Geophysical hazards usually involve multiphase flow of dense granular solids and water. Understanding the mechanics of granular flow is of particular importance in predicting the run-out behaviour of debris flows. The dynamics of a homogeneous granular flow involve three distinct scales: the microscopic scale, the meso-scale, and the macroscopic scale. Conventionally, granular flows are modelled as a continuum because they exhibit many collective phenomena. Recent studies, however, suggest that a continuum law may be unable to capture the effect of inhomogeneities at the grain scale level, such as orientation of force chains, which are micro-structural effects. Discrete element methods (DEM) are capable of simulating these micro-structural effects, however they are computationally expensive. In the present study, a multi-scale approach is adopted, using both DEM and continuum techniques, to better understand the rheology of granular flows and the limitations of continuum models. The collapse of a granular column on a horizontal surface is a simple case of granular flow; however, a proper model that describes the flow dynamics is still lacking. In the present study, the generalised interpolation material point method (GIMPM), a hybrid Eulerian ? Lagrangian approach, is implemented with the Mohr-Coloumb failure criterion to describe the continuum behaviour of granular flows. The granular column collapse is also simulated using DEM to understand the micro-mechanics of the flow. The limitations of MPM in modelling the flow dynamics are studied by inspecting the energy dissipation mechanisms. The lack of collisional dissipation in the Mohr-Coloumb model results in longer run-out distances for granular flows in dilute regimes (where the mean pressure is low). However, the model is able to capture the rheology of dense granular flows, such as the run-out evolution of slopes subjected to lateral excitation, where the inertial number I < 0.1. The initiation and propagation of submarine flows depend mainly on the slope, density, and quantity of the material destabilised. Certain macroscopic models are able to capture simple mechanical behaviours, however the complex physical mechanisms that occur at the grain scale, such as hydrodynamic instabilities and formation of clusters, have largely been ignored. In order to describe the mechanism of submarine granular flows, it is important to consider both the dynamics of the solid phase and the role of the ambient fluid. In the present study, a two-dimensional coupled Lattice Boltzmann LBM ? DEM technique is developed to understand the micro-scale rheology of granular flows in fluid. Parametric analyses are performed to assess the influence of initial configuration, permeability, and slope of the inclined plane on the flow. The effect of hydrodynamic forces on the run-out evolution is analysed by comparing the energy dissipation and flow evolution between dry and immersed conditions.

Inertial granular flows lie in a region of parameter space between quasi-static and collisional regimes. In each of these phases the mechanisms of energy dissipation are often taken to be the defining features. Frictional contacts between grains and the transmission of energy through co-operative force chains dominate slowly sheared flows. In the opposite extreme infrequent high-energy collisions are responsible for dissipation in so-called gaseous granular flows. Borrowing from each of these extremes, it is postulated that during liquid-like flow, grain energy is transferred through frequent frictional interactions as the particles rearrange. This thesis focuses on the μ(I)-rheology which generalises the simple Coulomb picture, where greater normal forces lead to greater tangential friction, by including dependence on the inertial number I, which reflects the frequency of grain rearrangements. The equations resulting from this rheology, assuming that the material is incompressible, are first examined with a maximal-order linear stability analysis. It is found that the equations are linearly well-posed when the inertial number is not too high or too low. For inertial numbers in which the equations are instead ill-posed numerical solutions are found to be grid-dependent with perturbations growing unboundedly as their wavelength is decreased. Interestingly, experimental results also diverge away from the original μ(I) curve in the ill-posed regions. A generalised well-posedness analysis is used alongside the experimental findings to suggest a new functional form for the curve. This is shown to regularise numerical computations for a selection of inclined plane flows. As the incompressibility assumption is known to break down more drastically in the high-I and low-I limits, compressible μ(I) equations are also considered. When the closure of these equations takes the form suggested by critical state soil mechanics, it is found that the resultant system is well-posed regardless of the details of the deformation. Well-posed equations can also be formed by depth-averaging the μ(I)-rheology. For three-dimensional chute flows experimental measurements are captured well by the depth-averaged model when the flows are shallow. Furthermore, numerical computations are much less expensive than those with the full μ(I) system.

