The general objective of the research effort reported in this thesis was to develop the knowledge required to optimize the design and operation of solid and semi-solid manure handling and land application equipment. Selected physical and rheological properties of manure products deemed to have an influence on the performances of manure handling and land application equipment were measured and general trends were identified among the measured properties. Relationships were also established between the measured properties and the type of manure as well as its total solids concentration. Field experiments were carried out to evaluate the effects of selected mechanical configurations, operating parameters and product properties on the discharge of manure spreaders. The influence of the type of conveying system (scraper conveyor and system of four augers) and the velocity at which it is operated, the geometry of the holding system and the position of a flow-control gate were all included in the analysis. The discharge rates of the machines as well as the specific energy required by the unloading operations were measured. A numerical modeling method called discrete element method (DEM) was used to create virtual manure, a numerical model of the real product. The measured physical and flow properties were used to develop and validate the virtual manure models. It was found that manure products could successfully be represented in a DE framework and that several parameters defining the contact constitutive model in the DEM had an influence on the behaviour of the virtual products. The DEM was then used to study machine-product interactions taking place in handling and land application equipment. Results from field experiments carried out using various land application equipment were used in the development and validation of the interaction models. The predicted flow rates and power requirements were in good agreement with measured data. The results obtained allowed for a better understanding of the flow of manure products in manure handling and land application equipment. It was found that the constitutive model used for the product influenced the results of the machine-product interactions models. A precision banded applicator under development at the University of Saskatchewan was also modeled. The discharge rate of this equipment is influenced by a number of parameters. The predicted mass distribution across the width of the banded applicator was well correlated to the experimental results. The models developed in this thesis have the potential to become powerful engineering tools for the design of improved machines for the handling and land application of solid and semi-solid manure.

In the past, most research on soil mechanical properties was carried out for cohesionless soils in the fields of civil and geotechnical engineering. Little research has been carried out for mechanical properties of agricultural soil, which are essential for designing soil engaging tools in agriculture. In this study, unconsolidated undrained triaxial compression tests were performed to study the effects of moisture level and confining pressure on a sandy loam soil. The soil specimens tested had three moisture levels, and they were high (27-29% d.b.), medium (19-21% d.b.) and low (9-11% d.b.). The confining pressures used for the triaxial tests were 50, 100, and 150 kPa. Soil specimen was loaded at a strain rate of 1%/min. Measurements from the tests included stress-strain curve, shear strength, Young’s modulus, Poisson’s ratio, angle of internal friction, and cohesion. A model was developed using the Discrete Element Method (DEM) and computed by Particle Flow Code in three dimensions (PFC3D), a common DEM software. The model simulated the triaxial compression tests, and the model specimen was an assembly of 5-mm spherical particles which were defined by a set of micro parameters. During simulations, soil shear strength was monitored under different confining pressures. Through sensitivity analysis, it was found that most of the micro parameters affected the simulated soil shear strengths and the stress-strain behaviours. The most influential micro parameter was particle friction coefficient. This micro parameter was calibrated with the data from triaxial tests for different combinations of soil moisture levels and confining pressures. The calibrated particle friction coefficients varied from 0.2 to 1.0. The calibrations were done through matching the shear strengths between simulations and measurements, and the relative errors ranged between 0 and 6 %. / October 2015

