Three-dimensional Discrete Element Model Research Articles

The Influence of an Unsupported Sleeper on the Vertical Bearing Characteristics of Heavy-Haul Railway Ballast.

In order to study the influence of an unsupported sleeper on the vertical bearing characteristics of heavy-haul railway ballast, a three-dimensional discrete element model (DEM) was established for a ballasted track, by removing ballast particles that come into contact with the bottom of the sleeper from the model to simulate the unsupported sleeper. Vertical bearing characteristics for ballast on different types of unsupported sleepers were studied. The results showed that an unsupported sleeper could reduce the bearing area of the ballast below the sleeper and reduce the number of ballast particles that were in contact. It could also lead to an increase in the maximum contact force between the particles, accelerating the deterioration of the particles (thus affecting the overall performance of the ballast) and reducing the vertical stiffness of the ballast. As the unsupported length and width increased, vertical stiffness gradually decreased. The vertical ballast stiffness for an unsupported sleeper was then used in a dynamic coupled vehicle/track model, and the effect of the unsupported sleeper on wheel/rail interaction was analyzed. Results showed that increasing the unsupported length and width leads to a decrease in the supporting force on the unsupported sleeper and to an increase in the supporting force on the adjacent sleepers.

Investigations of bioinspired soil penetration strategies via a numerical model: Does radial expansion improve soil intruder performances?

This paper investigates the performances shown during underground exploration by a plant root-inspired soil intruder. Plant roots are efficient soil explorers, moving by growing at their apical extremities and morphing their bodies in response to mechanical constraints. A three-dimensional (3D) discrete element model (DEM) was developed to mimic selected features of plant roots and verify their usefulness in soil penetration operations. Specifically, the model is used to simulate the penetration of an intruder that grows at the tip into both cohesionless granular and cemented soils. In the former case, dense and loose granular media are considered. The model is adopted to compare penetration performances with purely axial growth and a combination of radial and axial growths. Radial growth is hypothesized to be adopted in roots to facilitate soil penetration. Results from our model suggest that implementing a radial growth preliminary to an axial growth is more advantageous in cohesionless dense granular soil, reducing the soil resistance experienced by the intruder for deeper penetration after radial enlargement. When the penetration occurs in cemented soil, the radial expansion results advantageous over a lower penetration depth, and its beneficial effect drops with increasing inter-particle contact adhesion values. The proposed 3D DEM numerical model provides a methodology for evaluating the intruder penetration efficiency and supports the design of artificial robotic systems for the autonomous exploration of soil by allowing the selection of the most performant penetration strategies for their artificial implementation.

Insights into the Movement and Diffusion Accumulation Characteristics of a Catastrophic Rock Avalanche Debris—A Case Study

In this study, the 1991 rock avalanche, in Touzhai, Zhaotong, Yunnan, China, was considered the study object. The investigation of the landslide accumulation body revealed that the Touzhai rock avalanche accumulation body has the characteristics of wide gradation and poor sorting. A combination of field investigations, indoor and outdoor experiments, and numerical simulations were used to invert the occurrence and spreading range of rock avalanche-debris flow hazards. To invert and analyze its dynamics and the crushing process, a three-dimensional discrete element modeling was performed on the real terrain data. Simulation results showed that the movement time of the numerically simulated Touzhai rock avalanche was approximately 200 s. After 50 s of movement, the peak velocity reached 32 m/s, and the velocity gradually decayed after the sliding mass rubbed violently against the valley floor and collided with the mountain. Due to the meandering nature of the gully, the sliding mass makes its way down the gully and constantly collides with the mountain, making particles appear to climb, with some particles being blocked by the valley. After 150 s of movement, the average velocity rate decreased substantially, and the landslide-avalanche debris reached the mouth of the trench. After 200 s of movement, the average sliding velocity tends to 0 m/s, where the avalanche debris tends to stop and accumulate. When the rock avalanche movement reaches the mouth of the gully, the avalanche debris spreads to the sides as it is no longer bounded by the hills on either side of the narrow gully, eventually forming a ‘trumpet-shaped’ accumulation, and the granular flow simulation matched the findings of the landslide site accumulation.

