We study a system of differential-algebraic equations, describing motions of a mass-spring-dashpot oscillator by three different forms of implicit constitu- tive relations. For some problems with fully implicit but linear constitutive laws for combined force, we find conditions for solution stability. Assuming monotone relationship between the displacement, velocity and the respective forces, we prove global existence of the solutions. For a linear spring and a dashpot with maximal monotone relationship between the damping force and the velocity, we prove the global existence and uniqueness result. We also solve this problem numerically for Coulomb-like damping term.

Thickened tailings production and disposal continue to grow in importance in the mining industry. In particular, the transport of oil sands tailings is of interest in this study. These tailings must be in a homogeneous state (non-segregating) during pipeline flow and subsequent discharge. Tailings are often transported in an open channel or flume. Slurries containing both clay and coarse sand particles typically exhibit non-Newtonian rheological behaviour. The prediction of the flow behaviour of these slurries is complicated by the limited research activity in this area. As a result, the underlying mechanisms of solids transport in these slurries are not well understood. To address this deficiency, experimental studies were conducted with kaolin clay slurries containing coarse sand in an open circular channel.<p> A numerical model has been developed to predict the behaviour of coarse solid particles in laminar, open channel, non-Newtonian flows. The model involves the simultaneous solution of the Navier-Stokes equations and a scalar concentration equation describing the behaviour of coarse particles within the flow. The model uses the theory of shear-induced particle diffusion (Phillips et al., 1992) to provide a number of relationships to describe the diffusive flux of coarse particles within laminar flows. A sedimentation flux has been developed and incorporated into the Phillips et al. (1992) model to account for gravitational flux of particles within the flow. Previous researchers (Gillies et al., 1999) have shown that this is a significant mechanism of particle migration.<p> The momentum and concentration partial differential equations have been solved numerically by applying the finite volume method. The differential equations are non-linear, stiff and tightly coupled which requires a novel means of analysis. Specific no-flux, no-slip and no-shear boundary conditions have been applied to the channel walls and free surface to produce simulated velocity and concentration distributions. The results show that the model is capable of predicting coarse particle settling in laminar, non-Newtonian, open channel flows. The results of the numerical simulations have been compared to the experimental results obtained in this study, as well as the experimental results of previous studies in the literature.

<p>Soils, in general, undergo both elastic and plastic deformations upon loading. Strain dependant anisotropic elasto-plastic models are required for realistic modeling for soil-tool mechanics that will address issues like stress history and soil anisotropy. Although several such models have been proposed, the science of coupled poro-mechanical analysis of an unsaturated soil has not been fully addressed.</p><p>Tillage tool modeling is primarily concerned with the analysis of soil deformation patterns and development of force prediction models for design optimization. Most of the models are based on quasi-static soil failure patterns that cause difficulty in accurately predicting soil-tool behaviour and soil forces for high speed operation. In recent years efforts have been made to improve the conventional analytical and experimental models by numerical approaches. Numerical simulations of soil-tool interactions using finite element modeling (FEM) and discrete element method (DEM) were mostly based on a solid mechanics approach. Due to limitations of constitutive relations, predictions of these numerical models have not been able to address tillage dynamics with high shear rates. The contribution of this research was to study the dynamics of soil-tool interaction using computational fluid dynamics (CFD) from the perspective of soil visco-plastic behavior.</p><p>A motorised soil rheometer was developed for evaluating soil visco-plastic parameters for CFD simulations. The apparatus was used to determine soil yield stress and viscosity at different soil moisture and compaction levels.</p><p>Three-dimensional CFD analyses were carried out using a commercial software CFX 4.4 to observe soil failure patterns around a tool and the pressure distribution on and around the tool. Duct flow as well as free-surface flow simulations of visco-plastic soil as a non-Newtonian Bingham material indicated soil deformation comprising of plastic flow and plug flow patterns. The soil failure front advancement demonstrated a critical speed range of 4 to 6.5 m s-1 where advancement of the failure front did not increase with speed. Soil pressure on the tool surface increased with the tool operating speed. Pressure distribution on the tool surface and draft requirement agreed well with the published literature based on experimental results and FEM analysis. The CFD approach, in its first attempt to tillage process, demonstrated its greater potential for dynamic modeling of soil-tool interaction.</p>

