Particle Flow Code In 3 Dimensions Research Articles

A meso‐damage‐based constitutive model for yellow sandstone under dry–wet cycles

AbstractThe mechanical properties of rocks weaken under dry–wet cycles. This weakening may significantly modify the safety reserve of underground caverns or reservoir bank slopes. However, meso‐damage has not been carefully studied based on micromechanical observations and analyses. Therefore, in this study, meso‐damage of a yellow sandstone is investigated and a meso‐damage‐based constitutive model for dry–wet cycles is proposed. First, computed tomography scanning and uniaxial compression tests were conducted on yellow sandstones under different dry–wet cycles. Second, the evolution of rock mesostructures and the damage mechanism subjected to dry–wet cycles were simulated using the discrete element method with Particle Flow Code in 2 Dimensions (PFC2D) software. Third, a constitutive model was proposed based on the meso‐statistical theory and damage mechanics. Finally, this constitutive model was verified with the experimental results to check its prediction capability. It is found that the radius and number of pore throats in the sandstone increase gradually with the number of dry–wet cycles, and the pore structure connectivity is also improved. The contact force of sandstone interparticle cementation decreases approximately linearly and the continuity of the particle contact network is continuously broken. The meso‐deformation and strength parameters show similar declining patterns to the modulus of elasticity and peak strength of the rock sample, respectively. This meso‐damage‐based constitutive model can describe well the rock deformation in the initial pressure density stage and the damage stage under the coupling effect of dry–wet cycles and loads.

Three-dimensional Meso-scale virtual strength test of steel slag porous asphalt mixture based on PFC3D

In recent years, steel slag has gained widespread utilization in pavement construction as a green, low-carbon building material. In this study steel slag aggregate (SSA) was used as a partial replacement for basalt aggregate in porous asphalt mixture. To gain an in-depth understanding of the microscopic cracking characteristics of steel slag aggregate porous asphalt concrete (SSA-PAC), laboratory three-point bending tests and numerical simulations were conducted. Based on CT scanning images, 3D models of SSA and basalt aggregates within particle size ranges of 4.75–9.5 mm and 9.5–13.2 mm were generated. These characteristic aggregates were then randomly placed to establish a three-dimensional model using PFC3D (Particle Flow Code in 3 Dimensions). The micro-contact parameters were derived through the conversion and calibration of macro and micro-mechanical parameters. The results of the 3D virtual strength test exhibited a close resemblance to those obtained from laboratory semi-circular bending (SCB) tests. The displacement trend chart of the aggregates revealed three distinct stages: vertical displacement, vertical displacement combined with a small amount of lateral displacement, and lateral displacement. Cracking mainly occurred at the interface between the aggregates and asphalt mortar, which aligned with actual cracking scenarios. The cracking behavior of the asphalt mixture was characterized by evaluating the number of cracks, notch width, and coordination number throughout the loading process. Additionally, the influence of loading rates on cracking behavior was analyzed. The results of this study demonstrated that the established 3D model effectively revealed the cracking characteristics of SSA-PAC.

Energy Evolution Law during Failure Process of Coal–Rock Combination and Roadway Surrounding Rock

The deformation and failure of a coal–rock system in a deep environment is affected by its own mechanical properties, natural endowments, and geological structures; it is very important to study the energy evolution law of coal–rock systems. For this purpose, a Particle Flow Code in 2 Dimensions (PFC2D) simulation was conducted to assess the coal–rock structure and roadway surrounding rock. The hard roof would produce a rebound “energy supply” phenomenon when the coal was destroyed, and the influence of rock strength on the energy evolution of the coal–rock combination was analyzed. In addition, the energy evolution law of roadway surrounding rock with different roof strength is studied; the energy evolution process of roof and coal seam and deep and shallow coal mass are compared, according to the energy storage characteristics of roadway surrounding rock in different areas; the partition energy storage model of roadway surrounding rock is established preliminarily and the concepts of energy storage area and energy supply area of roadway surrounding rock are proposed; the prevention and control methods of near-field rock burst in deep roadways are discussed, and the research conclusions can provide theoretical reference for the research on the mechanism of rock burst in deep coal mines.

