Concrete Mix Design: Art and Science – Statistical Overdesign by ACI 318 (Part 2)

When determining the required average compressive strength, f’ cr , by ACI 318, the Structural Concrete Building Code, the Code cites the preferred option of using 30 consecutive tests to determine the sample standard deviation, then to use that standard deviation to calculate the overdesign above specified strength, f’ c . Fortunately the Code recognizes that not every concrete producer will have 30 consecutive tests for every combination of materials and provides options for other alternatives. In my last blog post we looked at determining required average compressive strength using 30 tests. In this post I would like to examine the other options. (NOTE: There are many details in ACI 318 that are not covered in this post. This post just covers one aspect of ACI 318. If you must develop a concrete mix in compliance with ACI 318 it is strongly suggested that you first obtain a copy of that document. Copies are available from ACI at .)

ACI 318 is very helpful for determining the overdesign requirements for a concrete mixture. In the 2011 edition, Section 5.3 starts off with a flowchart, shown below, that details the options for determining the overdesign.

ACI 318 Strength Overdesign Flowchart

Are there 30 or more tests from a single mix design?

To use this option the tests must be:

  • Consecutive
  • Using similar materials and cast under similar conditions
  • Cast within the last 24 months (ACI 301-10, Specifications for Structural Concrete, requires that the tests be within the last 12 months and cover a span of more than 60 days. I don’t know if this will change after ACI 318-14 comes out without the statistical overdesign sections, but I hope so.)
  • From a mix that has a design strength that is +/- 1000 psi (6.8 MPa) from the design strength of the new mix

As a reminder, this method uses the “sample standard deviation”, which uses an “(n-1)” coefficient under the divided-by sign. This is different from the “population standard deviation” which divides by “(n)”. If you are using a spreadsheet to calculate the standard deviation, make certain to use the correct one.

What if you only have 15-29 tests from a single mix?

If you have at least 15 tests but less than 30 tests that cover a span of at least 45 days, you can multiply the standard deviation of those tests by a factor set out in Table

Then perform the calculations as set out in my previous blog post at

What if you have 2 different mixes whose tests total 30 or more?

This procedure isn’t followed very often, since if there are tests that comply with it, they also comply with the procedure for 15-29 tests shown above. However, this procedure can result in a lower standard deviation, which will allow the use of less cementitious material. Also, this procedure isn’t really defined in the paragraph section of ACI 318, but is better described in the flow chart and the Commentary. To use this method calculate the standard deviation of each set of data, then calculate the average standard deviation using the following equation:

Where s s1 and s s2 are the standard deviations of mixes 1 and 2 respectively and n 1 and n 2 are the number of tests in each set. It is really much easier to do the calculations for a single mix with 15-29 tests shown above.

What do you do if you don’t have a single mix with at least 15 tests?

This actually addresses the issue of “What do you do if you don’t have 2 mixes with at least 30 tests combined?”, since one of the mixes must have at least 15 tests. First the strength overdesign must be determined. Table displays the overdesign values required for each of 3 ranges of strength targets:

The trick is to provide test data that shows the desired mix will achieve the required average compressive strength shown in the table.

If there are 10-14 tests available for the desired mix then as long as the average of those 10-14 tests exceeds f’ cr then the mixture complies with the table.

If 10 tests are not available for the desired mix then the issue becomes very unclear. Para 5.3.3 of ACI 318 states, “Documentation that proposed concrete proportions will produce an average compressive strength equal to or greater than required average compressive strength fcr ′ (see 5.3.2) shall consist of one or more field strength test record(s) or trial mixtures.” The trouble is that ACI 318 never defines just how a single strength test record is to be used.

Even the Commentary seems to be written to be vague. Para R5.3.2.2.e reads,” The compressive strength test results may be analyzed graphically or using regression models to determine the water-cementitious  material  ratio  and  the  relative proportions of cementitious materials, if other materials in addition to portland cement are used, that will produce concrete  satisfying  the  required  average  compressive strength fcr ′ .” This implies that you can use a single test from each of two mixes if you graphically analyze the data, but you would need at least 3 tests if you are going to do a regression analysis.

NOTE: I have not been able to find a standard method for developing a w/cm curve for the above method. Some people use 3 mixes, some use 4. Some use lab mixes while others use field data. ACI provides guidance on the allowable tolerances for slump and air, but ASTM contradicts those tolerances. The NRMCA is working on guidelines for preparing a w/cm curve, but it will probably be a year or more before they are available.

The code never really states how 2-9 tests of the same mix can be used to document strength of the mix.

What if you don’t have any data at all?

Para 5.4.1 states, “5.4.1 — If data required by 5.3 are not available, concrete proportions shall be based upon other experience or information, if approved by the licensed design professional. The required average compressive strength fcr ′ of concrete produced with materials similar to those proposed for use shall be at least 1200 psi greater than fc ′. This alternative shall not be used if fc ′ is greater than 5000 psi.”

About the only scenario if can see this working for is if emergency repairs have to be made on a structure with no experience and no time to develop it.

Gaps in the ACI 318 approach

One of the biggest gaps in the ACI 318 approach is there is no way to relate the required average compressive strength, f’ cr to cementitious content. If the standard deviation from a 3500 psi mix is used to determine f’ cr for a 4000 psi mix design, how do you determine the cementitious content in the 4000 psi mix. In the real world the typical ways to do this are by making proportional adjustments to cementitious content or by using the cementitious efficiency expressed as psi/lb of cementitious material to make the adjustment. While there is no standard unit of measure of cementitious efficiency in either Imperial or metric units, psi/lb works well for Imperial and I use MPa/100 kg cementitious material for metric. Both methods result in numbers in the 0-20 range.

Another gap in the 318 approach is determining what tests are to be used as the basis for the overdesign calculation. For example, if a previous project required 6% air +/- 1.5% and the new project requires 6.5% air +/- 1%, can you just use the tests from the previous project where the air content is between 5.5% and 7.5% or must you start fresh with a w/cm curve for a new mix?

A third gap is how mixes are selected for use in the analysis. Let’s say that the new mix has a 3500 psi design compressive strength. According to 318 we can use the standard deviation of data from a 3000 psi design mix to determine the strength overdesign. But what happens if that 3000 psi design mix also has a maximum 0.40 w/cm ratio and produces an average strength of 6500 psi? Can we still use the “3000 psi” design mix?

While it isn’t really a gap, another concern is the fact that there are numerous discrepancies between how ACI 318, the Code, and ACI 301, Specification for Concrete, address strength overdesign. It would take a lot more time and space than is available on this blog post to detail all the discrepancies. These discrepancies will be addressed once 318 drops the overdesign requirements, but then a whole new set of requirements will apply.

This concludes our discussion of statistical overdesign techniques using ACI 318. Next time I intend to explore the method used in EN-206, the Eurocode, which relies on “characteristic strength.”

Please let me know your comments and opinions.

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.


Any idea about concrete mix design for segmental retaining wall units?They need low slump concrete with maximum diameter of 6 mm of aggregate.

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