Discrete Element Numerical Simulation Research Articles

Research on crack propagation and rock fragmentation efficiency under spherical tooth dynamic indentation

Rock dynamic indentation is the most basic form of rock dynamic fragmentation, understanding the rock failure mechanism and influence factors of breaking efficiency plays important roles in improving impact drilling efficiency. According to the research achievements of Marshall, the theoretical model of radial crack and lateral crack length considering confining pressure and hydraulic pressure was established, analyzing the influence of confining pressure, hydraulic pressure on crack propagation, and the influence of loading rate on rock fragmentation effect. In addition, the discrete element numerical simulation method was used to study the characteristics of crack formation and propagation and the influence of loading rate on breaking effect under spherical tooth dynamic indentation. The results indicate that theoretical analysis and numerical simulation results are basically identical, with the increase of dynamic load, the damaged area and lateral crack growth, and radial crack initiates from the damaged area and propagates towards the rock free surface, forming rock fragments eventually; under the same dynamic load amplitude and duration, the increase of confining pressure has an inhibitory effect on damaged area, lateral crack, and radial crack, the increase of hydraulic pressure has a promoting effect on damaged area and lateral crack but has an inhibitory effect on radial crack; under the same dynamic load amplitude, rock breaking volume first increases and then decreases with the duration shortening, and when the dynamic load amplitude is 8.5 kN, duration is 1.25 ms, the crushing volume is the largest. The research achievements of this paper can provide reference for understanding dynamic fragmentation mechanism and improving impact drilling efficiency.

Study on the Large Deformation Characteristics and Disaster Mechanism of a Thin‐Layer Soft‐Rock Tunnel

In view of the large deformation of thin‐layer soft rock in the No. 2 inclined shaft of the Muzhailing Tunnel, we performed an experimental investigation on the mineral composition, physical characteristics, and uniaxial compressive strength of the surrounding rock of the tunnel. The characteristics of the large deformation of the surrounding rock of the tunnel were analyzed, and the main factors influencing the deformation of the tunnel were revealed. The influence of various factors on the large deformation of the surrounding rock was analyzed using the 3DEC‐Trigon discrete element numerical simulation method. The results show that (1) the deformation of the surrounding rock of the tunnel has remarkable asymmetry, the deformation of the initial support of the tunnel is significant, and the buried depth of the area where the maximum deformation of the tunnel exceeded 1 m is greater than 500 m; (2) the main factors influencing the deformation of a thin‐layer slate tunnel include joint inclination, buried depth, water absorption, and softening of the surrounding rock; and (3) the maximum deformation of the surrounding rock is observed for a joint angle of 45°, at which the buried depth is directly proportional to the deformation and failure of the tunnel. Furthermore, after the surrounding rock was softened by water absorption, the floor of the tunnel, the left shoulder socket, and the right side of the tunnel are deformed greatly. The results of this study will provide a theoretical basis for the study of similar deformation control methods and supporting measures for tunnels excavated in thin‐layer soft rock.

Extended kinetic theory for granular flow over and within an inclined erodible bed

We employ kinetic theory, extended to incorporate the influence of velocity correlations, friction and particle stiffness, and a model for rate-independent, elastic components of the stresses at volume fractions larger than a critical value, in an attempt to reproduce the results of discrete-element numerical simulations of steady, fully developed, dissipative, collisional shearing flows over and within inclined, erodible, fragile beds. The flows take place between vertical, frictional sidewalls at different separations with sufficient total particle flux so that differently inclined, erodible beds result. Numerical solutions of the spanwise-averaged differential equations of the theory and the associated boundary conditions are seen to be capable of reproducing profiles of stresses, solid volume fraction, average velocity and the strength of the particle velocity fluctuations, both in the rapid collisional flow above the bed and in the slower creeping flow within the bed. The indication is that extended kinetic theory has the unique ability to faithfully describe steady, inhomogeneous, granular shearing flows, ranging from dilute to extremely dense, using balances of momentum and energy and employing boundary conditions that are associated with the balances, with a small number of physically determined, microscopic parameters.

Measurement of Restitution and Friction Coefficients for Granular Particles and Discrete Element Simulation for the Tests of Glass Beads.