Numerical investigation of hydrolysis failure of aggregates in loess

Large numbers of aggregates in loess are vital components of the skeletal structure of loess. In this study, a simulation of the water stability of aggregates using coupled computational fluid dynamics and the discrete-element method (CFD–DEM) is presented. For the simulation, the ‘fixed coarse-grid’ method of the Particle Flow Code in 3 Dimensions (PFC3D) software program was employed to simulate the particle–fluid coupling. With respect to the degradation law, a customised code was developed using Python, which transformed through the CFD–DEM model the hydrolysis of cement into the degradation process for the bond strength between particles. Under the action of different hydraulic gradients, the rate of hydrolysis of the aggregates increased rapidly with an increase in water pressure, and many piles of particles were denuded from the aggregates, thus causing the destruction of the aggregates. At the same time and under the same water pressure, the rate of hydrolysis of the multi-aggregates was always lower than that of the single aggregate. Also, the density and porosity of the aggregates would affect, to varying degrees, the water stability.

Analysis of the Influence of Fault Fracture Zone on Mining Response Based on FDM-DEM Coupling

Fault slip will cause a change in mining stress at the longwall face, which will cause adverse effects. In this study, on the basis of Fast Lagrangian Analysis of Continua in 3 Dimensions (FLAC3D) and Particle Flow Code in 3 Dimensions (PFC3D), the sliding of the fault fracture zone and its impact on the longwall working face were analyzed. The rock mass of the fault fracture zone with a certain thickness was constructed using rigid random model particles. The coupling between the wall element of PFC3D and the zone element of the continuous medium in the software was used to realize the transmission of force and displacement, and the interaction between the fault fracture zone and the working face was studied. The influence of the slip of different fault zone positions on the fault and working face was also explored using the method of externally disturbing the fracture zone of the fault. The numerical results showed that as the distance between the fault and the working face continued to decrease, the peak stress concentration in front of the longwall face first increased, then decreased, and gradually shifted to the vicinity of the fault zone. The stress mutation and fault slip occurred within a certain distance of the longwall face from the fault. When fault slip activation begins, the stress near the fault zone showed a sudden change of varying degrees with the advancement of the longwall face. This sudden change was caused by the influence of mining activities from the activation distance of the rock in the fault fracture zone and the rolling extrusion of the rock mass in the fracture zone. When the fault zone closer to the working face was disturbed, the influence on the fault zone and longwall face was greater. When the fault zone near the coal seam was disturbed, the rock mass and working face near the fault zone brought different degrees of dynamic responses, which were mostly instantaneous and had high frequency and amplitude. The results of this research could help in the mining of longwall mining affected by fault zones and have a certain guiding role in coal mining before crossing faults.

Using DEM method to study graphite migration of copper-based graphite composites during friction

The self-lubrication of copper-based graphite composites depends on the formation of a graphite lubricating film on the frictional interface, which results from the graphite migration from the matrix. In fact, the graphite migration process is difficult to observe and record during friction by experimental methods. In our work, a discrete element method (DEM) software “the Particle Flow Code in 2 Dimensions (PFC2D)” was employed to simulate and analyze the graphite migration dynamic process of copper-based graphite composites sliding against 45 steel. The simulation results show that a migrated graphite particle layer was formed on the composite surface during friction, and maintained dynamic equilibrium relied on graphite migration from the matrix. The graphite migration was affected by applied load: the larger the applied load was, the greater the migration depth and number of migration particles were. And the sliding speed has little effect on graphite migration. With increase of graphite content, the migration depth first decreased and then increased, and the number of migration particles increased. With increase of graphite cluster size, the migration depth first decreased and then increased, and the number of migration particles decreased. The simulation results were verified by test analysis on a self-made in-situ observation tribometer, the test results was consistent with simulation results.

