The main objective of this research was to model the airflow paths through grain bulks and predict the resistance to airflow. The discrete element method (DEM) was used to simulate the pore structures of grain bulks. A commercial software package PFC3D (Particle Flow Code in Three Dimension) was used to develop the DEM model. In the model, soybeans kernels were considered as spherical particles. Based on simulated positions (coordinates) and radii of individual particles, the characteristics of airflow paths (path width, tortuosity, turning angles, etc.) in the vertical and horizontal directions of the grain bed were calculated and compared. The discrete element method was also used to simulate particle packing in porous beds subjected to vertical vibration. Based on the simulated spatial arrangement of particles, the effect of vibration on critical pore structure parameters (porosity, tortuosity, pore throat width) was quantified. A pore-scale flow branching model was developed to predict the resistance to airflow through the grain bulks. Delaunay tessellation was also used to develop a pore network model to predict airflow resistance. Experiments were conducted to measure the resistance to airflow to validate the models. It was found that the discrete element models developed using PFC3D was capable of predicting the pore structures of grain bulks, which provided a base for geometrically constructing airflow paths through the pore space between particles. The tortuosity for the widest and narrowest airflow paths predicted based on the discrete element model was in good agreement with the experimental data reported in the literature. Both pore-scale models (branched path and network) proposed in this study for predicting airflow resistance (pressure drop) through grain bulks appeared promising. The predicted pressure drop by the branched path model was slightly (<12%) lower than the experimental value, but almost identical to that recommended by ASABE Standard. The predicted pressure drop by the network model was also lower than the measured value (2.20 vs. 2.44 Pa), but very close to that recommended by ASABE Standard (2.20 vs. 2.28Pa). / February 2017

Soil disturbance and cutting force are two of the most common performance indicators for soil-engaging tools. In this study the interaction of two soil-engaging tools (a disc opener for fertilizer banding and a hoe opener from an air drill) with soil were modeled using Particle Flow Code in Three Dimensions (PFC3D), a discrete element modeling software. When comparing the disc model to the experiment results, the relative error was 11% for the average soil throw, 1.9% for the average draft force, and 51% for the average vertical force. Results from the soil-hoe model showed a relative error of 15% between the simulated soil throw and the measured one. In conclusion, both the soil-disc and soil-hoe models could simulate the selected soil dynamic properties (except for the vertical forces of the disc opener) with a reasonably good accuracy, considering the highly variable nature of the soil. / October 2016

Since the beginning of the last century, many studies have been performed in order to improve our understanding on the milling process. Recently, Mishra and Rajamani (1992) applied the Discrete Element Method (DEM) to solve the milling problem. Since then, this method gained considerable success due to its ability to predict load motion and power draw by tumbling mills as affected by operating conditions. The application of this method at an industrial stage requires a more rigorous validation in order to produce realistic output. Lifter profiles play a key role in the performance of tumbling mills since they influence the motion of mill charge. Since lifters change profiles during their useful life due to wear, the performance of tumbling mills will correspondingly vary as a function of time. There is therefore a need to predict forces and wear on mill lifters in order not only to chose or design an initial lifter profile which optimizes tumbling mills performance over the lifters’ useful life but also to evaluate lifter replacement time and type and also modifications which can be performed on lifters and/or operating mill conditions in order to extend the lifters’ useful life. Despite the importance related to this subject, few works has been done in this field. In this thesis, we firstly assess the ability of the Discrete Element Method to model the tangential and normal forces exerted by the mill charge on lifters. Data from an experimental two-dimensional mill designed in order to record the normal and tangential forces exerted on an instrumented lifter were available. The measured results obtained at different speeds and percentages of filling have been compared to the Discrete Element Method simulated results in the same conditions. A good agreement has been found between the experimental and the simulated results in terms of toe, shoulder positions and amplitude of forces. After this validation of the DEM, we secondly assess the ability of this method to predict the wear of lifters in dry milling conditions. We derived a mathematical wear equation describing the removal of materials from lifters which takes into account all types of wear occurring in dry milling environment. We introduce a new approach to implement this equation in the DEM code in order to produce realistic simulated profiles. Our new method developed has been tested against laboratory and industrial data of evolving lifter profiles due to wear. Good agreement has been found between the simulated and the measured profiles. The variation of the load behaviour as a function of lifter wear in industrial tumbling mills studied was also investigated in this thesis. The objectives were to improve the understanding of the grinding process and quantify the variation of load behaviour as a function of lifter wear. Lifter modifications were also explored in order to extend lifters useful life. An attempt was also made in this thesis to derive, from the description of the load behaviour, equations in order to predict the wear of lifters without using the Discrete Element Method. Equations derived show the difficulty to use this approach. Success in this case was achieved only in a particular case where no significant changes occur in the load behaviour as a function of lifters wear. This finding confirms the DEM as the adequate tool to model forces and wear of tumbling mill lifters. The results obtained are of great economical significance since they can improve the profitability of mineral processing plants. A step forward in the use of the DEM not only to design milling equipments but also to improve the understanding, optimise and quantify the change occurring as a function of lifters wear was achieved.