Tobulėjant skaitiniams metodams ir kompiuterinei technikai atsivėrė galimybė naujų, sudėtingesnių mechaninių objektų modeliavimui. Turėdami naujus sudėtingesnių objektų modelius tyrėjai gali pritaikyti aprašytas ir sumodeliuotas šių objektų savybes su mikro struktūros ypatumais esamų ar busimų savybių nustatymui bei naujų medžiagų kūrimui. Tam intensyviai naudojami kaip eksperimentiniai taip ir skaitiniai metodai, kurių tobulinimui šiuo metu yra skiriamas labai didelis dėmesys. Skaitinis eksperimentas, kaip medžiagos tyrimo būdas pasitelkiamas dar ir todėl kad yra pigesnis ir leidžia interpretuoti jau žinomus eksperimentų rezultatus, o taip suteikia žinių naujiems tyrimams. Vienas iš metodų, kuris modeliuoja makroskopines medžiagų savybes remdamasis medžiagos mikro savybėmis yra diskrečiųjų elementų metodas (DEM). DEM metodas remiasi idėja, kad bet kokia fizikinė struktūra gali būti aprašyta kaip judančių dalelių sistema. Ši idėja pradėta taikyti ir vientisam deformuojamam kūnui aprašyti. Skirtingai nuo biriųjų medžiagų, vientiso kūno dalelės ir tarp jų egzistuojančios sąveikos yra kitokios prigimties, o jų modeliai yra fizikinės ir matematinės abstrakcijos rezultatas. Vientiso deformuojamo kūno modeliavimas diskrečiais elementais yra tik pradinėje stadijoje, o vientiso požiūrio į diskrečių elementų modelius dar nėra. Yra kelios hipotetinės versijos, grindžiamos skirtingais požiūriais. Taikant DEM kūnui, pirmas žingsnis būtu tampriųjų savybių modeliavimas. Tai yra... [toliau žr. visą tekstą] / Development of numerical methods and computation environments opened the possibility of new, more sophisticated mechanical objects modelling. In this context it is natural desire of the researchers to describe macroscopic mechanical characteristics of the materials by their microstructure, which can be adapted for simulation of the existing and future materials. For this purpose researchers are using intensively experimental and numerical methods for the development of which the highest priority is given. Numerical experiments are used because they are cheaper and allow the interpretation of already known results of experiments and provide information to new investigations. One of the methods used for modelling of macroscopic properties modelling is based on microscopic properties of material is discrete element method (DEM). The DEM traditionally was applied for the granular materials. The basic idea of DEM is that any physical structure could be described as a system of moving particles. This idea could be also applied to the description of solid deformable body. Particles forming solid body and existing interaction between them are of different nature than the granular materials because their models are often the result of physical and mathematical abstraction. The modelling of solid deformable body with the discrete elements is just at the initial stage and the unified approach to discrete elements models doesn’t exist. There are several versions of models, based... [to full text]

Development of numerical methods and computation environments opened the possibility of new, more sophisticated mechanical objects modelling. In this context it is natural desire of the researchers to describe macroscopic mechanical characteristics of the materials by their microstructure, which can be adapted for simulation of the existing and future materials. For this purpose researchers are using intensively experimental and numerical methods for the development of which the highest priority is given. Numerical experiments are used because they are cheaper and allow the interpretation of already known results of experiments and provide information to new investigations. One of the methods used for modelling of macroscopic properties modelling is based on microscopic properties of material is discrete element method (DEM). The DEM traditionally was applied for the granular materials. The basic idea of DEM is that any physical structure could be described as a system of moving particles. This idea could be also applied to the description of solid deformable body. Particles forming solid body and existing interaction between them are of different nature than the granular materials because their models are often the result of physical and mathematical abstraction. The modelling of solid deformable body with the discrete elements is just at the initial stage and the unified approach to discrete elements models doesn’t exist. There are several versions of models, based on... [to full text] / Tobulėjant skaitiniams metodams ir kompiuterinei technikai atsivėrė galimybė naujų, sudėtingesnių mechaninių objektų modeliavimui. Turėdami naujus sudėtingesnių objektų modelius tyrėjai gali pritaikyti aprašytas ir sumodeliuotas šių objektų savybes su mikro struktūros ypatumais esamų ar busimų savybių nustatymui bei naujų medžiagų kūrimui. Tam intensyviai naudojami kaip eksperimentiniai taip ir skaitiniai metodai, kurių tobulinimui šiuo metu yra skiriamas labai didelis dėmesys. Skaitinis eksperimentas, kaip medžiagos tyrimo būdas pasitelkiamas dar ir todėl kad yra pigesnis ir leidžia interpretuoti jau žinomus eksperimentų rezultatus, o taip suteikia žinių naujiems tyrimams. Vienas iš metodų, kuris modeliuoja makroskopines medžiagų savybes remdamasis medžiagos mikro savybėmis yra diskrečiųjų elementų metodas (DEM). DEM metodas remiasi idėja, kad bet kokia fizikinė struktūra gali būti aprašyta kaip judančių dalelių sistema. Ši idėja pradėta taikyti ir vientisam deformuojamam kūnui aprašyti. Skirtingai nuo biriųjų medžiagų, vientiso kūno dalelės ir tarp jų egzistuojančios sąveikos yra kitokios prigimties, o jų modeliai yra fizikinės ir matematinės abstrakcijos rezultatas. Vientiso deformuojamo kūno modeliavimas diskrečiais elementais yra tik pradinėje stadijoje, o vientiso požiūrio į diskrečių elementų modelius dar nėra. Yra kelios hipotetinės versijos, grindžiamos skirtingais požiūriais. Taikant DEM kūnui, pirmas žingsnis būtu tampriųjų savybių modeliavimas. Tai yra... [toliau žr. visą tekstą]

