An investigation on the collisional behaviour of granular flows

Granular materials are encountered in a diverse range of geophysical contexts such as landslides and debris flows. This research aims to improve our knowledge of debris flows by means of experimental, numerical and theoretical work with a specific focus on the recently developed extended kinetic theory (EKT) for dry granular flows over bumpy bases. Debris flows undergo rapid rates of deformation in which momentum transfer is mainly carried by frictional and collisional stresses. The random components that generate particle stresses through collisions can be related to the concept of granular temperature. This entity represents the basic concept underpinning the kinetic theory of granular flows. Fundamental characteristics of mobile granular flows are reproduced in laboratory experiments and numerical simulations. The results obtained are used in this thesis to test the predictions and validate the predictions of velocity, granular temperature and solid concentration obtained from the application of extended kinetic theory (EKT). In the first part of this thesis, dry granular flows are studied. Two imaging techniques proposed for the measurement of velocity and granular temperature, namely Particle Image Velocimetry (PIV) and Particle Tracking Velocimetry (PTV) are critically assessed. Due to lack of guidelines for the correct investigation of granular flows using PTV, an error framework for this technique is presented. The influences of errors generated during the PIV and PTV procedures are examined in experiments on dry monodisperse granular flows made of angular and nearly spherical particles down an inclined chute geometry. For the spherical particles, profiles of velocity, granular temperature, solid concentration and stresses are obtained. In terms of granular temperature, the accuracy of the results is still unclear for flows of angular particles while, for the nearly spherical particles, it is shown how the choice of image resolution and the sampling interval affects both the magnitude and the profile shape of granular temperature. Based on the experimental investigations, discrete element simulations of steady, fully-developed, inclined flows of identical spheres over bumpy bases, in the presence and absence of flat, frictional sidewalls are conducted. The main features of these flows are described and new insights in the behaviour of numerically simulated flows over a bumpy base is given. A method to include the influence of rolling resistance in the numerical simulations is examined by comparing to the results of one selected experiment. A good agreement between the two approaches is found. The simulations in the absence of sidewalls are also used to generate synthetic images upon which PIV and PTV are assessed. It is found that PTV is a better technique to measure granular temperature when the appropriate sampling interval is used, at least for dry monodisperse granular flow of identical spheres, while PIV tends to to damp the magnitude of this quantity in some parts of the flow. The predictions of extended kinetic theory in terms of dimensionless pressure are compared with those obtained from experiments and numerical simulations. In the first case, the results obtained considering the error framework for PTV and the validation via synthetic images find good agreement in the limit of validity of solid concentration measurement. In the second case, a good agreement is also found but it is shown that the constitutive relation for the pressure of EKT must be modified in the proximity of the boundary, because of the influence of currently available radial distribution functions at the bottom boundary. It is also noticed that currently available boundary conditions for flows over bumpy planes underestimate the energy dissipation. These two observations generate a the lack of agreement of EKT with the simulations, in terms of the maximum angles of inclination for which steady flows are possible. However, whenever a solution is possible, the predicted measurements of EKT satisfactorily match the numerical measurements. In addition, for granular flows between sidewalls, it is confirmed that the sidewalls exert, on average, a Coulomb-like resistance to the flow. However, when EKT is tested against the experimental results, a strong disagreement is shown. It is thought that the cause may be connected to the introduction of rolling resistance in the numerical simulations, which in EKT has not yet been accounted for. In second part of the research, solid-fluid mixtures made of transparent materials are investigated. Monodisperse and polydisperse granular flows are studied. In simple monodisperse granular flows, spherical particles are used to improve the quality of the flow visualization and allow particle tracking. The information obtained from these flows is used to test the prediction of EKT in terms of dimensionless pressure. A qualitative agreement with kinetic theory is found, although the theory underestimates the experimental results. Improvements in the accuracy of the measured flow properties may lead to better agreement. Polydisperse granular flows are performed to match the characteristics of real debris flows. However, the selected particle size distributions, made of spherical particles or a combination of spherical and angular particles, produced unexpected depositional profiles. This may have to do with the boundary conditions imposed at flow release, which were designed to enable steady flows to develop. While these flows are part of preliminary testing used to increase a step further the complexity of the monodisperse granular flows, better consideration should be made in future to find a balance between flow visualization, experimental apparatus and boundary conditions, and the generation of appropriate mechanics that are characteristic of real debris flows

Capturing of the internal mechanics of liquid-granular flows comprised of polydisperse spherical particles

This paper presents a series of flume experiments designed to examine the motion and arrest of concentrated granular-fluid flows, with a view to understanding the role of polydispersity in debris flows. A non-intrusive technique is used to investigate the internal behaviour of small scale experimental flows. Three different particle size distributions comprised of polydisperse spherical particles and one with the finer component made of angular particles were analysed. The choice of using spherical shaped particles was made to improve the visualization of the internal mechanics without reducing overmuch the complexity involved in the study of these flows. We examined and compared the internal velocities of the flows and their depositional spreads. While the optical performance of the non-intrusive technique was improved, some of the characteristics commonly seen in these types of granular flows were not observed. Velocity profiles obtained in the body of the flows were similar in shape but with differences in velocity magnitude depending on the amount of fines and the angularity of the particle in one case. Depositional runouts between flows were similar at low inclinations when little internal energy was supplemented to the system or when the viscous effects dominated the mechanics at steeper angles

Extended kinetic theory applied to inclined granular flows: role of boundaries

We compare the predictions of extended kinetic theory (EKT), where the roles of surface friction and correlation in fluctuation velocities are taken into account, with discrete element simulations of steady, fully-developed, inclined flows of identical spheres over bumpy bases, in the presence and absence of flat, frictional sidewalls. We show that the constitutive relation for the pressure of EKT must be modified in the proximity of the boundary, because of the influence of excluded volume and shielding associated with collisions of particles with the boundary itself. We also note that currently available boundary conditions for flows over bumpy planes in kinetic theory underestimate the energy dissipation. These two observations explain the lack of agreement of EKT with the simulations, in terms of the maximum angles of inclination for which steady, fully-developed flows are possible. That is, for some high angles of inclination, EKT does not have solutions, while steady flows are predicted in DEM. However, whenever a solution to the system of differential equations of EKT does exist, the predicted distributions of velocity, solid volume fraction and granular temperature satisfactorily match the numerical measurements. The incompressible, algebraic approximation of EKT, which ignores the conduction of energy in the energy balance, admits solutions for a wider range of angles of inclination, as in the simulations, but fails to reproduce the quantitative and qualitative behaviour of solid volume fraction and granular temperature in the two conductive layers at the top and bottom of the flow. When frictional sidewalls are added to the domain, we show that the spanwise ratio of shear stress to pressure is linearly distributed in the dense core region of the flow, confirming that the sidewalls exert, on average, a Coulomb-like resistance to the flow with an effective friction coefficient which is less than half the actual particle-wall friction