Stress Propagation and Arching in Static Sandpiles

Abstract

We present a new approach to the modelling of stress propagation in static granular media, focussing on the conical sandpile constructed from a point source. We view the medium as consisting of cohesionless hard particles held up by static frictional forces; these are subject to microscopic indeterminacy which corresponds macroscopically to the fact that the equations of stress continuity are incomplete -- no strain variable can be defined. We propose that in general the continuity equations should be closed by means of a constitutive relation (or relations) between different components of the (mesoscopically averaged) stress tensor. The primary constitutive relation relates radial and vertical shear and normal stresses (in two dimensions, this is all one needs). We argue that the constitutive relation(s) should be local, and should encode the construction history of the pile: this history determines the organization of the grains at a mesoscopic scale, and thereby the local relationship between stresses. To the accuracy of published experiments, the pattern of stresses beneath a pile shows a scaling between piles of different heights (RSF scaling) which severely limits the form the constitutive relation can take ...

38 pages, 24 Postscript figures, LATEX, minor misspellings corrected, Journal de Physique I, Ref. Nr. 6.1125, accepted

Cited by in corpus (28)

• Jamming, Force Chains and Fragile Matter
• Footprints in Sand: The Response of a Granular Material to Local Perturbations
• Green's Function Measurements of Force Transmission in 2D Granular Materials
• Stress distribution in static two dimensional granular model media in the absence of friction
• Statistical Mechanics of Stress Transmission in Disordered Granular Arrays
• Stresses in silos: Comparison between theoretical models and new experiments
• Stresses in isostatic granular systems and emergence of force chains
• Development of Stresses in Cohesionless Poured Sand
• Small and Large Scale Granular Statics
• From the stress response function (back) to the sandpile `dip'
• Stress in frictionless granular material: Adaptive Network Simulations
• Elastic medium confined in a column versus the Janssen experiment
• Jamming and Stress Propagation in Particulate Matter
• A Ball in a Groove
• Effects of Friction and Disorder on the Quasi-Static Response of Granular Solids to a Localized Force
• Sensitivity of the stress response function to packing preparation
• Stress in planar cellular solids and isostatic granular assemblies: Coarse-graining the constitutive equation
• Isostaticity and Mechanical Response of Two-Dimensional Granular Piles
• Stress response function of a two-dimensional ordered packing of frictional beads
• The Stress Transmission Universality Classes of Periodic Granular Arrays
• The missing stress-geometry equation in granular media
• Anisotropic elastic theory of preloaded granular media
• Statics of loose triangular embankment under Nadai's sand hill analogy
• Stress Propagation in Sand
• Incipient failure in sandpile models
• Contact forces in regular 3D granular pile
• Statistical Physics of the Jamming Transition: The Search for Simple Models
• Stress Response in Confined Arrays of Frictional and Frictionless Particles