POSTERS
GRANULAR SESSION

Yann BERTHO
Laboratoire FAST, Orsay, France
Instability in an inertial standpipe flow
Y. Bertho, F.Giorgiutti-Dauphine, Ch. Ruyer-Quil, and J.-P. Hulin
We present a two-phase model for an air/grain standpipe flow. We achieve the determination of the stress tensor for the solid phase through a non-linear stability analysis coupled with experimental data. The experiment consists of a one dimensional vertical pipe where air and grains are flowing down. For some values of air and grain flow rates, a saturated density wave is observed and characterized. By means of these experimental results, we are able to close the system of equations, namely define the proper solid pressure $p_s$ and viscosity $\eta_s$ for this system. A first estimation for $p_s$ and $\eta_s$ is provided by a linear stability analysis of the steady dilute free fall regime. We establish that the density travelling waves result in an instability of the free fall regime and we define a stability criterion. In a second step, non-linear travelling waves have been computed; $p_s$ and $\eta_s$ have been adjusted so that the main features of the waves correspond to the experimental findings.

Philippe BOLTENHAGEN
PMMH, ESPCI, Paris, France
Surface fluctuations on cylindrical silos during granular drainage
Philippe Boltenhagen, Gustavo Gutierrez and Eric Clement
Sudden changes in the production process of many grains used in food industry forces the extensive development of storage for grains in order to maintain the necessary supplies when production falls. Collapse of silos is frequent and very damaging to many industries. It is important to understand well the different causes of silo collapse to develop prevention strategies to avoid this pervasive problem. We are studying experimentally the fluctuating small elastic deformations on the surface of open cylindrical paper silos filled with glass beads, during drainage. For sufficiently large grains we change the height of the granular bed, near the threshold of collapse. Knowledge of the characteristic of these fluctuations can help to design mechanisms to prevent the collapse. Measurement of these fluctuations can give the signal to stopping the granular flow before any irreversible deformation of the surface develops. We investigate the characteristics of the fluctuations that appear as elastic deformations in the lower part of the surface of the silo during the discharge of the grains. These fluctuations develop a short time before the actual buckling appears so that they play the role of precursors that signal the buckling and subsequent collapse of the silo. We examine the surface of the silo to measure the deformations at the scale of individual grain sizes and focus on the connection between the fluctuations of the surface of the silo with the buckling and the under pressure that develops inside the cylindrical shell during the discharge of the grains.

Rachid BOUAMRAME
Universite des Sciences et de la Technologie d'Oran, Algeria
Electric transport properties in conductor-insulator composite granular material
Rachid Bouamrane
The D.C, A.C and intermittent charge flow through a conducting thin films with granular structure is studied by numerical simulations. The film is modeled as a pure resistor or a resistor-capacitor regular and non-regular network. Systems of different sizes ratio conductor/insulator and disorder are considered.

Chris CAWTHORN
Department of Applied Maths and Theoretical Physics, Cambridge, UK
Static/Flowing interfaces in granular media
Christopher J. Cawthorn, E. John Hinch and Herbert E. Huppert
The presence of interfaces between static and flowing regions in granular media present an interesting free-boundary problem. Moreover, the boundary conditions to be applied at such a interface are not universally agreed upon. We shall present the early findings of our research into such interfaces, illustrating some theoretical predictions for simple flows, and discuss results of our numerical computations. In addition, we shall describe applications to time-dependent cases such as avalanches, and granular collapse or dam-break problems.

Eric CLEMENT
ESPCI, Paris, France
Mechanics and dynamics of weakly vibrated granular packing
Eric Clement, Chay Goldenberg, Rim Harich, Gabriel Caballero, Geoffroy Lumay and Nicolas Vandewalle
A granular medium is a macroscopic and athermic system. However, providing vibration energy will lead to the emergence of a slow dynamics characterizing the passage between multitudes of local metastable states. This is characterizing a new state of matter midway between a liquid and a solid, very much akin to usual glassy material or a fluid when the agitation energy is increased. We present here the result of several experiments performed on simple model granular packing both in 3D and in 2D. The set-up have the advantage to be able to follow directly the grains dynamics. We analyse the jump statistical distribution and show the existence at short times, of a sub-diffusive motion followed at by al long time regular diffusion process; this cross-over defines a ìcageî which size may vary strongly with the agitation energy. The jump correlation statistics shows the existence a collectively synchronized motion between the particles. We also compare these results on the drag of an intruder particle in the same environment and test the existence of a Fluctuation-Dissipation theorem.