Rock Strength Determination Based on Rock Drillability Index and Drilling Specific Energy: Numerical Simulation Using Discrete Element Method

In the present research, two real-time rock strength determination models based on the drilling parameters were studied. Firstly, a discrete element software named Particle Flow Code in 2 Dimensions (PFC2D) was used to analyze the applicability of rock drillability index and drilling specific energy, in which graded particle assemblies were created to simulate the rock behaviour. In the numerical models, Weibull distribution was used to randomize the bonds between particles and make the assembled rock model with different heterogeneity. The drilling process of a PDC (polycrystalline diamond compact) cutter was modelled in two steps: horizontal linear rock cutting and vertical pressing-in progress. From the horizontal linear rock cutting process, the peak cutting forces were obtained and vertical pressing-in process outputs the relationship between normal force and cutting depth. Subsequently, the methods for calculating rock drillability index and drilling specific energy were proposed in the discrete element model. Then, the relationship between the calculated indexes and rock strength was investigated (supported with the regression analysis). Moreover, the effect of rock heterogeneity, along with error comparison between the above two indexes, were discussed. The results showed that the rock drillability index is more accurate than drilling specific energy in rock strength assessment (The error is about 10% smaller).

The influence of aggregate shape properties on aggregate packing in porous asphalt mixture (PAM)

Aggregate shape properties is one of the factors that determine the packing conditions of asphalt mixtures. The influence of aggregate shape properties was evaluated by utilising aggregates in three shapes, namely cubical, blade, and disk. Three shape parameters, namely sphericity, shape factor, and roundness, were defined to quantify the shape properties of the aggregates. Herein, the influence of aggregate shape on the packing of porous asphalt mixture (PAM) was evaluated via comparative studies of PAM’s mechanical properties in laboratory measurements versus discrete element method (DEM) algorithmic simulations. PG-76 binder was used in the PAM, with compaction by a gyratory compactor. Simulation models of PAMs were built in Particle Flow Code in 3 Dimensions (PFC3D) algorithm simulation. The results showed that aggregate packing structure is greatly affected by aggregate shape properties, in terms of volumetric properties and mechanical properties. Statistical analysis results indicated that cubical shape is the recommended shape to optimise the quality of aggregate packing structure of PAM. The research provided in-depth analysis of PAM packing structure, in terms of volumetric and mechanical properties. The results of these experiments indicated that DEM simulation is an appropriate method to evaluate aggregate packing structure of PAM.

Evaluation of aggregate gradation on aggregate packing in porous asphalt mixture (PAM) by 3D numerical modelling and laboratory measurements

The packing conditions of unbound aggregate blends and porous asphalt mixture (PAM) are investigated via comparative studies between mechanistic laboratory measurements versus discrete element method (DEM) algorithmic simulations. Nine aggregate gradations with variations in 2.36–4.75 mm and 6.3–9.5 mm fractions were studied. For PAM, PG-76 binder which is a polymer-modified asphalt was used in the mixture, with compaction by gyratory compactor. Simulation models of unbound aggregate blends and PAMs were built in Particle Flow Code in 3 Dimensions (PFC3D) algorithm simulation. The simulation results were compared with the volumetric measurements of laboratory specimens. The results showed that the proportion of 6.3–9.5 mm fraction does not have notable influence on the aggregate packing structure, while 2.36–4.75 mm size fraction has notable influence. The 2.36–4.75 mm fraction has a tendency to either fill the voids of aggregate packing or affect re-orientation of stone-on-stone interlocking of the coarser fraction. DEM modelling provides a valuable aid to design feasible PAMs with a desired packing condition, which shall be supplemented with limited laboratory verifications.

Discrete element simulation on failure mechanical behavior of transversely isotropic rocks under different confining pressures

A large number of experimental investigations on anisotropic behavior of transversely isotropic rock have been conducted recently, and the strength and deformation anisotropy and macroscopic failure behavior and failure mechanism were studied in detail. However, the internal variation and microscopic failure mechanism of transversely isotropic rock have been rarely determined by laboratory tests, and few studies have reported these types of results. This paper presents an investigation of particle flow code in 2 dimensions (PFC2D) simulation on transversely isotropic rock under different confining pressures based on laboratory experiments. The transversely isotropic PFC2D model is established by the bonded-particle model (BPM) and the smooth-joint model (SJ) to represent the layer materials and weak planes, respectively. To reflect the experimental specimens accurately, BPM and SJ microparameters are calibrated first. The simulated strength and deformation anisotropy of transversely isotropic rock under different confining pressures are all consistent with the experimental specimens and can reflect the macroscopic failure behavior and failure mechanism of experimental specimens very well. On a microscopic level, the internal variation and microscopic failure mechanisms of transversely isotropic rock are studied in detail, and four types of microcracks, namely PB tensile cracks and PB shear cracks, which exist in the layer materials, and SJ tensile cracks and SJ shear cracks, which exist in the weak planes, are recorded and counted to reveal the microscopic failure mechanisms of transversely isotropic rock at different orientation angles. The evolution processes of microcracks and PB forces are also analyzed to investigate internal variations during the failure of transversely isotropic rock under different confining pressures.