The shear rupture of massive (intact non-jointed) brittle rock in underground high stress mines occurs under a variety of different boundary conditions ranging from constant stress (no resistance to deformation) to constant stiffness (resistance to deformation). While a variety of boundary conditions exist, the shear rupture of massive rock in the brittle field is typically studied under constant stress boundary conditions. According to the theory, the fracturing processes leading to shear rupture zone creation occur at or near peak strength with a shear rupture surface created in the post-peak region of the stress-strain curve. However, there is evidence suggesting that shear rupture zone creation can occur pre-peak. Limited studies of shear rupture in brittle rock indicate pre-peak shear rupture zone creation under constant stiffness boundary conditions. This suggests that the boundary condition influences the shear rupture zone creation characteristics. In this thesis, shear rupture zone creation in brittle rock is investigated in direct shear under constant normal stress and normal stiffness boundary conditions. It is hypothesized that the boundary condition under which a shear rupture zone is created influences its characteristics (i.e., shear rupture zone geometry, load-displacement response, shear rupture zone creation relative to the load-displacement curve, and peak and ultimate strengths). In other words, it is proposed that the characteristics of a shear rupture zone are not only a function of the rock or rock mass properties but the boundary conditions under which the rupture zone is created. The hypothesis is tested and proven through a series of simulations using a two dimensional particle based Distinct Element Method (DEM) and its embedded grain based method. The understanding gained from these simulations is then used in the analysis and re-interpretation of rupture zone creation in two mine pillars. This is completed to show the value and practical application of the improved understanding gained from the simulations. The re-interpretation of these case histories suggests that one pillar ruptured predominately under a constant stress boundary condition while the other ruptured under a boundary condition changing from stiffness to stress control.

The Distinct Element Method (DEM) and Discontinuous Deformation Analysis (DDA) are the two most commonly used discrete element methods in rock mechanics. Discrete element approaches are computationally expensive as they involve the interaction of multiple discrete bodies with continuously changing contacts. Therefore, it is very important to ensure that the method selected for the analysis is computationally efficient. In this research, a general assessment of DDA and DEM is performed from a computational efficiency perspective, and relevant enhancements to DDA are developed. The computational speed of DDA is observed to be considerably slower than DEM. In order to identify reasons affecting the computational efficiency of DDA, fundamental aspects of DDA and DEM are compared which suggests that they mainly differ in the contact mechanics, and the time integration scheme used. An in-depth evaluation of these aspects revealed that the openclose iterative procedure used in DDA which exhibits highly nonlinear behavior is one of the main reasons causing DDA to slow down. In order to improve the computational efficiency of DDA, an alternative approach based on a more realistic rock joint behavior is developed in this research. In this approach, contacts are assumed to be deformable, i.e., interpenetrations of the blocks in contact are permitted. This eliminated the computationally expensive open-close iterative procedure adopted in DDA-Shi and enhanced its speed up to four times. In order to consider deformability of the blocks in DDA, several approaches are reported. The hybrid DDA-FEM approach is one of them, although this approach captures the block deformability quite effectively, it becomes computationally expensive for large-scale problems. An alternative simplified uncoupled DDA-FEM approach is developed in this research. The main idea of this approach is to model rigid body movement and the block internal deformation separately. Efficiency and simplicity of this approach lie in keeping the DDA and the FEM algorithms separate and solving FEM equations individually for each block. Based on a number of numerical examples presented in this dissertation, it is concluded that from a computational efficiency standpoint, the implicit solution scheme may not be appropriate for discrete element modelling. Although for quasi-static problems where inertia effects are insignificant, implicit schemes have been successfully used for linear analyses, they do not prove to be advantageous for contact-type problems even in quasi-static mode due to the highly nonlinear behavior of contacts.