Les fluides magnétorhéologiques sont des dispersions de micro-particules magnétiques dans un fluide porteur non magnétique. Leurs caractéristiques varient avec l'application d'un champ magnétique. Le modèle de Bingham décrit le comportement des FMR pour des grandes vitesses de cisaillement. En dessous du seuil de Bingham, le comportement des FMR a reçu moins d'attention, cependant sa compréhension est nécessaire dans les interfaces homme-machine où de faibles contraintes de cisaillement sont observées. Une analyse expérimentale du comportement des FMR au cisaillement linéaire par une plaque, à de faibles taux de cisaillement, montre une réponse gouvernée par deux régimes successifs limités par un phénomène d'interface. Dans le régime initial, le FMR se comporte comme un matériau pseudo-élastique, l'élasticité observée est indépendante du champ magnétique et de la fraction volumique des particules. Le revêtement extérieur des particules magnétiques par des polymères (révélé par microscopie) est à l'origine de cette cohésion non-magnétique. Ce régime est limité par un seuil proportionnel au carré du champ magnétique et à la fraction volumique de particules. Dans le régime suivant, la déformation en cisaillement est non uniforme dans le liquide. La moyenne de la contrainte de cisaillement augmente linéairement avec la moyenne du cisaillement. Le coefficient de variation est proportionnel au carré du champ magnétique et diminue avec la fraction volumique de particules. Ce régime est limité par une perte d'adhérence des agrégats magnétiques avec la plaque de cisaillement, en cas de cisaillement avec une plaque amagnétique, ou avec le pôle magnétique en cas de cisaillement avec une plaque magnétique. La perte d'adhérence se produit à un seuil proportionnel au carré du champ magnétique et à la fraction volumique des particules et dépend de la nature de la plaque de cisaillement. Ce seuil peut être localisé au-dessus du seuil de Bingham.

<p>Soils, in general, undergo both elastic and plastic deformations upon loading. Strain dependant anisotropic elasto-plastic models are required for realistic modeling for soil-tool mechanics that will address issues like stress history and soil anisotropy. Although several such models have been proposed, the science of coupled poro-mechanical analysis of an unsaturated soil has not been fully addressed.</p><p>Tillage tool modeling is primarily concerned with the analysis of soil deformation patterns and development of force prediction models for design optimization. Most of the models are based on quasi-static soil failure patterns that cause difficulty in accurately predicting soil-tool behaviour and soil forces for high speed operation. In recent years efforts have been made to improve the conventional analytical and experimental models by numerical approaches. Numerical simulations of soil-tool interactions using finite element modeling (FEM) and discrete element method (DEM) were mostly based on a solid mechanics approach. Due to limitations of constitutive relations, predictions of these numerical models have not been able to address tillage dynamics with high shear rates. The contribution of this research was to study the dynamics of soil-tool interaction using computational fluid dynamics (CFD) from the perspective of soil visco-plastic behavior.</p><p>A motorised soil rheometer was developed for evaluating soil visco-plastic parameters for CFD simulations. The apparatus was used to determine soil yield stress and viscosity at different soil moisture and compaction levels.</p><p>Three-dimensional CFD analyses were carried out using a commercial software CFX 4.4 to observe soil failure patterns around a tool and the pressure distribution on and around the tool. Duct flow as well as free-surface flow simulations of visco-plastic soil as a non-Newtonian Bingham material indicated soil deformation comprising of plastic flow and plug flow patterns. The soil failure front advancement demonstrated a critical speed range of 4 to 6.5 m s-1 where advancement of the failure front did not increase with speed. Soil pressure on the tool surface increased with the tool operating speed. Pressure distribution on the tool surface and draft requirement agreed well with the published literature based on experimental results and FEM analysis. The CFD approach, in its first attempt to tillage process, demonstrated its greater potential for dynamic modeling of soil-tool interaction.</p>

