PFC3D Simulations Research Articles

Study on the macro–micro evolution of compaction characteristics of coal gangue with different grain sizes under side-limit compression conditions

Currently the main method of mine solid waste disposal and utilization is to apply gangue to underground filling. For the grading characteristics of coal gangue in the hollow zone in underground filling, the state of pressure and the mechanical properties of coal gangue filling materials under different particle sizes. In this paper, through laboratory tests and numerical simulations, the bearing characteristics and deformation damage of gangue are deeply investigated and analyzed from both macroscopic and microscopic perspectives. The results of the study show that when the axial pressure reaches a certain threshold, the strain increases accordingly with the increase in grain size. Under the axial pressure condition of 15MPa, the bearing capacity of gangue with different grain sizes under the lateral pressure of steel cylinder showed obvious positive correlation. In the software PFC3D simulation, as the particle size of gangue particles increases, it has a significant effect on the natural stacking porosity of the specimen, and gangue particles are more prone to force chain instability and failure. Mixed particle size gangue can significantly reduce the natural accumulation porosity of the specimen, thus improving its overall stability. Significant displacement triangles existed in the top and lateral directions of the B1 (0–5 mm), B2 (5–10 mm), and B5 (0–20 mm) specimens under the same circumferential pressure conditions. The results of the study are of great significance for further selection of reasonable gangue gradation and determination of its mechanical properties.

Study on multi-scale damage and failure mechanism of rock fracture penetration: experimental and numerical analysis

In natural rock masses, joints or fractures usually occur at different penetrations. To study the deformation and failure behavior of rock mass with different fracture penetrations, a series of triaxial compression experiments were conducted on rock specimens containing prefabricated fracture at penetrations of 0%, 25%, 50%, 75% and 100%. The results show that the greater the fracture penetration and the smaller the strength of the rock sample, the more obvious the plastic deformation section of the stress–strain curve. Confining pressure can greatly improve the compressive strength of rock samples. For intact rock samples, confining pressure will change the failure mode from tensile failure to shear failure. For fractured rock samples, the confining pressure will aggravate the degree of damage to the rock sample. PFC 3D simulation shows that the failure process of rock samples is accompanied by the transformation of strain energy to damping energy and particle sliding energy, which can quantitatively characterise the damage process of rock. The increasing trend of crack number is slow-steep-slow, which is the ‘S’ type. It began to grow rapidly after reaching peak strength and gradually stabilised after reaching residual strength. It is consistent with the trend of energy change.

Influences of true 3D twin flaws on principal stress status and crack occurrence of brittle rock-like samples under uniaxial compression: Insights from experimental and DEM studies

Fracture structures commonly have negative impacts on the strength and safety of rock mass, and various combinations of 2D and 3D flaws make the destruction procedure becomes more complicated. Therefore, laboratory tests based on three types of flawed rocks (symmetric twin flaws with different 2D-3D occurrences) are finished to detect the mechanical, optical and acoustic characteristics of fractured rocks during the uniaxial compression test; PFC3D simulations are conducted for analyzing the deformation features, principal stress distributions, and detailed failure mechanism of the fractured rocks. The main results are as follows: 1) Different combinations of 2D & 3D preset flaws directly influence the results of deformation, stress distribution, and failure developments. 2) Rotation of the intermediate stress axes only appear near the flaw inclination boundary (when the monitoring position moves outwards), while the directions of intermediate principal stress axes remain stable near the flaw strike boundary. 3) Separating cracks by various occurrences helps to construct local failures along different directions, and make some local failures visible and clear; the traditional cracks (short line or thin oval shape) are induced by the uneven deformation in x-o-z planes, and the separated cracks (wide oval or standard disc shape) result from the uneven deformation in y-o-z planes. 4) Surrounding rocks at different positions suffer various modes of failures, the non-ignorable thickness of preset flaw leads to simultaneous Mode I and Mode II failure at the flaw tip, and the mixed Mode II&III failure only occurs in the rocks adjacent to the flaw strike boundary.