Debris flows, avalanches and other geophysical mass flows pose a significant hazard to settlements in or near mountainous regions. Understanding the physical processes that govern these flows is an essential part of hazard assessment and mitigation strategies. This thesis addresses two aspects of geophysical mass flows: flow self-channelisation due to the formation of lateral levees, and granular shocks, which occur when a rapidly-moving debris flow or avalanche collides with an obstacle. We present the results of large-scale debris flow experiments in which the flow is channelised by coarse-particle levees that form at the flow margins. The flow surface velocities are measured with high speed overhead photography, and the deposits both sampled to obtain the grain size distribution and excavated to recover the deposited locations of tracer pebbles that were introduced in to the flow. We propose a model, supported by evidence from the large-scale experiments, that describes in detail the size segregation and kinematic transport processes responsible for the deposition of lateral levees. The second problem addressed in the thesis concerns granular shocks, or jumps, which are rapid changes in the depth and velocity of granular avalanches. We investigate these through experiments in which a falling jet of granular material impacts on an inclined plane, generating a steady granular jump, which is either teardrop-shaped or 'blunted'. Numerical solutions of a depth-averaged flow model agree quantitatively with many of the observed flow features. We use this model show that the transition between the teardrop-shaped and blunted jump regimes corresponds to a transition between two shock reflection structures, known as a regular and a Mach shock reflection. On planes inclined at a shallow angle, we demonstrate a wide variety of unsteady and channelised flows, which occur due to the complex interaction between flowing and stationary regions of granular material.

This thesis develops and tests a two-dimensional discrete dynamic model for the simulation of granular flows in silos and hoppers. The granular material considered is assumed to be an assembly of viscoelastic discs and the motion of such a particle system is shown to be governed by a set of nonlinear first order ordinary differential equations. This system of equations is then solved numerically using the centered finite difference scheme. Based on the model presented, a computer program has been developed and used to analyse the flow behaviour of granular materials during filling and emptying of a silo. The results show that the discrete dynamic model developed is capable of modelling granular flows in silos, particularly predicting wall pressures and analysing flow blockage.

Εισάγουμε σταθερή εισροή υλικού στο πρώτο δοχείο με σκοπό να περιγράψουμε τις συνθήκες κάτω από τις οποίες η ροή θα είναι ομαλή και συνεχής μέχρι και το τελευταίο δοχείο. Σε αντίθεση με τα κανονικά ρευστά, τα κοκκώδη υλικά έχουν την τάση να δημιουργούν συσσωματώματα (λόγω της μη-ελαστικής σύγκρουσης των σωματιδίων τους [Goldhirsch and Zanetti, 1993]). Όταν συμβαίνει αυτό η ροή σταματά και η εκροή από το τελευταίο δοχείο μηδενίζεται. Δεδομένης της δύναμης ανατάραξης και των διαστάσεων του διαδρόμου, καθορίζουμε την οριακή τιμή της εισροής πέρα από την οποία η δημιουργία συσσωματωμάτων είναι αναπόφευκτη. Δείχνουμε ότι η κρίσιμη αυτή κατάσταση αναγγέλλεται εκ των προτέρων (ήδη πριν από την οριακή τιμή της εισροής) από την εμφάνιση ενός κυματιστού προφίλ πυκνότητας υλικού κατά μήκος του διαδρόμου. Η οριακή ροή καθώς και το κυματιστό προφίλ εξηγούνται σ΄αυτή την εργασία, τόσο ποιοτικά όσο και ποσοτικά, μέσω ενός μαθηματικού μοντέλου ροής [Eggers 1999, Van der Weele et al., 2001]. Τέλος, βασιζόμενοι σε αυτό το μοντέλο προτείνουμε πρακτικές λύσεις ώστε να βελτιωθεί σημαντικά η παροχή του διαδρόμου. / We study the flow of granular material on a conveyor belt consisting of K connected, vertically vibrated compartments. A steady inflow is applied to the top compartment and our goal is to describe the conditions that ensure a continuous flow all the way down to the Kth compartment. In contrast to normal fluids, flowing granular matter has a tendency to form clusters (due to the inelasticity of the particle collisions [Goldhirsch and Zanetti, 1993]); when this happens the flow stops and the outflow from the Kth compartment vanishes. Given the dimensions of the conveyor belt and the vibration strength, we determine the critical value of the inflow beyond which cluster formation is inevitable. Fortunately, the clusters are announced in advance (already below the critical value of the inflow) by the appearance of a wavy density profile along the K compartments. The critical flow and the associated wavy profile are explained quantitatively in terms of a dynamical flux model [Eggers, 1999; Van der Weele et al., 2001]. This same model enables us to formulate a method to greatly increase the critical value of the inflow, improving the capacity of the conveyor belt by a factor two or even more.

