Particle Breakage Behavior Research Articles

Fractal Analysis of Particle Size and Morphology in Single-Particle Breakage Based on 3D Images

The accurate modeling of single-particle breakage based on three-dimensional (3D) images is crucial for understanding the particle-level mechanics of granular materials. This study aims to propose a systematic framework incorporating single-particle breakage experiments and numerical simulations based on a novel 3D particle reconstruction technique for fractal analysis of particle size and morphology in single-particle breakage. First, the vision foundation model is used to generate accurate particles from 3D images. The numerical approach is validated by simulating the single-particle breakage test with multiple Fujian sand particles. Then, the breakage processes of reconstructed sand particles under axial compression are numerically modeled. The relationship between 3D fractal dimensions and particle size, particle crushing strength, and morphology is meticulously investigated. Furthermore, the implications of these relationships on the particle breakage processes are thoroughly discussed, shedding light on the underlying mechanisms that govern particle breakage. The framework offers an effective way to investigate the breakage behavior of single sand particles, which will enhance understanding of the mechanism of the whole particle breakage process.

Application of Multibody Dynamics and Bonded-Particle GPU Discrete Element Method in Modelling of a Gyratory Crusher

The gyratory crusher is one of the most important mineral processing assets in the comminution circuit, and its production performance directly impacts the circuit throughput. Due to its higher energy utilisation rate for rock breakage than semi-autogenous (SAG/AG) milling, it is a common practice in operations to promote and optimise primary crushing before the downstream capacity can be enhanced. This study aims to develop a discrete element modelling (DEM) and multibody dynamics (MBD) cosimulation framework to optimise the performance of the gyratory crusher. An MBD model was initially established to simulate the gyratory crusher’s drivetrain system. A GPU-based DEM was also developed with a parallel bond model incorporated to simulate the particle breakage behaviour. Coupling of the MBD and GPU-based DEM resulted in a cosimulation framework based on the Function Mock-up Interface. An industrial-scale gyratory crusher was selected to test the developed numerical framework, and results indicated that the developed method was capable of modelling normal and choked working conditions. The outcome of this study enabled more realistic gyratory crusher improvement and optimisation strategies for enhanced production.

The 7th Bishop Lecture: The mechanics of coarse-grained geomaterials at meso- and micro-scales

In order to move towards discrete analyses of soil behaviour, we need to develop a new range of apparatus and testing techniques. The lecture describes attempts to develop these new apparatus and presents data for a range of coarse-grained geomaterials at the single particle scale. The roles of the particle morphology and hence geological origin are discussed and are shown to influence both the contact mechanics and particle breakage behaviour. The mechanics of single particles are shown to be more complex than generally assumed and will require new means of modelling to account for the significant plasticity that occurs at particle contacts and patterns of breakage that are strongly influenced by the origins of particles and their effect on their morphology.

Exploring particle breakage in sand under triaxial shearing using combined X-ray tomography and particle tracking method

In this paper, a novel investigation of the particle breakage behaviour of sands is made using combined techniques of X-ray micro-computed tomography (μCT) and sand particle tracking. First, an in situ μCT triaxial test on a miniature sand specimen is conducted to allow the visualisation of particle-scale morphology and movement. Then a two-step particle tracking method is developed and applied to track the sand particles that experience a zero or slight degree of particle breakage. Making use of the power of the particle tracking method, the individual intact particles within a sheared sand specimen containing a mixture of crushed and uncrushed particles were tracked for the first time. The results show that the degree of particle breakage in the consolidation stage is very low, and before the peak stress is reached, more than half of the particles were crushed for the first time; also significant particle breakage occurred at the centre of the specimen during the post-peak stage. The particle shape and gradation analyses reveal that larger grains with lower values of sphericity and convexity are prone to breakage, with the angularities of the crushed particles being closely related to their mother particles.

Effect of realistic shape on grain crushing for rounded and angular granular materials