A slant plate flat throw test system for measuring the restitution coefficient of granular materials and a sliding friction test instrument for measuring the friction coefficient between discrete particles and continuum boundary surface materials are developed. The restitution coefficients of the glass bead particles, the glass beads relative to the glass plate, the composite of glass plate and the rubber membrane and the friction coefficients between the glass beads and the rubber film and the filter paper are measured by the designed methods. Based on the measured restitution coefficient and friction coefficient, the discrete element numerical simulation is carried out for triaxial test and plane strain test. Through comparing the experimental results and the discrete element numerical simulation results, the feasibility and rationality of the designed measurement methods and the discrete element numerical simulation are verified. The measuring methods developed in this paper can be further applied to the tests of other fine particles.

Three dimensional steady‐state locus for dry monodisperse granular materials: DEM numerical results and theoretical modelling

SummaryIn this paper, steady‐state conditions for ideal monodisperse dry granular materials are both theoretically and numerically analysed. A series of discrete element (DEM) numerical simulations have been performed on a periodic cell by imposing stress paths characterized by different Lode angles, pressures, and deviatoric strain rates. The dependence of the material response on both inertial number and loading path has been discussed in terms of void ratio, fabric, and granular temperature. DEM numerical results have been finally compared with the prediction of an already conceived model based on both kinetic and critical state theories, here suitably modified to account for three‐dimensional conditions.

Evaluation of injection well patterns for optimum fracture network generation host-rock formations: An application in in-situ leaching

Artificial fracture stimulation in host-rock using soundless cracking demolition agents (SCDAs) is a potential alternative for rock fragmentation in enhanced in-situ leaching applications of mineral ores because conventional mining techniques are becoming increasingly uneconomic with declining ore-grade. In this study we investigated the impact of different injection well patterns on the fracture network propagation of an SCDA charged rock mass using a discrete element numerical simulation. First, a laboratory scale fracturing experiment was conducted on a simple specimen having two injection wells filled with SCDA. The results of the experiment were used to validate the numerical simulation, and the model was then extended to assess the SCDA charged fracture propagation in a host-rock formation with different injection well patterns typically found in the field. A two-staged fracturing process was identified from the numerical simulation observations and was defined as pre-fracture coalescence and post-fracture coalescence stages. The expansive pressure development within injection wells from the SCDA charging and the corresponding fracture growth was found to be dependent on the number of injection wells surrounding a centre injection well. With the increasing number of injection wells, the fracture connectivity between wells was found to decrease and consequentially a diminishing return of fracture density was observed. This is a result of the larger compressive stress fields generated within the rock mass with the increasing number of SCDA injection wells. The optimum number of injection wells surrounding a centre injection well was found to be four or five (five or six injection well pattern), which produces the highest fracture connectivity and the fracture density for enhanced ISL applications.

Numerical Experiments on Triaxial Compression Strength of Soil‐Rock Mixture

Soil‐rock mixture is a kind of unfavorable geologic material, and it is composed of low‐strength soil particles and high‐stiffness rock blocks. Mechanical properties of soil‐rock mixture were controlled by the internal mesoscopic medium, thus resulting in great difficulties of determination of mechanical parameters. In this paper, influences of rock content, mesoscopic features, and random distribution of mixture in soil‐rock mixture on its shear strength were discussed through discrete element numerical simulation of the laboratory triaxial test. Results demonstrated that, with the increase of rock content, the internal friction angle of soil‐rock mixture increased continuously, while the cohesion of soil‐rock mixture decreased firstly and then increased. The stress‐strain curve belonged to a nonlinear hardening type, which was close to soil characteristic. However, the shear strength was affected by mesoscopic medium of mixture particles significantly, resulting in the strong discreteness of strength, and only by large amounts of data statistics can we get a better regularity of strength. The research results can provide references to determine mechanical parameters of soil‐rock mixture.

Energy Dissipation and Storage in Underground Mining Operations

In this paper, we focus on the energy alteration during longwall mining in an attempt to mimic the conditions of a coal mine in Western Turkey. We verify the proposed model using existing analytical and numerical solutions in terms of stress components. Based on the verified numerical model, the energy balance during longwall retreat is studied rigorously. It is found that excavation-induced increment of external work increases linearly with time, while the stored strain energy increment is quadratic. Meanwhile, the strain energy increment rate gradually decreases with longwall progress because of excavation-induced higher stored energy within the adjacent coal block. The energy dissipation process during lonwall mining, corresponding to crack propagation, is divided into four stages, namely initiation stage, steady growth stage, sharp increment stage, and stabilisation stage. Our results provide new insights into energy evolution during longwall mining both from the reversible and irreversible points of view. The current paper shows, for the first time, that the extended finite element method is suitable to describe the crack propagation during longwall mining. The excavation induced crack propagation in the roof strata predicted by the model is in agreement with the “arch-shaped” patterns obtained using laboratory tests and Discrete Element numerical simulations.

