Mechanical response of a static granular piling
- PDF / 694,676 Bytes
- 6 Pages / 612 x 792 pts (letter) Page_size
- 10 Downloads / 247 Views
Mechanical response of a static granular piling Guillaume Reydellet, Loic Vanel, Eric Clément Laboratoire des Milieux Désordonnés et Hétérogènes – UMR 7603 Université Pierre et Marie Curie Boîte 86 4, Place Jussieu, F-75252 Paris ABSTRACT We present the results of different experiments which aim is to investigate the response of a static granular assemblies to various local perturbations. We design a sensitive experimental method to probe the response of a localized stress at the top of a granular piling. The piling is an horizontal 3D granular layer confined in a box and the spatial distribution of loads at the bottom is monitored. This analysis defines some crucial experimental test to inform a currently debated issue on the mechanical status of static granular assemblies. INTRODUCTION Understanding the exact mechanical status of static or quasi-static granular assemblies is still an open and debated issue (see for example [1] and refs inside). Models typically used in soil mechanics assume an elasto-plastic behavior for a granular material subjected to applied loads [2,3]. Relations between components of the stress tensor and deformations are determined empirically from triaxial test experiments. These relations may be quite complex if they are to reproduce the behavior of “real” granular assemblies (piece-wise, non-linear, anisotropic…) and many empirical constant may enter in the description. But overall, below the plastic threshold, the constitutive relations between stresses and deformations give to the system of partial differential equations (PDE) describing static equilibrium, the structure of elasticity (elliptic equations). Beyond the plastic threshold, the system is described using an adaptation of the Coulomb plasticity theory and we have a situation where a propagative character for the PDE (hyperbolic equations) will appear in regions experiencing yield[3]. An alternative theoretical approach was propose recently and is based on a microscopic viewpoint that incorporates a propagative character for the contact forces between the grains [4]. When extended to the continuum limit, this model predicts simple relations between components of the stress tensor, and a set of hyperbolic PDEs is obtained to solve for the distribution of stresses. A particular example of such a relation is called the Oriented Stress Linearity model (OSL) [5]. These models are dramatically different in character (below the plasticity threshold). The difference in the two approaches is manifested in the nature of the boundary conditions. In a propagative (hyperbolic) model, stresses must be specified on just a part of the boundaries, (for example at the free surface) and propagate in the bulk. The equation solutions and the boundary reflection properties determine stresses on the other boundaries. For an elliptic equation, stresses and/or strains must be specified at all boundaries [4,6,7] and influence the whole solution in the bulk. Recently several reproducible experiments were performed in a sand-pile (see[8] and references the
Data Loading...