Annie COLIN
Universite de Bordeaux 1, France
How does an emulsion flow in confined geometry?
J Goyon, G Ovarlez and A Colin
In this work , we study how does an emulsion flow in confined geometry. The local rheology of a concentrated emulsion is measured in various geometry (large Couette cell and micrometric channel). The velocity profile are measured using NMR velocimetry or Particule imaging velocimetry. We point out for the first time the effect of the confining on the flow. Confining induces a decrease of the yield stress and of the viscosity of the emulsion. Due to the rearrangements, the fluidity of the emulsion increases near the walls which induces the above behavior.

Stephanie DEBOEUF
Laboratoire FAST, Orsay, France
Dynamics of Grains Ejection during Impact Cratering in Deep Layers
StÈphanie Deboeuf, Philippe Gondret and Marc Rabaud
When a solid sphere impacts a deep granular layer, the sphere sinks in [Walsh, Holloway, Habdas, and de Bruyn, 2003; Uehara, Ambroso, Ojha, and Durian, 2003], and grains are ejected forming an axisymetric corrola. These phenomena lead to the formation of a crater at the free surface of the pile, as observed and studied in the case of a shallow granular layer [Boudet, Amarouchene, and Kellay, 2006]. Using a fast camera, we are able to study the dynamics of the ejected grains involving in the corrola. Some impact parameters, such as the mass, size and kinetic energy of the solid sphere, are systematically varied, allowing to quantify their influence on the characteristic time-scales and length-scales of the dynamics of ejection.

Antoine FOURRIERE
PMMH, ESPCI, Paris, France
Turbulent boundary layer over a relief in air or water, and application to the formation of ripples, dunes and mega-dunes granular material
Antoine Fourriere, Philippe Claudin, Bruno Andreotti and Fouzia Ould-Kaddour
We revisit the stability of an erodible bed in a turbulent shear flow to explain the formation of aeolian dunes and mega-dunes or ripples and dunes in rivers. Because there is only few physical differences between air and water, we study the formation of both aeolian dunes and ripples in water by introducing an infinite boundary layer flow that interacts with a bumpy bottom. As river dunes form due to the presence of a free surface, we then investigate different finite depth effects that could be responsible of the formation of aeolian mega-dunes too. We compare the results to experimental observations in free surface flows. Finally, using a classical linear stability analysis, we access the complete relation of dispersion in rivers and we show that dunes formation does not result from a linear instability.

Rim HARICH
PMMH, ESPCI, Paris, France
Experimental study of a 2D vibrated granular packing
Rim Harich, Eric Clement, Geoffroy Lumay and Nicolas Vandewalle
We present an experimental study of a 2D granular model made of a bidisperse cylinders confined between two glass plates. The packing is vibrated by individual pistons situated at the bottom of the cell. The setup allows the direct visualisation of transport properties, collective modes of relaxation and rheological characteristics of the flow. In particular, we analyse the particle trajectories and we evidence, at short times, a sub-diffusive motion followed at times by regular diffusion. Hence it shows a dynamical caging effect depending on the energy transferred to the packing by agitation. We characterize this constrained sub-diffusive behaviour by analyzing the local jumps statistics. We also directly evidence the internal modes of packing vibration that we propose to relate to the individual particle motion in a constrained environment. We also compare these results on the drag of an intruder particle in the same environment.

