Green’s Function Measurements of Force Transmission in 2D Granular Materials

We describe experiments that probe the response to a point force of 2D granular systems under a variety of conditions. Using photoelastic particles to determine forces at the grain scale, we obtain ensembles of responses for the following particle types, packing geometries and conditions: monodisperse ordered hexagonal packings of disks, bidisperse packings of disks with different amount of disorder, disks packed in a regular rectangular lattice with different frictional properties, packings of pentagonal particles, systems with forces applied at an arbitrary angle at the surface, and systems prepared with shear deformation, hence with texture or anisotropy. We experimentally show that disorder, packing structure, friction and texture significantly affect the average force response in granular systems. For packings with weak disorder, the mean forces propagate primarily along lattice directions. The width of the response along these preferred directions grows with depth, increasingly so as the disorder of the system grows. Also, as the disorder increases, the two propagation directions of the mean force merge into a single direction. The response function for the mean force in the most strongly disordered system is quantitatively consistent with an elastic description for forces applied nearly normally to a surface, but this description is not as good for non-normal applied forces. These observations are consistent with recent predictions of Bouchaud et al. [Bouchaud et al., Euro. Phys. J. E4 451 (2001); Socolar et al., Euro. Phys. J. E7 353 (2002)] and with the anisotropic elasticity models of Goldenberg and Goldhirsch [Goldenberg & Goldhirsch, Phys. Rev. Lett. 89 084302 (2002)]. At this time, it is not possible to distinguish between these two models. The data do not support a diffusive picture, as in the q-model, and they are in conflict with data by Rajchenbach [Da Silva & Rajchenbach, Nature 406 708 (2000)] that indicate a parabolic response for a system consisting of cuboidal blocks. We also explore the spatial properties of force chains in an anisotropic textured system created by a nearly uniform shear. This system is characterized by stress chains that are strongly oriented along an angle of 45o, corresponding to the compressive direction of the shear deformation. In this case, the spatial correlation function for force has a range of only one particle size in the direction transverse to the chains, and varies as a power law in the direction Preprint submitted to Elsevier Science 29 February 2008 of the chains, with an exponent of -0.81. The response to forces is strongest along the direction of the force chains, as expected. Forces applied in other directions are effectively refocused towards the strong force chain direction.