Triaxial test analysis and discrete element simulation of CFBC

In order to explore the mechanical behavior and crack propagation of cement fly ash stabilized brick-concrete gravel (CFBC) base mixture under three-dimensional compression, firstly, the triaxial loading tests of three different proportions of mixtures were carried out through laboratory tests. The axial load is controlled by a load control loading system, the sampling frequency is 5 Hz, and the triaxial specimen is loaded at a rate of 0.1 MPa /s.The stress–strain curves of the mixture under four different confining pressures were obtained, and the failure characteristics and strength characteristics were analyzed. Secondly, the SEM analysis of the specimens under different confining pressures was carried out, and the microstructure parameters of the mixture under four different confining pressures of 0 MPa, 0.5 MPa, 1.0 MPa and 1.5 MPa were studied based on the PCAS analysis software. On this basis, a three-dimensional discrete element model was established to numerically reproduce the triaxial test of the specimen. The results show that the failure mode of the specimen is mainly related to the confining pressure, and the crack shape has the characteristics of top-down in the direction of principal stress.Through the stress–strain curve, it can be seen that with the increase of confining pressure, the peak stress of the specimen is also increasing. In the BCA1 ratio, the peak stress of the 1.5 MPa confining pressure is increased by 23 % compared with the non-confining pressure. In addition, the cement fly ash stabilized brick-concrete gravel mixture specimen has a larger bearing capacity than other concrete brittle materials.PCAS pore analysis showed that the main controlling factors affecting the porosity of the mixture were brick content and confining pressure, which in turn affected the shear strength and peak stress of the mixture, and the porosity of BCA1 < BCA3 < BCA5; the numerical simulation results show that the failure mode and stress–strain curve of the specimens with the shear strength error of less than 3 % and the friction angle error of less than 6 % are in good agreement. The maximum displacement particle clusters appear on the upper and lower edges of the specimen, and the sliding zone angle of the specimen is about 45° under all stress paths except the horizontal sliding zone under the uniaxial stress state, which reflects that the numerical model is consistent with the mechanical response at the macro scale. The use of three-dimensional discrete element models in the field of construction engineering can simulate and optimize the use of the above materials in construction sites to minimize waste and maximize efficiency.

Three-dimensional discrete element model of crack evolution on the crack tip with consideration of random aggregate shape

In this paper, a method for concrete three-dimensional random polyhedral aggregate mesostructure is proposed. Moreover, a concrete discrete element fracture mesoscopic analysis model is established. The mesoscopic destruction mechanism of three-dimensional fracture of concrete three-point bending specimens is investigated. Three-dimensional evolutionary extension morphology of crack tip and fracture process zone (FPZ) of small-size concrete specimens in an indoor laboratory is simulated and analyzed. Furthermore, the entire fracture process of concrete specimens is investigated. The three-dimensional morphology of the crack tip and fracture process zone is analyzed via normal distribution statistics. Consequently, the size effect law of crack extension and fracture process zone evolution is derived. The fracture process of actual large-scale concrete specimens is predicted based on deficiencies of small-scale specimens in indoor tests. The results show that the proposed model is an effective method to characterize the three-dimensional fracture process of concrete and predict mechanical properties of large-scale specimens in actual structures.

Three-dimensional DEM tillage simulation: Validation of a suitable contact model for a sweep tool operating in cohesion and adhesion soil

Discrete element modelling (DEM) is widely used to estimate soil-tool interaction and tillage forces. To run an accurate simulation, it is essential to determine the appropriate DEM contact model and parameters. Although previous work has been introduced to determine the DEM contact model and parameters, the accuracy of numerical simulation is not high because of the soil differences when tillage tools operate in cohesion and adhesion soil in the middle and lower reaches of the Yangtze River in China. In this paper a Hertz-Mindlin with JKR Cohesion contact model and Linear Cohesion contact model were used to predict soil disturbance area and draft forces. The DEM parameters were determined using cone penetration, and uniaxial unconfined compression as an assisted test. The field experiment using sweep tool was used to validate the simulation results. A good agreement has been showed between simulation results and experiment results. Using verified model, the relative error for the predicted soil disturbance area at speeds of 0.50, 0.75 and 1.00 m/s were 5.3, 3.6 and 7.1 %, respectively. The maximum and average relative errors between simulated and measured draft forces were 6.98 and 3.91%, respectively. The effect of tillage depth and speed at soil disturbance area and draft forces were found which can provide some guidance for the selection of parameters during actual operation.

