4,085 research outputs found
Stress Propagation and Arching in Static Sandpiles
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 ...Comment: 38 pages, 24 Postscript figures, LATEX, minor misspellings corrected,
Journal de Physique I, Ref. Nr. 6.1125, accepte
Development of Stresses in Cohesionless Poured Sand
The pressure distribution beneath a conical sandpile, created by pouring sand
from a point source onto a rough rigid support, shows a pronounced minimum
below the apex (`the dip'). Recent work of the authors has attempted to explain
this phenomenon by invoking local rules for stress propagation that depend on
the local geometry, and hence on the construction history, of the medium. We
discuss the fundamental difference between such approaches, which lead to
hyperbolic differential equations, and elastoplastic models, for which the
equations are elliptic within any elastic zones present .... This displacement
field appears to be either ill-defined, or defined relative to a reference
state whose physical existence is in doubt. Insofar as their predictions depend
on physical factors unknown and outside experimental control, such
elastoplastic models predict that the observations should be intrinsically
irreproducible .... Our hyperbolic models are based instead on a physical
picture of the material, in which (a) the load is supported by a skeletal
network of force chains ("stress paths") whose geometry depends on construction
history; (b) this network is `fragile' or marginally stable, in a sense that we
define. .... We point out that our hyperbolic models can nonetheless be
reconciled with elastoplastic ideas by taking the limit of an extremely
anisotropic yield condition.Comment: 25 pages, latex RS.tex with rspublic.sty, 7 figures in Rsfig.ps.
Philosophical Transactions A, Royal Society, submitted 02/9
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