Aggregate strength, gradation, and shape play a vital role in controlling asphalt mixture performance. Many studies have demonstrated the effects of these factors on asphalt mixture performance in terms of resistance to fatigue cracking and rutting. This study introduces numerical and analytical approaches supported with imaging techniques for studying the interrelated effects of aggregate strength, gradation, and shape on resistance of asphalt mixtures to fracture. The numerical approach relies on the discrete element method (DEM). The main advantage of this approach is the ability to account for the interaction between the internal structure distribution and aggregate properties in the analysis of asphalt mixture response and performance. The analytical approach combines aggregate strength variability and internal force distribution in an asphalt mixture to predict the probability of aggregate fracture. The numerical and analytical approaches were calibrated and verified using laboratory tests on various aggregate types and mixtures. Consequently these approaches were used to: (1) determine the resistance of various mixture types with different aggregate properties to fracture, (2) study the effects of aggregate strength variability on fracture, (3) quantify the influence of blending different types of aggregate on mixture strength, (4) develop a mathematical expression for calculating the probability of aggregate fracture within asphalt mixture, and (5) relate cracking patterns (cohesive: aggregate - aggregate and matrix - matrix, and adhesive: aggregate - matrix) in an asphalt mixture to internal structure distribution and aggregate properties. The results of this dissertation established numerical and analytical techniques that are useful for developing a virtual testing environment of asphalt mixtures. Such a virtual testing environment would be capable of relating the microscopic response of asphalt mixtures to the properties of the mixture constituents and internal structure distribution. The virtual testing environment would be an inexpensive mean to evaluate the influence of changing different material and design factors on the mixture response.

This study considered using a relatively new method to study soil-tool wear which could drastically reduce the time and associated costs of traditional wear studies. The goal was to utilize discrete element method (DEM) simulations to recreate the results of a circular soil bin test in order to develop a relationship that could be used to predict wear under different conditions. Through the application of DEM, simulations could be used to study different materials or designs intended to result in improved wear performance.<p> Three replications of aluminum cylindrical bars were worn during 400 km of travel in a circular soil bin. Wear was quantified by measuring the change in radius of the cylinders at 18-degree intervals around their circumference. Mass data were also obtained to provide an overall average of wear occurring on the bar and to validate the radii measurements.<p> The DEM simulations were executed using EDEM software. Conditions present in the physical soil bin trials were simulated by recreating components in the soil bin and incorporating soil properties that were directly measured, using representative soil samples. Forces exerted on the bar by the soil and the relative velocities between the soil and tool were used to generate a relationship to predict wear of the bar. The wear equation was verified using a portion of the experimental data from the soil bin.<p> The wear model showed promise in predicting the amount of wear recorded in the soil bin through the application of DEM-predicted compressive forces and relative velocities between the tool and soil particles. The Archard equation for wear was modified to create a non-linear equation. Plotting the measured wear against the wear predicted from the fitted equation produced a trendline with a slope of 0.65. Although a perfect correlation would have produced a slope of 1, the model was able to predict a large portion of the wear that occurred. Refinement of the model could further be achieved with changes in the design of the geometry used in the simulation and through verification of force predictions with experimental data. Because of the variable nature of wear, additional replications of tools in the soil bin would have increased the number of data points available to create the model and reduced the impact of outlying data. With these recommended improvements, the wear model has the ability to very accurately predict the wear of a cylindrical bar.