Macroscopic Mechanical Properties of Brittle Materials with a 3D Internal Crack Based on Particle Flow Simulations

Pre-existing cracks significantly influence the macro-mechanical properties of rock. The macro-mechanical properties and crack propagation process of brittle materials with a 3D internal crack were investigated with PFC3D simulation in this paper. To determine the micro-parameters, the influence of micro-parameters on the macro-mechanical properties and ultimate failure mode was discussed. SJM’s parameters had little influence on the macro-mechanical properties and ultimate failure mode. Peak axial stress was changed greatly by strength parameters and friction coefficient, and the macro-elastic modulus was influenced greatly by Young’s modulus and changed slightly with other parameters. The failure mode changed gradually with all micro-parameters except Young’s modulus, which had a strong but irregular impact on it. The peak stress was 138 MPa in the simulation of the sample with a 3D internal crack, which agreed well with the experimental result (137 MPa). The crack propagation process can be divided into three stages: 17% of total crack was generated in the initial stage; 76% of the total crack was propagated when main failure surface coalesced; finally, the failure surface expanded downwards and caused the sample to be destroyed. Cracks initially appeared near the end of the lower major axis of the internal crack, which was in agreement with experimental results. The results demonstrated that PFC3D is a reliable method to simulate the failure process of brittle materials with internal cracks.

Research on longitudinal vibration suppression of underwater vehicle shafting based on particle damping

A particle damper is applied to suppress the longitudinal vibration of underwater vehicle shafting in order to reduce vibration level and improve silence and stealth of underwater vehicles. The model of rubber-coated steel particle damper was established with discrete element method and PFC3D simulation software, the damping energy consumption law of collision and friction between particle and damper and between particle and particle investigated, the effects of particle radius, mass filling ratio, cavity length, excitation frequency, excitation amplitude, rotating speed and both stacking and motion states of particles on the system vibration suppression were discussed, and the bench test was carried out to verify the law. It revealed the mechanism of longitudinal vibration suppression of particle damping, established the intrinsic relationship between of total energy consumption of particle and vibration of system, and put forward the evaluating method of longitudinal vibration suppression effect by total energy consumption of particle and vibration reduction ratio. The research results show that the mechanical model of particle damper is reasonable and the simulation data is reliable; the rotating speed, mass filling ratio and cavity length have significant effects on the total energy consumption of particle and vibration reduction ratio.

Experimental test and PFC3D simulation of the effect of a hole on the tensile behavior of concrete: A comparative analysis of four different hole shapes

In this article, the effects of porosity and its geometry on tensile features of concrete were investigated, using the Brazilian test and three dimensions PFC model. In the first step, the PFC sample was calibrated by indirect tensile lab outcomes and uniaxial compression test outputs. In the next step, indirect tensile tests were done on the models consisting of various pore shapes. Cylindrical models consisted of internal pores with different shapes such as rectangular, circular, horizontal notch, and vertical notch. The diameter and or the length of these porosity changes in various values, i.e., 10 mm, 20 mm, and 30 mm. Twelve different configurations of samples were prepared by varying the porosity shapes. The mechanical behavior of samples has been provided in form of stress–strain curves at a constant and slow loading rate of 0.05 mm/min for ensuring the static condition based on Newton’s first law. Concurrent with numerical simulation, an experimental test was done on the concrete slabs containing different pores. The outcomes showed that porosity geometry plays an important role in the fracturing pattern. It was found that the porosity geometry has potent consequences on fracturing process stress and the value of the UCS for rocks. Numerical simulation shows that fracture energy decreased by increasing the dimension of the defect. Crack initiation stress was close to final stress in vertical notch configuration while the difference between the final stress and crack initiation stress has a high value for horizontal notch configuration. The sharper the hole tip, the faster the progressive failure occurred.