The shear rupture of massive (intact non-jointed) brittle rock in underground high stress mines occurs under a variety of different boundary conditions ranging from constant stress (no resistance to deformation) to constant stiffness (resistance to deformation). While a variety of boundary conditions exist, the shear rupture of massive rock in the brittle field is typically studied under constant stress boundary conditions. According to the theory, the fracturing processes leading to shear rupture zone creation occur at or near peak strength with a shear rupture surface created in the post-peak region of the stress-strain curve. However, there is evidence suggesting that shear rupture zone creation can occur pre-peak. Limited studies of shear rupture in brittle rock indicate pre-peak shear rupture zone creation under constant stiffness boundary conditions. This suggests that the boundary condition influences the shear rupture zone creation characteristics. In this thesis, shear rupture zone creation in brittle rock is investigated in direct shear under constant normal stress and normal stiffness boundary conditions. It is hypothesized that the boundary condition under which a shear rupture zone is created influences its characteristics (i.e., shear rupture zone geometry, load-displacement response, shear rupture zone creation relative to the load-displacement curve, and peak and ultimate strengths). In other words, it is proposed that the characteristics of a shear rupture zone are not only a function of the rock or rock mass properties but the boundary conditions under which the rupture zone is created. The hypothesis is tested and proven through a series of simulations using a two dimensional particle based Distinct Element Method (DEM) and its embedded grain based method. The understanding gained from these simulations is then used in the analysis and re-interpretation of rupture zone creation in two mine pillars. This is completed to show the value and practical application of the improved understanding gained from the simulations. The re-interpretation of these case histories suggests that one pillar ruptured predominately under a constant stress boundary condition while the other ruptured under a boundary condition changing from stiffness to stress control.

Blending processes in a silo minimise the fluctuations in the property of bulk solids with the blending performance being strongly influenced by the flow pattern and operating mode among other process parameters such as batch size and type of input fluctuations. An accurate prediction of flow characteristics such as flow channel boundary and velocity profiles is important for understanding and quantifying the blending performance, thereby increasing the scope for new design by minimising the number of expensive pilot scale experiments required. In this thesis, the Discrete Element Method (DEM) is deployed to predict and understand the flow characteristics and blending of cylindrical plastic pellets in a planar flat bottom silo and a multi-flow blender (a silo with an insert and a blending tube). The predictions are validated against high-resolution velocity measurements analysed using Particle Image Velocimetry (PIV) technique. A planar model silo was built to measure the flow of pellets using PIV technique. The existing GeoPIV Matlab module was customised to extract the velocity fields in the Eulerian frame of reference and its accuracy has been verified. The developed tool was then applied to quantitatively investigate the mechanism of evolution of flow in a flat bottom silo and the dependency of the state of developed flow on the depth of the planar silo. It was shown that the development of flow during discharge can be divided into two stages: a rapid upward propagation of plug flow followed by a widening of the flow channel with increasing shearing boundaries. The size of the flow channel was found to be increasing with the depth of the silo. For the 100 mm deep silo, the flow is three dimensional with significant retardation in velocity at the frontal walls, whilst a negligible retardation was found for the 20 and 40 mm deep model silos. The thickness and frontal wall friction in planar silos thus play an important role in the development of flow patterns in model silos. In this thesis, DEM model calibration relating the macro-scale bulk friction and micro- scale particle friction at different rolling friction values was developed from DEM simulations of Jenike direct shear box. During the direct shear simulation, a constant normal force was achieved with the use of a shear lid geometry made with glued spheres thereby eliminating the use of a traditional servo control function. The