This study considered using a relatively new method to study soil-tool wear which could drastically reduce the time and associated costs of traditional wear studies. The goal was to utilize discrete element method (DEM) simulations to recreate the results of a circular soil bin test in order to develop a relationship that could be used to predict wear under different conditions. Through the application of DEM, simulations could be used to study different materials or designs intended to result in improved wear performance.<p> Three replications of aluminum cylindrical bars were worn during 400 km of travel in a circular soil bin. Wear was quantified by measuring the change in radius of the cylinders at 18-degree intervals around their circumference. Mass data were also obtained to provide an overall average of wear occurring on the bar and to validate the radii measurements.<p> The DEM simulations were executed using EDEM software. Conditions present in the physical soil bin trials were simulated by recreating components in the soil bin and incorporating soil properties that were directly measured, using representative soil samples. Forces exerted on the bar by the soil and the relative velocities between the soil and tool were used to generate a relationship to predict wear of the bar. The wear equation was verified using a portion of the experimental data from the soil bin.<p> The wear model showed promise in predicting the amount of wear recorded in the soil bin through the application of DEM-predicted compressive forces and relative velocities between the tool and soil particles. The Archard equation for wear was modified to create a non-linear equation. Plotting the measured wear against the wear predicted from the fitted equation produced a trendline with a slope of 0.65. Although a perfect correlation would have produced a slope of 1, the model was able to predict a large portion of the wear that occurred. Refinement of the model could further be achieved with changes in the design of the geometry used in the simulation and through verification of force predictions with experimental data. Because of the variable nature of wear, additional replications of tools in the soil bin would have increased the number of data points available to create the model and reduced the impact of outlying data. With these recommended improvements, the wear model has the ability to very accurately predict the wear of a cylindrical bar.

Aggregate strength, gradation, and shape play a vital role in controlling asphalt mixture performance. Many studies have demonstrated the effects of these factors on asphalt mixture performance in terms of resistance to fatigue cracking and rutting. This study introduces numerical and analytical approaches supported with imaging techniques for studying the interrelated effects of aggregate strength, gradation, and shape on resistance of asphalt mixtures to fracture. The numerical approach relies on the discrete element method (DEM). The main advantage of this approach is the ability to account for the interaction between the internal structure distribution and aggregate properties in the analysis of asphalt mixture response and performance. The analytical approach combines aggregate strength variability and internal force distribution in an asphalt mixture to predict the probability of aggregate fracture. The numerical and analytical approaches were calibrated and verified using laboratory tests on various aggregate types and mixtures. Consequently these approaches were used to: (1) determine the resistance of various mixture types with different aggregate properties to fracture, (2) study the effects of aggregate strength variability on fracture, (3) quantify the influence of blending different types of aggregate on mixture strength, (4) develop a mathematical expression for calculating the probability of aggregate fracture within asphalt mixture, and (5) relate cracking patterns (cohesive: aggregate - aggregate and matrix - matrix, and adhesive: aggregate - matrix) in an asphalt mixture to internal structure distribution and aggregate properties. The results of this dissertation established numerical and analytical techniques that are useful for developing a virtual testing environment of asphalt mixtures. Such a virtual testing environment would be capable of relating the microscopic response of asphalt mixtures to the properties of the mixture constituents and internal structure distribution. The virtual testing environment would be an inexpensive mean to evaluate the influence of changing different material and design factors on the mixture response.