Evaluation of CBR of Graded Crushed Stone of Flexible Base Structural Layer Based on Discrete Element Model

In order to study the mechanical properties of graded crushed stone, the discrete element method is used to simulate the CBR test of graded crushed stone. Aiming at the composition structure of graded crushed stone material, the PFC3D simulation software is used to construct the test model, and the process of constructing the virtual specimen model of the graded crushed stone discrete element model is discussed in detail. A servo mechanism is used to control the speed of the wall in the software, so as to control the virtual confining pressure imposed on graded crushed stone by the wall and simulate the real CBR test environment. The micro-parameter calibration of the virtual test is carried out by comparing the indoor and virtual CBR specimens of a single particle size specimen and three groups of graded crushed stone specimens. The comparison result shows that the stress-strain characteristics of the graded crushed rock obtained by the discrete element simulation during the uniaxial penetration process have a high degree of similarity, which can verify the accuracy of the model establishment. With the increase in the penetration depth, the penetration force of the aggregates of various particle sizes gradually increases, and the penetration force and the penetration depth are basically linear, and when the particle size is greater than 9.5 mm, the increase in particle size has little effect on the CBR test results. Under the certain conditions, the contact stiffness of graded crushed stone particles with particle sizes of 4.75 mm, 9.5 mm, 13.2 mm, 16 mm, and 19 mm should be 0.88 × 107 (N/m), 0.98 × 107 (N/m), 1.10 × 107 (N/m), 1.25 × 107 (N/m), and 2.05 × 107 (N/m), respectively. The recommended value of the contact stiffness of the small spherical particles increases with the increase in the particle size. This model can provide a basis for studying the micromechanical state of graded crushed stone and physical mechanics tests.

Research on fracture behavior and reinforcement mechanism of fiber-reinforced locally layered backfill: Experiments and models

Locally fiber-reinforced layered cemented paste backfill (FR-LCPB) were prepared for three-point bending experiments to examine the influence of fiber content and reinforcement position on its fracture resistance properties, in an effort to reduce the significant demand for cement during mine filling and improve the characteristics of the CPB brittle damage. Further, scanning electron microscopy (SEM) and PFC 3D numerical simulation were used to investigate the failure mode of FR-LCPB and the reinforcement mechanism of fibers. The results demonstrated that the addition of fibers significantly affects the FR-LCPB's fracture resistance, with 0.6% being the ideal fiber content. Flexural strength, peak deflection, and bending modulus of FR-LCPB increase with the decrease of the distance between the fiber reinforcement position and the lower layer. Additionally, the addition of fibers enhances the CPB's brittle damage characteristic, ensuring that it retains some strength even after failing. It is primarily due to the fibers' ability to deform and rub against the surrounding matrix while resisting the external load that FR-LCPB retains its strength even after damage. PFC 3D simulation results demonstrated that FR-LCPB damage exhibits hysteresis. FR-LCPB breaks down in the fiber-containing layer after first cracking through the non-fiber layer during the loading process, which differs from the damage pattern of regular layered CPB and further suggests that the fiber has an inhibitory effect on the FR-LCPB's fracture. The outcomes will serve as a guide for low-carbon mining development and safe mining operations.

Influence of aggregate reinforcement treatment on the performance of geopolymer recycled aggregate permeable concrete: From experimental studies to PFC 3D simulations

In this paper, industrial solid wastes such as fly ash and slag powder were used as the main components to prepare geopolymer cementitious materials. The geopolymer recycled aggregate permeable concrete (GRAPC) was prepared by reinforcing the recycled coarse aggregate with the geopolymer slurry. The mechanical properties and water permeability of GRAPC were investigated by slump test, compressive strength test, water permeability test and effective void ratio test. The effects of aggregate reinforcement treatment on slurry migration and pore structure changes were investigated by building a 3D virtual model of the fresh-mixed GRAPC mix using discrete element PFC3D. It was found that with the increase of the target void ratio, the aggregate reinforcement treatment increased the compressive strength of GRAPC by 5.6 %, 5.8 %, 11.7 %, and 23.2 %, respectively, compared with the control group. Aggregate reinforcement treatment increased the permeability coefficient of GRAPC by 15 %, 6.8 %, 6.5 %, and 5.7 %, respectively, compared with the control group. The geopolymer slurry reinforced treatment aggregate can effectively enhance the mechanical strength of GRAPC and improve its permeability coefficient and effective void ratio. At 0–0.4 s vibration loading, the slurry in the aggregate reinforced group was more likely to migrate downward. At 0.4–0.8 s vibration loading, the slurry floating range inside the aggregate reinforced group was smaller and the slurry migration was more uniform. Under the action of vibration, the uniformity of the slurry and the uniformity of the pore structure inside the aggregate reinforcement group were greater than that of the control group. The geopolymer slurry reinforcement treatment enhanced the permeability coefficient and effective void ratio of GRAPC by affecting the pore structure distribution.

