Originally Posted by
ckelloug
greybeard,
First, from what I've read about Silicon dioxide sand, the grains are relative spherical at least much more so that something like garnet. Secondly, and this is pragmatic to use fyffe555's euphemism for not thorough, everyone else doing packing studies seems to assume assumes spherical sand.
The paper you cited from NISS was random packing of spheres of different sizes. The 70% fill rate that they achieve with random packing is only 5% less than the packing of uniform sized identical spheres. They also state that as the size of the spheres added approaches 0 the packing approaches 100%. They got 70% stopping at an arbitrary size some ratio away from the biggest sphere. My gut instinct is that it will scale well to most semi-spherical shapes. Something I saw said the some types of packings actually work better with ellipsoids ?!
Ultimately, there are probably an uncountably infinite number of good aggregate sizing strategies. Fuller's Formula, a formula based on the NISS paper, and the Reichhold formula are but three. Fuller's formula has 100 years of testing in ordinary concrete. I don't have an implementable formula from the NISS paper yet. Finally, the Reichhold formulation was recommended to help them sell resins so it was obviously thoroughly tested.
One must remember that randomness is not something to fear in engineering. It can be controlled and often used to advantage. The niss paper when extended down to the tiniest particles actually approaches 100% packing. Dense packed spheres of any single size do not and I imagine that Dense packet spheres of any number of uniform sizes also may very well not.
Randomness in particle size should essentially cancel out randomness in particle placement.
Thanks c for the posting.
Having some drink taken last night while trying to explain close packing to number one grandson, I think I got random packing of one size particles mixed up with random sized random packing. (chair)
I think it's the former that gives the much lower fill now the head is a little clearer. :tired:
I, too, have some dim memory(25 years ago ?) of the discovery that ellipsoid packing could achieve higher fill ratios than 75% for spheres.
Re mixing and placement of the mix. I have had two ideas.
1. Could a better packing be achieved for the diy molder by mixing all the aggregates except the biggest with the total volume of epoxy first. This would give a lower viscosity "sludge".
Pour a thin layer of this into the mold, followed by a single layer of the largest stones, which would then be pushed down into the sludge, such that excess sludge oozes up just enough to fill the gaps under the stones.
Then another thin pour of sludge, followed by another single layer of stones.
Repeat till the mold is full.
If possible, vacuum reduction of air entrapment, vacuum bagging or vibrating could each or all be applied during the process, along with any other embeddings(sp?) needed.
The idea is to calculate all the different component quantities first, but handle them in a different way. Leaving the stones out of the small aggregate mix giving a better pour, and placing the largest separately giving more controlled distribution, but bringing the final mix back to the required fill density.
2. Could spinning the mold be used as a method of compaction/air release ?
I envisage taking two (for balance)rectangular steel hollow sections held together and parallel, and spun about their central long axis. Each filled with E/G, spinning would drive the fill to the outer sides and the air toward the inner sides of each beam. These would then become the bottom(tension) side of the finished beams.
John
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