was created using DEM and grains were progressively deleted to simulate the sink. The surface settlement trough was determined and, when normalised by the maximum settlement, its shape was nearly constant and closely fitted a Gaussian curve. The deformations observed gave a good approximation to the displacement field predicted using the Verruijt and Booker analytical line-sink model. This preliminary study suggests that a simple line-sink DEM may provide a robust basic frame of reference for the complex mechanisms of ground movement around soft ground tunnels. More generally the results demonstrate the potential of using particulate DEM to study ground response to tunnelling.

Revised drag calculation method for coarse grid Lagrangian–Eulerian simulation of gas–solid bubbling fluidized bed

In discrete element model (DEM) for simulation of gas–solid fluidized bed, drag force is correlated by use of local parameters which would be excessively smoothed within coarse grid. This work studies the method of calculating drag force for coarse grid DEM simulation of bubbling fluidized bed. The so-called complete circumstance-dependent local porosity (CCLP) model is proposed to correlate drag force taking the local circumstance of particle into account. The resulting circumstance-dependent drag force is employed in two-dimensional DEM simulations of a real small-scale bubbling fluidized system, using coarse grid. The local porosity is shown to be revised to a greater extent at the junctions of the gas-rich and particle-rich regions by the proposed CCLP model, which indicates that the circumstance influences on drag force are highlighted in the dense–dilute transitional regions. The parameter, i.e. the amplification factor, involved in the CCLP model is rationalized by investigating the comprehensive capability of predicting the fluidization features. The bubble size and shape simulated at the optimal parameter are generally consistent with the experimental observations. The simulated fluctuation time scales and amplitudes of solid volume fraction, relative pressure and bed layer height are close to the experimental results. Simulations show that DEM performs well in modeling the time-varying waveforms for the physical quantities in bubbling fluidized bed by use of the revised drag calculation method, which proves the unfamiliar merits of coarse grid simulation in some ways.

Modeling of the permanent deformation characteristics of SMA mixtures using discrete element method

Recently, significant advancements in the modeling of asphalt concrete have been made in micromechanics to describe the behavior and performance of asphalt pavements using the properties of their component materials. On the other hand, this approach has great potential benefits in the field of asphalt technology for reducing or eliminating costly tests to characterize asphaltic mixtures. In this study, two-dimensional Discrete Element Modeling (DEM) was employed to investigate the deformation characteristics of Stone Matrix Asphalt (SMA). Instead of the randomly generated initial models Image processing techniques were employed to make it possible to compare the actual and virtual test results. For this purpose, a series of Unconfined Dynamic Creep tests were also carried out in the laboratory according to British Standards. It has been concluded that the developed 2D-model can well predict the deformation characteristics of SMA mixes, however the results of simulations under-predict the accumulated permanent strain obtained through laboratory tests.

Discrete element modeling of Martian pit crater formation in response to extensional fracturing and dilational normal faulting

[1] Pit craters, circular to elliptical depressions that lack a raised rim or ejecta deposits, are common on the surface of Mars. Similar structures are also found on Earth, Venus, the Moon, and smaller planetary bodies, including some asteroids. While it is generally accepted that these pits form in response to material drainage into a subsurface void space, the primary mechanism(s) responsible for creating the void is a subject of debate. Previously proposed mechanisms include collapse into lave tubes, dike injection, extensional fracturing, and dilational normal faulting. In this study, we employ two-dimensional discrete element models to assess both extensional fracturing and dilational normal faulting as mechanisms for forming pit craters. We also examine the effect of mechanical stratigraphy (alternating strong and weak layers) and variation in regolith thickness on pit morphology. Our simulations indicate that both extensional fracturing and dilational normal faulting are viable mechanisms. Both mechanisms lead to generally convex (steepening downward) slope profiles; extensional fracturing results in generally symmetric pits, whereas dilational normal faulting produces strongly asymmetric geometries. Pit width is established early, whereas pit depth increases later in the deformation history. Inclusion of mechanical stratigraphy results in wider and deeper pits, particularly for the dilational normal faulting, and the presence of strong near-surface layers leads to pits with distinct edges as observed on Mars. The modeling results suggest that a thicker regolith leads to wider but shallower pits that are less distinct and may be more difficult to detect in areas of thick regolith.