3D DEM simulations of the variability of rock mechanical behaviour based on random rock microcracks

In this study, to investigate the variability of mechanical parameters of rock, a three-dimensional (3D) discrete element model (DEM) with the consideration of random microcracks was proposed. The random microcracks follow the negative power-law distribution with upper and lower limits of microcrack size. The results showed that coefficient of variations (COVs) and average values of elastic modulus, Poisson's ratio, unconfined compression strength and tensile strength of Lac du Bonnet granite are well matched through the present model. The present simulations indicate that the large COVs were induced by the interconnected large microcracks. The parametric study clearly indicates that the random microcracks significantly affect COVs, while the effect of grain size variation can be ignored. The size of microcracks determines the variability of mechanical parameters, and the volume density of microcracks can significantly influence the COVs. The correlation between the fractal dimension of microcrack size distribution and COVs is not linear. The increasing variability of microcrack density can result in the increase of COVs. Finally, a calibration procedure was proposed to determine the present model's parameters.

Effect of cutting blind zones on the performance of the rectangular pipe jacking machine with multiple cutterheads: A DEM study

Due to the shape discrepancy between the rectangular machine shell and the circular cutterhead, rectangular pipe jacking machines inevitably have cutting blind zones, which could waste thrust force and reduce tunneling efficiency. Few studies have been done in the past on the effects of the cutting blind zones on the jacking behavior of the rectangular tunneling machine. To investigate the performance of the rectangular pipe jacking machine under the influence of excavation blind zones, three-dimensional discrete element modeling was performed in this study, where various blind zone ratios (i.e. the area ratio of excavation blind zones to the rectangular excavation face) ranging from 2% to 10% were considered. The resultant velocity distributions of soil particles indicate that the soil stagnation phenomenon in the cutting blind zone near the non-overlapping zones between adjacent cutterheads can be alleviated by the staggered front-to-back arrangement of multiple cutterheads, while the stagnation phenomenon in the cutting blind zone close to the pipe shell is remarkable. Besides, it was advisable to keep the cutting blind zone ratio at about 5% in practical construction in view of the extra costs of over-arranging multiple cutterheads for a small cutting blind zone ratio as well as the waste of thrust force caused by an excessively large cutting blind zone ratio. Additionally, structural optimization strategies were proposed, which were intended to provide some guidance for the future design and improvement of rectangular pipe jacking machines.

Characteristics and treatment measures of tunnel collapse in fault fracture zone during rainfall: A case study

This paper analyzes the characteristics and mechanism of the collapse of a tunnel in Wenzhou in fault fracture zone during rainfall based on the failure theory of surrounding rock, three-dimensional discrete element numerical simulation and in-situ deformation monitoring. It was demonstrated that the continuous erosion and expansion of rock fissures caused by the scouring of water seepage on surrounding rock fissures is the main reason for the continuous reduction of surrounding rock stability in fault fracture zone after tunnel excavation. The failure process of surrounding rock was simulated by a three-dimensional discrete element model, and the results were consistent with the engineering practice. Treatment measures of collapse are adopted, including surface grouting, grouting in tunnel, and pipe-roof. The effect of reinforcement was evaluated through monitoring. The lessons and experience in this case has reference value for the prevention of tunneling collapse in fault fracture zone.

Constitutive modelling of natural sands using a deep learning approach accounting for particle shape effects

Particle shape plays a vital role in the macroscopic mechanical behaviour of a quasi-statically sheared granular material. However, most of the previous studies neglected the particle shape effects or characterized the particles with simplified geometries when predicting the constitutive behaviour of granular materials. This paper proposes a paradigm-shifting methodology for the constitutive modelling of granular soils subject to triaxial shearing which integrates the techniques of X-ray micro computed tomography (micro-CT), three-dimensional discrete element modelling and deep learning. Firstly, the micro-CT data of Leighton Buzzard sand particles used to reconstruct particles in discrete element method simulations are obtained separately. Secondly, the tomography data of a series of representative sand particles is used to construct the three-dimensional discrete element model of the sand sample which is then used to generate the numerical datasets for the subsequent deep learning task. Thirdly, a deep learning model called the long short-term memory network is developed to capture the combined effects of particle shape, confining pressure, and initial sample density on the constitutive behaviour of sands. Lastly, the effectiveness of the deep learning model is shown by comparing the model prediction on the testing datasets with the numerical simulation results. Furthermore, the capability of the model on predicting the real sand behaviour is demonstrated by an excellent agreement between the model prediction based on the input of tomography data and the soil response measured from the triaxial test.

