This work is done as a part of CEGEO french research project by

1. PARTICLE SHAPE DESCRIPTORSandTHEIR INFLUENCE ON THE MECHANICAL BEHAVIORM. ChazeUniversité 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 CHAZE 36, avenue Guy de Collongue F - 69134 Écully cedex Tél. +33 (0)4 72 18 62 24 Marie.Chaze@ec-lyon.fr

2. The purpose of the present study is to analyze the influence of the grain’s 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 affect • the 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

3. G F H R E A DR B D C • 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 octagon • Inscriptible (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 regular

4. Generations of different samples Some typical octagons using the h evolution. Square Regular octagon

5. Illustrations 0.1 double contact edge-to-edge 0.2 0.3 simple contact vertex-to-edge 0.4 0.4 Columnar structures Facetisation

6. Bi Axial Test The 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 background The contact law (Signorini-Coulomb) with inelastic quasi-shocks (B. Cambou & M. Jean). All simulations have been performed with the Open Source platformLMGC90 http://www.lmgc.univ-montp2.fr/~dubois/LMGC90 • We create one sample square, by applying a constant velocity on the right and on the upper wall. This procedure allows • to obtain homogeneous samples • to reduce the preferential direction of contact normal, (which does not occur with the gravity) • interparticle friction µ=0 for a dense confined packing

7. Isotropic Compression by applying a constant stress, confining stress (10 kPa) ISOSTATIC PACKING Some observations: Evolution of the contacts number with h 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.

8. Summary table

9. Fn normal contact force

11. Répartition des fn

12. The vertical compression state • is simulated • at constant mean controlled stress • by displacement loaded • with • interparticles friction µ=0.5 • && • interparticles and walls friction µ=0. • To avoid dynamics effects, the velocity is chosen such as the inertiaparameter I ~ 10-4. • These calculations are drived on intensive calculator.

13. MechanicalAnalysisof the microscopicresponse of the tests Coordinence Z Contact_number The proportions of contacts are correlatedwith the grain’sshapeslightlyincreasewithhigher values of h. Similartendencywith the z. For the discs theybecome stables rapidly

14. In the residual state Independent of h?

15. Volumetric strain versus axial strain stress ratio Strain-stress response Octagons show steeperdilatancyslopethan discs.

16. Frictionangles fpeak&&fcritincrease with h

17. 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).

18. Analysis of local kinematics distribution of branchvector set histogram of branchvector set

20. Strainlocalization in the samples • (using local strainmapscomputedlikeDelauney triangulation) View of e11for compressive displacement ande22 for extension displacement for h = 0.3 near the peak value of the internal angle of friction

21. Percentile of a dataset e11, e22, e12, e21 • according to deformation’s definition

23. Other directions (areas of futur investication) are:The 3D extensionDiscretisation Delaunay 3D Volumetric strain versus axial strain Stress Strain response

25. Discretisation Delaunay 3D

26. 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 octagons…To explain there are, two factors the most relevant : the anisotropy of stress transmission is due to the shapeanisotropy (Azema et al. 2007) • With the variation of h, octagons become irregular, regular, and square with change of vertex number • The 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.

27. ACKNOWLEDGEMENT The author is indebted Cambou B., Radjai F., Jean M. for theirs stimulations