# theoretically the strongest concrete

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From one book on masonry I get a mix for concrete as such:

1.6 cement :: 3.2 sand :: 6 gravel

From another masonry book I get this for concrete mix:

5 cement :: 12.5 sand :: 20 aggregate or gravel

For mortar I get this as a mix ratio:

1 portland cement :: 1 lime :: 4 to 6 parts sand

What I am wondering is like a checkerboard or chess board where the white squares are each one particle of portlandcement and the black squares are each one grain of sand. And that the strongest and ideal mix to make both Concrete and to make Mortar is simple this ratio:

1 portland cement to 1 of sand

So that each sand particle is connected to other sand particles by the portland cement between them. Trouble is getting a mix so that it is perfectly mixed as to result in a 3-dimensional perfect packing such as a chessboard is a perfect 2 dimensional packing.

Has anyone done experimental tests to see at what ratio of portlandcement to sand yields the strongest most durable concrete??

I would hazard to guess that if uniformly mixed that the 1 to 1 mix is the strongest.

Is there any proof to my above assertion?

Archimedes Plutonium, a snipped-for-privacy@hotmail.com whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies

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What you are asking isn't as easy as it sounds. Concrete is not like a checkerboard, where all the squares are the same size and shape. Concrete is a combination of rock, sand, cement and water, all of varying sizes and shapes (or amorphous).

Think of it this way - in woodworking the strongest glued joint is the thinnest one. Concrete is sort of the same way. Water surrounds the cement particles to make paste, and you want the least amount of water. Paste surrounds sand particles to make mortar, and you want the least amount of paste. Mortar surrounds the rock particles to make concrete, and you want the least amount of mortar. You could theoretically calculate all this for spheres, or using computer simulations, but the National Institute of Standards and Technology uses super-computers to do it, and is just now, after about 10 years, getting to the point where they can do it. Actually, their program doesn't optimize the concrete, it just tries to predict what the specified concrete will do.

If you are familiar with the subject, you might comment on my question on "Predicting spherical packing of multiple particle sizes" from last week.

Jay Shilst>From one book on masonry I get a mix for concrete as such:

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I would imagine that civil engineers have studied topic this just about to death. The answer is probably dependent upon the sand particle size, salt, temperature history of the cement, amount of water available, etc.

Michael

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It should be easy to research and find the answer. One easily can get a uniform grade of sand and see if a 1 :: 1 mix is stronger than say a 1:: 2 mix and various other mixes.

What is intriguing about the strongest concrete is that it is sort of like another Kepler Packing Problem where the spaces between the balls is filled with portland cement.

So, in the Kepler Packing Problem in 3-d, each sphere is surrounded by how many gaps?

Perhaps the strongest concrete is a direct result of the Kepler Packing Problem.

I proved the Kepler Packing Problem as that of "kissing points".

So if you are going to pose a different problem with variable particle sizes, this new problem is also solvable once you factor in the adjustment of "kissing points". For example, say you have 60 balls of which 1/3 are one size, and 1/3 another and the last 1/3 another, then once you factor in the new kissing points to determine the smallest packing, well, you are on the way to a generalized formula for variable packing sizes.

As for Concrete and the maximum strength, I believe it is somewhere near a

1 :: 1

mix, where 1 is portland cement and the 1 part sand is of uniform size and where the mix is so well mixed.

Archimedes Plutonium, a snipped-for-privacy@hotmail.com whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies

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As I understand it, the cement is much smaller than the sand, and chemically reacts with the water as it solidifies. The actual material giving strength to the material is the sand and gravel, the cement just holds that together and fills in the gaps between the particles. The use of steel rebar is a common way to strengthen the concrete (concrete is an ideal environment for normal steels as long as salts aren't present), but fiberglass, rubber, and perhaps other materials can also add useful characteristics to the concrete (respectively, resistance to crack formation and flexibility).

Water in the original mix is bad. You've probably already noted that the recipes state to use as little water as possible to wet the mixture. There are surfactants that can reduce the amount of water required for your concrete. Reducing water in the mix is another way to strengthen the concrete since little water pockets in the concrete apparently create flaws in the material.

The mix ratios you mention have been tried and tested IMHO and are probably really close to being optimal. Incidentally, when I looked on the Internet for details on small batch preparation of concrete, I found a lot of useful information from instructions for small house projects to art-related websites. You should be able to find good information on small-scale concrete projects if that's your inclination.

Karl Hallowell snipped-for-privacy@hotmail.com

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Okay, it is hard to get a uniform sand mix.

So let us do a research on something that is perfectly uniform. That of steel balls of the size of marbles and BBs. Where the marbles are gravel and the BBs are sand.

