How many cylinders: a pot roast story

How many cylinders does it take to determine the compressive strength of concrete for acceptance testing? To quote ACI 318,

A strength test shall be the average of the strengths of at least two 6 x 12 in. cylinders or at least three 4 x 8 in. cylinders made from the same sample of concrete and tested at 28 days or at test age designated for f’c.

The accompanying commentary explains that we need three 4 x 8 in. cylinders in order to maintain confidence in the strength measurement “because 4 x 8 in. cylinders tend to have approximately 20 percent higher within-test variability than 6 x 12 in. cylinders.” It cites a 1994 paper by Carino et al. in support of this statement.

A brief history

In 1945, John Tucker, Jr., applied the strength summation theory to the compressive strength of concrete. This theory predicts a 50% higher standard deviation with strengths of 4 x 8s than with 6 x 12s. In addition, it indicates that if you want the same confidence in the measurements as you’d get with two 6 x 12s, you’d need to test enough 4 x 8s to give the equivalent total cross-sectional area. That is, four and a half 4 x 8s are as good as two 6 x 12s. You can decide whether you want slightly less confidence with four 4 x 8s or slightly more with five.

As you saw above, Carino et al. found the variability of the strengths of 4 x 8s to be about 20%, not 50%, higher than with 6 x 12s. However, they did not consider the difference in variability between the two cylinder sizes to be statistically significant:

Analysis of dispersion indicated that the 100-mm [4-in.] cylinders had higher within-test variability, but the differences were not statistically significant.

It’s not clear why differences that the authors didn’t consider to be statistically significant became the reason for different treatment of 4 x 8-in. cylinder specimens.

Day, also in 1994, statistically analyzed data from eight published studies comparing cylinder size. He concluded,

The coefficient of variation for strength for 100-mm [4-in.] cylinders is equivalent to that of 150-mm [6-in.] cylinders. Some specifications require the testing of two 150-mm cylinders to determine strength. Due to the equivalence of coefficients of variation, there is little justification for future specifications to require the testing of 3 rather than 2 cylinders when 100-mm plastic molds are used.

More recent data

The 6 x 12s were the standard specimen for strength testing until 2006. Individual municipalities such as Phoenix, Arizona, had adopted 4 x 8s, but in most places everyone used 6 x 12s.  ASTM C31 allowed 4 x 8s “when specified” by the engineer. However, engineers are usually conservative, and many were unwilling to specify a nonstandard test specimen. Even though ASTM C39, the standard test method for compressive strength of concrete, was decades old, it lacked a precision statement for 4 x 8s. Without that, they couldn’t be standard the way 6 x 12s were.

In 2005 a group of Minnesota laboratories agreed to conduct the required testing. Technicians made hundreds of specimens, cured them overnight under simulated field conditions, and transported them to 20 labs for testing. A statistician collected and analyzed the data and proposed a precision statement. ASTM incorporated these data with those from another study to develop its own precision statement. The relevant standards changed, paving the way for ACI 318 to allow 4 x 8s for acceptance testing. However, citing the Carino paper, ACI 318 decided to require three 4 x 8s rather than two.

To try to persuade them to treat 4 x 8s and 6 x 12s the same, one Minnesota lab provided data from two years’ worth of testing for statistical analysis. These two years were the transition period when the lab kept using 6 x 12s on existing projects, but 4 x 8s on new projects. Where ACI 318 applied, they used sets of three 4 x 8s. Where it didn’t, they used sets of two. Over 70,000 individual cylinders were cast and initially cured under field conditions. The same technicians made and tested both sizes of cylinders using the same equipment over the same two-year period.

Statistical analysis

Analysis of the within-test variability showed that tests of two 4 x 8s actually had lower variability than tests of two 6 x 12s. Consistent with Day’s findings, the data clearly indicate that

… tests of two 4 x 8s do not result in greater within-test variability than tests of two 6 x 12s cast under a wide variety of field conditions.

By the time this study came out in 2009, there were already two other big studies, Day 1994 and Detwiler 2006, in support of treating 4 x 8s and 6 x 12s the same, along with two decades of satisfactory results in the Phoenix area. Even so, ACI 318 continued to require three 4 x 8s.

The pot roast story

pot roast with carrots and potatoes
The apocryphal story of the pot roast illustrates an important truth. Shutterstock image.

It’s kind of like the story of the pot roast. A man watching his wife make a pot roast saw her cut off about an inch from each end before putting it in the pot. When he asked her why, she replied that her mother had done it that way. Curious, she asked her mother why she cut the ends off the pot roast. “My mother always did it that way,” was the response. When she asked her grandmother about it, her grandmother said, “I had to cut off the ends to make it fit into the pot.”

There are variations on this story all over, which suggests that it may be more urban legend than true story. However, it does illustrate a true principle. Sometimes you need to ask why rather than just doing it “the way we’ve always done it.”

In the case of cylinder size, the strength summation theory predicts much higher variability than anyone has obtained in actual tests. That suggests that the theory either doesn’t apply here or isn’t the whole story. Why do we act as if it were?