Concrete Mix Design: Art and Science – Using w/c curves

It sounds so easy to say, “Design a concrete mix using a water/cement ratio curve”, but it isn’t. Finally in this mix design series we are talking about concrete and not just components. However, there are a number of steps we have to go through before we cast our first trial batch.

Before we get started, I want to make one thing crystal clear. Many times QC people will say “I know how much cement I need to reach the design strength, f’c, so I will determine my water by multiplying the cement content by w/c.” DO NOT EVER DO THIS!!! It takes a certain minimum amount of water to produce plastic concrete and this calculation does not take this into consideration. If not enough water is included in the design, the water will be added somewhere else in the process, usually in an uncontrolled manner. I consider this procedure at best ignorant, and at worst fraudulent. (I don’t think I can make things any clearer than I have.)

Step 1 – Concrete Requirements: Before we even begin discussing what strength the target mix needs to achieve we need to ask ourselves, “What is this mix for?” “Are there specifications for the mix?” More specifically we need to ask:

  • What are the durability requirements?
  • Will the concrete be subject to freezing and thawing? If so, what air content do we need?
  • Will the concrete be subject to chemical attack? If so, what kind?
  • Are there requirements for the concrete element to be cast, such as for slump and set time? What is our placing environment, such as haul time or climatic conditions?
  • Are there other requirements, such as restrictions on shrinkage?
  • Are there material requirements, such as maximum aggregate size or a restriction on the type of cement that can be used?

Basically these questions fall into 4 areas:

  • What kind of materials do we need to use?
  • What are the construction requirements
  • How is the concrete supposed to perform?
  • Will the concrete be in an aggressive environment?

Step 2 – Material Selection: For most concrete this is an easy choice. We use what everyone else is using. The problem arises whenever we are trying to create a concrete that no one else has created before. An aggregate that has been used successfully for decades in a region may not be suitable for high-strength concrete with a high cement factor. Either dust on the aggregate, weak fracture planes, or susceptibility to ASR formation may manifest itself. If any of these considerations is important the only solution is to test, test, test, which means that work on developing mixtures may need to start months, or even a year prior to needing to produce concrete.

Step 3 – Determining Water Demand, Admixture Requirements and Aggregate Ratios: Let’s say we have waved a magic wand and we now know we need an air entrained concrete using a ¾” maximum aggregate size (19mm) that will not be exposed to chemical attack and that we need to produce 4000 psi (about 28 MPa). The plant is 30 minutes from the jobsite and the concrete will need to be pumpable for a total of 90 minutes after it is batched. Our objective is to produce a maximum 6” slump (150mm) with a 5.5% air content +/- 1.5%. The concrete temperature is expected to be 80-85 deg. F (27-30 deg. C), so we will use a normal set high range water reducer.

If we were using ACI 211 to determine the estimated water content all that we would need to know was that the concrete was air entrained and the aggregate had a ¾” maximum aggregate size. From that we could determine the estimated water content. However, Duff Abrams, in his historic publication Design of Concrete Mixtures, 1918, had a different first step. First he determined the combination of rock and sand that had the lowest water demand. There are many different ways to estimate this, most of which we have already discussed, but the easiest way is to cast a trial batch of concrete using the proportions of aggregate that you think will work and determine the water demand from that. You may need to cast more than one trial batch if your initial mix is too rocky or sandy. In any case, you will need to determine how much water needs to be added to the materials in order to produce a 2” slump (50mm), then how much admixture needs to be added to produce a 6” slump (150 mm). These trial batches should be cast at the design air content, but with the understanding that air tolerances will affect water demand. Higher air contents usually require less water than lower air contents.

Step 4 – Calculate Mixture Proportions: Even though many sources only require 3 mixtures to produce points on a w/c ratio curve, I usually try to do 4. It gives you better data to draw on if one of your mixtures doesn’t test well. Start with the water required to produce the concrete at the desired slump, then determine cementitious content based on the target water/cementitious ratios. (Just a note, even though I have been saying “water/cement ratio”, I usually mean “water/cementitious ratio”. It is just easier to say “water/cement ratio”.) If you only want to generate a single mix design from the water/cement ratio curve, include points at least + 0.10 above and -0.10 below where you think the desired design w/c should fall. If you are creating a mix family (a group of mixes using similar materials, but covering a range of strengths) include points at least 0.05 above the highest expected w/c ratio and 0.05 below the lowest expected w/c ratio.

As part of the mix design you will need to determine the target air and slump for the trial batches. I have always tried to design for the highest allowable slump and air content, but I can no longer find the reference that required this, so it may be you can just design for the target slump and air content.