Thickened tailings production and disposal continue to grow in importance in the mining industry. In particular, the transport of oil sands tailings is of interest in this study. These tailings must be in a homogeneous state (non-segregating) during pipeline flow and subsequent discharge. Tailings are often transported in an open channel or flume. Slurries containing both clay and coarse sand particles typically exhibit non-Newtonian rheological behaviour. The prediction of the flow behaviour of these slurries is complicated by the limited research activity in this area. As a result, the underlying mechanisms of solids transport in these slurries are not well understood. To address this deficiency, experimental studies were conducted with kaolin clay slurries containing coarse sand in an open circular channel.<p> A numerical model has been developed to predict the behaviour of coarse solid particles in laminar, open channel, non-Newtonian flows. The model involves the simultaneous solution of the Navier-Stokes equations and a scalar concentration equation describing the behaviour of coarse particles within the flow. The model uses the theory of shear-induced particle diffusion (Phillips et al., 1992) to provide a number of relationships to describe the diffusive flux of coarse particles within laminar flows. A sedimentation flux has been developed and incorporated into the Phillips et al. (1992) model to account for gravitational flux of particles within the flow. Previous researchers (Gillies et al., 1999) have shown that this is a significant mechanism of particle migration.<p> The momentum and concentration partial differential equations have been solved numerically by applying the finite volume method. The differential equations are non-linear, stiff and tightly coupled which requires a novel means of analysis. Specific no-flux, no-slip and no-shear boundary conditions have been applied to the channel walls and free surface to produce simulated velocity and concentration distributions. The results show that the model is capable of predicting coarse particle settling in laminar, non-Newtonian, open channel flows. The results of the numerical simulations have been compared to the experimental results obtained in this study, as well as the experimental results of previous studies in the literature.

Grouting is performed in order to decrease the permeability and increase the stiffness of the material, especially soil and rock. For tunnelling and underground constructions, permeation grouting is done where cement based materials are pumped inside drilled boreholes under a constant pressure, higher than the ground water pressure. The aim of permeation grouting is to reduce the water flow into tunnels and caverns and to limit the lowering of the surrounding groundwater table. Cement based materials are commonly used as grout due to their availability and lower costs. To obtain a proper water sealing and reduce the lowering of the ground water table, a desired spread of grout must be achieved and the rheology of the cement grout is the governing factor for estimating the required spread. Rheological properties of cement grout such as viscosity and yield stress are commonly measured off-line using laboratory instruments, and some simple tools are available to make field measurements. Although the rheological properties of the grout that is used play a fundamental role in design and execution, no method has yet been developed to measure these properties in-line in field work. In addition to the real time measurement, there is no standard method for determining the yield stress for grouting applications. Despite the common usage of Bingham model fitting to determine the yield stress, the range of shear rate is often not specified or is neglected.   In this work, an in-line rheometry method combining the Ultrasound Velocity Profiling (UVP) technique with Pressure Difference (PD) measurements, known as “UVP+PD”, was successfully tested for continuous in-line measurements of concentrated micro cement based grouts. A major obstacle of using the ultrasound based methodology was the transducers, which would be capable of emitting sufficient acoustic energy and can be used in field conditions. The transducer technology was developed in a parallel project and the Flow-Viz industrial rheometer was found to be capable of detail measurement of the velocity profiles of cement grout. The shape of the velocity profiles was visualized, and the change in the shape of the profiles with concentration and time was observed. The viscosity and yield stress of the grout were determined using rheological models, e.g. Bingham and Herschel-Bulkley. In addition, rheological properties were determined using the non-model approach (gradient method) and the tube viscometry concept and were compared with results obtained using the rheological models. The UVP+PD method was found to be capable of determining the rheological behavior of cement grout regardless of the rheological model. The yield stress of cement grout was investigated using off-line rheometry techniques and UVP+PD in-line measurements. Tests were performed applying different shear histories and it was found that two ranges of yield stress indeed exist. Therefore, the design value of yield stress should be chosen with respect to the prevailing shear rate at the grout front for the required spread of grout. In addition, an appropriate shear rate range should be used when a Bingham fitting is done to determine the yield stress. In order to estimate the shear rate, plug thickness and velocity for one dimensional and two dimensional geometry, a non- dimensional nomogram was developed. The advantage of using the nomogram is that it does not depend on the applied pressure and the rheological properties of the grout and can therefore, be used as a simple design tool. Analytical approaches were used for the estimation and good agreements were found with numerical calculations and experimental results. In conclusion, in this work, it was found that it is possible to continuously measure the velocity profiles and determine the change of the rheological properties of cement grout using the ultrasound based UVP+PD method under field conditions. The yield stress was also investigated and it was found that two range of yield stress exist depending on the prevailing shear rate of the grout, which should be used for designing the grouting time at different conditions. In order to decide the design value of yield stress for grouting applications, a non-dimensional nomogram was developed that can be used to estimate the plug thickness, shear rate and velocity of the grout. / <p>Funding for the project was provided by the Swedish Rock Engineering Research Foundation (BeFo), The Swedish Research Council (FORMAS) and The Development Fund of the Swedish Construction Industry (SBUF), who are gratefully acknowledged. QC 20151112</p>

