1. PARTICLE SHAPE DESCRIPTORS and THEIR INFLUENCE ON THE MECHANICAL BEHAVIOR M. Chaze Université 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 DEM the mechanical behavior during the intensive computer simulation with DEM methods

3. We characterized the discrepancy from a disc (suggestion F.Radjai) using the scalar parameter R the radius of the largest circle containing the particle  R difference between the ex- and the in-circle of particle  R = 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 A B C D E F G H RR R With the variation of  from 0.1 to 0.4 octagon become irregular and regular CEGEO II

4.  0.2  0.3  0.4  0.0824  0.414 Generations of different samples Some typical octagons using the  evolution. Regular octagon Square CEGEO II

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

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 platform LMGC90 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 CEGEO II

7. 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  CEGEO II

8. Summary table Shape s indicator 0.0.10.20.30.4 µ = 0. Z 0 Mean number of contacting neighbors per particle 3.7834.74.44.454.5 Compacity C iso  affects the compactness 0.8450.8510.8630.8740.876 CEGEO II

9. Fn normal contact force CEGEO II

11. Répartition des fn CEGEO II

12. 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 inertia parameter I ~ 10 -4.  These calculations are drived on intensive calculator. The vertical compression state CEGEO II

13. Coordinence Z Contact_number Mechanical Analysis of the microscopic response of the tests The proportions of contacts are correlated with the grain’s shape slightly increase with higher values of . Similar tendency with the z. For the discs they become stables rapidly CEGEO II

14. Shapes indicator0.0.10.20.30.4 Z Mean number of contacting neighbors per particle 3.163.343.43.783.84 Ziso/Zcrit Degree of connectivity 1.2 1.41.31.2 Compacity Space-filling aptitude 0.810.7840.79090.8030.809 In the residual state Independent of  ? CEGEO II

15. Volumetric strain versus axial strain Octagons show steeper dilatancy slope than discs. Strain-stress response stress ratio  0.0.10.20.30.4 sin  0.2790.39640.39700.3810.435 StD0.006240.065960.09650.05490.00465 CEGEO II

16. Friction angles  peak &&  crit increase with  Shapes indicator 0.0.10.20.3 0.4 carr é  * residual state Mean 16,3357 Std D 0,3225 Mean 23,05 Std D 0,4 Mean 23,35 Std D 0,55 Mean 23,72 Std D 0,718 Mean 24,45 Std D 0,177 CEGEO II

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). CEGEO II

18. Analysis of local kinematics distribution of branch vector set histogram of branch vector set CEGEO II

20. Strain localization in the samples (using local strain maps computed like Delauney triangulation) View of   for compressive displacement and   for extension displacement for  = 0.3 near the peak value of the internal angle of friction CEGEO II

21. Percentile of a dataset         according to deformation’s definition CEGEO II

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

25. Discretisation Delaunay 3D CEGEO II

26. The parameter  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 shape anisotropy (Azema et al. 2007) With the variation of , 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. CEGEO II

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