The deformation characteristics of granular materials in the field of geotechnical engineering largely depends on particle breakage behavior, which remains unresolved to date due to complex grain morphology. In this paper, a combination of experimental and numerical study was conducted to investigate the effect of realistic shape on grain crushing behavior for two groups involving rounded and angular rock grains. A shape library was established after acquirement of grain morphology via three-dimensional scanner, in addition, statistical analysis of grain shape indicates that four indices including sphericity, convexity, inscribed circle sphericity and volume sphericity, are useful for distinguishing shape characteristics of two rock grain groups. The experimental results exhibit a marked difference in force–displacement curve, fragmentation mode and Weibull survival probability for the two rock grain groups, moreover, these results were reproduced by discrete element method (DEM) simulation of grain crushing considering realistic shape. Finally, on the basis of DEM simulation method, deeming the grain shape as the sole variable, its influence on strength distribution was explored by modifying realistic complex shape of grains without altering microscopic mechanical parameters of DEM simulation. A conclusion can be reached that realistic irregular shape enhances grain crushing strength variability, and more angular edges (indicating higher degree of shape irregularity) leads to greater variability of grain crushing strength. Meanwhile, the role of particle microstructure in weakening or strengthening the effect of grain shape was also confirmed. These findings provide a deeper insight into the effect of morphological features on grain crushing behaviours.

Discrete element numerical analysis for bearing characteristics of coral sand foundation considering particle breakage

Owing to the construction demands of island and reef engineering, studying the bearing and deformation characteristics of coral sand foundations is significant. This study used the discrete element method to simulate the plate loading test of coral sand foundations based on the actual experiments of coral sand foundations. The particle breakage of coral sand was considered by the fragment replacement method, and the influence of relative compactness on the particle breakage behaviour and compression deformation characteristics of coral sand foundations was analysed. The results show that the compression process of the coral sand foundation undergoes three stages: compaction, shear deformation, and failure. The bearing capacity, deformation modulus, and particle breakage rate of the coral sand foundation increase with the increasing relative compactness, but the growth trends are different significantly at different relative compactness. The numerical analysis indicates when the relative compactness of the foundation increases, the contact force and coordination number would increase, the relative displacement would decrease, causing more particle breakage. This microscopic phenomenon explains why the increasing trend of bearing capacity and deformation modulus of the foundation decreases with the increasing relative compactness.

Experimental investigation of the impact breakage characteristics between grinding media and iron ore particle in ball mills

The particle breakage of the ball mill is an extremely complicated breakage process. It is difficult to quantify and describe the particle breakage behavior. In this study, a drop-ball experimental setup was developed to demonstrate the impact process of grinding media on ore particles. The quantitative analysis of the effects of particle size, impact energy, and the number of impacts on particle breakage behavior was performed separately. The results show that the breakage probability model and product size distribution model used can be excellent to predict the particle breakage behavior for the single-particle impact experiments. The breakage probability of particles is highly sensitive to impact energy and particle size, exponentially increasing with the increase of impact energy. In addition, the application of the tn-t10 relationship provides a convenient means to characterize and predict the particle size distribution. In multi-layer particle impact experiments, the captured thickness of ore particles is approximately 2 layers during the crushing process. The broken mass of iron ore particles is proportional to the number of concessive impacts at different impact energies. This paper provides theoretical and methodological support for the evaluation and optimization of particle breakage in ball mills.

On single particle breakage behavior of crushable weathered sands

On single particle breakage behavior of crushable weathered sands

Effects of Loading Stress and Velocity on Compression and Particle Breakage Behaviour of Waste Rocks in Backfill Coal Mining

Coal mine waste rocks, mainly broken gangue, can be used as filling materials to backfill into goafs. Under the overburden load, the backfill body is vulnerable to compressive deformation and particle breakage. With the increase in mining depth, the overlying strata will impose different loads on waste rock filling materials at different loading velocities, which further affect the material compressive deformation and particle breakage. In this paper, an experimental scheme and a loading device are designed to study the influence of loading stress and velocity on the compressive deformation and particle size distributions of the backfill materials before and after compression. The results show that the axial strain of the gangue filling materials increases rapidly with the axial stress and then gradually stabilizes, showing a logarithmic functional relationship. Increasing the loading velocity will destroy the contact structures among the gangue particles and cause a larger deformation to the filling materials. When the loading stress is relatively low (5 MPa), the gangue particles with a size larger than 20 mm have a stronger bearing capacity compared with particles of 16–20 mm, which are the first particles to be crushed under these conditions. Further increasing the loading velocity will increase the breakage degree of the filling materials. The breakage ratio (BM) has a logarithmic functional relationship with the loading stress and the loading velocity. When the ground stress is lower than 5 MPa, the content of coarse particles should be increased to enhance the bearing capacity of the gangue materials; when the ground stress is higher than 10 MPa, the content of fine particles should be increased to reduce the porosity ratio and the particle breakage ratio.