Although the flow of granular material in silos and the pressure acting on the silo walls have been studied for over a century, many challenges still remain in silo design. In particular, during the discharge process some dynamic phenomena in silos can often be observed to display large, self-induced and dynamic pulsations which may endanger the stability of the silo structure. The aim of this thesis is to study the flow and pressure in silos using numerical modelling and analytical methods, and to further understand the mechanical behaviour of granular material and mechanism of dynamic phenomena during silo discharge. The Finite Element (FE) method can be used to analyse the behaviour of the granular material in silos by considering the material as a continuum. In this thesis, FEM modelling of silo flow was developed using the Arbitrary Lagrangian-Eulerian (ALE) formulation in the Abaqus/Explicit program and the key parameters that affect the predictions of the flow and pressure during discharge were identified. Using the ALE technique, almost the entire silo discharge process can be simulated without mesh distortion problems. The mass flow rate and temporally averaged discharge pressure predicted by the FE model were first investigated in a conical hopper and were found to be in good agreement with those from the most commonly quoted theoretical solutions. The transient dynamic pressure fluctuations during incipient silo discharge were predicted and the causes for these dynamic events have been investigated which led to the conclusion that the stress wave propagation and the moving shear zone phenomena within the bulk solid were responsible for the dominant higher and lower frequencies effects respectively. A one-dimensional dynamic model of granular columns subject to Coulomb wall friction was developed to investigate the propagation of stress waves, focusing on the effect of geometry by examining converging and diverging tapered columns. The analytical solutions of this model are compared to the FE model based on the ALE formulation. This FE model was first validated using the known behaviour for cylindrical columns. In all cases, the stress impulse set off by incipient discharge at the silo outlet grew with the distance travelled up the column, however the rate was shown to depend on the halfangle of the taper. Over a range of small angles, the proposed analytical model was found to accurately predict this behaviour. After the successful application of the ALE technique for a conical hopper, the FE model was extended to simulate the granular flow in a flat-bottomed model silo. The FE predictions were compared with the silo pressure measurements in a model silo (Rotter et al, 2004). Pressure cells mounted along a vertical line on the silo walls were used to measure the pressure distribution in the silo tests using dry sand. The FE model was further extended to simulate the granular flow in a model silo consisting of a cylindrical section with a conical hopper. The prediction was compared with the experimental observations from a model silo (Munch-Andersen et al, 1992), together with the well-known theoretical solutions. Two numerical issues were addressed in some detail: one is the numerical treatment of the abrupt transition between the cylinder section and the conical hopper, the other is the interaction between the granular solid and the silo walls that was modelled using a dynamic friction model. In addition, the dynamic pressure events during discharge were examined and plausible explanations were given. Finally, this thesis deployed a non-coaxial elastoplastic constitutive model to explore the effect of non-coaxiality on silo phenomena. The non-coaxial FE modelling was performed on three problems: a simple shear test under various initial conditions, a steep hopper and a flat-bottomed silo. The results show that non-coaxiality did not influence the prediction of wall pressure during filling and storing, on the other hand, the discharge pressure was predicted to be larger when non-coaxiality is considered.

