Concrete Mix Design: Art and Science – Coarseness/Workability Factor

Probably the most common request I receive is for an explanation of the Coarseness/Workability Factor method of mix design, sometimes called the “Shilstone method”. About 6 months ago I did a survey of concrete producers around the world about mix design methods and was astounded to find out that 50% of them, including international, used the Coarseness Factor method to design concrete mixes. My father would have been very proud of this, since he developed the method. If you want the long, more technical explanation of the method you can download an article my father wrote about it at For this blog post I will be giving you a summary of the process.


It all began in about 1975. My father, Jim Shilstone, was working with the U.S. Army Corps of Engineers on the Saudi Arabia National Guard Headquarters. The Corps was trying to use local materials for the concrete, but the materials were outside of ASTM limits (the sand was very fine) and ACI 211 wasn’t applicable. Their original mixes were not performing as they wanted. Finally my father and the Corps decided to start from the beginning.

The Corps shipped a bunch of the local Saudi material to their Materials Lab in Athens, Greece. (Wouldn’t you like to run trial batches in Athens?) First they cast a series of mixes with a fixed 6 sacks of cement (564 lbs/cyd or 335 kg/m^3, but this was back when they still talked about “sacks”) and had increasing percentages of coarse aggregate. The mixes had no air entrainment and all produced a constant slump. They discovered that for a given stone and sand, there was an optimum proportion of the two which resulted in the lowest water demand and the highest strength. Presumably, adding more sand to the mix increased surface area, which increased water demand. Adding more stone resulted in a greater stone-to-stone contact, meaning more water had to be added to provide lubrication to the mix. The problem with the optimum combination mix was that it was too rocky. Even though the mix was good for footings, grade beams and larger masses of concrete, more sand was necessary to develop a mix for pumping or finishing in a slab. The amount of additional sand necessary depended on the application, such as pump line diameter and thickness of slab.

Optimum Blend of 2 Aggregates
Optimum Blend of 2 Aggregates

After determining there was an optimal combination of the original rock and sand, the question came up regarding how different types of rock and sand should be combined. Various mixes were cast using differing maximum aggregate sizes and aggregate gradings. The resulting hodge-podge of mixes couldn’t just be compared using a single number like the coarse aggregate percentage. Instead it was necessary to evaluate the mixes in a fashion that reflected the percentage of coarse and fine aggregate, and the relative size and fineness of each aggregate. After looking at the work done by Weymouth on particle size distribution, my father started to look at aggregate as shown in the image below.

Aggregate Sizes
Aggregate Sizes

Coarse aggregate typically ranges from 1-1/2” (37.5mm) to the #8 sieve (2.36mm). Yes, it is defined as material that is retained on the #4 sieve, but some of that material can pass the #4 and act like sand. Sand is the material that passes the 3/8” (9.5mm) sieve and goes down to the pan. When you look at the coarse and fine aggregate together, you find that +3/8” material all comes from the stone, – #8 material mostly comes from sand, but in the middle, from 3/8” to #8, the material can come from either coarse or fine aggregate. My father created the Coarseness Factor chart, where the X axis indicated the relative coarseness or fineness of the +#8 aggregate and the Y axis indicated the quantity of sand passing the #8 sieve. Thus 3 variables could be plotted on a 2 dimensional chart. The mixes that the investigating team produced were plotted as follows:

Original Coarseness Factor Chart
Original Coarseness Factor Chart

The Y-axis is easy to understand. To move a mix “up” on the curve, use a higher percentage of sand. To move it “down” add more rock. The X axis is a little harder to understand in that it shows the relative size of the coarse and intermediate aggregate. To move to the “right” you must either use a smaller maximum aggregate size or add intermediate aggregate (passing the 3/8” sieve) to the mix.  To move to the “left” you must increase the maximum aggregate size or remove material passing the 3/8” sieve. If you have only 1 rock and 1 sand, moving up and down is easy. To move the blend left and right you really need to have 3 aggregates – a coarse, intermediate and fine aggregate. Unfortunately this caused a major problem in the U.S. and other places with older batch plants that only had 2 aggregate bins, or that had 3 bins but 2 of them were dedicated to a single size of coarse aggregate.

Where did the optimum band in the middle of the chart come from? The Coarseness Factor Chart is the result of plotting the optimum combination curves for a number of different coarse aggregates side-by-side. The optimum combination curves typically run up and down on the graph. The S-shaped band in the middle of the chart is simply the location of the optimal percentages of aggregate for all those bands. It is the point at which you achieve maximum strength and minimum water demand for a set of materials. It has long been recognized that a pea gravel mix needs more sand than a large stone mix. The upward slope of the optimum band just reiterates this.


The equations for the coarseness and workability factors are:

Q (Quality) = % of combined aggregate (all materials including sand) retained on the 3/8” sieve
I (Intermediate) = % of combined aggregate passing the 3/8” sieve and retained on the #8 sieve
W (Workability) = % of combined aggregate passing the #8 sieve

CF (Coarseness Factor – X axis) = Q / (Q+I)
W (Workability – Y axis) = W

Please note that the two values, CF & W, do NOT add up to 100.