Three-Dimensional Discrete Element Analysis of Crushing Characteristics of Calcareous Sand Particles

Particle crushing is an important factor affecting the mechanical characteristics of calcareous sand, but at present, most of relative studying methods rely on physical experiments. In order to study the influence of particle crushing characteristics on the micromechanics of calcareous sand, the 14-fragment replacement method satisfying the Apollonian distribution is used to simulate the calcareous sand particles, and the fragment replacement method (FRM) is used to simulate the particle crushing. The three-dimensional discrete element model of calcareous sand particle crushing is established, and the development of relative crushing rate and the evolution laws of coordination number, porosity, and sliding contact ratio in triaxial consolidated drained shear test are analyzed. The results show that the three-dimensional model considering particle breakage can well reflect the micromechanical properties of the internal structure of the sample. The micromechanical response with and without particle crushing is quite different, which can be well reflected by the numerical test under high confining pressure. In addition, the modified relative crushing rate proposed by Einav based on the research of Hardin can better describe the relative crushing rate of calcareous sand under wide gradation and can provide a reference for the study of particle crushing characteristics of laboratory test of calcareous sand under wide gradation.

Three-dimensional discrete element modeling of the shear behavior of cemented hydrate-bearing sands

Understanding the shear behavior of hydrate-bearing sands is fundamental for the safe exploitation of natural gas hydrates. Calibration is necessary to accurately capture the shear behavior of hydrate-bearing sands when using the three-dimensional discrete element method (DEM). In this study, a new method is developed to quantify the hydrate saturation of hydrate-bearing sands by using a DEM model with Voronoi partitions. A series of DEM simulations with various hydrate saturations and confining pressures were performed to calibrate the DEM model, which was then compared with experimental results. The results demonstrate that the DEM can effectively capture the macroscopic properties, including the shear strength, secant modulus, cohesion, and friction angle of hydrate-bearing sands. The bond strength and inter-particle friction coefficient of hydrates mainly impact the shear strength of hydrate-bearing sands, whereas the bond stiffness of hydrates affects both the shear strength and secant modulus of hydrate-bearing sands. The number of broken hydrate-sand bonds is much larger than the number of hydrate-hydrate bonds, indicating that the contribution of the former bonds is more significant than the latter bonds during the shearing process. This calibration method helps improve the reliability and accuracy of the DEM simulations for hydrate-bearing sands under triaxial compression tests.

Experimental study and discrete element analysis on lateral resistance of windblown sand railway

The lateral resistance of ballast bed is an important parameter to prevent track expansion and maintain track stability. The invasion of sand particles can cause the change of lateral resistance of ballast bed and affect the stability of track structure, but little attention has been paid to the change characteristics of nonlinear lateral resistance of sandy ballast bed. In this paper, the field tests on the lateral resistance of windblown sand ballast bed were carried out to establish a multiscale three-dimensional discrete element model of sleeper-ballast bed. A systematic analysis on the evolution of lateral resistance, resistance to lateral deformation, micro-contact characteristics and lateral stability of ballast bed is performed. The results show that sand intrusion can increase the lateral resistance of ballast bed, which is approximately 40 % higher than that of clean ballast bed. In nonlinear strengthening stage and yield stage, the enhancement effect of sand particles on the lateral resistance of ballast bed is relatively weaker in comparison with the linear growth stage. With the increase in sand intrusion depth, the lateral resistance and resistance work of ballast bed both gradually go up, and the contribution of ballast shoulder to lateral resistance tends to play a leading role. Sand intrusion can increase the lateral stiffness of ballast bed and reduce the elasticity of track structure. Therefore, the maintenance operation should be carried out in time for the section with severe sandstorm.

