Breakage Parameters Research Articles

A Laboratory Investigation of Particle Breakage Parameters in Carbonate and Quartz Sands

A Laboratory Investigation of Particle Breakage Parameters in Carbonate and Quartz Sands

New critical state constitutive model considering particle breakage implicitly for uncemented carbonate sands

One of the main problems of carbonate sands is the fragile nature of particles and their susceptibility to breakage. Carbonate sands are affected by volumetric strain even at low stress levels, which is not the case with silicate sands. By defining a simple breakage model, the current study develops an elastoplastic critical state constitutive model that considers the impact of particle breakage on the mechanical behavior of carbonate sands. The particle breakage model depends on mean effective stress and critical breakage stress, which is assumed to correspond with the precompression pressure of soil in the oedometer test. In the proposed model, critical state line movement with the breakage parameter (α) considers the particle breakage effect. Based on the unified clay and sand model (CASM), a novel dynamic yield surface with a shape parameter affected by particle breaking has been created. Certain modifications are made to the modified Cam-Clay stress dilatancy to predict the behavior of carbonate sand. The current model has only ten parameters that simulate the carbonate sands’ behavior even at high-stress levels without any breakage test. Experimental data with different soil densities, loading stress paths, and stress levels were compared with the model, and the results demonstrated satisfactory conformance.

Discrete Element Modeling of the Breakage of Single Polyhedral Particles in the Rotary Offset Crusher

Innovation in comminution is expected to continue unabated to address the inefficiencies that are inherent in comminution circuits. The rotary offset crusher (ROC) is a new comminution device with a promising performance potential in terms of throughput due to the enhanced speed of transportation induced by the centrifugal force of the discs. However, the processes driving the comminution of particles trapped in the conical space between the two discs of the crusher are not fully understood. To gain a better insight into the comminution process in this device, discrete element modeling (DEM) simulations were conducted to study the breakage of a single particle for the crusher operated under two different dynamic conditions, i.e., (1) a stationary top disc and (2) both discs rotating at the same speed. For both scenarios, the speed of the discs was varied between 550 and 2350 rpm. Experimental testwork was also conducted with the laboratory prototype to generate the data that were used to calibrate the breakage parameters of the Ab × t10 breakage model. Simulations were performed using polyhedral UG2 ore particles that were generated with the in-built particle generator in the DEM simulator. The simulated ROC, which is operated with both discs rotating, outperformed the ROC with a stationary top disc in terms of the specific input energy and throughput. The crusher with a stationary top disc is characterized by high shear forces (suggesting a higher wear rate), specific input energies greater than 1 kWh/t, and low throughputs (<50 kg/h). The ROC operated with a stationary disc is not recommended for hard rock applications due to expected excessive wear of crushing surfaces and higher energy consumption. The freewheeling discs are recommended, but there is scope to optimize the crusher performance in terms of the power draw, size reduction, and throughput by manipulating the difference between the speeds of the discs. There is also scope to optimize the crusher performance when it is simulated with many particles. Once the full performance potential of the ROC is established, it will then be important to benchmark it against the existing crushers in the minerals industry as well as other industries where crushers are used.

Influence of particle crushing on the critical state line of rockfill materials

The mechanical behaviour of rockfill materials is strongly affected by particle breakage, which causes a continuous variation of the grain size distribution (GSD) until a stationary condition. Although the evolution of grain crushing caused among others by the initial grading, the relative density and stress level has been extensively studied, the relationship describing the influence of the current GSD on other soil properties such as the critical state line is not uniquely defined. In this study, a series of triaxial compression tests with various stress paths under monotonic loading were performed on a rockfill to examine the effect of particle breakage on the position of the critical state lines (CSLs) in the compression plane. Specimens were prepared with the same initial grading and relative density to investigate the evolution of the GSD as a result of grain breakage determined by different stress paths applied in a large triaxial apparatus. In addition, a recently proposed simplified procedure is employed to capture the evolution of the CSLs of the tested crushable rockfill as a function of a breakage parameter related to the breakage index Bg. Experimental results obtained for the tested rockfill demonstrate that the abovementioned procedure is capable to predict the position of the CSL linked to the GSD reached at the end of the triaxial test, also when the critical state condition, defined as the ultimate condition in which shearing could continue indefinitely without changes in volume or effective stresses, is not reached.