Shear Failure Mechanism and Numerical Simulation Analysis of Rock-like Materials with an Embedded Flaw

In this study, the failure characteristics of self-made rock with internal flaws under shear were studied and a numerical simulation analysis was carried out. Firstly, based on basic physical and mechanical tests, the shear strength characteristics of rocks with built-in 3D defects were summarized. PFC3D simulation software was used to model the samples with flaws, and the microscopic parameters were calibrated according to the test results. From the simulation results, it was found that the generation mode of microcracks from the flaw tip was different. The microcracks of forward shear and reverse shear were mainly generated from the horizontal direction, while the microcracks of lateral shear gradually increased from the upper and lower ends of the flaw in the opposite direction. When the peak shear strength was reached, the total number of cracks was the largest in lateral shear and the smallest in forward shear. When studying the particle velocity vector field, it was found that when reaching the peak shear strength, the particles on both sides of the prefabricated flaw appeared to be in vortex motion. When α = 45° and σn = 2 MPa, the failure mode of forward shear and lateral shear was shear-tensile-shear (S-T-S), and that of reverse shear and the intact specimen was shear-shear-shear (S-S-S). The lateral shear tensile effect was the most obvious and was mainly concentrated in the middle part of the sample.

Experimental and numerical studies of brittle rock-like specimens with unfilled cross fissures under uniaxial compression

Unfilled cross fissures are defects that widely exist in natural rock, and their existence has a significant impact on the mechanical behaviour of the rock. To investigate the effects of different fissure cross angles (α) and fissure lengths (Lh and Li) on the macroscopic mechanical behaviour, crack development law, ultimate failure mode and final crack distribution of preflawed rock-like specimens, four groups of rock-like material specimens with unfilled cross fissures are fabricated and subjected to uniaxial compression tests using digital image correlation (DIC) technology monitoring, computerized tomography (CT) scanning, and three-dimensional particle coding (PFC3D). These results reveal that the uniaxial compression strength (UCS) and elastic modulus (E) of the specimens all show a nonlinear increase–decrease-increase changing law with increasing α and are all weakened to a certain extent. However, the peak strain (εf) of the specimens shows a nonlinear decrease-increase changing law with increasing α. Based on DIC technology, the influence of α and Lh and Li on the crack development law can be observed. These three parameters mainly affect the crack initiation location of all specimens, and two kinds of ultimate failure modes (shear-tensile mode and tensile mode) can be observed. Based on CT scanning and PFC3D numerical simulation, it can be seen that the final crack system inside the specimen is a 3D system, and the analytical method used to analyse it should contain 2D (DIC technology) and 3D aspects (CT scanning and PFC3D simulation) at the same time.

Fracture behavior of cylindrical sandstone specimens with two pre-existing flaws: experimental investigation and PFC3D simulation

Fracture behavior of cylindrical sandstone specimens with two pre-existing flaws: experimental investigation and PFC3D simulation

Macroscopic and Mesoscopic Mechanical Properties of Mine Tailings with Different Dry Densities under Different Confining Pressures

