Nov. 8, 1999 DURHAM, N.C. -- Researchers at Duke University have shown in careful experiments that not all sandpiles are the same. The pressures under some are highest at their centers. But the stresses under others get shifted outwardly much like loads are transferred from the walls of some medieval cathedrals.
It all depends on how the sand heaps are formed, and the take-home message is that "small changes in the history of preparation have an extraordinarily dramatic effect," said Robert Behringer, a Duke professor of physics.
These experiments, which were supported by the National Science Foundation, have practical importance because unbalanced distributions of stresses can lead to the self destruction of structures like coal and grain silos, he said. Coal, like sand, is a granular material, a class that includes objects as diverse as breakfast cereals and ice crystals.
Behringer, who recently became chairman of Duke's department of physics, is a long-time investigator of granular materials, which are regarded as almost a separate state of matter because they exhibit features of both solids and liquids.
In a report published in the Nov. 1 issue of the journal Physical Review E, Behringer, his doctoral student Daniel Howell, collaborators from France, and Dahl Clark û a then-high school student at the North Carolina School of Mathematics and Science who is now a Duke undergraduate û found that sand flowing unimpeded out of funnels builds up piles with an underlying pressure "dip" where logic would say there shouldn't be.
Contrary to what intuition would suggest, the largest stresses do not get concentrated under these piles' very centers, but are instead shifted to a surrounding zone some distance away.
The picture reverses itself when sand is made to "rain" down in generally distributed showers instead of pouring out in a concentrated granular torrent. Then the resulting sandpiles don't transfer their stresses from the center but instead focus them there, just like reason would suggest.
These experiments, done in collaboration with French researchers Loic Vanel and Eric Clement, addressed a controversy that has been raging among scientists who study the flow of granular materials.
"There were a lot of very strong words that flew back and forth," Behringer said in an interview. "People were fighting it out in public meetings with very strong statements about the quality of each other's models."
When some physicists' mathematical models and experiments began showing that sand piles could concentrate their stresses off-center, scientific skeptics were quick to object. According to Behringer, detractors blamed these results on subtle defects in the way the experimental sandpiles were constructed. Another possibility was stress detector inaccuracies.
The experimenters at Duke joined the others at the University of Pierre and Marie Curie in Paris to dispel the controversy by designing new tests that were especially precise.
They build up sandpiles in two different ways. In one, sand flowed out of narrow openings at the bottom of cone and wedge shaped funnels. In the other, sand was more generally distributed by showering it out through an additional pattern of sieves.
They also took special pains to keep the energy of falling sand constant by raising each funnel's and sieves's height as the sand piled higher underneath. And they made stress measurements at different places under the piles, using sensors of different thicknesses.
Their results were consistent. Sand that poured directly out of the mouths of the funnels always formed piles with off-center stresses. But sand whose flows were broken up by sieves didn't.
To study why, the researchers also built skinny "2-dimensional" versions of the experiments out of clear plastic and cardboard. That way, they could watch what amounted to cross sections of both types of sandpiles building up.
But instead of sand, the experimenters substituted special flexible "photoelastic" disks that affect light differently in response to pressure and thus appear to glow. By shining light through the them, they could thus observe where stresses were forming within the growing 2-D piles of disks.
Each disk that glowed represented a sand grain that was carrying more stresses than others. The glowing disks linked up into networks of "stress chains," which look like jagged lightning bolts when so illuminated. And, by comparing the results, the researchers found that stress chains inside the two different kinds of sand piles formed different patterns, Behringer said.
He and Howell previously reported on their stress chains research at a March 1998 meeting of the American Physical Society.
"If you pour grains directly out of a funnel, they avalanche down to the surface and what that does is create stress chains that are aligned almost like flying buttresses," he added, pointing to a picture of Paris's Notre-Dame cathedral on his office wall.
Flying buttresses are curved structures that transfer some of the wall loadings of such cathedrals towards the ground some distance from the center. And in the case of funnel-poured sand piles, "you are literally building similar arches into the granular material," he said.
In contrast, "if you pour the sand out through a sieve instead you don't build up those outward-slanting arches," he noted. "Everything is piled straight up and down as with a big chunky wall. So the force at any given spot will be determined by how much material is directly overhead." That means the highest pressure is under the central peak.
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