Effect of Size-Distribution Environment on Breakage Parameters Using Closed-Cycle Grinding Tests.

The so-called population balance model (PBM) is the most widely used approach to describe the grinding process. The analysis of the grinding data is carried out using-among others-the one-size fraction BII method. According to the BII method, the breakage parameters can be determined when a narrow particle size fraction is used as feed material to the mill. However, it is commonly accepted that these parameters are influenced by changing the particle size distribution in the mill. Thus, this study examines the breakage parameters through kinetic testing in different natural-size distribution environments generated by closed-cycle grinding tests that simulate industrial milling conditions. The differentiation of the milling environments was accomplished using various reference sieves in the closed-cycle tests. The experimentally determined breakage parameters were back-calculated and then used to simulate the closed-cycle tests using the MODSIMTM software. Additionally, the energy efficiency was evaluated based on the specific surface area of the grinding products and the energy consumption. The results of the kinetic tests showed that the breakage rate of the coarse particles increases as the aperture size of the reference sieve decreases, and consequently, the content of fines in the mill increases. The back-calculated breakage parameters can be reliably used to simulate closed-cycle circuits, thus helping control industrial milling operations.

Fine-grained damage detection of cement concrete pavement based on UAV remote sensing image segmentation and stitching

A hybrid model for pavement damage segmentation, stitching, and detection based on unmanned aerial vehicle (UAV) remote-sensing pavement images was proposed as high-resolution panoramic images are required to analyze pavement damage feature parameters during the inspection process. Based on target recognition, active stereo vision was used to determine the autonomy awareness of the UAV system in the 3D structure. Then, incremental search strategy was employed to triangulate scale-invariant feature transform (SIFT) point features based on geometric constraints. Perspective-n-point and random sample consensus (PNP-RANSAC) algorithm were combined to find the best matching surface for mis-matching rejection, and the trigonometric function theory was used to fuse images. Subsequently, the semantic segmentation framework based on deep learning context encoder network (CE-Net) was employed to train suitable models to simultaneously detect and segment pavement damages. Finally, the stitching technique and hue, saturation, value (HSV) segmentation technique were combined to obtain the feature parameters to be detected. This method achieved fast and accurate stitching, feature parameter segmentation, and pavement health condition assessment of long-threaded pavement disease image datasets. The splicing accuracy rate and the global feature segmentation overlap rate were greater than 84% and 80%, respectively. The experimental data show that the method is able to detect full-width pavement breakage parameters better than existing optical sensor-based automotive or drone inspection methods.

Simulating large-diameter industrial ball mills from batch-grinding tests

Phenomenological models of ball milling are routinely used to optimize size reduction operations. A usual method adopted in the minerals industry relies on batch-grinding tests to calibrate models in a population balance model formulation describing the breakage behaviour and then scale-up the breakage parameters using an energy-based relationship. Despite the important advances and application of these methods, their application in describing grinding in large-diameter (>7.5 m) mills has not been widely demonstrated. The work demonstrates the calibration of industrial-scale ball mill model parameters from laboratory milling tests on Platinum Group Metals (PGM) and Itabirite iron ores. Minor fine-tunning of a single model parameter was required to simulate the large-diameter industrial mills, demonstrating the validity of the approach for ores as distinct as PGM and Itabirite iron ores. Estimation of the Arbiter Flow Number below 4.1 showed a regular slurry transport for all mills studied. This model can then be used in optimization of the ball mill performance.

Compaction-deformation behaviors and breakage characteristics of loose broken coal under various stress–temperature coupling loads

This study probed the compaction-deformation and breakage characteristics of loose broken coal under stress–temperature coupling loads. The constitutive model of loose broken coal under stress–temperature coupling loads was first constructed. Then, we quantificationally investigated the particle size distribution (PSD) evolution for the compacted loose coal using the fractal and Weibull functions. In addition, the relative breakage rate, energy evolution, and particle breakage degree of the loose coal compacted were quantificationally evaluated. Results suggest that stress is the prominent factor leading to the breakage of loose broken coal, while increased temperature exacerbates the particle breakage process in combination with the axial stress. Changes in temperature have a distinctive influence on particle breakage for loose broken coal under low-stress conditions, whereas less conspicuous under high-stress conditions. Finally, the evolution of PSDs and related breakage parameters for the entire loose broken coal compaction process were mathematically predicted utilizing the grey model.

