Microscopic origins of shear stress in dense fluid-grain mixtures

A numerical model is used to simulate rheometer experiments at constant normal stress on dense suspensions of spheres. The complete model includes sphere-sphere contacts using a soft contact approach, short range hydrodynamic interactions defined by frame-invariant expressions of forces and torques in the lubrication approximation, and drag forces resulting from the poromechanical coupling computed with the DEM-PFV technique. Series of simulations in which some of the coupling terms are neglected highlight the role of the poromechanical coupling in the transient regimes. They also reveal that the shear component of the lubrication forces, though frequently neglected in the literature, has a dominant effect in the volume changes. On the other hand, the effects of lubrication torques are much less significant. The bulk shear stress is decomposed into contact stress and hydrodynamic stress terms whose dependency on a dimensionless shear rate - the so called viscous number $I_v$ - are examined. Both contributions are increasing functions of $I_v$, contacts contribution dominates at low viscous number ($I_v$ 0.15, consistently with a phenomenological law infered by other authors. Statistics of microstructural variables highlight a complex interplay between solid contacts and hydrodynamic interactions. In contrast with a popular idea, the results suggest that lubrication may not necessarily reduce the contribution of contact forces to the bulk shear stress. The proposed model is general and applies directly to sheared immersed granular media in which pore pressure feedback plays a key role (triggering of avalanches, liquefaction).Comment: to appear in Granular Matte

Pore-scale modeling of fluid-particles interaction and emerging poromechanical effects

A micro-hydromechanical model for granular materials is presented. It combines the discrete element method (DEM) for the modeling of the solid phase and a pore-scale finite volume (PFV) formulation for the flow of an incompressible pore fluid. The coupling equations are derived and contrasted against the equations of conventional poroelasticity. An analogy is found between the DEM-PFV coupling and Biot's theory in the limit case of incompressible phases. The simulation of an oedometer test validates the coupling scheme and demonstrates the ability of the model to capture strong poromechanical effects. A detailed analysis of microscale strain and stress confirms the analogy with poroelasticity. An immersed deposition problem is finally simulated and shows the potential of the method to handle phase transitions.Comment: accepted in Int. Journal for Numerical and Analytical Methods in Geomechanic

From elasto-plasticity to visco-elasto-plasticity for saturated granular materials

A recent extension of the discrete element method is reported for the simulation of dense mixtures of non-colloidal particles and viscous fluids in the non-inertial regime. The numerical model includes sphere-sphere contacts using a soft contact ap- proach [2], short range hydrodynamic interactions defined by frame-invariant expressions of forces and torques in the lubrication approximation, and drag forces resulting from the poromechanical coupling computed with the DEM-PFV technique [3]. The proposed model is general and applies directly to sheared satured granular media in which pore pressure feedback plays a key role. A partitioned solver makes the algorithm trivially parallel, which enables the coupled problems to be solved with nearly the same wall-clock time as uncoupled dry materials simulations. The shear stress in a dense suspension is analyzed, and decomposed into contact stress and hydrodynamic stress. Both contributions are shown to be increasing functions of a dimensionless shear rate Iv, in agreement with experimental results [4]. In contrast with a popular idea, the results suggest that lubrication may not necessarily reduce the contribution of contact forces to the bulk shear stress

DEM simulations of unsaturated soils interpreted in a thermodynamic framework

The behavior of granular materials (e.g. soils) strongly depends on the interactions between particles at the grain scale. In addition, in multiphase systems, the presence of water and interfaces between different phases in the soil adds complexity to the study [1,2,5]. The main purpose of this work is to introduce some concepts that are able to fill the gap between discrete element method simulations [3,4] and thermodynamics in order to develop constitutive laws able to better describe the behavior of unsaturated granular medium. The problem is studied in a thermodynamic framework where energies are calculated at low water content for a simple system of two particles of different sizes connected by a liquid bridge. The effect of gravity is considered to be negligible in this study. The energy supplied to the simple system is divided into two parts: a) the energy due to the change of the matric suction in the system and b) the energy resulting from the movement of the particles with respect to each other. Comparisions with the first law of thermodynamics show that there are some features that have significant importance in the macro formulation of energies. These features may be related to the interfacial areas in the medium

Discrete element modelling of bedload transport

International audienceWe present a model for the description of bed load transport at the particle scale. The granular phase was modelled using discrete element method while the fluid phase was characterized by a fluid profile taken from the experiment. The coupling between the two phases was done considering only the effect of the fluid on the particle, through the drag force. The results of the model were compared to particular experimental results. A good agreement was obtained on the particle velocity and solid volume fraction in function of the depth considering the simplicity of the coupling

Physical and numerical modelling of sand liquefaction in waves interacting with a vertical wall

International audienceWave induced liquefaction at a coastal structure is studied. Experiments in a glass-wall flume filled with a partially saturated bed of light-weight sediment are presented. Periodic waves and single wave loadings are simulated. For large enough wave conditions an excess pore pressure is recorded within the soil and a liquefaction threshold is reached. Velocity fields obtained from video recordings display large zones of the bed that behave as a fluid. Phases of soil compaction and dilatation are identified. Moreover, a Discrete Element Method - Pore-scale Finite Volume model is used to simulate the wave-sediment interactions. The computation of the coupling between the flow and the motion of the particles enables to reproduce the excess pore pressure that lead to liquefaction and the progressive compaction of the bed

Modélisation micro-mécanique des milieux granulaires non saturés

Un modèle tridimensionnel polydisperse aux éléments discrets a été développé afin d'étudier le comportement des milieux granulaires non saturés. La présence d'eau interparticulaire est prise en compte grâce à l'introduction de forces spécifiques, décrites dans le cadre de la théorie de la capillarité. Afin de considérer les mécanismes de transfert d'eau au sein du milieu, le modèle est piloté en succion: à chaque niveau de succion, les forces capillaires et la teneur en eau sont calculées à partir d'une résolution numérique de l'équation de Laplace-Young

Evaluating force distributions within virtual uncemented mine backfill using discrete element method

This paper investigates the distribution of intergranular forces within uncemented mine backfills using the discrete element method (DEM) and compares it with the existing analytical method. The virtual backfilling is modeled via the DEM to simulate the underground mining stopes backfilling with uncemented granular materials. Normal and shear forces of all particle contacts within the model backfill are tracked and analyzed with particular attention to the effect of sidewall friction. The DEM evaluates normal force chains and reveals a concentration of high forces within the model backfill. The DEM shows profiles of forces that are distinctly different from those obtained from analytical solutions. Quantitative analyses of the spatial distribution of forces, number of contact points, and changes in the orientation of forces are presented. The DEM demonstrates its capacity as a good tool for looking closely into the backfill on a particle scale. It highlights potential force distribution and concentration within a backfill and shows the limitations of analytical solutions, which helps engineers in the mining industry to better understand the possible mechanisms within backfill

On granular rheology in bedload transport

The local granular phase rheology in bedload transport is investigated from discrete numerical simulations. The numerical model is based on a coupled Discrete Element Method with a 1D space-averaged fluid momentum balance. Using this model the averaged granular stress tensor profile can be computed from particle-particle interactions. In bed-load transport, the granular media exhibits quasi-static and dynamical behaviors. This physical situation can be used as a rheometer and the actual granular rheology can be deduced from a single simulation. Preliminary results suggests that the denser part of the flow, close to the static bed, is well described by a a μ(I)/Φ(I) rheology. Above this layer, the dense granular flow rheology fails to explain the observed shear and normal stresses, meaning that other mechanisms come into play