influence of particle rotations and rolling friction on the limiting bulk friction for different particle sliding friction coefficients was explored. The accuracy of the calibration data was assessed by simulating the flow in a flat bottom silo and comparing the model predictions of flow rate, velocity profiles and flow channel boundary with the experiments. A good quantitative agreement was found between the experiment and simulations. The DEM model predictions were also compared with the kinematic model. Following the validation of the model, it was shown that the frontal friction and rolling friction are the influential parameters in simulating the flow patterns such as semi-mass and internal flow. It was further shown that flow transits from semi-mass flow to internal flow with the increase of frontal wall friction. The drastic influence of frontal wall friction on stress, flow patterns and force chains were analysed highlighting its implications on interpretations in 2D test silos. Finally, the developed DEM and PIV tools are employed to investigate blending in a flat bottom and multi-flow blender silo for different flow patterns. The analysis showed that the blending is more effective with the internal flow when compared to semi-mass flow in a flat bottom silo, in both continuous and discontinuous modes for a variety of process conditions such as batch size, the number of recirculation and frequency of input fluctuations. An algorithm was developed to evaluate the blending performance from the spatially averaged Eulerian velocity fields. The flow in a relatively large-scale multi-flow blender comprising nearly 606,000 particles, thereby fully replicating the test silo, was simulated and the challenges in reproducing the test conditions of continuous and discontinuous modes of operation were discussed. The flow patterns and blending were first analysed from the experiments in different configurations of the insert. Using the same input parameters for the model, it was shown that the model predictions of the velocity profiles along the height of the silo are in good agreement with the experiments. Internal flow, mixed flow and mass flow were predicted for the diverging, straight and converging insert configurations respectively and the blending performance for each of these configurations suggests an optimal configuration of the blender thereby demonstrating the potential of PIV and DEM in design optimisation. The possibility of conducting the DEM simulations under increased gravity in order to reduce the computational time has also been explored.

O processo de dano em materiais quasi-frágeis pode ser caracterizado pela perda de isotropia para certos níveis de carga. A localização de deformações, o efeito cooperativo entre regiões danificadas e a avalanche de rupturas são características particulares na medição do dano neste tipo de material. As características mencionadas criam diferentes formas de dissipação de energia, que não são fáceis de representar utilizando métodos baseados na hipótese dos meios contínuos. No presente trabalho uma versão do Método dos Elementos Discretos Formado por Barras é empregado. Neste método a massa do contínuo é concentrada nos nós, os quais são interconectados por barras sem massa. Essas barras possuem uma lei constitutiva bilinear, que é usada para simular a ruptura da estrutura em estudo. A distribuição dos nós permite formar uma treliça tridimensional regular, e a partir dessa discretização espacial é possível chegar a um sistema de equações de movimento, que é resolvido com um esquema explícito de integração numérica (diferenças finitas centrais). Neste método a fratura e a fragmentação são levadas em conta de forma natural, já que as barras que rompem durante o processo são desativadas, respeitando o balanço energético. É possível introduzir heterogeneidade no modelo considerando as propriedades do material como campos espaciais aleatórios com distribuição de probabilidades de Weibull e comprimento de correlação conhecido. Nessa dissertação, é analisado o processo de dano que aparece em estruturas de geometria simples quando solicitadas até o colapso. Diferentes índices são apresentados para realizar a medição do dano. O desempenho desses índices, e a maneira com que eles ajudam na interpretação da evolução do dano, são discutidos nesse trabalho. / The process of damage in quasi-fragile materials is characterized by loss of isotropy for certain load levels. The strain localization, the cooperative effect between damaged regions and the avalanche of ruptures are particular features in measuring the damage in this kind of material. The mentioned features create different forms of energy dissipation, which