Comparing modeling approaches in simulating a continuous pilot-scale wet vertical stirred mill using PBM-DEM-CFD

Vertical stirred mills have become increasingly popular in size reduction operations in the fine and ultrafine range, being normally used in industry in continuous operation. The present work describes the application of a mechanistic mill modeling approach based on the population balance (PBM) to describe the performance of a pilot-scale gravity-induced continuous stirred mill using 6 mm steel grinding media. At first, DEM and coupled DEM-CFD were compared in simulation of the mill, clearly demonstrating the significant effect of incorporating explicitly the fluid flow in describing the motion of the grinding media. The work then uses data from the stirred mill grinding calcite in multiple passes for model calibration and validation, besides breakage parameters from previous studies. It shows that the population balance-based mechanistic mill model predictions vary depending on the number of mixers-in-series used to predict product size, but that are capable of describing very well the milling operation considering the mill as three perfectly mixed grinding zones in series.

The relationships between the kinetic grinding parameters with interstitial fillings and the liberation degree of a chromite ore

In this study, the relationships between the liberation degree and the kinetic breakage parameters of a chromite ore obtained from the Burdur (Türkiye) were examined under the laboratory conditions. Firstly, liberation degrees for chromite particles were determined by the particle counting method in a metal microscope for 4 different size groups. Secondly, the breakage parameter of chromite ore which was dry ground with a ball mill was obtained using standard test methods. Additionally, the model parameters were also determined for the fractional interstitial fillings (U) of the chromite sample. Thirdly, the kinetic grinding parameters were compared with the liberation degree of the chromite sample. As a result of the tests, a very good correlation was obtained with R2=0.998, and regression analysis in the grinding processing of the chromite ore was used to verify the validity of the relationship parameter of Si that was produced. To these, it was found that interstitial fillings (U=0.6, 0.8, 1.0, and 1.2) have an effect on the grinding.

Performance Comparison of the Vertical and Horizontal Oriented Stirred Mill: Pilot Scale IsaMill vs. Full-Scale HIGMill

Varied types/geometries of stirred mills have been produced by different manufacturers, and the comparison task has been accomplished for some of the technologies, i.e., Tower mill vs IsaMill. However, the main drawbacks of these comparisons were the uncommon characteristics of the milling environment, such as media size. In this study, HIGMill and IsaMill, which were vertically and horizontally chamber oriented, respectively, were compared for a regrinding process of copper ores with similar characterization and almost the same milling environment. Detailed characterization studies of the two ore types, such as work index, ore breakage and chemical composition, were performed. Modeling of the two mills was also performed to show the variation in the rate of breakage parameters. The entire assessments were based on comparing the signature plots, energy and shape of the product size distribution as well as the stress analyses. The results showed that HIGMill and IsaMill technologies behaved in a different manner for coarse and fine tail of comminution. IsaMill with horizontal orientation was found to be more energy-efficient, particularly at the fine grind size, and produced finer product when it was operated at the same stress level of HIGMill.

A novel oblique impact model for unified particle breakage master curve

Many experimental and numerical studies have been performed on the impact breakage of particulate solids, leading to a variety of impact breakage models developed to predict breakage probability. Ideally, impact breakage models would be mechanistic in nature, mathematically simple and inclusive of critical breakage parameters. In this paper, a critical review of the most widely used impact breakage models is presented, with the conclusion that the majority of existing breakage models inadequately predict breakage probability under oblique impact. In this work, a novel oblique impact model is proposed where the effect of impact angle is considered by the equivalent velocity. A breakage database compiled from the literature is deployed to interrogate the validity of the proposed model across a variety of oblique impact circumstances. In this way, the new oblique impact model is shown to provide excellent predictions of breakage probability, requiring only one set of fitting parameters under various impact angles. The unique feature of this oblique impact model is not necessarily required to be used with any specific normal impact breakage models, but can instead be universally applied with any of the assessed normal impact breakage models to establish unified breakage master curves for any oblique impact.

