## Concrete Mix Design: Art and Science – Statistical Overdesign using EN-206

My past couple of posts have been about statistical overdesign using ACI 318, so I thought this time I would discuss the overdesign technique used in EN-206. After all, EN-206 uses a similar statistical method to ACI 318, right? Wrong! What started out as a simple 2 hour exercise in paraphrasing EN-206 has turned into a major effort involving about 20 people on 3 different LinkedIn groups. One of my favorite sayings has come to be, “If you want to make God laugh, tell him your plans.” My only consolation from this blog post is that God must have gotten a real belly laugh.

On the surface EN-206 use a technique that is slightly different from ACI 318. Instead of determining a minimum recommended average strength, EN-206:2001 uses something called characteristic strength. The characteristic strength is a value determined statistically such that 95% of the strength tests will fall above the characteristic strength and 5% below. In other words, there is a 95% probability that a test for a mix will be above the characteristic strength. The Engineer will specify the minimum characteristic strength of the concrete for the structure, then the concrete producer will select or design a mix that meets or exceeds that minimum characteristic strength. (In case you are wondering why I am using EN-206:2001 when there is a new version out, I think from 2013, the 2001 edition is the only one I have.)

I’m going to attempt to explain in plain English why this issue is so complicated, but if anyone out there can do better, I invite you to submit an article in non-statistical jargon to explains this. I will be happy to publish it on my blog.

How is the characteristic strength determined?

The characteristic strength is determined just as the minimum recommended strength is determined by ACI 318 – from the average strength and the standard deviation of the concrete tests. However, ACI 318 uses the following criteria:

• 99% chance that the moving average of 3 tests will exceed specified strength, f’c
• 99% chance that an individual test will exceed f’c – 500 psi or, for designs over 5000 psi f’c, that an individual test will exceed 90% of f’c

EN-206 uses the following criteria:

• 95% of the tests will exceed specified strength

Looking at it graphically the 95% confidence limit looks like this for a 30 MPa design strength with a 36 MPa average strength and a 4 MPa standard deviation:

In this particular case the concrete mix does comply because the characteristic strength is below the design strength of 30 MPa.

To calculate the characteristic strength, you would normally use the following equation:

f ck = average strength – ( t x σ )

where σ is the population standard deviation and t is the student t-value for the probability you want. (In case you have never heard of a t-value, it comes from a table you can find in most statistics books and it is based on the probability of low tests you want and the number of tests you have already made.)

For EN-206 based on a 5% probability of low strength, the equation for f ck would appear to be:

f ck = average strength – ( 1.65 x σ)

Right off the bat, we are forced to realize that there are a number of assumptions being made in the above equation.

Average strength = the mean strength

t is based on the student t-test for 5% below a value (which is called a “single tailed” test as opposed to “double-tailed” test. You don’t need to understand this except to know that it is an assumption that is being made.)

σ is the population standard deviation and not the sample standard deviation, which is what is used in ACI 318

How does EN-206 actually define f ck ? As nearly as I can tell it doesn’t. It just defines it as the value below which 5% of the tests will fall. If anyone knows where f ck is defined with a real equation in the Eurocode, please let me know, and preferably provide a screenshot of the section.

How does EN-206 define strength overdesign requirements?

Like ACI 318, EN-206 uses two criteria for determining concrete overdesign requirements, but there are only two situations defined in EN-206.

For “Initial” production the concrete must meet the following requirements:

• The average of 3 tests >= f ck + 4 N/mm 2
• An individual test >= f ck – 4 N/mm 2

For those unfamiliar with the units “N/mm 2 ”, they are the same as MPa, megapascals.

Once the producer has accumulated 35 tests [note: I originally stated 15 tests, but once the producer accumulates 35 tests they can use the average of 15 tests], they can use the two following criteria:

• The average of 15 tests >= f ck + 1.48σ
• An individual test >= f ck – 4 N/mm 2

Even here there are a couple of questions. Why are we using the population standard deviation when we only have 15 tests and why not the sample standard deviation? Also, according to a nice publication from the British Quarry Products Association called “Guidance on the application of the EN 206-1 conformity rules”, which I think is no longer available, the standard deviation should be based on 35 tests, not the 15 tests.

The next question that comes up is, “Where does the 1.48 in the first equation for continuous production come from?” It is much lower than the 1.65 student t-factor described above and from ACI 214, Statistical Analysis of Concrete Tests, Table 5.4. and actually results in about a 7% probability of low strength according to the student t-table. The answer becomes a major “rabbit hole” that the average reader of this blog doesn’t want to go down. In fact, it is one that I don’t think I adequately understand, but I will try to give a “short answer” and references for the reader to find the “long answer” if they really want to pursue it.

Short answer: The 1.65 student t-factor comes from an assumption that the data we are examining is “normally distributed” (which means it looks like a bell curve) and that each “datum” (the singular of “data”) point is independent of every other data point other than that they are produced by the same process. It is also based on the assumption that we have a relatively large number of data points. It seems that EN-206 may be assuming at least 35 points over a 3 month period. Apparently the 2013 version of EN-206 allows for either a 3 month period or a 3-6 month period, with different criteria for both.

In reality concrete test results are not independent of each other, they are closely related to the test result most recently prior to the current test. This is called a “time series”. If you have a large number of tests taken over a short period this becomes apparent. However, in a situation like in the U.S. where concrete producers rely on sporadic data from outside third party laboratories, the data looks more like independent normally distributed data. Since Europe and many other parts of the world rely on in-house producer-generated test data that is more frequent than in the U.S. it makes sense to use the time-series approach, which allows for a lower safety factor for the probabilities involved.

Long answer: If you really want to jump down the rabbit hole most of the references on this that I have seen relate to a publication by Luc Taerwe entitled “A general basis for the selection of compliance criteria” which is available at

I haven’t given this a hard look yet, but what I have provided in my short answer is based on comments about references to Luc’s paper. You can find the threads on this subject at the following LinkedIn group locations: 1) American Concrete Institute – ACI, 2) Concrete Society Technologist, and 3) The Concrete Producer Network. I looked at posting links, but discovered that my LinkedIn member number would be embedded in all the links and I didn’t think that would work. Besides, some of the groups are “Members Only”, so you probably want to join those groups.

My thanks to the following people who contributed to increasing my understanding of the issues involved:

• Ioannis P. Sfikas
• Claus V Nielsen
• Yasin Engin
• Selim Y.

Many other people contributed to peripheral aspects of the conversation and I would like to thank everyone who offered feedback. This is a great example of how LinkedIn discussion groups can assist in international cooperation.

Summary:

I wrote a blog post, entitled “Thereby Hangs a Tale”, on the need to understand the story behind a technical presentation before you try to apply “sound bites” from that presentation. You can find the article at http://www.commandalkonconnect.com/2013/01/14/thereby-hangs-a-tale/ . The case of the overdesign calculations and the use of characteristic strength is a case in point. In order to be able to properly apply EN 206 techniques you must first be operating in an environment comparable to that for which EN 206 was developed. If a concrete producer who did not test as frequently as is assumed in EN-206 attempted to use the EN-206 equation they would achieve a 7% failure rate rather than a 5% failure rate, which could result in a huge financial impact on the company.

This posting has become a bit longer than I normally like to do, and is certainly more technical, but I think it is important to understand the “big picture” as well as the details.

I hope you find this post meaningful. If anyone has any comments, please let me know. If you want to provide a more comprehensive, but understandable, article that explains the concepts used in EN-206, I will be happy to print it.

Until next time,

Jay Shilstone 