Now the question is, what mix ratio of Portland cement to make a cubic foot of concrete that has marbles and BBs and is the strongest cubic foot.

I still suspect the final answer to be a cubic foot wherein only BBs are used and the ratio is close to a 1 :: 1 in terms of volume. Say perhaps 10 liters of portland cement and 10 liters of BBs.

Trouble with various sizes of aggregate is that it allows air pockets which diminish strength and cause cracking.

So I am guessing that the strongest mix ratio is a 1 to 1 ratio using only BBs and portland cement.

And I am guessing that the perfect piece of concrete is one in which there is a Kepler Packing and where the portland cement is in between the voids of the Kepler Packing.

I wonder if someone can arrange for a Kepler Packing of steel BBs and infuse the crevasses between the BBs or take marble size steel balls and Kepler Pack them and then infuse the interstatials with portlandcement. I have the hunch that such a block of concrete would be the strongest such block over any other such block having a different arrangement of those BBs and marbles. And obviously the ratio is no longer a 1 :: 1 because if memory serves me (mathematician would know) that in a Kepler Packing that the gaps are something like 23% of the volume and so the ration of cement to balls would be closer to that of 1 :: 4

Archimedes Plutonium, a snipped-for-privacy@hotmail.com whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies

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I can't imagine the answer being independent of the actual particle shapes. When studying the suitability of different sources of crumb rubber as an asphalt filler, for instance, it was found that rubber that was ground after cryogenic treatment resulted in a drastically less strong compound than rubber that was ground at room temperatures. This was determined to be because the cryogenically treated crumb had shear surfaces, like faceted gems, which provided less surface area to grip its binder than the more complex surfaces of the other crumb.

If different sources of sand produce significantly different particle surface textures, then I would think the strengths of compounds made of them would have different physical properties. I am no expert on sand, though, so I have no idea if particle surface texture varies or not.

Getting back to the original question, I think it would depend on exactly what kinds of "strength" was needed from the concrete compound. Adding different things to the mix (straw, dung, sawdust, rubber, steel rebar, hardware cloth, etc) can improve the strength/density ratio, or the resilience, or the total blunt trauma energy absorbed per unit mass of the compound, albeit possibly at the detriment of hardness or absolute flexural, shear, or tensile strength. Even if the concrete is only used to support a load which is static most of the time (eg, the foundation of a building), there may be other factors which complicate things, like occasional dynamic loading (Californian earthquakes), or water erosion (rain), etc. There is no single best formula for everything.

-- TTK

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Sharp sand and aggregate makes much stronger concrete than smooth sand and aggregate.

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well, they have, but as any empirical science (sorry, I just had to write that) there is still a lot of room for improvement. Unfortunately i don't know the right english words for the coming remarks; i hope it is still understandable. Often highest strength is not the aim, but early strength to allow quick formwork removal, or low porosity (high density) to make a barriers for ground water protection etc. Concretes are optimized to set under suboptimal circumstances like low/hi temperatures, short times in formwork, low viscosity, very long/short pot life.

The posed 1:1 optimal concrete theory has no basis... a sand grain is a sand grain is a sand grain...silicon dioxide... a dead dog.. the "cement" however is more or less reactive depending on where it comes from, it is not a defined substance.. pure CaO has completely different setting behaviour than fly ash cements. Silica fume, plasticizers and thousands of other additives make this a real witchcraft system. So no 1:1 ratio, neither m:m, nor v:v or mol:mol have the slightest chance of being a general rule, let alone specify some concrete mixture. The quality of the concrete widely varies even with the same cement/sand ratio (and using the exact same materials in different experiments) with different water/cement ratios. Depending on water content of the sand, its specific surface, the quality of the cement etc., the "brickie" on the building site has to slightly modify the recipe every day to just get the ideal, same consistence.

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Well yes, there is a direct link with theory and with analysis. We have the Kepler Packing to be applied to concrete and to see if the Kepler Packing is a better concrete than the theory of 1 :: 1 mix of a 3-d chessboard mix.

I forgotten the 3-d Kepler Packing percent of voids. Was it somewhere around

23% voids? Let us say it was. So that a Kepler Packing Concrete mix would not be a 1 :: 1 mix but a 23% :: 77% mix or a 1 :: 3 mix.

Experiment: It should be easy to experiment as to whether a Kepler Packing concrete mix is superior to a 1 :: 1 chessboard mix. In that we get marble sized

balls and Kepler pack them in wet cement. We then pack some marbles in a configuration of a chessboard where the marbles and cement are in a 1 :: 1 ratio. We wait for the two samples to dry and harden. We then test them for superiority of one over the other.