Irene IPPOLITO
Conicet-Universidad de Buenos Aires, Argentina
Velocity profiles of granular materials during the drainage of a hopper
Ulissi Facundo, Ippolito Irene, Calvo Adriana, Martorello Leandro, Galliano Pablo, Calvo Adriana
We analyse the flow of granular materials inside a quasi-two-dimensional silo as it drains and compare the datawith some existingmodels. The particle flows inside the silo are recorded and analysed by PIV (Particle Image Velocimetry) in both space and time to obtain their velocity profile. Grains used in the experiments are: sand river grains, glass beads and quartz grains with irregular geometry. The data obtained by varying the hopper angle and the grain geometry and size allow us to understand driven flows inside these geometries. On the other hand, we study the influence of the rougness of the lateral walls on the velocty profiles. We have chosen the geometrical parameters of the silo (aperture angle, width orifice) in order to perform the experiments in a continuous flow regime. During the drainage, we find that the mean velocity profile can vary from gaussian to a plug profile depending on the position of the free surface of the packing in motion. Finally, we discuss the flow rate as a function of the orifice width and hopper angles.

Payman JALALI
Lappeenranta University of Technology, Finland
Experimental observations in granular shear flows of monodisperse and bidisperse packing
Payman Jalali, Jouni Ritvanen, and Pertti Sarkomaa
We introduce our facilities built up for experiments of granular shear flow in an annular shear cell. We present the results of hundreds of experiments done using perfectly-round steel balls of different sizes (2 and 3 mm). Monodisperse and bidisperse packings of steel spheres have been tested in our experiments and instantaneous variation of overall force, overall torque, vertical displacement and local force fluctuation have been measured and compared for different loading conditions. Particles are also tracked during shear flow experiments using high-speed video camera. In a typical shear flow experiment, we observe a sheared region of certain depth below which the material is not practically sheared. Depending on the granular bed height and the shear rate and the compressing force the shear flow of the granular bed can significantly change.

Oistein JOHNSEN
University of Oslo, Norway
Coupled granular and fluid flow in a linear Hele-Shaw cell
O. Johnsen, R. Toussaint, K. J. Maloy, E. G. Flekkoy, and Jean Schmittbuhl
We investigate experimentally the pattern formation process during air injection into a granular material confined in a linear Hele-Shaw cell. The behavior and characteristics of the patterns is largely dependent on the injection pressure and the separation between the cell plates. Varying these two parameters we distinguish four hydrodynamic regimes with different flow properties: 1) A pure seepage regime where the air simply permeates through the granular packing without creating any particle motion. 2) Typical patterns formations within the second pressure regimes is recognized by nearly linear to slightly bulged displacement fronts. The material ahead of the pattern formation is compacted and can be visualized and studied using image subtraction. The structure is stabilized and stops advancing when the mobilized friction between the granular packing and the confining plates balance the hydrodynamic drag on the particles. 3) Within the third pressure regime patterns are bigger and increasingly bulged with a radii of curvature depending on cell spacing. The patterns will saturate under friction mobilization for a transient waiting time before resuming and developing into a finger breaking through the entire granular packing. Failure is observed to be induced by local decompaction and fluidization, resulting in reduced friction. 4) In the fourth regime instability is more pronounced. The finger formations penetrates the granular packing without undergoing a rest state. The transition from a seepage regime to regimes where flow of air and grains are shown to be strongly coupled and instable is governed by the competition between the pressure gradient as a driving force and friction mobilization between the granular packing and the confining plates as the stabilizing mechanism. The fact that the phases are interpenetrating also contributes to stabilization due to smoothening of the pressure gradient while air flows through the granular pore space. Characteristic times for events defining the flow regimes and the dynamical properties of these categorized structures are studied and compared for the parameter space.