Main topic of this thesis are magnetic fluids. These are specific type of fluids which can simplistically be considered as Bingham fluids. Main issues regarding the magnetic fluids mentioned in this thesis are: rheological properties of the magnetic fluids, behaviour of the magnetic fluids and the use of the magnetic fluids in industrial applications. Main goal is to apply Binghams model on the the magnetic fluids assuming that this model can be applied with a good accuracy. Equations which describe behaviour of the Bingham fluids are constructed. Some assumptions which have to be respected to use this analytical equations for magnetic fluids are formulated. Flow of bingham fluid is analytically solved in some simplificated cases with consideration of laminar flow. Analytical results are confronted with numerical ones obtained from CFD software Fluent for the purpose of verification.

This work deals with the research of degradation of magnetorheological (MR) fluid during long-term loading under conditions that correspond to the real load in the linear MR devices such as dampers. The behaviour of MR fluid is described by a Bingham model of viscoplastic fluid. The parameters of this model are the yield stress and viscosity. Their values are determined by the shear rate from 1 to 2,8104 s-1. Results of durability tests show a significant decrease in viscosity of MR fluid, a gradual increase in yield stress in the off-state and a significant decrease in MR effect. The paper also described the effect of temperature on these parameters and there is also designed a method of non-assembly diagnostic of the MR fluid state in the damper using the "rate of pulsation."