are not easy to represent with a continuous approach. In the present work a version of the Lattice Discrete Element Method is employed. In this method the mass of the solid is concentrated on node points, which are interconnected by uniaxial elements. These elements have a bilinear constitutive law, which is used to simulate the rupture of the structure under study. The node distribution allows the formation of a regular three-dimensional lattice, and from this spatial discretization it is possible to arrive at a system of equations of motion, which is solved by an explicit numerical integration scheme (central difference). In this method the fracture and fragmentation are taken into account in a natural manner, since the bars that reached their limit strength during the process are disabled of the system, respecting the energy balance. It is possible to introduce heterogeneity in the model considering the material properties as random fields with spatial Weibull probability distribution and known correlation length. In this dissertation, the damage process, which appears in structures of simple geometry, when they are loaded until collapse, is analysed. Different indexes are presented to perform the measurement of the damage. The performance of those indexes, and the way they help in the interpretation of the damage evolution, are discussed in this paper.

A demanda por estruturas mais leves implica num ganho em economia, porém o aumento de esbeltez da estrutura pode tornar ela susceptível a instabilidade frente a tensões compressivas estáticas ou dinâmicas. A instabilidade acontece em várias escalas da estrutura analisada e pode interagir com outras formas de colapso como a propagação instável de fissuras, problema governado pela mecânica da fratura, pela plastificacão do material, ou por uma combinação dos efeitos citados. Neste contexto, no presente trabalho, se explora a capacidade do método dos elementos discretizados por barras (LDEM) na simulação de problemas de instabilidade estática e dinâmica devido as tensões de compressão. Este método permite simular o sólido como um arranjo de barras com rigidez equivalente ao contínuo que se quer representar. Leis constitutivas não lineares permitem modelar ruptura de forma simples. A equação de movimento resultante da discretização permite formular uma equação de movimento desacoplada que pode ser integrada no domínio do tempo com um método explícito (Método das Diferencias Finitas Centrais). O fato das barras serem rotuladas nos seus extremos e a solução do problema ser obtida de forma incremental permite capturar problemas com não linearidade geométrica, entre eles a instabilidade estrutural frente a tensões compressivas. Como último exemplo se realiza a análise de um painel sanduiche por flexão em três pontos, que é composto por um núcleo de poliuretano, com duas lâminas externas de material compósito, neste caso a instabilidade estrutural está associada a flambagem da camada da lâmina comprimida. Finalmente a potencialidade da metodologia de análise utilizada é discutida. / The demand for lighter structures implies a gain in economy, but the increase in slenderness of the structure may make it susceptible to instability against static or dynamic compressive stresses. Instability occurs at various scales of the analyzed structure and may interact with other forms of collapse such as unstable crack propagation, problem governed by fracture mechanics, plastification of the material, or a combination of the cited effects. In this context, in the present work, we explore the ability of the discrete elements methods by bars (LDEM) in the simulation of problems of static and dynamic instability due to the compression stresses. This method allows to simulate the solid as an arrangement of bars with rigidity equivalent to the continuum that one wants to represent. Constitutive non-linear laws allow simple modeling of rupture. The equation of motion resulting from the discretization allows us to formulate a decoupled motion equation that can be integrated in the time domain with an explicit method (Central Finite Differences Method). The fact that the bars are labeled at their ends and the solution of the problem is obtained in an incremental way allows to capture problems with geometric non-linearity, among them the structural instability against compressive tensions. The last example, the analysis of a sandwich panel by three-point bending, which is composed of a polyurethane core, with two external blades of composite material, in this case the structural instability is associated with buckling of the layer of the compressed blade . Finally, the potential of the analysis methodology is discussed.