For as long as I have been around concrete the two primary methods of proportioning concrete mixtures have been ACI 211 and British Road Note 4. Of course it seems that every country, government office and consultant has their own favorite mix design method, but as far as I know, those are still the only two internationally recognized methods for “concrete mix design”. Of course, growing up on the west side of the “pond”, I learned ACI 211. So why am I lumping ACI 211 in with particle packing procedures? It doesn’t use the ternary packing diagram so common in contemporary particle packing discussions. Instead ACI 211 simplifies particle packing by starting with the maximum packing of the largest particles (coarse aggregate), then provides a guide to reducing the coarse aggregate to produce a workable mix.
Before I get too much into the basis of ACI 211, let’s go back and look into its origins. I really need to go back and learn more about the early history of concrete mix designs, but my understanding is this. Back in the early 1900’s there were no “standard practices” for developing concrete mix designs. In 1907 Fuller & Thompson performed their studies, The Laws of Proportioning Concrete (1906), on optimized aggregate grading. Apparently there were also studies by others based on maximum density, but Duff Abrams dismissed them in Design of Concrete Mixtures, Bulletin 1. Instead Abrams developed the Fineness Modulus and based his mix design theories on combined fineness modulus of both the coarse and fine aggregate. Then, in 1942, A.T. Goldbeck and J.E. Gray published their seminal work, A Method of Proportioning Concrete for Strength, Workability and Durability (http://aftre.nssga.org/Technical_Reports/A_Method_of_Proportioning_Concrete_for_Strength_Workability_and_Durability_1968.pdf) for the National Crushed Stone Association. This is where the b/bo concept, which is used in ACI 211, was first introduced. Although the original document addressed pavement concrete mixes, the b/bo method is applicable to all types of concrete.
The b/bo method can be summarized as this: First, fill a container (like a cubic foot, cubic yard or cubic meter) with the maximum amount of coarse aggregate possible and weigh the coarse aggregate. This is bo. Next, since the aggregate in a container isn’t workable, figure out how much stone you have to take out of the the container, b, and replace that stone with mortar plus fill the voids between the remaining stone particles. The ratio b/bo is the percent of the maximum stone quantity that can be used in concrete while still producing a workable mix. NOTE: If you compare the b/bo table in Goldbeck and Gray’s report with that used in ACI 211, the two are different. That is at least partly because the Goldbeck and Gray table was for pavements while the ACI 211 table is for all concrete.
The original Goldbeck and Gray table is below:
The corresponding ACI 211 table is as follows:
If you read between the lines of the b/bo tables you can deduce a couple of other truisms about concrete mixture proportioning:
1) As the maximum aggregate size of the stone becomes smaller it is necessary to have a higher proportion of sand (the b/bo value goes down)
2) As the sand becomes coarser (the fineness modulus increases) it is necessary to have more sand (again, the b/bo value goes down)
So even though ACI 211 doesn’t use fancy ternary packing diagrams (that even I have a hard time understanding) in reality it is a particle packing technique which considers not only maximizing coarse aggregate, but also obtaining a workable concrete mix. It takes into consideration aggregate grading, as well as empirically accommodates particle shape and texture, two things we can’t currently quantify otherwise (at least not easily).
This raises and interesting question for me. If this technique works for stone particles separated by mortar, why can’t it work for sand particles separated by paste, or cementitious particles separated by water and air? Based on what little “research” I have been able to do, which amounts to asking a couple of friends in the ready mix business to perform dry rodded unit weight tests on sand, the technique does work. When you make mortar you have to separate the sand particles by a similar percentage as is found in the b/bo table. When you make paste you have to separate the cement particles by a similar percentage.
CALL TO ACTION!: If you are a student looking for a thesis topic, here is a great one. It shouldn’t be too hard. The hardest part would probably be assembling a variety of aggregates (rounded vs. crushed, flat vs. cubical) and cements to produce a valid range of values to include in a b/bo table. I just ask that if you do the work, you let me see your results.
As a final thought, all of the above theory is based on conventional concrete, where we maximize coarse aggregate to minimize paste demand while still producing workable concrete. If we want to switch to self-consolidating concrete there are other factors at play, such as increasing fluidity while maintaining cohesiveness. My first assumption is that for SCC we need to start the mix design not with the coarsest aggregate sizes, but with the amount of water and cement necessary to produce a fluid, yet cohesive paste, then use the aggregate to create a “home” for the paste. Do any of you SCC gurus out there have a comment on how SCC and b/bo relate?
This concludes my post for the day. As always I look forward to any comments you have.
Just a little orientation note – I try to post to my blog every other Monday at about 1:00PM Dallas time. Sometimes, when I have special topics such as an industry technical meeting, I will post on the Mondays between. For the next few weeks I will be addressing more aggregate topics, such as particle packing and combined grading techniques, then move on to paste determination. After that, who knows? If you have a topic you would like for me to address, just let me know.
Until next time,