Fluid–solid transition in unsteady, homogeneous, granular shear flows

Discrete element numerical simulations of unsteady, homogeneous flows have been performed by shearing a fixed volume of identical, soft, frictional spheres. A constant, global, shear rate was instantly applied to particles that are initially at rest, non interacting, and randomly distributed. The granular material exhibits either large or small fluctuations in the evolving pressure, depending whether the average number of contacts per particle (coordination number) is less or larger than a critical value. When the coordination number is less than the critical value, the amplitude of the pressure fluctuations is dependent on the shear rate, whereas, it is rate-independent in the opposite case, signatures, according to the case, of fluid-like and solid-like behaviour. The same critical coordination number has been previously found to represent the minimum value at which rate-independent components of stresses develop in steady, simple shearing and the jamming transition in isotropic random packings. The observed complex behaviour of the measured pressure in the fluid–solid transition can be predicted with a constitutive model involving the coordination number, the particle stiffness and the intensity of particle agitation.

Numerical and experimental study on the formation mode of a landslide dam and its influence on dam breaching

The deposition morphology of a landslide dam determines the position of initial breach and sequentially affects the direction of lateral erosion. Twenty-seven discrete element numerical simulations were carried out to investigate the deposition morphology of landslide dams concerning three factors, which include the valley shape, the valley bed inclination and the landslide velocity. The simulation results show that the valley shape and the landslide velocity affect the dam morphology in both transverse and longitudinal directions, while the valley bed inclination mainly affects the longitudinal morphology of dams. Further, a flume experiment was carried out to investigate the specific effects of the dam morphology on the overtopping erosion of landslide dams. The results of experiment show that for the dams in different deposition morphologies and with different initial breaches, the breach widths and the total sediment discharges induced by overtopping erosion are different.

Sinking during earthquakes: Critical acceleration criteria control drained soil liquefaction.

This article focuses on liquefaction of saturated granular soils, triggered by earthquakes. Liquefaction is defined here as the transition from a rigid state, in which the granular soil layer supports structures placed on its surface, to a fluidlike state, in which structures placed initially on the surface sink to their isostatic depth within the granular layer. We suggest a simple theoretical model for soil liquefaction and show that buoyancy caused by the presence of water inside a granular medium has a dramatic influence on the stability of an intruder resting at the surface of the medium. We confirm this hypothesis by comparison with laboratory experiments and discrete-element numerical simulations. The external excitation representing ground motion during earthquakes is simulated via horizontal sinusoidal oscillations of controlled frequency and amplitude. In the experiments, we use particles only slightly denser than water, which as predicted theoretically increases the effect of liquefaction and allows clear depth-of-sinking measurements. In the simulations, a micromechanical model simulates grains using molecular dynamics with friction between neighbors. The effect of the fluid is captured by taking into account buoyancy effects on the grains when they are immersed. We show that the motion of an intruder inside a granular medium is mainly dependent on the peak acceleration of the ground motion and establish a phase diagram for the conditions under which liquefaction happens, depending on the soil bulk density, friction properties, presence of water, and peak acceleration of the imposed large-scale soil vibrations. We establish that in liquefaction conditions, most cases relax toward an equilibrium position following an exponential in time. We also show that the equilibrium position itself, for most liquefaction regimes, corresponds to the isostatic equilibrium of the intruder inside a medium of effective density. The characteristic time to relaxation is shown to be essentially a function of the peak ground velocity.

Brittleness Evaluation of Shale Based on the Brazilian Splitting Test

Brittleness is an important mechanical parameter of shale reservoirs and has a significant effect on hydraulic fracturing. Traditional evaluation methods of shale brittleness are mainly based on complete stress-strain curves under compressive loading, which can barely describe the fracture characteristics of shale during hydraulic fracturing. This paper proposes to define the brittleness index based on the Brazilian splitting test and establishes a corresponding evaluation method, forming a tensile brittleness evaluation system for noncontinuous shale. The Brazilian splitting test and discrete element numerical simulation are carried out to study the crack distribution characteristics after tensile failure as well as the influence of anisotropy and scale effect on the brittleness of shale. The results show that the tensile brittleness index is more accurate and sensitive to condition changes than the compressive brittleness index. The experimental shale cores are from the Longmaxi formation, Silurian system, Sichuan basin.