Coupled Discrete Element-Finite Difference Method for Analysing Effects of Cohesionless Soil Conditioning on Tunneling Behaviour of EPB Shield

A computational scheme coupling PFC3D (Particle Flow Code in 3 Dimensions) and FLAC3D (Fast Lagrangian Analysis of Continua in 3 Dimensions) was performed to investigate influences of sand conditioning on the tunneling behaviour of earth pressure balance (EPB) shield in sandy ground. A detailed EPB shield and its near ground were modelled in the PFC3D while the other ground was simulated in the FLAC3D. Decreasing friction coefficients were used to characterize the fluidity improvement of conditioned muck particles. The results indicate that the residence time of muck in the excavation chamber is associated with its position and rotation directions of the spoke. The muck pressure and its difference in front of and behind the cutterhead decrease with the improvement of conditioning degree in a certain conditioning range, and an appropriate soil conditioning scheme can facilitate the control of chamber pressure. In addition, the torque of cutterhead decreases more significantly than the thrust with an improvement of soil conditioning degree within a normal conditioning range.

Numerical simulation of the dynamic evolution of the friction interface of PTFE/45 steel friction pair

The software of the Particle Flow Code in 2 Dimensions (PFC2D) was employed to simulate the dynamic evolution of the friction interface of the PTFE/45 steel friction pair. The simulation results showed that the PTFE material near the friction interface can be divided into three different layers: (1) the transfer particle layer; (2) the quasi-fluid layer; and (3) the elastic-plastic deformation layer. The direction of the horizontal component force applied on the PTFE particles within the quasi-fluid layer and elastic-plastic deformation layer kept consistent with the movement direction of the 45 steel. A ‘non-contact area’ was formed at the moving front of the PTFE surface, and the area size was affected by applied load and sliding speed. The higher the load is, the shorter the ‘non-contact area’ is; the greater the speed is, the longer the ‘non-contact area’ is. The size of non-contact area has little effect on the number of transfer particles, but the worn particles decrease with the increase of ‘non-contact area’. The simulation results are significant for optimizing material design and improving the friction performances.

Discrete Element Modeling of Soil Displacement Resulting from Hoe Openers

Abstract. Soil displacement is the most important performance indicator for seed openers, as it affects the uniformity of seeding depth. In this study, a hoe opener was modeled using Particle Flow Code in 3 Dimensions (PFC3D), a discrete element modeling software program. The objective was to simulate soil displacement in terms of soil throws. To validate the model, an air drill with hoe openers was tested in a field with clay soil at a working depth of 38 mm and travel speed of 8 km h-1. Soil throw resulting from the hoe opener was measured. To calibrate the model, a virtual soil shear test was created within PFC3D, and the output soil shear torque was compared to the torque measured in the same field. The result showed that the calibrated effective modulus, a critical micro-parameter of model particles, was 5.692 × 107 Pa. With this calibrated value, the simulated soil throws agreed well with the measured throws, with a relative error of 15%. The model was used to compare different hoe opener designs: single-shoot spread, double-shoot side-band, double-shoot paired-row, and triple-shoot openers. Among all these openers, the side-band opener resulted in the least lateral soil throw, and the paired-row opener resulted in the lowest vertical soil throw but the highest lateral throw. The developed model was effective for examining the effects of opener geometry on soil displacement. Keywords: DEM, Hoe, Opener, PFC3D, Soil displacement.