Henning KNUDSEN
University of Oslo, Norway
Modelling and simulation of a maze-forming process in granular-fluid systems
Henning Arendt Knudsen, Bjornar Sandnes, Knut Jorgen Maaloy, Eirik Grude Flekkoy
Experiments on granular-fluid systems in confined geometries may produce labyrinth patterns. This is the case when the fluid from a particle/fluid dispersion in a Hele-Shaw cell is slowly withdrawn, resembling a drying process. The particles, initially sedimented and uniformly spread out in a disc, are slowly pulled inwards and together by capillary forces. Invading air forms branching fingers, whereas the particles are compiled into comparably narrow branches. These branches are connected in a tree-like structure, taking the form of a maze. We model the competing forces in the process. Firstly, the capillary forces that pull on the particles are estimated to some extent, taking into account the local geometry of the air fluid interface. Secondly, the friction that is mobilized against the top and bottom plates are modelled using a Janssen assumption. Based on the modelling of the forces we present a simulator designed to reproduce the whole process. Qualitative characteristics and quantitative measures are compared between simulations and experimental data and found to agree. In particular, a characteristic wavelength within the structure is found to decrease with the volume fraction of the particles and increase with the plate separation in the Hele-Shaw cell. This finding is also supported by analytic predictions.

Henning KNUDSEN
University of Oslo, Norway
From Janssen to inverse Janssen effect by tapping
Henning Arendt Knudsen, Knut Jorgen Maaloy, Eirik Grude Flekkoy
When a tube is filled with a granular packing a state of equilibrium between gravity and the friction from the walls is rapidly established. In other words, the weight of the grains is locally carried by the walls, an effect which is known as the 'Janssen effect'. The Janssen effect is caused by an upwards polarization of the friction force on the grains. However, the state of a system supporting the Janssen effect is a fragile one, the local direction of the friction is readily changed by perturbing the system. This is demonstrated in our experiment where a tube containing grains is subjected to vibrations, and the resulting force on the bottom measured. Contrary to our initial expectation that the force on the bottom would converge to the weight of the grains, we measure forces 2-3 times the grain weight. Preliminary studies indicate that for sufficiently rigid grains the bottom force increases quadratically with filling height. This would mean that the direction of the friction force changes and that the vibrations of a tube or a silo containing grains induces a transition from compressive to tensile forces in the silo walls.

Romain LANIEL
LMGC, Montpellier, France
Description of wire-reinforced geomaterials by numerical discrete experiments granular material
Romain Laniel, Pierre Alart, Stephane Pagano
A lot of different solutions can be used to reinforce soil, columns, micro-piles, geomembranes, geogrids and geotextiles. The TexSol is a soil reinforcement process releasing in the last reinforcement category. This one mix sand and wire, and it has a higher strength than the sand alone. Although the wire volume is negligible compared to the sand one, the wire becomes a strong reinforcement when it tangles up inside sand. This type of material is adapted for the embankments requiring a strong slope or works which may be subjected to a dilatation strain (protection dome of a gas reserve for example). Indeed, the wire works in tensile directions and the wire network maintains the structure (when the wire density is big enough); the TexSol can be regarded as a composite material. But the reinforcement micromecanisms remain relatively obscure. Phenomena like the tangles or the remote forces roughly explain the macroscopic maintain of the structure even if they remain difficult to highlight and to quantify. We modelled it by continuous and discrete methods to emphasize its reinforcement mechanisms. In one hand, the formulation of a thermodynamic law which take into account for the wire network unilaterality, models consistently this material. In the other hand, the Non Smooth Contact Dynamics (a disscrete element method) is use to highlight reinforcement micro phenomena. This needs a modelling effort to have realistic samples with a consistent discrete model of the wire. Numerical investigations are carried out with both large transformation and small strain one to show the differences of the wire network action on the structure. Some averaged fields which are not accessible for experimenter can be computed from such a numerical experiments. They allow us to identify the continuous law parameters.

