PARTICLE SHAPE DESCRIPTORSand THEIR INFLUENCE ON THE MECHANICAL BEHAVIOR M. Chaze Universit de Lyon,Ecole Centrale de Lyon

This work is done as a part of CEGEO french research project by LTDS U. Lyon, C. Nouguier, M. Chaze (regulars and irregulars polygons)LMGC U. Montpellier, F. Radjai et al. (clumps)3S-R U. Grenoble, G. Combe, P. Villard et al. (non-convex clumps)Marie CHAZE36, avenue Guy de CollongueF - 69134 cully cedexTl. +33 (0)4 72 18 62 24Marie.Chaze@ec-lyon.fr

The purpose of the present study is to analyze the influence of the grains form indices upon the micro- and the macroscopic mechanical parameters.Do they reflect the quasistatic behavior and shear resistance volumetric change of complex soil behavior ?

And how the indices affectthe contact strong and weak force network the force transmission patterns the compactness of the samples the coordination numbers the stick-slip phenomenon

the mechanical behavior during the intensive computer simulation with DEM methods

We characterized the discrepancy from a disc (suggestion F.Radjai) using the scalar parameter

R the radius of the largest circle containing the particle DR difference between the ex- and the in-circle of particle ( DR = 0. when the particle is a disc) We begin by considering octagonInscriptible (all the vertices are on the same circle)Octagon circumscribed in circle

Geometrical octagon design

With the variation of h from 0.1 to 0.4 octagon become irregular and regularCEGEO II

Generations of different samplesSome typical octagons using the h evolution.Regular octagon SquareCEGEO II

h = 0.2h = 0.3h = 0.4

h = 0.0824h = 0.414

Illustrations0.10.40.20.30.4double contact edge-to-edgesimple contactvertex-to-edgeColumnar structuresFacetisationCEGEO II

Bi Axial TestThe granular model 2D assembly of 5000 polydisperse frictional particles (discs && octagons)Their radius ranges vary from 3.e-2 to 9.8 e-2 m, the density is equal to 2800 kg.m-3. Modelling backgroundThe contact law (Signorini-Coulomb) with inelastic quasi-shocks (B. Cambou & M. Jean).All simulations have been performed with the Open Source platform LMGC90 http://www.lmgc.univ-montp2.fr/~dubois/LMGC90We create one sample square, by applying a constant velocity on the right and on the upper wall. This procedure allows to obtain homogeneous samplesto reduce the preferential direction of contact normal, (which does not occur with the gravity)interparticle friction =0 for a dense confined packingCEGEO II

by applying a constant stress, confining stress (10 kPa)ISOSTATIC PACKING Some observations:Isotropic Compression Evolution of stick (edge-to-edge) and slide (vertex-to-edge) contacts

Evidence for large class of weak (dashed line) forces carried by vertex-to-edge slide contacts. Strong force chains (plain line) are composed of edge-to-edge stick contacts acts as the skeleton.Evolution of the contacts number with hCEGEO II

Summary tableCEGEO II

Shapes indicator0.0.10.20.30.4 = 0.Z0Mean number of contacting neighbors per particle 3.7834.74.44.454.5Compacity Cisoh affects the compactness 0.8450.8510.8630.8740.876

Fn normal contact forceCEGEO II

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Rpartition des fnCEGEO II

is simulated

at constant mean controlled stress by displacement loaded with interparticles friction =0.5&&interparticles and walls friction =0.

To avoid dynamics effects, the velocity is chosen such as the inertia parameter I ~ 10-4. These calculations are drived on intensive calculator.The vertical compression stateCEGEO II

Coordinence ZContact_numberMechanical Analysis of the microscopic response of the testsThe proportions of contacts are correlated with the grains shape slightly increase with higher values of h.Similar tendency with the z. For the discs they become stables rapidlyCEGEO II

In the residual stateIndependent of h ?CEGEO II

Shapes indicator0.0.10.20.30.4ZMean number of contacting neighbors per particle 3.163.34 3.43.783.84Ziso/ZcritDegree of connectivity1.21.41.31.21.2CompacitySpace-filling aptitude0.810.7840.79090.8030.809

Volumetric strain versus axial strain

Octagons show steeper dilatancy slope than discs.

Strain-stress responsestress ratioCEGEO II

h0.0.10.20.30.4sin f*0.2790.39640.39700.3810.435StD0.006240.065960.09650.05490.00465

Friction angles

fpeak && fcritincrease with hCEGEO II

Shapes indicator0.0.10.20.30.4carrf*residual state Mean 16,3357Std D0,3225Mean 23,05Std D0,4Mean23,35Std D 0,55 Mean23,72 Std D 0,718Mean24,45 Std D 0,177

Snapshot of radial forces(thickness propotional)Force transmission of octagonal particles. The side to side contacts not transmit torques. Class of weak forces carried by vertex-to-edge slide contacts (dashed lines).strong force chains are composed of edge-to-edge sticks contacts (plain lines). CEGEO II

Analysis of local kinematicsdistribution of branch vector sethistogram of branch vector setCEGEO II

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Strain localization in the samples (using local strain maps computed like Delauney triangulation) View of e11 for compressive displacement and e22 for extension displacement for h = 0.3 near the peak value of the internal angle of frictionCEGEO II

Percentile of a dataset e11, e22, e12, e21 according to deformations definitionCEGEO II

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Other directions (areas of futur investication) are:The 3D extensionDiscretisation Delaunay 3D

Volumetric strain versus axial strain Stress Strain responseCEGEO II

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Discretisation Delaunay 3DCEGEO II

The parameter h is a good shape parameter for our 2D granular packings?

There are clear differences in the behavior of discs ( the geometry overestimate the role of rotations) and convex octagonsTo explain there are, two factors the most relevant : the anisotropy of stress transmission is due to the shape anisotropy (Azema et al. 2007)

With the variation of h, octagons become irregular, regular, and square with change of vertex numberThe face-to-face or edge-to-edge contacts create facets, and form columnar structures. Also, locking may happen, the evolution of the grains is not possible or is possible only if the reaction forces increase dramatically, and in rough case, if at last some errors are allowed. These behaviors are favored in collections of octagons which have a tendency to organize as crystals, like clusters, while collections of poly-sized disks are easier to deform.

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ACKNOWLEDGEMENT

The author is indebted Cambou B., Radjai F., Jean M. for theirs stimulationsCEGEO II

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