The mechanism of hysteretic ground settlement caused by shield tunneling in mixed-face conditions

Shield is used more and more widely, such as coal mine roadway, hydropower tunnel, traffic tunnel and so on. But Tunneling with a tunnel boring machine (TBM) may cause inevitable ground subsidence. Though over the world numerous researches have been conducted for surface settlement induced by TBM in soft ground, the researches of surface settlement induced by TBM in a sandy cobble stratum are limited and a comprehensive study of the mechanism of delayed settlement induced by TBM in a sandy cobble stratum is unavailable. A ground stable state or surface settlement can be determined based on real-time monitoring data for surface dynamic subsidence. Subsequently, TBM tunneling parameters can be adjusted to accommodate various geological conditions. A sand-pebble-soil matrix is a typical heterogeneous material. The macro-mechanical performance of this matrix significantly differs from any material. In a general situation with a low water level and minimal disturbance, a stratum can stabilize by itself for a long period of time. Considering the characteristics of the stratum, ground loss can be divided into two phases: immediate settlement, which tends to stabilize, and delayed settlement, which tends to occur in sand-cobble strata, where settlement develops at a much slower rate than in single-medium strata. Monitoring data is not sufficient to guide the construction in the case of delayed settlement. Cobble-soil matrix can be treated as a spatial structural system that is constituted by single granular soil, aggregates of granular soil and pebble grains. Based on Particle Flow Code in 2 Dimensions (PFC2D), the mechanical characteristics of the matrix and the TBM tunneling process were numerically simulated. Movements of the pebble grains were traced and recorded in real time. The model addressed the mechanism of surface collapse from the perspective of mesomechanics. According to the model, a matrix formed self-stabilizing arch that overlies an underground cavity seems gradually wear out with expanding the cavity and eventually penetrating to the ground surface. The law of ground movement and the formation mechanism of ground subsidence in TBM advancement were investigated. The main factors that affect surface subsidence are the speed of advancement, the underground water level and the supporting period. In the numerical analysis, the surface-loss lag was reproduced and the field monitoring data were verified. The findings of this study provide a new method for investigating ground subsidence in similar strata.

Investigation of Various Parameters Effect on Cerchar Abrasivity Index with PFC3D Modeling

The Cerchar test is one of the appropriate and routine tests for determining the rock abrasion; but as for the costs and pin wear measurement errors in laboratory procedures and lack of access to laboratory equipment, using of numerical modeling can lead to use of greater number of samples required during the course of mechanized excavation and reduce the costs and errors in the laboratory test. In this study, the Cerchar abrasivity test was modeled using PFC3D (Particle Flow Code in 3 Dimensions) software. In order to verify the simulation results, Cerchar laboratory test results obtained by Rostami (Rock Mech Rock Eng 47(5):1905–1919, 2014) were compared with the numerical modeling results. In modeling studies, the effects of some parameters such as apply load, test speed, pin hardness and scratching distance on pin wear were investigated. As a conclusion of the study, good agreement between modeling and experimental results was obtained for a given condition. As in the experiment with various loads in both laboratory tests and modeling, with increasing applied load the Cerchar abrasivity index also increased in the experiment with Rockwell hardness HRC (An abbreviation for Rockwell Hardness measured on the C scale. The Rockwell test determines the hardness by measuring the depth of penetration of an indenter under a large load compared to the penetration made by a preload, that on the C scale use from a indenter with 120° cone and 150 kgf load) 42.

A PFC2D model of the interactions between the tire and the aggregate filled arrester bed on escape ramp

The stopping distance of a runaway vehicle is determined by the entry speed, the design of aggregate-filled arrester bed and the longitudinal grade of escape ramp. Although numerous previous studies have been carried out on the influence of speed and grade on stopping distance, taking into account aggregate properties is rare. Firstly, this paper analyzes the interactions between the tire and the aggregate. The tire and the aggregate are abstracted into a big particle unit and a particle combination unit consisting of lots of aggregates, respectively. Secondly this paper proposes an assumption that this interaction is a kind of particle flow. Later, this paper uses some particle properties to describe the tire-particle unit and aggregate-particle unit respectively, then puts forward several simplified steps of modeling by particle flow code in 2 dimensions (PFC2D). Therefore, a PFC2D micro-simulation model of the interactions between the tire and the aggregate is proposed. The parameters of particle properties are then calibrated by three groups of numerical tests. The calibrated model is verified by eight full-scale arrester bed testing data to demonstrate its feasibility and accuracy. This model provides escape ramp designers a feasible simulation method not only for predicting the stopping distance but also considering the aggregate properties.