Aurelie LE QUINIOU
CEMAGREF, France
Granular Flow under the action of centrifugal force
A. Le Quiniou and F. Rioual
In many real situations, the granular flows are non stationary and the properties of these flows are still little known. In agro-environment, the centrifugal action is an effective mean of propulsion of a granular material. The crucial challenge is to get an optimized quantity of fertilizers in the field. This requires to know the properties of the granular flow in the spreader. This device consists essentially in a spinning disk with vanes which subjects the grains to the centrifugal force and the Coriolis force. Our study focuses on the modelling of this type of flow in this particular geometry. Along the wall, after a transient state, the grains are distant one from another so that we can use the single particle approximation. At first, we study particles of spherical shapes. We model a flow of grains along a wall under the centrifugal action, using the discrete element method under the quasi-static assumption; We suppose that the material goes through a succession of steady states following Hertzian Contact theories. This assumption has to be checked because the particles can reach high speeds and undergo fast deformations, dependent of the speed of request (~10 m/s). Our study focuses on the identification the modes of energy dissipation during the contact. The interactions of frictional/collisional types between particles and the wall, in particular introducing viscosity or plasticity must be examined through various laws of contact and be confronted with pilot experiments. Moreover the shape of the particle appears to have a crucial importance. For a spherical ball, the phenomenon of bearing without slip seems to prevail in the phase of contact with the wall. For an ellipsoidal particle, modelled by using a cluster of sphere, the slip seems to have priority. We treat the importance of this effect in the appearance of a new phenomenon of granular segregation within the flow.

Maniya MALEKI
PMMH, ESPCI, Paris, France
Pattern formation in a confined suspension by an oscillating shear
Maniya Maleki, Hector Pacheco, Jesus Carlos Ruiz Suarez and Eric Clement
Suspensions of polystyrene particles in pure water/water-salt solution are studied experimentally in a rectangular Hele-Shaw cell. The cell is rotated around its longest axis in such a way that a compact suspension sediments will form at the bottom or top edge, depending on the density of the solution. Thereafter, an oscillating shear is applied to the cell via an air pump. For large enough amplitudes of shearing, we evidence ripple formation at the sediment-clear liquid interface. We varied many parameters, namely the amplitude and frequency of shearing, bead diameter, salt concentration (which allows to change the density contrast between the particles and the liquid), and the angle of the cell before shearing. By changing these parameters, the wavelength and the height of the ripples change. We also observe a slow coarsening process of the surface modulation. We measured the threshold amplitude of shearing, above which the pattern formation occurs. We show that this amplitude increases with the angle and the density differenece between the grains and the liquid, but decreases with frequency. Below this threshold, the grains oscillate, but no surface instability is observed. We evidence an expansion of the sediment layer before the pattern starts to form. This experiment provides an important test to several mechanisms of re-suspension that have been proposed earlier to model the dynamics of a fluid/ grain interface. Also, our study aims to understand unraveled erosion/deposition processes present in natural environment and addresses the issue of micro-fluid transport and mixing usually taking place in confined cells.

Bjornar SANDNES
University of Oslo, Norway
Pattern formation in a confined granular-fluid system
B. Sandnes, H. A. Knudsen, K. J. Måløy and E. G. Flekkøy
Beautiful labyrinth patterns emerge during slow drainage of a granular-fluid system confined between the parallel glass plates of a Hele-Shaw cell. A mixture of glass beads and fluid is loaded into the cell, and after some time the grains sediment out onto the lower plate. The mixture is then drained by slow withdrawal of fluid through a central outlet. The receding fluid/air interface at the perimeter gradually compiles a layer of compacted mass and becomes unstable, resulting in fingers of air invading the granular-fluid mixture. The final branching labyrinth of compacted granular material is random, simply-connected, and space-filling. We show that the labyrinth formation is governed by a competition between capillary forces and the frictional stress mobilized by grain-grain contact networks. These two opposing forces are implemented in a simulator program that reproduces the dynamics of the pattern formation process, and also produces the same pattern length-scales as seen in the experiments. In an alternative approach we present an analytic theory that gives a prediction for the length-scale that is also in agreement with experiment and simulations. The characteristic length-scale of the labyrinth structure is shown to decrease with volume fraction of granular material, and increase with system thickness.