The next area of concern was the amount of cement in the mix. All the original studies were based on 6 sacks of cement per cubic yard (564 lbs/cyd or 335 kg/m^3). What happens when more or less cement is used? When you think about it the answer becomes intuitively obvious. If you add cement to a mix the mix becomes “stickier”. To counteract this you need to remove sand and add rock to the mix. If you take cement out of a mix it becomes harsher and you need to add more sand to lubricate the mix. Ultimately the team decided that every sack of cement (94 lbs/cyd or 55kg/m^3) added to a 6 sack mix increased the Workability factor by 2.5 points. Every sack deducted from a 6 sack mix decreased the Workability factor by 2.5 points. Thus the Adjusted Workability Factor, or W-Adj, was born. It is the W-Adj that we actually use to evaluate a concrete mix. If you want an equation for the W-Adj, it is:

W-Adj (Adjusted Workability – Imperial) = W + ((wt. cementitious/94lbs) – 6 ) * 2.5
W-Adj (metric) = W + ((wt. cementitious/55kg) – 6) * 2.5

What happens when you use fly ash or GGBFS to replace cement? You simply add the cement and fly ash weights together to come up with the total cementitious material. (In case you are wondering, yes, we should have recalculated the cementitious based on volume and not weight, but all these studies were done back in the 1970’s, which was before personal computers and spreadsheets. It was just a lot easier to do it by weight and after the computers came out, we had already built up a history of doing it by weight.)

Using the Coarseness Factor Chart

The first use of the Coarseness Factor Chart is to evaluate existing mixes. To do so you must do the following:

  1. Calculate the percentage volumes of each aggregate
  2. Calculate the combined grading
  3. Determine the Coarseness Factor
  4. Determine the W-Adj
  5. Plot the CF and W-Adj on the graph

The most common mistake people make is that they think all mixes should plot in the optimum band. That is FALSE. True, those mixes will typically have the highest strength, but they are also too harsh to pump or finish. As was previously stated, for different applications you need to add more sand to the mix. You rarely need to add more stone to a mix unless it is an architectural mix that is supposed to contain a high coarse aggregate factor in the finish. Special vibrators are necessary to place these mixes. Concrete for most applications will typically plot about 5-7 points above the top of the band.

Particle shape and texture have an impact on where the best mix is located on the chart. Mixes containing crushed manufactured sand or angular coarse aggregate will typically need to plot higher on the chart, sometimes by an additional 3-5 points. However, mixes with rounded gravel and well-graded natural sand can often be pumped or finished even though they plot right at the top of the band.

The best thing to do is to plot mixes that have worked well in the past and find out where they plot on the chart. Then compare the good mixes to problem mixes and notice the difference. You will usually find a distinct difference in where the two types of mixes plot.

While it may sound difficult to calculate the combined grading and coarseness factor, most modern concrete mix design software, including COMMANDqc, will do it for you. You can read more about COMMANDqc at

COMMANDqc Coarseness Factor Chart
COMMANDqc Coarseness Factor Chart

After analyzing mixes, it is obvious that the next best use of the Coarseness Factor Chart is to use it to design new mixes. Using simultaneous equations, it is easy to blend 2 aggregates to a desired W-Adjust. We’ll leave that as an exercise to the reader to determine how to do that (boy, I’m sounding like a college professor I once had).

The third use for the Coarseness Factor Chart is to develop a specification. ACI 302, the U.S. Federal Aviation Administration and numerous state Departments of Transportation have done this. Overall I feel that using the Coarseness Factor Chart in specifications has improved the quality of concrete that is acceptable, but the procedure has limitations that must be recognized. First, the Coarseness Factor chart depends on only 2 sieves – the 3/8” (9.5mm) and #8 sieves (2.36mm). You can have an infinite number of gradings that plot on the same CF/W-Adjust combination, but all those mixes will be different. Secondly, the Coarseness Factor Chart doesn’t take into consideration particle shape and texture. A mix that works well using rounded gravel and natural sand will not perform as well using angular stone and manufactured sand.

I think it is safe to say that the Coarseness Factor chart has revolutionized the modern concrete industry. It has provided a means of evaluating concrete mixes other than just by strength, slump and air content. It has also provided a means to both specify and proportion concrete mixtures using any materials, including those that don’t comply with ASTM or EN specifications. It can tell you if a mix is too rocky or too sandy and if a large stone mix is gap-graded (I’ll get into that in a different article). However, the Coarseness Factor Chart doesn’t solve all of concrete’s issues. It must be used with common sense and a familiarity with the materials in the concrete mix. However, I think it is safe to say that any concrete mix design method must be used with common sense.

Again, to find out more about the development of the Coarseness Factor Chart, read the article at

Until next time.

Yours truly,

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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