Force distribution in a two dimensional sandpile (original) (raw)
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The role of particle shape on the stress distribution in a sandpile
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2008
The results of an experimental investigation into the counter-intuitive phenomenon that a local minimum in the normal stress profile is sometimes found under the apex of a sandpile are presented. Specifically, the effects of particle shape on the stress distribution are studied and it is shown that anisotropy of the particles significantly enhances the dip. This amplification is attributed to the mechanical stability induced by boundary alignment of the anisotropic particles. Circular, ellipsoidal and pear-shaped cylinders are used and the stress propagates principally towards the sides of the pile through primary stress chains. Secondary chains are also present and we propose that the relationship between the magnitudes of the ratio of primary to secondary chains is correlated with the size of the dip.
Forces in piles of granular material: an analytic and 3D DEM study
Granular Matter, 2001
We investigate the stress distribution at the base of a conical sandpile using both analytic calculations and a three dimensional discrete element code. In particular, we study how a minimum in the normal stress can occur under the highest part of the sandpile. It is found that piles composed of particles with the same size do not show a minimum in the normal stress. A stress minimum is only observed when the piles are composed of particles with different sizes, where the particles are size segregated in an ordered, symmetric, circular fashion, around the central axis of the sandpile. If a pile is composed of particles with different sizes, where the particles are randomly distributed throughout the pile, then no stress dip is observed. These results suggest that the stress dip is due to ordered, force contacts between equiheight particles which direct stress to the outer parts of the pile.
Geotechnical and Geological Engineering, 2011
This work is a contribution to the understanding of the mechanical properties of non-cohesive granular materials in the presence of friction and a continuation of our previous work (Roul et al. 2010) on numerical investigation of the macroscopic mechanical properties of sand piles. Besides previous numerical results obtained for sand piles that were poured from a localized source (''point source''), we here consider sand piles that were built by adopting a ''line source'' or ''raining procedure''. Simulations were carried out in two-dimensional systems with soft convex polygonal particles, using the discrete element method (DEM). First, we focus on computing the macroscopic continuum quantities of the resulting symmetric sand piles. We then show how the construction history of the sand piles affects their mechanical properties including strain, fabric, volume fraction, and stress distributions; we also show how the latter are affected by the shape of the particles. Finally, stress tensors are studied for asymmetric sand piles, where the particles are dropped from either a point source or a line source. We find that the behaviour of stress distribution at the bottom of an asymmetric sand pile is qualitatively the same as that obtained from an analytical solution by Didwania and co-workers (Proc R Soc Lond A 456:2569-2588, 2000).
On the stress depression under a sandpile
Powder Technology, 1994
The observed minimum in the normal stress beneath the highest portion of a 'sandpile' (a pile of granular material) is a counter-intuitive result that has long remained unexplained.
Simulation study on micro and macro mechanical behaviour of sand piles
Powder Technology, 2010
We investigate numerically the micro and macro mechanical behaviour of non-cohesive granular materials, especially in the static limit. To achieve this goal we performed numerical simulations generating twodimensional "sand piles" from several thousands of convex polygonal particles with varying shapes, sizes and corner numbers, using a discrete element approach based on soft particles. We emphasize that the displacement (strain) fields inside sand piles have not been measured in experiments on sand piles. Averaging is made reproducible by introducing a representative volume element (RVE), the size of which we determine by careful measurements. Stress tensors are studied for both symmetric and asymmetric sand piles in two-dimensional systems, where the particles are dropped from a point source. Furthermore, we determine the fabric tensor inside the sand piles. A surprising finding is the behaviour of the contact density in this kind of heap, which increases where the pressure is at a minimum. The fabric is linearly proportional to the product of the volume fraction and the mean coordination number for a pile consisting of monodisperse mixture of particles. We observe that the macroscopic stress, strain and fabric tensors are not collinear in the sand piles.
Exact calculation of force networks in granular piles
Physical Review E, 1998
We present calculations of forces for two-dimensional static sand pile models. Using a symbolic calculation software we obtain exact results for several different orientations of the lattice and for different types of supporting surfaces. The model is simple, supposing spherical, identical, rigid particles on a regular triangular lattice, without friction and with unilateral springlike contacts. Special attention is given to the stress tensor and pressure on the base of the pile. We show that orientation of the lattice and the characteristics of the supporting surface have a strong influence on the physical properties of the pile. Our results agree well with numerical simulations done on similar systems and show, in some specific cases, a dip, i.e., a depression under the apex of the pile. We also estimate that the algorithm we have developed can be easily adapted to other configurations and models of granulates and can be used in other physical cases where piecewise linear systems are encountered. ͓S1063-651X͑98͒09607-X͔
Effect of Particle Shape on the Stress Dip Under a Sandpile
Physical Review Letters, 2007
The results of an experimental investigation into the effects of particle shape on the stress dip formed under a 2D sandpile is reported. We find good agreement with previous results of a small dip for mixtures of disks poured from a localized source. The new finding is that the dip is significantly enhanced when elliptical particles are used. We attribute the amplification of the effect to orientational ordering induced by the shape of the grains which removes the degeneracy of circular particles.
Stress dip under a two-dimensional semipile of grains
Physical Review E, 2008
The origin of stress dip under the apex of a standard sandpile has stimulated significant debate within the scientific community. On the other hand, it could be argued that a semipile built against a vertical wall is of more practical interest since it serves as a model of dams, dykes, and embankments. There is surprisingly little information available for the stress distribution in this case. Here we show clear experimental evidence that the presence of the wall enhances the dip under a granular pile significantly. Our investigation provides insight into the influence of walls on the orientation of force chains and this appears to be key in enhancing the dip. Moreover, numerical simulations and experiments with different kinds of particles show that the vertical wall induces an alignment of isotropic particles.
The averaged stress and strain response functions of granular aggregates are investigated numerically. We use the discrete-element method (DEM) to generate granular packings consisting of soft convex polygonal particles, i.e., the simulation geometry is two-dimensional. Packings are prepared in a rectangular container. To determine the stress response of a packing, we apply an external load to a single grain from the top layer of the assembly, with a force small enough not to cause structural rearrangements. Measuring the average vertical normal stress response at different heights of the sample, we find that the shape of the stress response function depends on the regularity of the granular assembly. For packings with strong spatial order, the average stress response shows a behaviour corresponding to that of hyperbolic continuum equations. As the amount of contact disorder increases, there is no wavelike stress propagation anymore and a behaviour emerges that would rather be predicted by elliptic equations. Furthermore, we show that not only geometric disorder but also large values of static friction coefficients, which may be linked to force disorder, lead to elliptic equations. Finally, we determine the strain response for a rectangular sample that consists of monodisperse particles.