Debris flows can be highly destructive and pose a significant threat to both life and property in those areas in which they naturally occur. Such flows can be especially hazardous when large amplitude surges form, which cause more damage than continuous flows of the same mass flux. It is therefore important to understand how these surges form and subsequently behave. The most likely explanation for their formation is the spontaneous development of roll waves - small shock-like disturbances typically observed in thin liquid films - which merge and coarsen as they travel downslope, in turn growing in amplitude and wavespeed. There have also been observations of naturally occurring debris flows which develop surges with regions of completely stationary material between them. The terminology of 'erosion-deposition' waves is introduced to describe these waves, according to the process by which they propagate steadily through a flow by eroding at the static layer ahead of the wave front and depositing a stationary layer behind it. This behaviour is particularly novel and the pulses can be even more destructive than their roll wave counterparts. A combination of experimental observations, travelling-wave solutions and numerical simulations are used here to study the behaviour of both roll waves and erosion-deposition waves in granular flows.

De nombreux procédés industriels nécessitent la manipulation de matériaux sous forme pulvérulente. L’émission de poussières générée par leur manipulation peut s’avérer dangereuse pour la santé des travailleurs ou bien causer un risque d’explosion. Afin de mieux comprendre les mécanismes de dispersion des poussières, le cas de la décharge d’un silo est étudié par simulation numérique avec une approche Euler-Euler. Deux configurations ont été étudiées au cours de cette thèse. La première, sans silo, a permis d’étudier l’influence de perturbations de vitesses imposées à l’entrée de la chambre de dispersion en lieu et place du silo. Cette étude a révélé que ces perturbations peuvent influencer l’élargissement du panache de poudre. Seules les perturbations avec une corrélation temporelle ont généré une ouverture importante du jet tombant semblable à celle relevée expérimentalement. Dans la deuxième configuration, le silo et la chambre de dispersion sont représentés afin d’étudier le couplage entre la dispersion du jet et l’écoulement dans le silo. L’une des difficultés de ces simulations est de prédire les différents régimes d’écoulements granulaires, allant de l’état quasi-statique dans le silo au régime très dilué lors de la dispersion du jet tombant, en passant par le régime collisionnel à la sortie du silo. La théorie cinétique permet de modéliser le régime dilué et collisionnel. En revanche pour la partie quasi-statique un modèle semi-empirique a été utilisé, implémenté et validé sur différentes configurations. La seconde étude a montré l’importance du rapport entre le diamètre de l’orifice et le diamètre des particules sur la structure du jet. En effet, lorsque ce paramètre est faible, le coeur du jet se contracte immédiatement après la sortie du silo puis s’ouvre en aval. Pour des valeurs grandes, l’ouverture du jet est négligeable. Cependant, il semblerait que l’angle du silo modifie le comportement de l’écoulement, ce qui nécessitera des études supplémentaires. / A wide range of industrial processes requires the handling of granular material in a pulverulent form. The subsequent dust emissions due to these processes can be harmful to the health of workers or hazardous explosion risks. In order to understand dust dispersion mechanisms, a case of a free falling granular jet discharged from a silo is studied by numerical simulations using an Euler-Euler approach. Two types of numerical simulation are conducted. First, the influence of velocity fluctuations at the inlet chamber is studied on the plume behavior, instead of the silo. This study reveals that fluctuations are enable to reproduce the jet expansion. It is established that only fluctuations with temporal correlation generate a large jet opening similar to the experiment. The second type of setup shows the coupling between the silo and the chamber. One of the major challenges is the ability to predict the different flow regimes going from quasi-static regime inside the silo, to the very dilute regime in the dust spread and include the collisional regime occurs through the silo. Kinetic theory allows modeling of the dilute and collisional regime. By contrast, frictional models have been used, implemented and validated in different cases. The second study highlights the key role of the ratio defined by the orifice diameter on the particle diameter. Indeed, when this parameter is small, the jet powder core contracts immediately after the exit of the silo dump plane and expands downstream. For high values, the granular jet does not exhibit dispersion anymore. This study suggests that the silo half-angle has an impact on the flow field which justifies the need for further investigations.

