In previous blogs we’ve discussed various aspects of acceptance testing of concrete. The standard concrete compressive strength specimen in North America is a cylinder, either 6 x 12 inches or 4 x 8 inches. In most of the rest of the world it’s a 150- or 100-mm cube. What’s the difference between concrete cylinder tests and concrete cube tests?
In the late 1980s I spent a year as a postdoctoral fellow in Trondheim, Norway. At first it was a struggle to process all the new impressions in a foreign language. Every time I started a new experiment, I’d have to learn new vocabulary—a process complicated by the various dialects spoken in the lab. Norway’s mountainous terrain makes travel difficult even today, so many dialects have developed over the centuries. That means not just different pronunciations of the same word, but entirely different words for the same thing.
But one thing that wasn’t difficult at all was using cubes instead of cylinders for concrete strength tests. We’ve discussed errors that can occur in concrete strength testing and the consequences of such errors. Some of them stem from the need for flat, even surfaces on which to apply the load. A finished surface is not good enough; you have to cut off the ends and grind them flat or cap them. With concrete cube tests, you just turn the cube on its side.
At first glance, the compressive strengths of concrete cubes and cylinders may look the same. In both cases the strength is the maximum load divided by the cross-sectional area. But there’s more to it than that.
Specimen geometry and Poisson’s effect
Suppose you have a large rubber band. If you pull on it, it stretches. It also contracts laterally—that is, perpendicular to the direction of loading. Similarly, if you press on both ends of a rubber eraser, it expands laterally. This lateral strain, known as Poisson’s effect, occurs in all materials. Poisson’s ratio is the ratio of lateral strain to longitudinal strain.
In concrete testing, compression causes the specimen to expand laterally. However, friction between the loading platen and the specimen surface provides some confinement, so that the concrete doesn’t expand as much as it would otherwise. Confinement increases the strength you measure.
The volume that’s confined extends from the surface into the specimen at a 45-degree angle. So in a cylinder with an aspect ratio of 2.0, only the cross section at mid-height is completely free of confinement. Not coincidentally, failure starts there. In a cube, the aspect ratio is 1.0, and there’s no cross section unaffected by confinement. All else being equal, cube specimens yield higher strength test results than cylinders.
When we test concrete cores, the aspect ratio is nearly always less than 2.0. For this reason we need to adjust the measured strength with a correction factor to compensate for the effects of confinement.
To complicate matters further, concrete begins to crack well before reaching its maximum stress. Thus the lateral expansion is greater than in an intact specimen. High-strength concrete reaches a higher percentage of its maximum stress before cracking, and once the cracks start they propagate rapidly. That means that the confinement effect is less significant for high-strength concrete. So differences due to aspect ratio and confinement effects aren’t the same for all concrete strengths.
Fabrication of specimens
In addition, there’s a size effect. If the size of the specimen is too small relative to the size of the aggregate, it may be difficult to consolidate the concrete properly. Also, if several large aggregate particles happen to line up, there could be a weak plane along the interfaces between aggregate and cement paste. That’s why testing standards have limits on the relative sizes of specimen and aggregates.
Size and shape aren’t the only differences between concrete cube tests and cylinder tests. Different standards specify different ways of fabricating the specimens. The number of layers and how they’re consolidated will affect how dense the concrete is. ASTM C31 requires rodding each layer 25 times, followed by tapping the sides of the mold to eliminate any voids the rod leaves in the fresh concrete. But rodding more or fewer times, making more or fewer layers, or using external vibration would give different results.
Once you’ve made the specimens, you need to cure them. The curing temperatures in the ASTM and EN standards are slightly different—23 and 20 C, respectively. At early ages, the higher temperature will make the specimens a bit stronger, as it causes the hydration of the cement to proceed faster.
To each his own
In the mid-1990s I was assigned the task of reducing the variability of ASTM C109, Standard Test Method for Compressive Strength of Hydraulic Cement Mortars (Using 2-in. or [50-mm] Cube Specimens). Before then, ASTM C109 and its EN counterpart had similar variability, so converting an ASTM C109 strength to its EN equivalent was straightforward. But improvements in the EN test had made it more precise, so the two tests were no longer equivalent. The Portland Cement Association commissioned me to study the two test methods.