Two-dimensional discrete element modeling of a spherical steel media in a vibrating bed

A discrete element model was developed to model granular flow in different vibratory beds and the results are compared with experimental measurements of bulk flow velocity and bed expansion. The sensitivity of the model predictions to the contact parameters was considered and the parameters were optimized with respect to the experimental results. The difference between the model predictions of the bulk flow velocity and the measurements was less than 10% at four locations in media beds of two depths. The average bulk density of the vibrating beds was also predicted to be within 10% of the measured values.

Dike-induced deformation and Martian graben systems

The Tharsis region of Mars is characterized by large volcanic and tectonic centers with distinct sets of graben systems. Many of the radially oriented grabens have been inferred to form in response to intrusion of magmatic dikes. This interpretation is based primarily upon early physical and numerical (boundary element) models that were developed originally to understand surface deformation associated with dike emplacement on Earth. In this study, we constructed and analyzed two-dimensional discrete element models to test the hypothesis of shallow dike emplacement and widening as a primary mechanism for the production of grabens on Mars. In particular, our models are designed to explore the extent to which a widening subsurface dike—in the absence of regional extension or pre-existing faults—will induce near-surface graben formation. The use of discrete element models allows for the permanent deformation and material heterogeneity to be captured as opposed to boundary element models that are limited by an assumption of homogeneous elastic behavior. Our analyses consider both homogeneous materials as well as mechanical stratification. The results indicate that forcible widening of a dike alone is unlikely to produce grabens at the surface. Furthermore, estimates of subsurface dike widths and emplacement depths based solely on measurements of surface graben widths may significantly over- or underestimate actual parameters. Finally, the model results suggest that the ability to distinguish between fault-induced or dike-induced graben formation mechanisms may not be possible unless the subsurface mechanical stratigraphy can be well characterized.

Vibration induced flow in hoppers: DEM 2D polygon model

A two-dimensional discrete element model (DEM) simulation of cohesive polygonal particles has been developed to assess the benefit of point source vibration to induce flow in wedge-shaped hoppers. The particle–particle interaction model used is based on a multi-contact principle. The first part of the study investigated particle discharge under gravity without vibration to determine the critical orifice size ( B c) to just sustain flow as a function of particle shape. It is shown that polygonal-shaped particles need a larger orifice than circular particles. It is also shown that B c decreases as the number of particle vertices increases. Addition of circular particles promotes flow of polygons in a linear manner. The second part of the study showed that vibration could enhance flow, effectively reducing B c. The model demonstrated the importance of vibrator location (height), consistent with previous continuum model results, and vibration amplitude in enhancing flow.

Micromechanical fracture modeling of asphalt concrete using a single-edge notched beam test

Cracks in asphalt pavements create irreversible structural and functional deficiencies that increase maintenance costs and decrease lifespan. Therefore, it is important to understand the fracture behavior of asphalt mixtures, which consist of irregularly shaped and randomly oriented aggregate particles and mastic. A two-dimensional clustered discrete element modeling (DEM) approach is implemented to simulate the complex crack behavior observed during asphalt concrete fracture tests. A cohesive softening model (CSM) is adapted as an intrinsic constitutive law governing material separation in asphalt concrete. A homogenous model is employed to investigate the mode I fracture behavior of asphalt concrete using a single-edge notched beam (SE(B)) test. Heterogeneous morphological features are added to numerical SE(B) specimens to investigate complex fracture mechanisms in the process zone. Energy decomposition analyses are performed to gain insight towards the forms of energy dissipation present in fracture testing of asphalt concrete. Finally, a heterogeneous model is used to simulate mixed-mode crack propagation.

PREDICTING SOIL-RIGID WHEEL PERFORMANCE USING DISTINCT ELEMENT METHODS

A two-dimensional discrete element model (DEM) for the interaction between a rigid wheel and soil is presented using PFC2D code. The soil particles are modeled by clumps of two discs. The contact model between the particles includes cohesion by a so-called softening model. The parameters of the model represent soil having a cone index (CI) of 200 kPa or 400 kPa. The model of the wheel is based on 30 grousers, spaced equally around a drum 200 mm in diameter and 100 mm in width. Dynamic simulations were performed with different combinations of drawbar force, vertical load, and soil conditions. The traction performance of the wheel was calculated, and the results were compared with known theories and reported test results. The simulation results show reasonably good correlation, quantitatively and qualitatively, with previously reported results and theories, and emphasize the ability of the DEM to simulate soil-wheel interaction for design purposes. Prediction of wheel performance as a function of slip for driven, self-propelled, and towed wheels is presented for different combinations of soil conditions and vertical loads. The ability to investigate soil deformation, stress distribution beneath the wheel, and the influence of slip on sinkage is shown. Contrary to the prediction of empirical theories, the simulations suggest that vertical load and soil CI have different influences on tractive performance; this point warrants further investigation. The model also predicts a different behavior of motion resistance and net traction at high slip rates compared with empirical and semi-empirical methods.

