Concrete Mix Design: Art and Science – Introduction to Particle Packing

The next few articles in this series will discuss particle packing techniques for proportioning aggregate. The concept behind particle packing is that the more coarse and fine aggregate that can be placed into a container, like one cubic yard or one cubic meter, the less room will be available for paste, meaning that both water and cement can be reduced. The part that is usually unspoken when discussing particle packing is that the resulting concrete mix must still be workable.

As mentioned in previous posts, both Duff Abrams and the SHRP program discovered that concrete mixes with maximum particle packing are not the best mixes. In Lewis Institute Bulletin 1 – Design of Concrete Mixtures, written in 1918, Abrams said “We have found that the maximum strength of concrete does not depend on either an aggregate of maximum density or a concrete of maximum density…” Unfortunately he never cites a reference for this statement. However, I think that since Bulletin 1 was based on over 50,000 concrete and mortar tests, Abrams had justification for his assertions. [Note: At one point I contacted the PCA to find out if Abrams original notes and data were still available and was informed that they were destroyed by a flood in their basement back in the 1960’s. What a loss! With today’s computer power I bet we could have improved on Abrams analysis using his own data.] Ultimately Abrams went on to use the Combined Aggregate Fineness Modulus as the basis for his work. We will discuss this in a future blog post.

Particle packing objectives

If we go back to basics of particle packing, we need to confirm our two objectives: 1) Minimize the void space between the aggregate particles (coarse and fine combined) so we can minimize water demand and so minimize cement content, and 2) provide a workable concrete mix. In looking at the first objective, we must understand that void content in aggregate will be dependent on two factors: 1) Particle size distribution, and 2) Particle shape and texture.

Particle size distribution is composed of two factors: 1) Maximum aggregate size, and 2) Combined aggregate grading. ACI 318-11, Structural Concrete Building Code, para. 3.3.2 cites requirements for maximum aggregate size based on the dimensions of the element being cast and the spacing between reinforcing steel bars. Of course there may be other limitations, such as the desire to pump the concrete or to avoid D-cracking in pavements. However, the actual maximum aggregate size is irrelevant for this discussion as the same concepts apply to all aggregate sizes. Typically we want to use the largest practical size of aggregate available, usually 3/8” to 1-1/2” (10mm-38mm).

Aggregate PackingThe combined aggregate grading objective is to first fill as much of the volume as possible with the largest available particle sizes, then fill the spaces between those particles with the largest particles that will fill those spaces. When people do this calculation theoretically, they usually simplify things by considering the particles as spheres. At this point these discussions start to get messy and use terms like “face centered packing (cubic packing)” and “body centered packing”, which I would like to avoid. If you really want to dig into it, check out the following reference:

Let’s take this to the extreme and assume you are able to perform this packing almost perfectly and produce a particle size distribution that has almost zero voids. (I say “almost zero” because even if you get down to atom sized particles, you will still have voids between the atoms.) If all the particles are perfect spheres, you might be able to get the mass of particles to flow. However, if there is any angularity to the particles at all, you will not be able to get the mass to flow unless you introduce excess paste (or fluid), which will increase the void spacing between the aggregate particles and you will no longer have perfect particle packing.

The Real World

SeparatingParticlesNow let’s come back to the real world. Mother Nature doesn’t give us perfectly spherical aggregates to work with. Even if she did, many of them would be too large and we would have to crush them, resulting in non-spherical aggregates. We actually have to separate the aggregates and fill the resulting space with a fluid (or semi-fluid like cement paste) to get the combined mass to flow. The more angular the aggregates the farther we have to separate them to produce a flowable mix. For example, assume you walk on to a crowded elevator. If you keep your arms at your sides, you can probably turn around as long as the elevator isn’t too crowded. However, if you stick your elbows out and try to turn, you will be unable to do so until some of the people get off the elevator. (If you are obnoxious about it and try to turn anyway, people will probably get off the elevator sooner, but only after making certain you have a few extra bruises for your efforts.)

In Bulletin 1 Abrams later went on to state that to get the best mix you must use a coarser blend of materials than is appropriate for maximum aggregate density.  He never explained his reasoning, but I assume it is to force there to be more voids in the concrete to accommodate more paste and produce a more workable mix. This is one reason I wish we had Abrams notes. He was working with a paste that was composed of only cement and water. He was also working with mixes with a limited slump range. I think that with today’s materials and our higher slumps, we have to consider a third factor – cohesiveness. Not only do we want to produce a workable mix, we also want to produce one that doesn’t segregate. However, this is a discussion I want to save for a future blog post.

OptimumAggregateBack to the matter at hand, if you want to prove or disprove Abrams’ assertions about the usefulness of a maximum density aggregate or mix, it is relatively easy. Back in the 1970’s, when my father was developing the Coarseness Factor Chart, he ran a series of mixes ranging from over-sanded to too rocky. He found that there was a combination of aggregates that had the lowest water demand required to produce a constant slump. In this series he held cement content constant, varied the ratios of coarse and fine aggregate, and added water to produce a constant 4 inch (100mm) slump. The actual optimum combination of materials he discovered is immaterial, since each pair of materials will have a different optimum. Finer sands will usually reach optimum with less sand while coarser sand blends will require more sand. For each combination of aggregates, create a batch of combined aggregates blended at the same percentage levels and perform a unit weight test on the combined aggregates (it won’t be easy since the aggregates will pack pretty well and rodding the combined aggregate will be difficult.) According to Abrams the highest strength concrete will not be at the maximum aggregate packing density. It would harder to prove Abrams other statement, that the maximum density concrete doesn’t result in the highest strength, since water content would be our only variable and the highest strength concrete would occur at the lowest water content, and presumably the highest density. You might have to cast a series with a constant w/c ratio paste, like 0.50, and add paste to each aggregate blend until you achieved a 4 inch slump, then measure the unit weight of the concrete.

Note: I just calculated the specific gravity of a paste with a 0.50 w/c ratio and it was about 1.83. If you believe the notion that you have to separate aggregate particles to get a workable concrete, that implies that you could produce a heavier concrete mix by not adding all the paste required to produce the designated 4 inch slump, but then that mix wouldn’t be as workable as the mix with the extra paste. If you held out sufficient paste, the resulting mix would be difficult to compact in test cylinders, resulting in a possible low concrete strength. Even though Abrams never explained his assertion that maximum density concrete didn’t produce the highest strength, this could be one possible explanation.

I still haven’t spoken much about particle shape and texture, but this post is getting long already. I will save the shape and texture discussion for a later post, but I think it is readily understandable that the more angular a particle is, the more space you will need between particles in order to get a flowable mix. Therefore it is desirable to minimize the number of angular particles or to reduce the angularity of the particles.

I also haven’t discussed the effect of gap-graded aggregates vs. well-graded aggregates. I have discussed that a bit in this series already and will add more later. If you want to read about it now, check out

If you really want to study voids and particle packing, check out Joe Dewar’s book, Computer Modeling of Concrete Mixtures, available  at Amazon at Also, Francois de Larrard’s book Concrete Mixture Proportioning is a great reference.

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.

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