I traveled to several laboratories that had participated in the modification of the EN standard. While there, I met with the relevant experts in the UK, France, Germany, and Switzerland and witnessed the details of the testing in each laboratory.
It was interesting to compare studies of variability between the two methods. When American technicians performed side-by-side comparisons of the ASTM and EN tests, the ASTM test proved to be less variable. When European technicians performed similar studies, they found the EN tests were less variable. These findings really aren’t surprising. American technicians conduct ASTM tests day in and day out, developing consistent ways of performing each step. Naturally they learn to produce consistent results. Similarly, European technicians perform EN tests routinely and consistently. When they have to perform a different test, they aren’t equally well practiced.
Of all the laboratories I toured, I was most impressed by Holderbank (now Holcim) in Switzerland. They had two cement testing rooms, one for ASTM and one for EN testing. Each had its own set of tools and equipment, and each maintained the appropriate standard temperature. Holderbank had personnel from various countries where they produced cement, so they benefited from the international perspectives.
Perhaps the most important difference between concrete cube tests and cylinder tests isn’t the tests themselves, but how we use them. Each is part of a whole design philosophy that forms the basis of its respective design code. All design codes seek to make efficient use of resources while ensuring against failure. However, they accomplish these goals by different means.
In graduate school, I learned from my European and Middle Eastern classmates about their methods of structural analysis. They emphasize the theoretical capacity, which has been validated experimentally. Ours spring from empirical measurements of capacity, which have been reduced to formulas using statistical methods. In each case, factors of safety compensate for uncertainties in the estimated loading and variability of the materials, fabrication methods, and so on.
When we calculate the structural capacity of a concrete beam, we include the compressive strength as one of many variables. In ACI 318, we usually estimate the tensile strength and the modulus of elasticity from empirical relationships between these values and the compressive strength. While it’s possible to measure these values directly, we almost never do. But our methods work: buildings and bridges that meet the relevant codes almost never collapse.
The EN codes also work. However, it’s not straightforward to determine the factor of safety for any given member and load condition. Partial factors of safety are inherent in each of the variables in the calculation. In a sense, the factor of safety is an indication of the uncertainty of an estimate of strength or imposed load. Some engineers refer to the factor of safety as a “factor of ignorance”—a way of managing the “known unknowns”. Because of the different design philosophies between the US and European codes, there’s no direct comparison between their factors of safety.
Comparing concrete cube tests with cylinder tests
Converting the results of concrete cube tests to cylinder tests isn’t straightforward. It’s not like, say, converting temperatures from Fahrenheit to Celsius. That is, you can’t just convert MPa to psi and call it good. Differences in the way we make, cure, and test cubes and cylinders all affect the measurement. And who does the testing—that is, whether the technician is expert in US or European test methods—will affect the precision of the tests.
Because the European and US codes developed from different design philosophies, it’s not prudent to use concrete cube tests with US codes. Factors of safety and underlying assumptions aren’t explicitly spelled out. Engineers using the codes don’t always fully understand the basis for them. Much of ACI 318, for example, is based on tests using concrete having strengths up to 6000 psi. At the time, that was high-strength concrete. The commentary accompanying ACI 318 and the references on which it is based provide insights as to when the formulas apply. When I studied structural engineering as an undergraduate and then a master’s student, we learned about the basis for the code as well as how to use it. Later, when I switched to civil engineering materials, I learned how the test methods affect the results and why we use the tests we do.
Both the US and European codes produce structures that perform adequately. But the EN codes are based on EN test methods, and US codes are based on ASTM test methods. The engineer may not know all the underlying assumptions, and structural engineers usually know little or nothing about materials and testing. Much as I prefer the simplicity of concrete cube tests, I think we’re better off keeping to ASTM C31 and C39 when we use US design codes.