Effect of Saturation on Shear Behavior and Particle Breakage of Coral Sand

Coral sand is the main filling material for the island–reef foundation. Under tidal actions, the saturation (Sr) of coral sand layers varies with the specific depths in the reclaimed foundation. Studying the Sr effect of coral sand’s mechanical behaviors is crucial for the stability of the reclaimed foundation of island–reefs. In this study, a “quantitative injection method” was designed to prepare coral sand with saturation ranging from 90% to 100%, and unconsolidated–undrained (UU) triaxial shear tests were conducted on coral sand under different effective confining pressures (σ3′). The results indicated that the stress–strain curves of coral sand under various conditions were of the strain-softening type. When σ3′ = 200, 400, 600, and 800 kPa, the shear strength of coral sand decreased exponentially by 13.1, 9.1, 16.8, and 15.2%, respectively, with the increase in Sr from 90% to 100%. As Sr rose, the internal friction angle (φ) dropped by 3.77°. The cohesion (c) was not significantly affected by Sr compared to φ. In consideration of the physical susceptibility of coral sand to breakage, relative breakage ratio (Br) and modified relative breakage index (Br*) were introduced to evaluate the particle breakage behaviors of coral sand samples with different Sr levels in the triaxial shear process. It was found that Br and Br* increase linearly with increasing Sr; the effect of Sr on the particle breakage of coral sand weakens significantly when σ3′ is sufficiently large. The median particle size (d50) of coral sand decreases with increasing Sr, and presents a negative linear correlation with both Br and Br*. Based on comparing the strength and particle breakage characteristics of coral sand samples with varying Sr levels, this study suggests that 92.5% should be considered as the Sr value of coral sand available for testing.

Particle breakage behavior of a foundation filling material on island-reefs in the South China Sea under impact loading

Particle breakage behavior of a foundation filling material on island-reefs in the South China Sea under impact loading

Cumulative deformations and particle breakage in calcareous sand subjected to drained high-cyclic loading: Experimental investigation

Transportation infrastructures filled with calcareous sand are subjected to a high-cyclic loading. Existing studies indicated that a key challenge in predicting the cumulative deformation of calcareous sand was a lack of thorough knowledge about the effects of various important field factors. This paper presents an experimental study on the drained monotonic and high-cyclic triaxial behavior of calcareous sand. The dependencies of cumulative deformation and particle breakage behavior on practical variables, such as mean effective stress (p'), cyclic stress ratio (ζ), void ratio (e), and stress-induced anisotropy, etc., were summarized for calcareous sand. It was found that a larger e and consolidation anisotropy led to a significant increase in the accumulated axial strain, transforming the stable shakedown behavior to transitional or unstable shakedown behaviors. The increase in anisotropy can cause a remarkable increase in dilatancy, as well as a severe failure. A phase transition state line (PTSL) was observed to exist in e-(p/pa)0.7 plane under high-cyclic loading, where the PTSL was found dependent on initial void ratios. As the p', ζ, e, and anisotropy increase, a larger particle breakage index (Br) of calcareous sand was observed, where the total input energy (Win) played a substantial role. The relationship between Br and Win was found to be unique under high-cyclic loading, regardless of the stress conditions and initial void ratios. Moreover, the relationship between Br and Win under high-cyclic loading was discovered to differ dramatically from that under monotonic loading. An appropriate equation was thus developed to describe the correlation between Br and Win for high-cyclic loading.

Fragmentation modes of single coral particles under uniaxial compression: Microstructural insights

Coral soils are being used increasingly as construction and building materials in ocean engineering. Because of their biological origins, coral soils have unique properties compared to rock and silica sands with physical or chemical origins. One of the most important properties of coral soils is particle breakage. The particle breakage behavior of coral soil exerts significant control over its mechanical properties including strength, stiffness, and hydraulic features, but despite extensive studies into coral particle breakage, the relationship between fragmentation mode and coral microstructure remains to be revealed. This paper reports uniaxial compression tests on single coral particles with various microstructural characteristics. How mineralogy, chemical composition, coral particle shape and size, water content, and loading rate affect coral particle breakage behavior is discussed. The test results reveal that the fragmentation mode of coral is controlled predominantly by the coral microstructure, with particle irregularity also playing a role. While underwater immersion does not alter the corresponding fragmentation mode of coral particles, it dramatically reduces the particle crushing strength and leads to a higher degree of particle breakage. An fragmentation mode classification system that considers the force–displacement responses, particle fragmentation features, and coral microstructural properties is proposed. The classification applies to not only coral particles but also other granular materials. This paper improves the understanding of the particle crushing mechanism of coral soils.