Archimedes Plutonium, a snipped-for-privacy@hotmail.com whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies

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Part of the problem also revolves around the fact that the more water that is added to the concrete, the lower the strength. We do not have a binary (marbles and B-Bs), or a ternary mix (marbles, B-Bs and cement), but a quaternary (4 part) blend of marbles, B-Bs, cement and water. Studies have shown that we can reduce water by getting a good blend of large and small particles (marbles and B-Bs). If we just have

1 size particle, the water demand goes up and strength goes down. Some studies have shown that reducing the maximum aggregate size will increase strength, but we still need a variety of particle sizes to minimize water demand.

I am a concrete technologist, not a mathematician. If you know of a computer program or web model that will predict voids in a Kepler Packing system using a variety of sphere sizes, I would like to know where.

Thanks, Jay Shilst>

balls of the size of

concrete that has marbles

and the ratio is close to

liters of BBs.

diminish strength and cause

and portland cement.

Kepler Packing and where

the crevasses between the

interstatials with

strongest such block over

me (mathematician would

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it may have to do with Kepler's problem, but a) using BBs will weaken it (too heavy), and b) "aerocrete" is actually stronger than that using sand: the aggregate has no tensional strength, between any two chunks. the thing about Portland Cement is that it's stronger, the longer it takes to dry -- so keep dousing it.

diminish strength and cause

and portland cement.

a Kepler Packing and where

the crevasses between the

interstatials with

strongest such block over

serves me (mathematician would

--Dec.2000 'WAND' Chairman Paul O'Neill, reelected to Board. Newsish?

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for uniform-ball "aggregate," teh cement is the complement to the volume of the ball, inscribed within a rhombical dodecahedron; I think it's got pi and 18 in the ratio, as per Kepler's problem, about a fifth left-over. (congratulations on your proof via kissing; you've beat Hale, at last .-) I wasn't aware taht "sharp" sand is better, either. however, assigning a simple "1/3" ratio of various sizes will not be easy

-- no easier than Kepler's problem.

--Dec.2000 'WAND' Chairman Paul O'Neill, reelected to Board. Newsish?

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balls of the size of

concrete that has marbles

and the ratio is close to

liters of BBs.

diminish strength and cause

Actually, I'm not sure that this is the case. I can see that the sand would fill in the gaps between the larger aggregate, and the cement in turn would fill in the gaps between the sand. OTOH, you probably would get more air than with sand-sized aggregate alone.

Also, would a marble sized glob of BB's cemented together be stronger than a steel marble of the same size? I think not. It indicates to me that the large aggregate is probably responsible for most of the strength (perhaps in some random almost kissing structure) with the spaces filled by cement and sand.

and portland cement.

a Kepler Packing and where

the crevasses between the

interstatials with

strongest such block over

serves me (mathematician would

This seems more reasonable to me. I notice that there appears to be a sparseness of the larger stronger stuff (by volume). Ie, the large gravel should be 4 over the smaller stuff and cement combined. Instead it's slightly better than 1. The sand to cement ratio is a little over

2-1 with pure sand in cement around 3 to 2.

I see a couple of reasons this theoretical limit isn't reached. First, the concrete when poured needs to be sufficiently fluid to be usable (and other people have mentioned the various other attributes that usable concrete needs depending on the application). That appears to be a significant constraint and may be the sole reason for the low ratios of large aggregate to the space filling material. Second, the material as you note is usually randomly packed. I don't know how inefficient that is. One way to improving the packing would be to compress the concrete while it's still wet. That would force the aggregate into a more optimal packing, and squeeze out air and perhaps some of the water. I seem to recall that this is done for some applications (and the weight of a large amount of concrete tends to compress the buried sections).

Karl Hallowell snipped-for-privacy@hotmail.com

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I consider the water as temporary.

If it turns out to be true that the best or optimum mix of concrete is a ratio of that corresponding to the Kepler Packing Problem where the density is

pi/3sqrt2 or approx 74%

Then that would entail a concrete mix of approx 1 :: 4 ratio for superior concrete.

Jay, you say you are a concrete expert. I wonder if you also have studied asphalt such as road blacktop.

Where instead of the glue as portlandcement, the glue then becomes tar.

Now, I wonder if the best or optimum asphalt blacktop is also a ratio of 1 :: 4 for 1 unit of tar to 4 units of aggregate.

It would seem to me that the Theory of glues for the optimum product that there should be no difference in ratio for the blacktop and for the concrete. And that the superior concrete should follow the same Kepler Packing theory as does the superior blacktop.

But, however, if the optimum concrete and blacktop follows the 3-d chessboard pattern and not the Kepler Packing pattern would indicate the the ratio is that of 1 :: 1 of 1 unit of portlandcement to 1 unit of aggregate, likewise blacktop of tar and aggregate.