A Three-Dimensional Discrete Element Modeling to Cyclic Response of Geosynthetic-Encased Stone Column

A Three-Dimensional Discrete Element Modeling to Cyclic Response of Geosynthetic-Encased Stone Column

Dynamic properties and fracture damage characteristics of granite under impact load

The goal of this research is to study the dynamic properties and fracture damage laws of granite at the meso-scale under impact load. The quasi-static and dynamic mechanical properties of granite were studied through laboratory tests (Uniaxial compression, split Hopkinson pressure bar). The establishment of three-dimensional coupled numerical model of rock specimen and split Hopkinson pressure bar was realized by new coupling technology of PFC-FLAC. Three wave superposition and end stress distribution were discussed to determine the stress balance of the specimen during the loading process. The dynamic compression mechanics response characteristics and crack growth laws of granite under different strain rates were studied. The results indicated that PFC-FLAC coupling technology can solve the problems of tedious modeling process and long calculation time in the past three-dimensional discrete element model, and can better describe the dynamic mechanical behaviour of rock. There is obvious rate dependency in the dynamic strength of rock material, and the dynamic compressive strength of rock increases with the increase of strain rate. The macro fracture of rock mass is the result of the continuous development, expansion, aggregation and connection of the internal microcracks. With the increase of strain rate, the increase and cross propagation of cracks lead transformation of rock from intact to crushing destruction. Under dynamic loading, the failure process of rock is crack initiation, propagation, crossing, transfixion and rupture.

Experimental study and discrete element analysis on dynamic mechanical behaviour of railway ballast bed in windblown sand areas

Due to the limitation of the geological environment, many railways around the world are built in desert areas. The intrusion of sand particles can increase the stiffness of ballast beds and cause corrosion and fracture of fasteners, turnout blockage, etc., even affecting the service safety of railways. In the paper, based on the results of field and laboratory tests, a three-dimensional discrete element model of the sandy ballast bed is developed to study the effect of sand intrusion on the load sharing ratio of sleepers, contact forces between ballast particles, displacements of ballast particles, and energy dissipation in ballast beds. The results show that the axle load in sandy tracks is mainly shared by three sleepers under the single-axle load and six sleepers under the dual-axle load. The maximum contact force under the sleeper in the sandy ballast bed is about 80% larger than that in the clean ballast bed and its normal and tangential contact forces are also larger than that in the clean ballast bed. The ballast particles at the ballast shoulder of the clean ballast bed move downward in the direction of less than 45°, while those in the sandy ballast bed move outward at the direction of 90°. The sand intrusion inhibits the movement of ballast particles and may cause a rheological phenomenon of ballast particles at the ballast shoulder. The intrusion of sand particles mainly affects the elastic strain energy and damping energy in ballast beds but has less effect on friction energy and kinetic energy.

Effect of particle size on the failure behavior of cemented coral sand under impact loading

The effect of particle size distribution (PSD) of coral sands on the failure behavior of cemented coral sand specimens is investigated in this study. A series of static and impact loading tests on the specimens with various grain grading curves have been carried out. Test results show that the compression strength and impact resistance of the cemented coral sand specimen are increased with the increasing of the uniformity coefficient of coral sand particles. The specimen with a higher value of the uniformity coefficient would have a smaller failure angle under the same impact loads. In addition, the micro mechanism of PSD on the macroscale mechanical behavior is explored by a three-dimensional discrete element model. Four typical realistic particles are scanned and incorporated in the numerical models. The numerical model is established with the same PSD and impact loading conditions. Calibration tests are carried out to verify the numerical model. Then, a series of numerical analysis are conducted to examine the effects of particle shape and PSDs on the failure behavior. Analysis results indicate that the contact force distribution and absorbed energy can be linearly influenced by the PSDs. The realistic particles with a lower shape factor will result in a higher impact resistance. Thus, an optimum PSD can be design to meet the requirement of impact loadings. The outcome of this study could benefit for the foundation design with the consideration of the impact loadings.