Particle flow numerical simulation software (PFC3D) was utilized to establish the consolidated-undrained triaxial compression test numerical models of mine tailings with different dry densities to deeply investigate the macroscopic and microscopic characteristics of mine tailings in a tailing pond in Hunan Province. Comparing the results of the simulation and the laboratory experiment, the mesoscopic parameters of the particle flow numerical simulation were obtained through continuously adjusting the mesoscopic parameter with the higher degree of agreement between the stress-strain curve, the peak strength, and the elastic modulus as the determining standard. The macroscopic and microscopic characteristics of mine tailings were studied from the perspectives of stress-strain, axial strain-volume strain, coordination number, particle velocity vector, and contact force between particles. After numerous numerical tests, it was found that the PFC3D simulation results are consistent with experiment results of the dry density tailing samples under different confining pressures; compared with the high confining pressure, the simulation test results at lower confining pressures were more with that of the laboratory tests; low density and high confining pressure both have inhibitory effect on the dilatancy characteristics of triaxial samples; with the same confining pressure, the dilatancy tendency of low dry density samples is suppressed comparing with the high dry density samples. The initial coordination number of the numerical model is large, which proves that the contact degree of the model is good to some extent.

Experimental and numerical study on the cracking characteristics of repetitive electrohydraulic discharge shock waves

The application of repetitive electrohydraulic shock waves (EHSs) is a developing underwater discharge technology; however, its cracking characteristics on rock under different loading modes are rarely studied. In this paper, an experimental platform of electrohydraulic discharge is built, and test results show that repetitive EHSs can cause obvious macroscopic cracks on samples. A fitting method is proposed for the time-domain waveform of the EHS. The mechanism of the EHS cracking process (liquid–solid interface transmission process, cracking process in rock) is analyzed, and the cracking criterion and fracture zone range of a single EHS on rock are given. In addition, PFC3D simulation is used to establish a three-dimensional numerical model of the test sample under the experimental conditions, and the development characteristics of the damage shape and crack density inside the rock under the action of repetitive EHSs are deeply analyzed. Under different repetitive loading modes with the same loading total energy, the simulation results show the following cracking characteristics: in single-level mode, the crack density is mainly related to the energy of the single loading. The higher the single-loading energy, the more conducive it is to the growth of the number of main cracks, but it will form a crushing zone to cause energy loss; lower single-loading energy is more favorable to the length of main cracks. In the multi-level loading mode, the degraded loading mode has a higher crack density than the upgraded loading mode. Compared to the single-level loading mode, the multi-level loading mode can effectively promote the development of the number and length of main cracks, and effectively reduce the range of the crushing zone. This paper provides theoretical and simulation guidance for the research and application of repetitive EHSs.

Numerical Simulation Study on The Degree of Submarine Cable Protection by Riprap Protection Layer Against Anchor

Based on the discrete element theory, the rockfill-anchor-cable discrete element model was built on the PFC3D simulation platform. Combined with the engineering practice, numerical simulation of the penetration process of anchor into the submarine cable riprap protection layer was carried out, the relationship between force and displacement and the sidewall pressure of the submarine cable under the anchor partial penetration were obtained, and the anti-anchor damage ability of the submarine cable was evaluated quantitatively. The results show that the resistance force of the riprap to the anchor increases gradually with the increase of anchor invasive displacement, and eventually stabilize, which reflects the forming, developing, rupturing and restructuring process of the physical chain of the ripped-rock. Furthermore, the riprap protection layer has a significant protective effect on the submarine cable.

NUMERICAL SIMULATION STUDY ON MOVEMENT CHARACTERISTICS OF TAILINGS DAM BREAK

Tailings pond is an artificial hazard source with high potential energy. Once the dam breaks, it will surely threaten the safety of people regarding property and ecological environment of downstream. Due to the complexity of factors and the uncertainty of movement and retention in the downstream channel or site, it is difficult to predict the movement characteristics of tailings dam break. In this paper, based on the mechanics theory of continuous media and discontinuous media, considering the current ability of fluid-solid coupling numerical simulation, using the software such as Massflow, PFC3D combination UAV measurement, analysis of field investigation and verification, conduct a research of simulation study on the movement characteristics of tailings dam break. It is found that the tailings movement process is different based on PFC3D and Massflow numerical simulation. Massflow simulation results show that most of the tailings sands move along the zigzag channel downstream of the tailings pond and accumulate at the culvert where the gully meets the Zhang-Tang railway; PFC3D simulation results show that most of the tailings sands follow the tailings ponds main body towards outburst overflow, and a few enter the zigzag channel downstream. According to the research, considering the uncertainty of geological mass and movement process, it is advisable to combine two simulation methods based on different theoretical bases for the simulation of movement characteristics, and make comprehensive analysis and prediction combining with the actual situation of tailings pond.