Bjornar SANDNES
University of Oslo, Norway
Emerging stripe patterns in drying suspension droplets
B. Sandnes and D. Molenaar
When a droplet of silica particles suspended in water dries out on a horizontal surface, one can observe an emerging pattern of interconnected stripes of sedimented mass. The evaporation generates a flow towards the perimeter of the droplet, and the stripes grow within the area of fluid flow (not at the pinned contactline as in the ìcoffee drop ring stainî). Particles of different sizes are carried with the flow. When the film thickness becomes comparable to the particle diameter, the largest particles are trapped first, clamped to the substrate by the surface tension of the meniscus. At this point, the friction between particle and substrate exceeds the viscous drag from the surrounding fluid flow. An aggregation of gradually smaller particles takes place, generating the visible stripes. From experimental observations and numerical simulations we determine that the mechanism for the pattern formation is a combination of meniscus shape perturbations and reorganization of the flow caused by the compiled mass, where a self-organized focusing of flow through gradually smaller channels induces the growth of stripes perpendicular to the overall direction of the flow.

Gilles SAUSSINE
SNCF, France
Behaviour of railway ballast under cyclic loading
Gilles Saussine & Pierre-Etienne Gautier
The ballast is an essential component of railway track which is employed for its mechanical properties and its flexibility from the point of view of construction and maintenance. This granular material is confined between concrete sleepers supporting the rail and the platform. To ensure the safety of running of trains, maintenance operations are performed in order to restore the quality of track geometry which decreases under repeated loading. A part of this phenomenon is due to the ballast grains reorganization. In this context it is important to carry on physical and numerical studies on the origins of settlement. The aim of this work is to propose by the mean of numerical computation to characterize the behaviour of ballast during the two degradation phase of track geometry. We distinguish the initial state, ´ unstabilise track ª with a fast evolution of settlement and ´ stabilised track ª with an asymptotic evolution of settlement. We choose the discrete element method with the contact dynamics approach. The ballast is modelled as a collection of rigid pentagons which respect its gradation. The lineic contact is considered as two contacts points which represent the contact segment between two polygons. This sample remains on a deformable layer in order to take into account the soil deformations. The loading cycle are applied on a particle with a specific shape which represents a sleeper. We focused on the behaviour of the thin granular layer confined between the deformable layer and the sleeper. >From the numerical computations we have shown that we can obtain after 60000 loading cycles the two characteristic phases in the evolution of settlement. The settlement curve can be fitted with a numerical model which predicts the final settlement. The stabilised state is characterised by a specific organisation of strong and weak contacts network with an important proportion of strong lineics contacts. These results allow preparing samples which respect the stabilised state in order to perform numerical studies on the increase of speed circulation.

Antoine SEGUIN
Laboratoire FAST, Orsay, France
Influence of confinement on granular penetration by impact
A. Seguin, Y. Bertho and P. Gondret
When a solid sphere drops in a granular medium, an impact crater is created. The morphology and the size of this crater depend on the granular medium (packing fraction,...) and many features of the projectile such as its diameter, its density or the energy dissipation involved during the collision.
The penetration of the projectile in the granular bed as a function of the impact energy is calculated theoretically using a simple friction law between the projectile and the grains and compared to experimental results.
When the projectile enters inside the granular material, the grains tend to move sideways, allowing the formation of the crater. The influence of a radial confinement of the grains is investigated experimentally by measuring the penetration depth of the projectile for different impact energies. A characteristic length beyond which the confinement has no influence is observed and quantified.

Zahra SHOJAAEE
Physics Institute-Computational and Statistical Physics, Univeristy of Duisburg-Essen, Germany
Phase Transition Characteristics of the Rheology of Granular Media
Zahra Shojaaee, Lothar Brendel and Dietrich E. Wolf
The Contact Dynamics method is being applied to investigate a two-dimensional non-cohesive granular material. The particles are hard discs, and Coulomb friction and volume exclusion forces are the only forces being exerted. The particles are confined between two parallel walls at the top and the bottom. The walls are being pushed inwards by the same perpendicular forces. They move horizontally with the same constant velocity in opposite directions. The velocity profile is being studied. In the case of a bidisperse system the flow as function of the shear velocity shows characteristics comparable to a phase transition. The key quantities are the velocity of the center of mass of the system as well as its fluctuations. A finite size analysis suggests that it is a continuous ``phase transition''. At high shear velocity the symmetry between the upper and lower wall is not spontaneously broken, whereas at slow shear rate the granular material has different slip at the two walls. For large systems the ergodic time seems to diverge exponentially below the critical shear velocity.

