Just when I was getting ready to produce my final entry on particle packing I realized that so far we haven’t discussed the second most important concept in particle packing – the “wall effect”. First, though, I would like to thank Joe and Mike for their recent guest blogs. I hope to have more guest columns soon.

The wall effect describes what happens when aggregate reaches the concrete form. Since aggregate can’t penetrate the form, only a small portion of the aggregate will be in contact with the form, reducing the density of aggregate adjacent to the formwork. This means that, particularly for a concrete member with a high surface area to volume ratio, the amount of coarse aggregate you can put into concrete is more limited than in mass concrete.

A good example of this is the comparison between a concrete core and a concrete cylinder. When you take a core, the core bit will have cut through coarse aggregate and you will see a lot of aggregate faces on the surface of the core. The aggregate quantity in a core will be consistent with the dry rodded (or dry loose) unit weight of the aggregate. With a cylinder, however, the coarse aggregate particles can’t penetrate the cylinder mold, so you will not be able to put as much coarse aggregate into the cylinder as the dry rodded unit weight would indicate. Either a corner, edge or face of an aggregate particle will contact the cylinder mold. If it a corner or edge the majority of the aggregate will be inside the concrete. Space around the corner or edge will then be taken up by the smaller coarse aggregate or by mortar. Even if you were to polish off the outside millimeter or concrete from a cylinder, you would see very little coarse aggregate.

This also has other implications. A concrete mix that is optimal for pumping through a 5” (125mm) pump line is different from a mix that is to be pumped through a 4” (100mm) diameter pump line. Concrete going into a 6” thick wall (150mm) will require less coarse aggregate than concrete going into a 12” (300mm) wall. Mass concrete can contain more coarse aggregate than any of the above examples. If you examine the next step in the mix design process, if you have less coarse aggregate then you need more mortar, which will require more water and so more cement in order to maintain the w/c ratio.

The wall effect not only applies to contact between the coarse aggregate and the form, but also between the aggregate particles themselves. If you combine a 1” stone (25mm) with a ¾” stone (19mm), the ¾” stone will see the 1” stone particles as a wall. It can’t fit between them easily. On the other hand, if you combine a 1” stone with a coarse sand (like a #8 sand, which is about 1/8” or 3mm) then the coarse sand can easily move around the 1” stone particles.

I haven’t done any tests to confirm this, but I think it is the wall effect that accounts for the fact that the curved line in Joe Dewar’s graph showing combined aggregate density, moves away from the straight lines. I think the amount of the difference will depend on both the difference in size between the two materials and the angularity of both particle sizes. The closer the two different aggregate sizes are to each other the greater the impact of the wall effect. In other words, if the smaller aggregate is too large, it can’t fill the voids created by the wall effect. In addition, the more angular both aggregate sizes are, the greater the likelihood of a point or an edge contacting the form and reducing the available space for coarse aggregate.

In summary, not only do we need to decrease the amount of the larger aggregate particles so they can spread apart and produce a workable mix, but we also need to reduce the larger aggregate particles to accommodate the wall effect. This not only applies to the large aggregate particles vs. intermediate or fine aggregate, but also to fine aggregate vs. paste and to cementitious materials vs. water and air. The wall effect exists for all solid particles, including cement grains.

Now that we have gotten the wall effect out of the way, I think I am ready to finish off the section on Particle Packing. In summary, my thoughts are as follows:

Particle packing is the best way to determine an optimal mix, but it is a real pain to implement. You have to perform a large number of either dry rodded or dry loose unit weight tests using a wide variety of aggregate combinations. Of course, it is easier to perform 10 DRUW tests than it is to perform 10 concrete trial batches. Even so, once you determine the maximum aggregate density blend, that still won’t necessarily produce the best concrete. What is better – take out more rock or to add coarser aggregate, remove intermediate aggregate and use more mortar? Does a mix that requires a high paste content (for whatever reason) need more fine aggregate to create surface area for the paste and reduce void spacing between sand particles? (Ding, ding, ding … can you say “graduate student research topic”?)

In talking to some friends who do this, it appears that it is better to perform dry loose unit weights, rather than dry rodded unit weights. I think this may be because concrete performs more like a loose material until you compact it. Of course, when doing a dry loose unit weight you have to be careful not to compact the material by dumping it rapidly or from a height into the measuring bucket.

Since performing the aggregate unit weight tests is so cumbersome, it would be nice if a computer program could reduce the amount of work necessary. I really haven’t spent the time I should with the MixSim program, but I hope to do so after my busy travel season is over. Francois deLarrard’s BetonLabPro program supposedly helps on this, but my French is awful and I am having trouble understanding it. I can’t find a copy of the Europak program that is supposed to do the calculations. The EMMA program, from Elkem and the Silica Fume Association says it does optimized particle packing, but it really requires that you determine the optimal grading first, then it calculates the best blend of aggregates to meet that grading. It doesn’t help you calculate the optimum combined grading.

It seems that if you could use the old COST program from the FHWA (which it seems is now integrated into COMPASS) you could use its “design of experiments” methodology to minimize the number of unit weight tests that need to be done, then do the tests and fill in the rest of the program. That should give you the optimum combination of materials. However, then you are still left with the dilemma of which direction do you come down off the ternary packing diagram “mountain” to get a workable concrete mix.

If you wanted to develop a mix design methodology for this, you could do the following:

- Calculate the maximum density blend of a coarse and intermediate aggregate. Calculate the b/bo value for the blend.
- Take that aggregate blend and then calculate the maximum density blend of the blended coarse and intermediate aggregate with a sand. Calculate the b/bo value of blended coarse aggregate vs. sand.
- Determine the blend of combined aggregate with a standard paste (like a 0.45 w/c with straight cement [CEM I for the Europeans]) which produces a workable mix. Calculate the b/bo for combined aggregate vs. paste.

I have a feeling the b/bo for all of the above size ranges will be on the order of 0.55 to 0.75. You could continue on to determine the optimal blends of straight cement with pozzolans to improve workability.

Ultimately you would have to look at the impact of different characters of pastes (low w/cm, high w/cm, low pozzolan, high pozzolan, low admix, high admix) and see how the characteristics of the paste impacts the b/bo of the aggregate blend, but that is a topic for another day.

I don’t know if any of this makes sense to anyone but me, but it helps me get a handle on the notion of optimized grading and, ultimately, SCC. If I have confused anyone, please let me know and maybe I can reword things to make them more clear.

Now that I have finished with particle packing, my next series of blog articles will deal with combined grading approaches to mix design. Stay tuned for more “exciting news” from the world of concrete mix design.

Until next time,

Jay Shilstone

### About Jay Shilstone

I am a concrete technologist for Command Alkon, Inc. and have been in the concrete industry for over 35 years. For 28 of those years I have been working on quality control software for the concrete industry. I am a Fellow of the American Concrete Institute and a member of multiple ACI, ASTM and NRMCA committees. I look forward to talking about concrete mix design and quality control with everyone.

## Henry Brummel says:

Another great article! Having been in construction for 50 plus years, I was quite dismayed with myself, that I did not know about the wall effect. Live and learn.