The rheological properties of cement-based grouts play a key role in determining the final spread in grouted rock formations. Rheologically, cement grouts are known to be complex thixotropic fluids, but their steady flow behavior is often described by fitting the simple Bingham constitutive law to flow curve data. The resultant Bingham parameters are then used in grouting design of e.g. tunnels, to estimate the penetration length. Since cement grouts are thixotropic suspensions, the interpretation of their flow curves as obtained from flow sweeps in concentric cylinder rotational rheometers is often complicated by: the presence of wall slip, sedimentation and unstable flow at low shear rates. A systematic approach to study these effects within the constraints of the concentric cylinder geometry (Couette) and for different cement grout concentrations was carried out as part of the Licentiate research work. Of particular interest was the influence of geometry and flow sweep measurement interval on flow curves, including the characteristic unstable flow branch that appears at applied shear rates that are below the critical shear rate. The unstable flow branch observed below the critical shear rate has been described as a characteristic feature in the flow curves of thixotropic suspensions, e.g. cement grouts, laponite. From a practical standpoint, this information can then be readily used to improve rheological measurements of cement grouts. The existence of the critical shear rate below which no stable flow occurs, plus the complex wall slip phenomenon are then discussed by considering how they affect actual spread in rough and smooth rock fractures. Another major part of the research presented in this thesis relates to the measurement of model yield stress fluid (YSF), i.e. Carbopol, velocity profiles within the radial flow geometry. Radial flow between parallel plates, is an idealized fundamental flow configuration that is often used as a basis for grout spread estimation in planar rock fractures. Compared to other flow configurations with YSFs, e.g. channels, only a limited amount of work has presented analytical solutions, numerical models and especially experimental work for radial flow. Thus, as a first step towards more systematic studies of the plug flow region of YSFs in radial flow the current work presents the design, manufacture and for the first time velocity profile measurements that were conducted by using the pulsed Ultrasound Velocity Profiling (UVP) technique. The current observations for tests carried out with different disk spacings and flow rates show a distinct plug region, coupled with wall slip effects for the Carbopol model YSF fluid that was used. The theoretically predicted velocity profiles and the measured ones agree reasonably well, and the main discrepancies are discussed. Future studies, would then be targeted at improving the current experimental setup, for detailed measurements of the plug flow region along the radial length, which remains a challenging issue for studies on YSFs and engineering applications such as rock grouting design. / Cementbaserade injekteringsmedels reologiska egenskaper har en stor påverkan på strömning och inträngningslängd i sprickigt berg. Medlens reologi är komplex, inklusive tixotropi, men strömningen beskrivs ändå oftast med den enkla linjära Bingham modellen i injekteringssammanhang. De två parametrarna från denna modell, flytgräns och viskositet, används sedan inom injekteringsdesign, för t.ex. tunnlar och dammar, för att bedöma inträngningen. Eftersom cementbaserade medel är tixoptropa suspensioner försvåras utvärderingen vid mätning med konventionella rotationsviskometrar på grund av glidning vid fasta begränsningsytor, sedimentation/separation av partiklarna och instabila flöden vid låga deformationshastigheter. En systematisk mätprocedur för att studera ovanstående problem med rotationsviskometer och koncentriska cylindrar samt olika vanliga vattencementtal, har utförts inom ramen för detta licentiatarbete. Av särskilt intresse har varit att studera effekten av olika geometrier och tidsintervallet mellan mätningarna, inklusive den instabila delen av flödeskurvan då deformationshastigheten är lägre än ett kritiskt värde. Denna del av kurvan har i litteraturen beskrivits som karakteristisk för tixotropa suspensioner, som t.ex. cementbaserade injekteringsmedel. Praktiskt kan ovanstående kunskap användas för att förbättra mätningen av de reologiska egenskaperna. Existensen av en kritisk deformationshastighet under vilken det inte finns något stabilt flöde, i kombination med glidning vid fasta begränsningsytor, diskuteras särskilt med hänsyn till dess påverkan på faktisk inträngning i släta och råa bergsprickor. Ett annat fokus i licentiatarbetet har varit att studera icke-Newtonska modellvätskors (Carbopol) radiella strömning mellan parallella plattor. Denna typ av strömningsgeometri används ofta som en idealiserad konfiguration för strömning i bergsprickor. I jämförelse med andra enklare geometrier, finns endast en begränsad forskning utförd för denna geometri både då det gäller analytiska och numeriska beräkningar men framförallt då det gäller experiment. Som ett första steg inför en mer systematisk undersökning av icke-Newtonsk radiella strömning presenteras i detta arbete framtagandet av en fysisk laboratoriemodell där hastighetsprofilerna mellan plattorna för första gången visualiserats med hjälp av ultraljud. De utförda mätningarna med tre olika öppningar mellan plattorna sam tre olika värden på det konstanta flödet, visar på en distinkt plugg som är ett resultat av vätskans flytgräns samt glidning i gränsskiktet mellan vätskan och plattornas fasta begränsningsytor. En jämförelse mellan uppmätta hastighetsprofiler och analytiskt beräknade diskuteras där resultaten överensstämmer relativt väl, med beaktande av de långtgående förenklade antaganden som krävs för beräkningarna. Fortsatta studier kommer att fokuseras på att förbättra laboratoriemodellen för en mer detaljerad studie av icke-Newtonska vätskors strömning och hur pluggen utvecklas under den radiella inträngningen, vilket fortsättningsvis är av betydelse för design av injektering i bergsprickor. / <p>QC 20190521</p>