ANALYSIS OF DISCRETE ELEMENT NUMERICAL SIMULATION FOR DEEP FOUNDATION PIT EXCAVATION WITH PCMW RETAINING STRUCTURE

The stability of deep foundation pit is an important engineering problem, in which effective supporting structure is the basis of foundation pit engineering. The discrete element method is employed in this paper, and a modeling and numerical simulation method of foundation pit and supporting structure is proposed. A close-packed discrete element model is used to build the model of initial layers, and the clump model of discrete element is used to build pipe piles with smooth surfaces. A deep foundation pit is taken as an example. The geometrical model can be built using the three-dimensional discrete element software MatDEM3D.The mechanical parameters of elements are determined according to the mechanical properties of soil. In numerical simulations, the soil layers are compacted using a pre-balancing operation, after which the deformation of soil and piles are simulated during the excavation process of foundation pit. The numerical simulation results are compared with the measured monitoring data to evaluate the effectiveness of foundation pit support structures. The discrete element numerical simulation method of foundation pit has potential application prospect in the stability prediction of foundation pit excavation process and the evaluation of the effectiveness of supporting structures.

Theoretical and simulation analysis of abrasive particles in centrifugal barrel finishing: Kinematics mechanism and distribution characteristics

Centrifugal barrel finishing processes, as a class of typical mass finishing methods, have been used to deburr and finish metallic components across a wide range of industries. For achieving excellent finishing effects and high efficiency, the determination of the process parameters, especially the transmission ratio, is necessary. Almost all the process parameters remain largely empirical owing to the motion uncertainty of the abrasive particles in the drum. The velocity and acceleration of arbitrary point in or on the drum were analyzed at different transmission ratios. Then, the kinematics mechanism and the distribution characteristics of the abrasive particles in the drum were analyzed to find the relationship between the transmission ratio and the motion status of the abrasive particles. By means of discrete element numerical simulation, the critical value of the transmission ratio was finally determined. The transmission ratio has a profound influence on abrasive particles' behavior for seeking the ideal motion status of the abrasive particles that can ensure the normal running of finishing processes.

Strength model and mesoscopic mechanism of intermediate principal stress effect on rock strength

Intermediate principal stress effect on rock strength, strain, energy dissipation and micro crack distribution are studied by using particle discrete element numerical simulation software PFC3D. Numerical simulation reproduces the typical phenomenon that rock strength has an initial increase and a subsequent decrease with the increase of intermediate principal stress. On micro level, the increase of intermediate principal stress makes the micro cracks distribution in horizontal plane from symmetrical to asymmetrical. When intermediate principal stress ratio b is large than 0.5, micro cracks have a substantial increase at yield stage and energy dissipated by frictional sliding also has a substantial increase. Intermediate principal stress restrains the expansion of micro cracks normal to intermediate principal stress direction (or with component in this direction), which makes rock strength increases. On the other side, intermediate principal stress promotes the expansion of micro cracks normal to minimum principal stress direction (or with component in this direction), which makes rock strength decreases. The restraint and promotion of micro cracks in different directions lead to the intermediate principal stress effect. Based on Weibull theory, a failure probability model is developed to describe the effect of the intermediate principal stress on rock strength. Using shear stress to express the computed strength of each micro-unit, a strength criterion is proposed to quantitatively reflect the intermediate principal stress effect on rock strength. New criterion can be regarded as a modified Mohr-Coulomb criterion with a uniformity coefficient and it becomes Mohr-Coulomb criterion when materials are absolutely homogeneous. New criterion matches previously published experimental results and numerical simulation results better than common strength criterion.

Segregation in inclined flows of binary mixtures of spheres

We outline the equations that govern the evolution of segregation of a binary mixture of spheres in flows down inclines. These equations result from the mass and momentum balances of a kinetic theory for dense flows of inelastic spheres that interact through collisions. The theory employed for segregation is appropriate for particles with relatively small differences in size and mass. The flow of the mixture is assumed to reach a fully developed state much more rapidly than does the concentrations of the two species. We illustrate the predictions of the theory for a mixture of spheres of the same diameter but different masses and for spheres of different diameters but nearly the same mass. We show the evolution of the profiles of the concentration fractions of the two types of spheres and the profiles in the final, steady state. The latter compare favourably with those obtained in discrete-element numerical simulations.