Effects of Relative Density and Grading on the Particle Breakage and Fractal Dimension of Granular Materials

Particle breakage was reported to have great influence on the mechanical property of granular materials. However, limited studies were conducted to quantify the detailed effects of relative density and initial grading on the particle breakage behaviour of granular materials under different confining pressures. In this study, a series of monotonic drained triaxial tests were performed on isotropically consolidated granular materials with four different initial gradings and relative densities. It is observed that particle breakage increases as the confining pressure or relative density increases, whereas it decreases with the increasing coefficient of uniformity. Due to particle breakage, the grading curves of granular materials after triaxial tests can be simulated by a power-law function with fractal dimension. As the confining pressure increases, the fractal dimension approaches the limit of granular materials, i.e., 2.6. A unique normalized relation between the particle breakage extent and confining pressure by considering relative density and grading index was found.

Numerical simulation study on particle breakage behavior of granular materials in confined compression tests

In order to study the fragmentation law, the confined compression experiment of granular assemblies has been conducted to explore the particle breakage characteristic by DEM approach in this work. It is shown that contact and contact force during the loading process gradually transform from anisotropy to isotropy. Meanwhile, two particle failure modes caused by different contact force states are analyzed, which are single-through-crack failure and multi-short-crack failure. Considering the vertical distribution of the number of cracks and the four characteristic stress distributions (the stress related to the maximum contact force, the major principal stress, the deviatoric stress and the mean stress), it is pointed out that the stress based on the maximum contact force and the major principal stress can reflect the distribution of cracks accurately. In addition, the size effect of particle crushing indicates that small size particles are prone to break. The lateral pressure coefficient of four size particles during the loading process is analyzed to explain the reason for the size effect of particle breakage.

Large-scale triaxial tests of reinforced coral sand with different grain size distributions

The strength, deformation and particle breakage behaviors of reinforced coral sand were analyzed by performing a series of large-scale consolidated drained triaxial tests on unreinforced and two-layer geogrid reinforced samples. Two grain size distributions, namely, the natural coral sand in the South China Sea (ISG) and the uniformly graded coral sand (UG), were used to investigate the effect of gradation on unreinforced and geogrid-reinforced specimens under dry and saturated conditions. The results indicated that the inclusion of geogrid offered a great improvement to the coral sand with respect to increasing its shear strength and reducing the shear dilation. The reinforcement effect of geogrid on dry sample was better than that on saturated one. Moreover, the UG sample exhibits high compressibility and distinct strain hardening behavior due to the significant particle breakage resulting from the lack of fine content compared with the ISG sample, which induced the better reinforcement effect of geogrid on ISG sample. The increase of particle breakage further led to the decrease of peak-state friction angle.

Particle breakage behavior in frozen sands during triaxial shear tests based on the energy principle

It is well known that particle breakage in frozen sands continues throughout the triaxial shearing process and is accompanied by irreversible energy dissipation. Accordingly, it is extremely meaningful to investigate the particle breakage characteristics of frozen sands from the perspective of energy dissipation. First, the contact relationships between particles in frozen sands were abstracted as point-to-point and point-to-surface contacts to determine the mechanism of particle breakage under a low stress state. The extra work or energy dissipation attributed to particle breakage results in a higher friction angle, whereas particle breakage suppresses the occurrence of dilatancy, resulting in a lower friction angle. Thus, the friction angle in the samples was continuously modified during testing to incorporate the comprehensive influence of particle breakage and dilatancy. In this study, a modified energy equation for frozen sands was developed considering the continuous variation in the internal friction angle during the loading process. According to this energy equation, the calculated energy dissipation of crushing during shearing is always greater than zero due to the irreversible crushing behavior and increases gradually until it reaches a stable value when no crushing occurs. Finally, a series of cryogenic triaxial compression tests at various temperatures and confining pressures were performed to systematically explore the particle breakage behaviors of frozen soil by using an improved apparatus, and the energy dissipation of frozen soils during the crushing process was further calculated and analyzed based on the improved energy equation. The results demonstrate that the degree of particle breakage is most severe when the axial strain ranges from 1.5% to 2.5% and that energy dissipation presents a hyperbolic trend with axial strain. The results also imply that the particle breakage energy consumption increases when the soil samples are subject to a higher confining pressure, higher shear stress or lower temperature. The aim of this research is to provide a theoretical basis for establishing suitable constitutive models for frozen soils by considering particle breakage from the perspective of energy dissipation.