Turbulent droplet breakage probability: Analysis of fitting parameters for two commonly used models

Droplet breakage in liquid–liquid systems is an important physical process in manufacturing operations throughout the chemical, food, and pharmaceutical industries. Although several mathematical models have been developed to describe droplet breakage in agitated liquid emulsions, the utility of these models is limited by the fact that they incorporate multiple fitting parameters that must be determined empirically for specified fluid pairs and flow conditions. In this work, analytical expressions that can be evaluated without need to perform droplet breakage experiments have been developed for parameters associated with droplet breakage probability in two commonly used breakage models. These expressions were derived by applying dimensional analysis and by using a hypothesis regarding breakage probability that is based upon competition between disruptive and restorative stresses on droplets. Data used for validation of the proposed equations for the breakage probability parameters were obtained from previously published reports of droplet breakage in heterogeneous flow devices, as well as from experiments performed in a von Kármán box designed to produce homogeneous turbulence. Comparison of the droplet breakage probability predictions using the derived expressions for the breakage parameters show generally good agreement with experimental data.

Evaluation of the Relationship between the Milling Breakage Parameters and Mineralogical Data: A Case Study of Three Copper Ores from a Multi-Mineralised Deposit

The study evaluated the milling kinetics of three copper ores, from a multi-mineralised deposit, which were identified as sulphide 1 (with bornite as a dominant copper mineral), sulphide 2 (mainly composed of chalcopyrite) and oxide (with malachite as a dominant copper mineral) and related the breakage parameters to the mineral composition data. Five mono-size fractions between 1000 µm and 212 µm were dry milled for short grinding times in the laboratory ball mill in order to obtain data for predicting breakage rate parameters. The analytical and mineralogical characterisation of the ores were performed using X-ray fluorescence (XRF) analysis, scanning electron microscopy energy dispersive spectroscopy (SEM-EDS) analysis, optical microscopy analysis and X-ray diffractometer (XRD). The mineralogy data showed that quartz was the abundant gangue mineral (average for each ore was above 60% (w/w)), followed by K-feldspar minerals (orthoclase and microcline) which constituted between 4% (w/w) and 6% (w/w) and the remainder are the minor calcite and dolomite minerals which are also in the host rock. The experimental milling kinetics parameters and mineralogical data were used to assess the robustness of the heterogeneous (two-component) and homogeneous (single-component) first-order rate breakage models. The mineral composition data were used for setting up the predictions of breakage parameters in the two-component and single-component first-order breakage models. The experimental data fitted better on the two-component breakage model than the single-component breakage model. These results highlighted the influence of two groups of minerals (generally classed as valuable and gangue minerals). The breakage data showed that the selection function for the hard component (the gangue minerals) has a dominant contribution to the overall selection function of the ores, with SiA correlating fairly well with experimental Si. The parameter a in the Austin empirical breakage model was relatively similar (approximately 1) for all three ores, which confirms similar milling conditions to which the ores were subjected to. The data suggests that there is a relationship between breakage parameter α (material-specific parameter) in the Austin empirical breakage model and brittleness index βi (calculated from the mineralogical composition of the gangue phase). No clear trends could be deduced from the cumulative breakage distributions of the three ores. This highlights the complexity of developing relationships between the mineralogical composition data and breakage distributions of the ores which are extracted from the same deposit and with comparable gangue composition.

Analysis of the breakage parameters of railway ballast based on the discrete element method

Analysis of the breakage parameters of railway ballast based on the discrete element method

Experimental measurement of particle crushing around model piles jacked in a calibration chamber

During installation of driven or jacked piles in sand, particle crushing occurs in a region below the base of these piles. Quantification of the degree and extent of particle crushing during driving or jacking in sand is necessary to improve current design methods. To study the effects of particle crushing on the capacity of piles jacked in uniform silica sand samples, a model pile was jacked and tested in a half-cylindrical calibration chamber with transparent observation windows in its front wall. Annular samples of crushed sand 3 mm in thickness were recovered after testing from several locations along the shaft and the base of the model piles and used to assess particle gradation changes and to calculate breakage parameters. Relationships between the load mobilized at the base of the model piles and three breakage parameters are proposed. Furthermore, the number of jacking strokes (ranging from 1 to 32 in this research) has a negligible effect on the degree of crushing produced during installation and on the measured stresses at the base of the model pile. Analyses of the digital images captured during pile jacking indicate that the silica sand particles in the path of the model pile crush mainly along irregularities and sharp edges. Different zones are identified below the model pile according to the degree of particle crushing. Digital images taken during static loading of the model pile allowed tracking of the displacement paths of individual sand particles during loading.