Flow of top coal and roof rock and loss of top coal in fully mechanized top coal caving mining of extra thick coal seams

This study investigates the flow and caving characteristics of top coal and roof rock, as well as top coal loss pattern in the fully mechanized top coal caving mining of extra thick coal seams. The two dimensional discrete element numerical simulation software program, particle flow code (PFC), is used for the simulation of top coal caving and the inversion analysis. The original locations, distribution, and migration pattern of caved top coal and lost coal were obtained. The analysis shows that in the initial site of caving, the caved bodies are in the form of arc shaped strips in front of the working face. During the caving, caved bodies of different heights move towards the lower rear of the face at different speeds. The lost coal and caved roof rock are originally located at the interface between coal seam and roof, the lost coal is mainly distributed in the goaf on the floor. Behind the support, the caved top coal bodies originally are arc shaped strips, with the highest points located at the midline of the caving opening. The strips are more curved near the goaf than those near the support. During top coal caving, the strips successively cave, with the adjacent outer strip replacing the caved one. The variations of top coal loss and waste rock ratio with time reflect the different phases of top coal caving. In order to improve coal recovery and limit the amount of caved roof rock, the waste rock ratio should be controlled below 10 %. When the waste rock ratio reaches this value, the caving opening should be closed. This paper provides theoretical bases for the improvement of top coal recovery in the fully mechanized top coal caving mining of extra thick coal seams.

Anisotropy and lack of symmetry for a random aggregate of frictionless, elastic particles: theory and numerical simulations

We consider a random aggregate of identical, frictionless spheres whose contact is maintained by an applied pressure. The aggregate is then subjected to an axial compression at fixed pressure. We show that the incremental elastic response of the resulting transversely isotropic material is characterized by six rather than by five independent coefficients and that the stiffness tensor does not have the major symmetry. This is because we permit deviations from an affine deformation that are determined by local equilibrium, when anisotropy is present. Discrete element numerical simulations confirm these findings.

THREE-DIMENSIONAL DISCRETE ELEMENT ANALYSIS OF RAILWAY BALLAST’S SHEAR PROCESS BASED ON PARTICLES’ REAL GEOMETRY

Ballast beds are made up of particles with diverse sizes and shapes. Particle shape plays a fairly important role in affecting ballast aggregate’s mechanical behaviors; however, conventional grading curves indicating particle unidirectional size distribution cannot describe ballast particle shape characteristics comprehensively. Computer-vision technology is applied to obtaining three orthogonal views of a ballast particle, then extracting outlines of these three views to compute particle shape characteristic parameters. Three dimensional discrete element numerical simulations of ballast aggregate are processed by a self-developed program using elements which are built based on a particle’s three orthogonal views and identical in shape characteristics to realistic ballast particles. The computer-vision based discrete element method is validated with predictions from discrete element simulations matching closely with laboratory direct shear test results. Ballast aggregate’s deformation features and micro-scale mechanical behaviors in direct shear tests are investigated in depth based on the validated discrete element method

Reply to comment by Chen et al. on “Controls on the size and geometry of landslides: Insights from discrete element numerical simulations”

Chen et al.'s comment presents limit equilibrium (LE) calculations of slope stability, which yield different landslide geometries compared with those obtained by Katz et al. (2014) using the Discrete Element Method (DEM). Previous work, however, has demonstrated excellent agreement in the slide geometries and sizes obtained by DEM vs. those obtained by limit analysis, thereby lending confidence to DEM and to limit analysis as methods to study slope instability and geometry. We suggest three reasons why the LE results may differ from DEM: (1) LE is a static method, which seeks a single failure surface to predict slope stability. Although it captures well the average slope conditions, the details of the stress distribution may be inaccurate. (2) DEM is a dynamic method that holistically simulates the evolution of stress and strain. Thus it is better suited to simulate far from equilibrium situations, such as overly steep slopes with FS<1, which have strong dynamic responses. (3) The geometries of the slides presented by Chen et al. appear to be constrained by the domain size. We expect that a larger simulation domain may allow exploration of additional slide geometries, potentially with better correspondence with those of the DEM simulations.