Le dimensionnement des digues paravalanches s’appuie sur la connaissance des processus physiques liés au ressaut, qui se forme lorsqu’un écoulement fin et rapide rencontre un obstacle suffisamment haut pour ralentir et épaissir l’écoulement incident. La hauteur du ressaut est aujourd’hui calculée à partir d’équations strictement valides pour des écoulements de matériaux non frictionnels et non compressibles tels que l’eau, sur fond plat et lisse. Or, les avalanches de neige dense sont des écoulements compressibles qui ne peuvent avoir lieu qu’en pente, et au sein desquels se produit de la dissipation d’énergie par friction et collisions entre les grains. Il est donc essentiel de mieux connaître le comportement des ressauts dans les écoulements granulaires en pente. Pour cela, la thèse s’appuie sur plusieurs approches. Les ressauts granulaires stationnaires sont d’abord étudiés de manière purement théorique, à l’aide des équations de conservation de la masse et de la quantité de mouvement moyennées dans l’épaisseur, afin de trouver une relation générale pour prédire la hauteur des ressauts quelques soient les conditions d’entrée. Nous simulons ensuite numériquement un grand nombre de ressauts granulaires en faisant varier plusieurs paramètres (la pente du plan incliné, le débit, le diamètre des grains, la friction entre les grains) à l’aide de la méthode aux éléments discrets. Cette méthode permet d’accéder à la structure interne des ressauts, et notamment à la mesure des champs de vitesse, de fraction volumique, ou encore de la dissipation d’énergie. Les simulations sont réalisées en deux dimensions. Enfin, un dispositif de mesure innovant, qui utilise la radiographie à rayons X dynamique, a été adapté à une expérience de laboratoire existante pour créer des ressauts granulaires stationnaires. Cette technique de mesure permet, en particulier, de mesurer la distribution spatiale moyennée dans la largeur de l’écoulement de la fraction volumique avant, à l’intérieur et après le ressaut granulaire. La comparaison du nouveau cadre théorique proposé avec les résultats expérimentaux et numériques nous permet de mettre en évidence une grande diversité des types de ressauts granulaires en fonction des conditions initiales. Pour chaque type de ressaut, les lacunes du cadre théorique classique, qui ne tient pas compte des forces mises en jeu dans le ressaut ni de la compressibilité, sont clairement établies. / The design of avalanche protection dams relies on the understanding and modelling of physical processes related to the formation of jumps that form when a thin and fast flow meets an obstacle high enough to slow down and thicken the incoming flow. The jump height is nowadays calculated through equations that are strictly valid for non-frictional incompressible flows on a horizontal and smooth bottom. However, dense-snow avalanches are compressible granular flows taking place on a slope, and inside which energy is dissipated through enduring frictional contacts and collisions between grains. It is then essential to decipher the behaviour of jumps formed during granular flows down inclines. To this extent, the thesis relies on several approaches. Standing granular jumps are first studied in a purely theoretical way, with the help of depth-averaged mass and momentum conservation equations, in order to find a relation to predict the height of the jumps regardless of the input conditions. A great number of granular jumps are then simulated by varying several parameters (the slope angle of the incline, the discharge, the grain diameter, the grain-grain friction) thanks to the discrete element method. This method allows us to access to the internal structure of the jumps, and in particular to the spatial distributions of velocity, volume fraction and energy dissipation. Those simulations are done in two dimensions. Finally, an innovative measurement technique using dynamic X-ray radiography was adapted to an existing small-scale laboratory device to produce standing granular jumps. This technique allows in particular the measurement of the width-averaged spatial distribution of volume fraction before, inside and after the granular jumps. The comparison between the new theoretical framework proposed and both the experimental and numerical data, allows us to evidence a rich variety of granular jump patterns as a function of the input conditions. For each type of jump pattern, the shortcomings of the classical theoretical framework, which does not account for the forces at stake within the jump volume nor the compressibility, are well established.