A Binary Medium Model for Frozen Silty Sand Simplified by Breakage Parameter

In order to investigate the strength-deformation characteristics of frozen silty sand, the triaxial compressive strength tests of saturated frozen silty sand under different fine particle contents were carried out, and the binary medium theory was introduced to interpret the stress-strain relationship. Due to the characteristics of the existing binary medium model with many parameters and complicated determination method, a simplified binary medium model based on breakage parameter is proposed. The derived model was verified by the triaxial tests of frozen silty sand. The results show that the stress-strain relationship can be divided into three stages with the increase of axial strain, namely, linear elastic deformation stage, plastic deformation stage, and strain softening stage. All three stages can be well explained by the transformation theory of bonded element and frictional element with the binary medium model. In the linear elastic deformation stage, the external stress is mainly borne by the bonded element. In the plastic deformation stage, the stress sharing ratio of the bonded element decreases and that of the frictional element increases. In the strain softening stage, the stress sharing ratio of the bonded element decreases rapidly, while that of the frictional element increases rapidly. Under the same confining pressure, both deviator stress and the maximum values of bulk expansion decrease, while the shear strength decreases linearly with the increase of fine particle content. By comparing the measured deviator stress in triaxial test with the calculated values of binary medium constitutive model simplified by breakage parameter, the proposed model can better simulate the stress-strain relationship of frozen silty sand. The results of the study can provide some theoretical reference for the constitutive model of seasonal frozen soil.

Application of artificial neural network method to predict the breakage properties of PGE bearing chromite ore

In the present investigation, systematic grinding experiments were conducted in a laboratory ball mill to determine the breakage properties of low-grade PGE bearing chromite ore. The population balance modeling technique was used to study the breakage parameters such as primary breakage distribution (Bi, j) and the specific rates of breakage (Si). The breakage and selection function values were determined for six feed sizes. The results stated that the breakage follows the first-order grinding kinetics for all the feed sizes. It was observed that the coarser feed sizes exhibit higher selection function values than the finer feed size. Further, an artificial neural network was used to predict breakage characteristics of low-grade PGE bearing chromite ore. The predicted results obtained from the neural network modeling were close to the experimental results with a correlation of determination R2 = 0.99 for both product size and selection function.

The effects on the grinding parameters of chemical, morphological and mineralogical properties of three different calcites in a Hardgrove mill

Recently, the kinetic model commonly uses the specific rate of breakage (Si) and the cumulative breakage distribution (Bi,j) functions to explain the grinding behavior of the material with respect to time in a laboratory batch mill. Until now, important researches have been published on these functions, especially in a tumbling ball mill. However, so far, there has been no study determining the effects of kinetic breakage parameters on calcites in a Hardgrove mill, which is a vertical roller mill. This study presents the kinetic breakage behavior of the three different calcites in a Hardgrove mill. Firstly, the Bond and Hardgrove grindability tests were performed. Secondly, kinetic breakage parameters (Si aT, α, γ, β, and ϕj) were determined from product size distributions for short grinding times and compared for three different calcite types. From the result of the tests, contrary to expectations, different results were obtained between the grindability data and kinetic breakage parameters. The reason for these different results was found to be due to the different chemical, morphological, and mineralogical properties of calcites.

Model driven design for twin screw granulation using mechanistic-based population balance model

This paper presents a generic framework of Model Driven Design (MDD) with its application for a twin screw granulation process using a mechanistic-based population balance model (PBM). The process kernels including nucleation, breakage, layering and consolidation are defined in the PBM. A recently developed breakage kernel is used with key physics incorporated in the model formulation. Prior to granulation experiments, sensitivity analysis of PBM parameters is performed to investigate the variation of model outputs given the input parameter variance. The significance of liquid to solid ratio (L/S ratio), nucleation and breakage parameters is identified by sensitivity analysis. The sensitivity analysis dramatically reduces the number of fitting parameters in PBM and only nine granulation experiments are required for model calibration and validation. A model validation flowchart is proposed to elucidate the evolution of kinetic rate parameters associated with L/S ratio and screw element geometry. The presented MDD framework for sensitivity analysis, parameter estimation, model verification and validation can be generalized and applied for any particulate process.