An investigation on the breakage behavior of olivine sand particles: An attainable region technique

This study investigates the breakage behavior of olivine sand particles to identify optimal operating parameters to get products in three different define particle size classes. This was achieved by a Los Angeles abrasion test with different numbers of steel balls (up to 12), weights of steel balls (up to 0.441 kg), and different grinding durations (up to 200 mins). The data obtained were then analyzed using a model-free and equipment-independent attainable region (AR) technique. The findings revealed that the required product fineness is a function of the grinding time, numbers and weight of steel balls, and feed material size. Using 9 steel balls of 0.441 kg, a higher mass fraction of materials in the fine-sized class (−75 μm) was obtained after grinding for 200 mins. The AR technique proved to be a practical approach to optimize olivine particle size during breakage, with a potential application in sustainable soil stabilization projects.

An Experimental Investigation of the Behavior of Single-Particle Breakage on Polymetallic Nodules

Abstract Underwater mining systems for mining polymetallic nodules use various transport systems through submersible pumps that can span across subsea platforms (i.e., flexible risers and subsea structures), despite the role of concentration of the medium, shape, and size of the particle and conduit. The crushing unit determines the particle's shape and size, which plays a vital role in transportation (slurry ores) in the subsea environment. The National Institute of Ocean Technology is currently working on a flexible riser transport system. The collected nodules vary in size, and the majority of the nodules are nearly spherical/spheroid in shape with sizes ranging from 3 to 7 cm (Vineesh et al., 2009). The planned vertical slurry transport pipe/flexible hose has an internal diameter of 10 cm for better handling, favorable flow rate, and peak pressure capabilities. The collected nodules are fragmented using a crusher to less than 3 cm (1/3 of the hose inner diameter) to form narrow particle size distribution to prevent layering of the different particle sizes and plug formation by the larger particles during vertical slurry transport. Impact tests were conducted with actual wet nodules of various sizes, using different striker shapes in a drop weight tester to assess the size of the crusher, design the impact surfaces, and estimate the power required. The tests were conducted in submerged conditions to assess the actual load and breakage results. The objective was to maintain low crusher power and have minimal fragmentation to the desired sizes. Single-particle breakage tests were conducted on irregular polymetallic nodules using customized drop-weight impact equipment and a uniaxial compression testing machine to analyze the effect of shape and size on the specific comminution energy (SCE) of three different particle sizes (i.e., 4‐5 cm, 5‐ 6 cm, 6‐7 cm). Furthermore, to understand the deformation behavior of the nodules, experiments are performed with different types of strikers (i.e., hemisphere, conical, and flat). The breakage behavior of ore particles with different particle arrangements and SCE were studied in the tests. Experimental studies indicate that the shape of particles significantly affected the impact-loading mode and the breakage progress. With the increase in the size of particles, the SCE for wet particles decreases for a fixed fraction of particles. Regulating the input power of the crushing machinery and optimizing the crushing technology, considering the influence of particle shape and size, can reduce the SCE consumption and improve energy efficiency. Results reveal that the shape of the striker has a pronounced effect on the SCE in dry, wet, and submerged water test conditions. Compared to wet particles, submerged water conditions show a noticeable increase in SCE consumption due to the associated drag inside water conditions. Our results develop reference data sets required to understand the fragmentation of particles due to intricate crushing and transporting in a submerged environment.

Experimental study on particle breakage of carbonate gravels under cyclic loadings through large-scale triaxial tests

Carbonate gravels are often used as a road base filling material in island area. To evaluate the feasibility of carbonate gravels as a filling material, a large-diameter cyclic triaxial testing system (LDCTTS) was adopted to investigate the particle breakage and long-term behavior of carbonate gravels under high-cycle loadings (N = 50000). The effects of cyclic deviatoric stress, initial static deviatoric stress, effective confining pressure and drainage conditions on the long-term behavior of carbonate gravels were investigated. Fractal theory and Einav’s relative breakage index were applied for the analysis of particle breakage. Test results show that the accumulated axial strain of carbonate gravels increases with the increase of cyclic deviatoric stress and initial deviatoric stress. Particle breakage occurs during the cyclic loading tests, especially for coarse particles with diameter>10 mm. The relative breakage index increases linearly with the cyclic deviatoric stress and the initial deviatoric stress, while decreasing exponentially with the effective confining pressure for the stress range studied. In addition, carbonate gravels in undrained tests exhibit more crushing than drained tests due to the positive pore water pressures accumulated. Einav’s relative breakage index is found to be in an exponential relationship with the input of plastic deformation energy, which can be used to predict the particle breakage of carbonate gravels under cyclic loadings.