Experimental and Numerical Analysis of the Effects of Curing Time on Tensile Mechanical Properties of Thin Spray-on Liners

The effects of curing time on tensile elastic material properties of thin spray-on liners (TSLs) were investigated in this study. Two different TSL products supplied by two manufacturers were tested comparatively. The “dogbone” tensile test samples that were prepared in laboratory conditions with different curing times (1, 7, 14, 21, and 28 days) were tested based on ASTM standards. It was concluded that longer curing times improves the tensile strength and the Young’s Modulus of the TSLs but decreases their elongation at break. Moreover, as an additional conclusion of the testing procedure, it was observed that during the tensile tests, the common malpractice of measuring sample displacement from the grips of the loading machine with a linear variable displacement transducer versus the sample’s gauge length had a major impact on modulus and deformation determination of TSLs. To our knowledge, true stress–strain curves were generated for the first time in TSL literature within this study. Numerical analyses of the laboratory tests were also conducted using Particle Flow Code in 2 Dimensions (PFC2D) in an attempt to guide TSL researchers throughout the rigorous PFC simulation process to model support behaviour of TSLs. A scaling coefficient between macro- and micro-properties of PFC was calculated which will help future TSL PFC modellers mimic their TSL behaviours for various tensile loading support scenarios.

Numerical Simulation on Combined Deformation of Tip-Loaded Cantilever Beam with Particle Flow Code

In order to calculate the combined deformations of an Euler-Bernoulli cantilever beam subjected to bending moment, twisting moment, transverse load and axial load, particle flow code in 3 dimensions (PFC3D) is used with parallel bonds model. The computed deformations, including transverse deflections, rotations about axis, maximum normal and shear stresses, were compared with the analytical beam-theory solution in terms of axial tension, axial compression and none axial load, respectively. Between computed results and analytical beam-theory solution, the error bands are greater than 99.7% at the beam tip, while the error of the transverse deflection of the whole beam is less than 0.6%. So, the PFC3D is able to precisely simulate the combined deformation of cantilever beam, and this work has special reference to engineering calculations and designs when PFC is applied to model the mechanical behaviors of continuum materials.

Simulation and Analysis on the Direct Shearing of Semi-Fixed Abrasive Tool

This paper firstly summarizes two-dimensional numerical simulation of semi-fixed abrasive tool (SFAT), then three-dimensional model of SFAT is established by PFC3D (Particle Flow Code in 3 Dimensions). In order to make the compression ratio simulation match to experimental one about SFAT, the mechanical parameters of model are adjusted. In the direct shearing simulation, the relation between the shear stress and the horizontal shear displacement under different parallel bond stiffness are obtained. By Comparative Analysis the numerical results and test experiments of the direct shearing, the three-dimensional model of SFAT is further proven rational.

Numerical simulation of the top coal caving process using the discrete element method

How to understand the top coal caving process and increase the top coal recovery ratio is one of the urgent problems to resolve for longwall top coal caving technology. This paper discusses a new theory and technology of top coal caving with vibration. The vibration device is mounted on the shield beam of the top coal caving support. The vibrator destroys the arch structure formed during the top coal caving process, which results in the smooth top coal caving process, and in this way the top coal recovery ratio is increased. The distinct element method (DEM) numerical software particle flow code in 2 dimensions (PFC2D) is used for the numerical simulation. It is proven that the vibration can easily destroy the arch structure which is formed during the top coal caving process. The parameters about when the arch structure would be formed during the top coal caving process have been obtained. The movement of the top coal caving process under the vibration condition makes a more stable layer uniform caving performance. The aim of the top coal caving with vibration technology, to increase the top coal recovery ratio and to lower the waste content rate, has been achieved.