I suppose I can conduct this Experiment but the blacktop would get awful messy.

If the Experiment turns out that Kepler Packing is the optimum blacktop and the optimum concrete mix, then the question arises as to whether this is a Coincidence or whether the Kepler Packing is the geometrical equivalent of the optimum material product of strength and endurance. I suppose physics would say that the density and the most dense object is tied to strength and durability.

Archimedes Plutonium, a snipped-for-privacy@hotmail.com whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies

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Karl Hallowell wrote: (snipped)

In the optimal strength and durability of concrete, I am not sure whether sand alone is superior or less superior than a sand and gravel mix. Mortar has to be tough to hold together block and brick and it is sand only.

Well the problem originally was concrete mixes and sure I can find a whole different material stronger than a concrete block.

This is where experiment is needed. To find out if a 1 :: 1 mix of portlandcement to sand is better than a 1 :: 4 mix of 4 parts sand.

I need to find out how the Kepler Packing relates to the optimal mix of concrete and blacktop. Where the density of the Kepler Packing is that of pi/3sqrt2 or about 74% which yields a mix ratio of somewhere between 1 :: 3 to 1 :: 4

Archimedes Plutonium, a snipped-for-privacy@hotmail.com whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies

• posted

The water isn't temporary, except that after 60 years all the cement that can combine with the water has done so. Water remains in the pores of the concrete for decades. Even in the desert it can exist inside the concrete for years. The product of the water - cement reaction is actually smaller than the individual components, so even when the water reacts, a space remains. However, the more water initially in the mixture, the lower the concrete strength at any given time.

I am not an asphalt expert, but I know a bit about it. There was some work done by Fuller and Thompson back in the 1950's that resulted in the .45 power chart, which is used in asphalt. A graph is drawn where the X-axis is the aggregate particle size taken to the .45 power (with a specific set of sieves used for determining the aggregate gradation). The Y axis is the percent of aggregate that passes each sieve. A line is drawn from the origin of the graph (0,0) up to 100% passing the largest nominal size of the aggregate (say 3/4"). The "optimal grading" for asphalt falls near this line. Some studies have shown that if the grading falls directly on the line (which can be done in the lab but not in real life during production) the aggregate can have so few voids there is insufficient room for the asphaltic binder. I don't know if Fuller and Thompson ever compared their work to Kepler's.

There is a guy named Joe Dewar in the UK who has done a lot of work with designing concrete based on aggregate voids. I won't post his email address in an open newsgroup, but you can probably find him on the web. He has a computer program called MixSim for concrete mix designs. (It competes with our seeMIX program.)

Jay Shilstone

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Thanks James. I am having a difficult time of envisioning that .45 power and how it relates to the quantity of tar versus aggregate. Whether it relates at all to the amount of tar used.

Just from looking at blacktop, I suspect the ratio of mix is that of 1 :: 1. Where one part is tar and the other part is aggregate. Am I correct or wrong, James?

Archimedes Plutonium, a snipped-for-privacy@hotmail.com whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies

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Our group in Grad school did quite a bit with particle packing. The computer algorithms were originally developed for a coal water slurry project (in the 70's). - size the coal - mix with water - pump and burn like oil. The short answer is - it worked - the DOE built built a large pilot facility in Fl and it was fully operational. (75 vol% coal with viscosities below 100cps and no dilatent behavior below

2000sec-1 shear rates) Why don't you see now? -
1. oil prices came down
2. railroads would not give right aways for the pipelines
3. you can see it in operation in china - they stole the technology.

The packing efficiencies can be calculated on a spread sheet from algorithms developed on a VAX (no super computers - just good imaginative science/ engineering) (Engineering is the key word because the model parameters and later confirmed by experiment - did not have any derived fundamental significance.) I know for years the group was trying to determine the fundamental significance of the parameter values with out much success. The procedures are given in detail in Predictive Process Control of Crowded particulate Suspensions by Funk and Dinger. ISBN 0-7923-9409-7

I know Dinger sells excel addins for \$100.00 or so. I use my own spreadsheet - very clunky - but it works

Gregg

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Look at an earlier post I made to this thread - If you need a spread sheet for the calculations I have one based on the Dinger-Funk distribution. e-mail me - it really clunky - if it works you may want to buy Dinger's ad-in It works extremely well for large particle size distributions. I found that when the distribution was under 1/2 decade it didn't predict packing as well.

steel balls of the size of

foot of concrete that has marbles

used and the ratio is close to

10 liters of BBs.

which diminish strength and cause

only BBs and portland cement.

there is a Kepler Packing and where

infuse the crevasses between the

the interstatials with

the strongest such block over

serves me (mathematician would

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