Numerical and experimental investigations of the flow of powder into a confined space

In this paper, the flow behaviour of a powder as it is delivered into a confined space from a moving shoe is investigated. An experimental system has been developed to model the filling process. Two-dimensional discrete element models (DEMs) have also been constructed to simulate the flow process. Through a combination of experimental and numerical studies, qualitative and quantitative results are obtained, which provide new insights into the complicated filling process. DEM and experimental results have demonstrated that the flowability of powders can be characterised by a novel concept—the critical velocity. The flowability of powders with different shaped particles is assessed in terms of its influence on the critical velocity. It is shown that two groups of particle shapes can be distinguished. The first group consists of particle shapes that can tessellate, so that in principle they could completely fill the die (such as monosized rectangular and hexagonal particles). The second group includes those particle shapes that cannot tessellate. It is found that the former generally has a lower flowability than the latter. The powder behaviour during the filling of a stepped die is also analysed. Two major features have been observed: the formation of a forward concave shrink zone and a merge surface, where two different flow regimes meet, which are both filled with a low intensity. A low packing density is likely to be found in these two regions. A more chaotic filling process is induced by the presence of air. The built-up of air pressure can significantly slow down the filling process. Comparison of experimental and simulation results indicates that DEM simulations can capture the major features observed during the flow of powder into a confined space.

Modeling of damage evolution in soft-wood perpendicular to grain by means of a discrete element approach

The anisotropy of wood within the radial–tangential (RT) growth plane has a major influence on the cracking behavior perpendicular to grain. Within the scope of this work, a two-dimensional discrete element model is developed, consisting of beam elements for the representation of the microstructure of wood. Molecular dynamics simulation is used to follow the time evolution of the model system during the damage evolution in the RT plane under various loading conditions. It is shown that the results are in good agreement with experiments on spruce wood, and that the presented discrete element approach is applicable for detailed studies of the dependence of the microstructure on mesoscopic damage mechanism and dynamics of crack propagation in microstructured and cellular materials like wood.

Discrete element modelling of a broken ice field — Part II: simulation of ice loads on a boom

A two-dimensional discrete element model which simulates the dynamics and interaction forces between individual ice floes in a broken ice field has been described in the paper “Discrete Element Modelling of a Broken Ice Field — Part I: Model Development”. The present paper elaborates on the application of this model using three examples. The first example presents a simulation of the forces exerted on a boom when it is pulled through a broken ice sheet. This example refers to small-scale tests, in which the kinematic behaviour and calculated forces are compared with, and calibrated against, tests with such a boom in the ice tank at the National Research Council Canada (NRC, Ottawa). The two other examples, utilizing the calibration from the small-scale testing, study the full-scale interaction between a broken ice field and the boom. Example 2 shows that for an ice thickness of 1.0 m and a boom speed of 0.2 m/s, the average forces on a 250 m wide boom were 50 kN and 119 kN for ice concentrations of 0.4 and 0.6, respectively. In Example 2 the floe diameters ranged from 20 m to 36 m. The values of the parameters in the visco-elastic-plastic rheology (linear spring constant, viscous damping coefficient and friction coefficient) appeared to have marginal influence on the force exerted on the boom. The average force increases with increasing ice concentration, ice thickness, boom speed and boom width. Keeping the ice concentration, ice thickness and boom speed fixed, the average force on the boom is proportional to the boom width.

Discrete element modelling of a broken ice field — Part I: model development

This paper describes a two-dimensional discrete element model which simulates the dynamics and interaction forces between distinct ice floes in a broken ice field. The ensemble of ice floes, is modelled as a granular material consisting of circular discs of different diameters, constrained in a domain with displacement controlled or periodic boundaries. The dynamic behaviour of the ensemble is determined by calculating the motion of the individual discs caused by interaction forces and body forcing (shear forces from air and water drag, surface tilt and Coriolis forcing). The interaction forces arise either directly from contacts between adjacent discs or by squeezing of brash ice which may be present between the distinct floes. Multiple contacts between discs are allowed and a viscoelastic-plastic rheology is applied at contacts. A computer algorithm is developed by which a cell structure is used to quickly identify neighbouring discs in the domain.