Step 5 – Calculate Batch Proportions: Determine the volume of concrete required to produce strength specimens and plastic concrete tests. If you are producing an air entrained mix, make certain to run an air test using the specified procedure (usually pressure meter, but often roll-a-meter for lightweight mixes). Always run a unit weight test, as it is an excellent test to confirm air and it is also typically required by the standard. Design your batch to produce at least 10% more material than you think you will need.

Make adjustments for the moisture of the aggregates, both coarse and fine aggregate. Spreadsheets make it too easy to make this calculation for it to be ignored. If you are batching dry or less-than-saturated material, follow the locally accepted procedure to make certain the material absorbs water and becomes totally saturated prior to batching.

Step 6 – Cast the Trial Batches: ASTM C192, “Standard Practice for Making and Curing Concrete Test Specimens in the Laboratory”, details all the steps you need to go through to produce a trial batch in the laboratory. If you don’t produce trial batches on a regular basis, have a copy of C192 available during the batching process and follow it religiously! I find that if I don’t do something on a regular basis I often miss the fine points of the procedure unless I have it in front of me.

Step 7 – Conduct the Plastic Concrete Tests and Make Test Specimens: At the least you should perform slump, concrete temperature and unit weight tests, then add the air content test for air entrained concrete. Follow the specified test procedure EXACTLY as it is spelled out in the standard. Cure the test specimens as required by the Project Specifications! You have done too much work to this point to invalidate your results by doing things part way.

Step 8 – Test the Strength Specimens and Plot them on a Chart: Make the X-axis the w/c value and the Y-axis the strength. If you want you can plot multiple ages on the same chart. This can help make it easier to spot outliers.

SHORTCUT: If you have field test data available on the desired concrete mixtures, you can skip Steps 5-7 and use the field data. In the U.S. neither ACI 318 or ACI 301 prohibit this. The results will be more conservative, since laboratory tests are usually higher than field tests, but that just increases the safety factor. The example shown contains actual field data from multiple mixes. Only the average strength for each mix is shown.

(This image has been changed from what was originally posted. The original image had an X axis that extended beyond the range of the available data, implying that the w/c curve could be extrapolated beyond the available data. At most I would extrapolate no more than 0.02 beyond the available data. If I had a narrower range of data, say 0.45 to 0.55, I would only extrapolate 0.01 beyond the data.)

Step 9 – Calculate the Required Overdesign and Determine the w/c: In the U.S. the required overdesigns in accordance with ACI 318 are as follows:

  • f’c design strength < 3000 psi: Overdesign = 1000 psi
  • f’c design strength 3000 psi – 5000 psi: Overdesign = 1200 psi
  • f’c design strength > 5000 psi: Overdesign = (f’c x 1.1) + 700 psi

I’m not certain I understand the procedure in EN-206 properly, but I think it means that the characteristic strength (which I will need to get into in a later article) must exceed specified strength by 4MPa. If anyone using EN-206 knows otherwise, please let me know.

In our example the design strength, f’c, is 4000 psi, which means that the target strength is 4000 psi + 1200 psi = 5200 psi. The w/c ratio required to produce 5200 psi is about 0.47. If you are using a spreadsheet to determine the relationship, it can probably show the equation to calculate the relationship. Excel includes multiple types of trendlines for this purpose. I usually try to use the one that has the greatest degree of correlation.

In summary, developing the actual water/cement ratio curve is the least difficult part of the process, since it just involves math and following directions. It is the determination of requirements and the selection of materials that is the most important and requires the most attention to detail.

I look forward to hearing from you. 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.

Brent Rollins

Beautiful, Jay! I especially liked “It takes a certain minimum amount of water to produce plastic concrete and this calculation does not take this into consideration.” This is a finer point that gets missed often. I am teaching Civil Engineering Materials this semester and have just made this blog post required reading.


Brent, thank you for your kind comments. I admit that I sometimes get annoyed with people who mis-apply concrete technology, but I get even more annoyed at those that taught them wrong in the first place. Changing our industry requires first providing accurate instruction from qualified educators. Thank you for improving the education process.


Many thanks to a sharp-eyed reader, who wishes to remain anonymous, who pointed out that the original w/c graph I posted had an X-axis extending way beyond the available data points, implying that the data could be extrapolated to extremes. I have updated the chart to show a narrower X range and explain that extreme extrapolation isn’t appropriate.

Kevin E. Miller

The first 2 paragraphs of your article are brilliant, I wish more engineers had the ability to think outside the box that the concrete industry has built!

Leave a Reply