Submitted by Silvana Teresinha Dornelles Studzinski (sstudzinski) on 2016-07-14T12:51:11Z No. of bitstreams: 1 Gabriel Cristiano Kuhn_.pdf: 1527987 bytes, checksum: dd028ed9d9ded68e948299bcc1bfb746 (MD5) / Made available in DSpace on 2016-07-14T12:51:11Z (GMT). No. of bitstreams: 1 Gabriel Cristiano Kuhn_.pdf: 1527987 bytes, checksum: dd028ed9d9ded68e948299bcc1bfb746 (MD5) Previous issue date: 2016-04-27 / FAPERGS - Fundação de Amparo à Pesquisa do Estado do Rio Grande do Sul / Válvula L é um tubo em forma de L destinado a conduzir partículas sólidas entre dois reservatórios. Este dispositivo usa injeção de um fluido e a sua geometria para o controle da vazão dos sólidos. A aplicação deste tipo de válvula não mecânica se dá em processos que visam o transporte de partículas, como linhas de transporte pneumático e reatores de leito circulante. O objetivo deste trabalho é desenvolver uma correlação para a vazão mássica de sólidos através da análise dos números adimensionais, calculados com base em variáveis do processo, e dados experimentais. Com uma correlação mais precisa torna-se mais fácil o controle e o projeto de uma válvula L. Este estudo desconsidera a influência dos reatores, levando em conta apenas a influência da geometria da válvula, a variação da injeção de ar e as propriedades das partículas. A bancada de ensaios foi projetada com duas válvulas L (diâmetros de 34 e 70 mm) feitas de acrílico. Foram utilizadas esferas de vidro (diâmetro Sauter 0,8 mm, massa específica efetiva 1580 kg/m3, grupo D da classificação Geldart), conduzidas por ar comprimido. Aplicando-se o teorema de PI de Buckingham às variáveis importantes do processo, três números adimensionais foram obtidos. Após uma bateria de testes, estes números adimensionais foram calculados para várias condições de ensaios. Com base nos dados experimentais, obteve-se uma equação de ajuste e uma correlação para o fluxo de sólidos. Calculou-se seis correlações, porém é possível dizer que apenas três descrevem o processo, mesmo que com alguma incerteza. Para as válvulas de 34 mm foi possível observar a máxima taxa de sólidos, ou seja, qualquer incremento na vazão injetada resulta em uma diminuição do escoamento de sólidos. / L valve is a right angled, L shaped pipe applied to transfer solids between two vessels. The device uses gas injection and pipe geometry for controlling the flow of particulate solids. This kind of non-mechanical valve is used in processes as pneumatic transport lines and circulating fluidized beds. This study aims to develop a new correlation to the solids mass flow rate through dimensional analysis, experimental data and equation fitting. An accurately way to estimate the flow of solids makes easier the valve design and control. This study does not consider the influence of the reactors that an L valve connect, in other words, this approach is limited to the influence of L valve geometry, gas injection and particle properties. A test section was built, comprising two valve diameters (acrylic pipes of 34 and 70 mm). Glass beads will be used as solids (Sauter diameter 0.8 mm, bulk density 1580 kg/m3, group D of Geldart classification) conveyed by air. Dimensionless numbers were calculated (by Buckingham PI theorem) from the variables of the process, then an experimental program was done. Based on experimental data, π_1, π_2 and π_3 values were calculated for various test conditions. Based on the experimental data, an equation fit and a correlation to the solids mass flow rate were obtained. Six correlation were calculated but only three are able to describe the L valve process with a minimum accuracy. Maximum solids flow were achieved for 34 mm L valve, in other words, if aeration rate is increased beyond this point, solids flow decreases.