Analysis of Failure Mechanism of Roadway Surrounding Rock under Thick Coal Seam Strong Mining Disturbance

Severe dynamic disturbance in extrathick coal seam mining has become one of the main factors threatening the stability of roadway surrounding rock. In this article, the #6 thick coal seam of Buliangou mine in Inner Mongolia, China, is taken as the engineering background. A mechanical model of the roadway roof structure is established to obtain an analytic formula of the key block subsidence. A three-dimensional discrete element model is established and used to verify the field measurement results. The fracture characteristics of the main roof above the F6104 transport roadway and the deformation and damage evolution law of the surrounding rock during thick coal seam mining are analyzed. The results show that because of the long-term breaking and falling of the roof rocks during extrathick coal seam mining, the F6104 transport roadway will undergo two severe mining disturbances at the locations of 10∼30 m and 50∼70 m ahead of the F6103 working face. During the two disturbance periods, the roadway roof displacement settles to 300∼350 mm and 750∼800 mm, and the deformation of the solid coal wall reaches 650∼700 mm and 1350∼1450 mm, respectively. The energy change curve of the total length of the fractured key roof is obtained, and when mining at 50 m, the basic roof is close to its tensile strength, and the strain energy can reach the peak value of 5.2 × 10 4 kJ, which easily leads to rock burst. The plastic damage zones on both sides of the roadway develop to the roof central area and eventually coalesce, and the deformation of the surrounding rock is obvious. When mining at 50∼70 m, the basic roof breaks and unloads, and elastic strain energy of 3.57 × 10 4 kJ is instantaneously released. These two dynamic disturbances are the main reasons for the instability of the roadway surrounding rock. The results clarify that the failure mechanism investigation of roadways in thick coal seam mining conditions can be effectively applied to control the stability of the roadway surrounding rock under strong mining disturbance.

Rock fragmentation induced by a TBM disc-cutter considering the effects of joints: A numerical simulation by DEM

The study of rock fragmentation mechanism significantly contributes to the advancing speed of tunnel boring machines (TBMs). In this sense, numerous factors are shaping the rock fragmentation mechanism of their disc-cutters. Among them, rock structural parameters, such as joint inclination, orientation, spacing, etc., considerably impact cutting force as well as rock-cutting process. However, detailed relationships between rock-cutting parameters and rock mass ones have not been to date proven, and rock fragmentation mechanism still needs to be investigated in depth. In this paper, a three-dimensional (3D) discrete element model of rock-cutting using a disc-cutter was established via the high-performance MatDEM software. To simulate the fragmentation performance of the rock undergoing the impact load, an elastic–plastic contact model was firstly proposed based on the linear elastic contact model, verified by several mechanical experiments. Then, the influence of different joint parameters (e.g., joint inclination, orientation, spacing, etc.) on cutting force and rock fragmentation volume was examined. At the same time, the effect of joint parameters on specific energy (SE) was calculated to explore the joint influence on rock-cutting efficiency. The simulation results show that the elastic–plastic contact model can better simulate the plastic deformation characteristics of the brittle rock, and the improved model can imitate the generation of the rock fragment structure. As well, the influence of the joint orientation and spacing on the mean value of the cutting force and the rock fragmentation volume is obvious, and the propagation mode of the internal cracks in the rock varies with reference to the joint orientation. The existence of the joints also decreases the rock-cutting SE, and consequently the rock-cutting efficiency can reach the highest level when the joint spacing is equal to 50 mm and the joint orientation is about 30°. The opposite inclination of the joint correspondingly leads to the opposite change in the rock-cutting parameters, which can be eliminated through rotating cutting in practice. This study explores the influence of joint parameters on rock-cutting ones and reveals crack distribution mechanism in jointed rock mass.

Mechanical Characteristics of Ballast Bed under Dynamic Stabilization Operation Based on Discrete Element and Experimental Approaches

To study the mechanical characteristics of ballasted bed under dynamic stability, a three-dimensional discrete element model of ballasted bed with 1000 mm × 700 mm × 550 mm is established based on the discrete element method. Meanwhile, a simulation test bench with the same size is built for simulation analysis and experimental research. The variation law and trend of settlement, lateral resistance, and compactness of ballasted bed under different excitation frequencies are analyzed comprehensively. The results show that when the excitation frequency is constant, the lateral resistance of sleeper, the settlement of sleeper, and the compactness of track bed under sleeper increase first and then tend to be stable. With the increase in horizontal excitation frequency, lateral resistance of ballast bed, sleeper settlement, and compactness first increase and then decrease after stable operation. The values of these parameters are maximized when the excitation frequency is 36 Hz which is the relative optimal horizontal excitation frequency of this model.