Irena SIELAMOWICZ
Civil Engineering Department, Structural Mechanics Chair, Bialystok Technical University, Poland
Optimization of granular material flow rate related to the moisture of the grains and the geometry of the hopper
Michal Czech and Irena Sielamowicz
The paper presents the results of investigations of granular material flow rate in the model of silo for both three values of the inclination of the bottom (X1) and moisture of the grains (X2). The flow rate W(X1, X2 ) was assumed as a polynomial of the second order with interaction. The constants of the model were determinated by the least square method. Both the adequacy of the model and significance were made. To state if the investigated area, where the regression function is given as a polynomial of the second order W(X1, X2 ), has the point in which the function reaches its maximum, this polynomial was reduced to the canonical form. On the base of the analysis of the canonical form of the equation of the investigated area, a point was found in which the function W(X1, X2 ) reaches its maximum. In the case if such a point did not exist in the investigated area, the directions of searching of points with greater values of the function W(X1, X2 ) than the values reached so far will be given.

Irena SIELAMOWICZ
Civil Engineering Department, Structural Mechanics Chair, Bialystok Technical University, Poland
Statistical modeling of the discharge process of granular material from the silo model
Irena Sielamowicz
Some experimental results of investigation of the discharge process of granularmaterial from silo model with vertical walls are presented in the paper. The model was made of Plexiglas at the scale 1:20. The relation of discharge flow rate, determined as function Y , [kg/(m2 ·s)], was investigated from some different factors as: the ratio of the batch height of millet grains to the height of the silo (factor X1), moisture of the grains (factor X2), angle of the inclination of the bottom (factor X3), the ratio of the length of the hopper to the height of the silo (factor X4), the ratio of the width of the outlet to the width of the silo (factor X5). On the base of the results the regression model of this relation was determined. It made it possible to detect the effects of influence of the factors and their common interactions. The results obtained can be used during design of silos in natural scale.

Vincent TOPIN
LMGC, Montpellier, France
Stress transmission in a multi-phase granular packing
Topin Vincent, Radjai Farhang, Delenne Jean-Yves, and Mabille Frédéric
We analyze stress transmission in granular media involving an interstitial cementing matrix of variable volume fraction. We rely on a lattice-type discretization of both the particles and cemented matrix and we show that the percolation of the particle phase results in stress concentration along particle chains. The signature of granular structure appears clearly on the probability density functions (pdf) of node stresses. From the shape of the pdf's we can discern large, intermediate and weak stresses. The large stresses occur mostly at the interparticle contact zones as in noncohesive granular media with a well-defined exponential distribution. The weak forces reflect the arching effect in compression and the presence of bare (uncemented) contacts in tension, and they occur in both the particles and the matrix. The intermediate stresses belong mostly to the bulk of the particles and their distribution is well fit to a Gaussian distribution. We also observe that the stress chains are essentially guided by the cementing matrix in tension and by the particulate backbone in compression. The stress pdf's are increasingly wider for a decreasing matrix volume fraction in tension. In other words, the stresses are more and more concentrated in the matrix phase. Finally, we compare in detail the contact force network computed from stresses localized at the matrix bridges between particles with that computed by means of the discrete element method with cohesive interactions and for the same configuration of the particles. We show that the two methods yield similar force patterns at low matrix volume fraction.

Ana Maria VIDALES
Departamento de Fisica y CONICET Universidad Nacio, Argentina
Compaction and arches in packings of pentagons
A. M. Vidales, L. A. Pugnaloni and I. Ippolito
We present results of the compaction and arching of regular pentagons from simulation. We analyze the behavior of density as a function of the number of taps performed on the system and we also make an annealing process on the packing. A detailed characterization of the problem of arch formation during the tapping process is also presented and we discus the role of arch distribution in the compaction of the system and in the final density attained by it. The results obtained show that pentagons display new features in the compaction dynamics as compared with round objects.