The main objective of the project was to develop a model for the motion of granular media under vibration in a tub vibrator. For such a system, it was decided that a discrete element method (DEM) was the most appropriate tool to model bulk velocity and circulation of media. In the first phase of the work, a vibratory finisher was modified to introduce planar vibration into a single layer of particles. The motion of the tub was measured using accelerometers and the corresponding granular media behavior was determined by video recording. A discrete element model, based on Cundall’s approach to contact, was developed to model granular flow in different vibratory beds, and the results were compared with experimental measurements of bulk flow velocity and bed expansion for the tub finisher. The sensitivity of the model predictions to the contact parameters was considered and the parameters were optimized with respect to the experimental results. After optimization, the difference between the model predictions of the bulk flow velocity and the measurements was less than 20% at four locations in media beds of two depths. The average bulk density of the vibrating beds was also predicted to be within 20% of the measured values. In the next phase, a two-dimensional discrete element model was developed to model single-cell circulation in vibratory beds that had both vertical and horizontal components of motion. The model predictions were compared with experimental measurements of the onset and growth of circulation in beds of steel and glass spheres as a function of bed depth, inter-particle and wall friction coefficients, and the amplitude of vibration. While the values from the DEM showed an error of up to 50% in the predicted circulation strength, depending on the type of the media and system conditions, the trends predicted by the model closely matched those in the experiments. Finally, a physical model was developed to describe the relationship between the onset and direction of circulation with the vibration of the container. A similar model was used to describe the experimental results as well as the transition in circulation patterns in terms of the resultant shear forces at the vibrating container walls and the interlocking of media close to the container walls. It was also demonstrated that a two-dimensional DEM could model a granular flow in which the media had three-dimensional contact and freedom of movement, but that was driven by vibrations in a plane. In summary, it was found that the linear optimization procedure for the contact parameters is an efficient way to improve the results from DEM. Additionally, the circulation in a tub-vibrator increased with the depth of the particulate media in the container, and with the magnitude of the wall-particle and particle-particle friction coefficients. The strength of circulation also increased with the amplitude of vibration. A strong correlation existed between the total shear force along the vibrating container walls and the circulation behavior. Bulk circulation increased sharply when increasing bed depth increased the pressure and the shear forces at the walls and between particle layers. It was also concluded that dimensionless bed depth (the ratio of bed depth to particle diameter) was not a proper dimensionless group when discussing the circulation behavior and it should act in conjunction with other parameters.

The main objective of the project was to develop a model for the motion of granular media under vibration in a tub vibrator. For such a system, it was decided that a discrete element method (DEM) was the most appropriate tool to model bulk velocity and circulation of media. In the first phase of the work, a vibratory finisher was modified to introduce planar vibration into a single layer of particles. The motion of the tub was measured using accelerometers and the corresponding granular media behavior was determined by video recording. A discrete element model, based on Cundall’s approach to contact, was developed to model granular flow in different vibratory beds, and the results were compared with experimental measurements of bulk flow velocity and bed expansion for the tub finisher. The sensitivity of the model predictions to the contact parameters was considered and the parameters were optimized with respect to the experimental results. After optimization, the difference between the model predictions of the bulk flow velocity and the measurements was less than 20% at four locations in media beds of two depths. The average bulk density of the vibrating beds was also predicted to be within 20% of the measured values. In the next phase, a two-dimensional discrete element model was developed to model single-cell circulation in vibratory beds that had both vertical and horizontal components of motion. The model predictions were compared with experimental measurements of the onset and growth of circulation in beds of steel and glass spheres as a function of bed depth, inter-particle and wall friction coefficients, and the amplitude of vibration. While the values from the DEM showed an error of up to 50% in the predicted circulation strength, depending on the type of the media and system conditions, the trends predicted by the model closely matched those in the experiments. Finally, a physical model was developed to describe the relationship between the onset and direction of circulation with the vibration of the container. A similar model was used to describe the experimental results as well as the transition in circulation patterns in terms of the resultant shear forces at the vibrating container walls and the interlocking of media close to the container walls. It was also demonstrated that a two-dimensional DEM could model a granular flow in which the media had three-dimensional contact and freedom of movement, but that was driven by vibrations in a plane. In summary, it was found that the linear optimization procedure for the contact parameters is an efficient way to improve the results from DEM. Additionally, the circulation in a tub-vibrator increased with the depth of the particulate media in the container, and with the magnitude of the wall-particle and particle-particle friction coefficients. The strength of circulation also increased with the amplitude of vibration. A strong correlation existed between the total shear force along the vibrating container walls and the circulation behavior. Bulk circulation increased sharply when increasing bed depth increased the pressure and the shear forces at the walls and between particle layers. It was also concluded that dimensionless bed depth (the ratio of bed depth to particle diameter) was not a proper dimensionless group when discussing the circulation behavior and it should act in conjunction with other parameters.

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