落石冲击棚洞结构的PFC3D数值模拟研究

落石冲击棚洞结构的PFC3D数值模拟研究

Crack coalescence behavior of sandstone specimen containing two pre-existing flaws under different confining pressures

Flaws widely exist in engineering rock masses, which significantly influence the overall mechanical behaviors (strength, elastic modulus and failure, etc.) of rock masses. The study of crack coalescence behavior of rock specimen containing pre-existing flaws enhances the understanding of failure mechanism of rock. In this study, a series of PFC3D simulations on numerical specimens were carried out to investigate the crack initiation, propagation and coalescence process under conventional triaxial compression. First, numerical model for cylindrical sandstone specimen was constructed and a set of micro-parameters were calibrated by comparing with the experimental results of intact sandstone with different confining pressures. Then, two pre-existing open flaws which were the same as the tested sandstone were created by deleting balls. Triaxial compression simulations were conducted on pre-flawed specimens for a range of confining pressures (10–40 MPa). The numerically simulated results were compared with the experimental results, which showed that the simulations were in agreement with the laboratory tests. The processes of crack initiation, propagation and coalescence for pre-flawed specimens were investigated by program in PFC3D. The relationships among the cracking process, stress-strain curve and number of micro-crack were analyzed in detail. Finally, the internal crack patterns in pre-flawed specimens were revealed by analyzing the cross-sections from X-ray CT scanning and PFC3D.

Application of transparent soil model test and DEM simulation in study of tunnel failure mechanism

With fast growing demand for modern transportation, more shallow tunnels are being constructed and planned. Understanding the deformation and failure mechanism of a shallow underground tunnel has been a topic of research. The influences of the surrounding material (rock and soil) strengths and buried depths on the deformation and failure mechanism are investigated through the transparent soil model test technique and PFC3D numerical simulation in this study. It can be observed from model tests that the failure mode of test 1 (relative density of 30%, buried depth of 60 mm) is similar with that of test 2 (relative density of 70%, buried depth of 60 mm), both showing the funnel shape. The difference lies in that the tunnel stability in test 1 is lower. On the other hand, tests 2 and 3 (relative density of 70%, buried depth of 120 mm) are of different failure shapes as the latter displays a chimney shape. PFC3D simulation is carried out to numerically examine the failure modes under different testing conditions. The stress field and the displacement field derived from the numerical results can help to interpret the tunnel failure mechanism. In addition, it is obvious from this study that the Peck formula (1969) is less applicable for the surrounding materials with low strength. Therefore, it should be amended according to the surrounding materials, especially for the granular soils.

PFC3D simulation of the effect of particle size on the single edge-notched rectangle bar in bending test

Three points bending flexural test was modeled numerically to study the crack propagation in the pre-cracked beams. The pre-existing edge cracks in the beam models were considered to investigate the crack propagation and coalescence paths within the modeled samples. The effects of particle size on the single edge-notched round bar in bending test were considered too. The results show that Failure pattern is constant by increasing the ball diameter. Tensile cracks are dominant mode of failure. These crack initiates from notch tip, propagate parallel to loading axis and coalescence with upper model boundary. Number of cracks increase by decreasing the ball diameter. Also, tensile fracture toughness was decreased with increasing the particle size. In the present study, the influences of particles sizes on the cracks propagations and coalescences in the brittle materials such as rocks and concretes are numerically analyzed by using a three dimensional particle flow code (PFC3D). These analyses improve the understanding of the stability of rocks and concretes structures such as rock slopes, tunnel constructions and underground openings.