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This article is reprinted with permission from ACI MATERIALS JOURNAL
ACI MATERIALS JOURNAL
Title no. 105-M68
Accurate determination of the compressive strength of very high strength concrete is currently a difficult proposition due to large testing machine capacity requirements and the need for cylinder end preparation. An experimental program was conducted to determine whether alternate specimen types can be reliably used to determine the compressive strength of an ultra-high-performance fiber-reinforced concrete (UHPFRC) in the strength range from 80 to 200 MPa (11.6 to 29 ksi). Fifty-one, 76, and 102 mm (2, 3, and 4 in.) cylinders were tested alongside 51, 70.7, and 100 mm (2, 2.78, and 4 in.) cube specimens. The 76 mm (3 in.) cylinder as well as the 70.7 and 102 mm (2.78 and 4 in.) cubes were found to be acceptable alternatives to the standard 102 mm (4 in.) cylinder specimen. The 70.7 mm (2.78 in.) cube specimen is recommended for situations where machine capacity and/or cylinder end preparation are of concern.
Keywords: compressive strength; cube; cylinder; ultra-high-performance fiber-reinforced concrete.
The continued advancement of concrete technology and the associated push to adapt advanced technology to production processes has resulted in the initial uses of 205 MPa (30 ksi) compressive strength concrete in the constructed environment.1,2 Producing concretes of this strength level presents a set of challenges to the concrete industry, many of which can be termed quality control/quality assurance issues. In North America, cylinder compressive strength is widely used as a proxy for any number of other concrete properties, in addition to its obvious role relating to the compressive strength of the structural concrete. In the history of modern structural concrete, compressive strength is one of the most, if not the most, important property in terms of verifying acceptability of a wide range of concrete behaviors to a structure’s performance. Accurately and reliably verifying the compressive strength of a 200 MPa (29 ksi) concrete, however, can be a challenge in and of itself.
The two standard methods for determining the compressive strength of concrete are the testing to failure of cylinder and cube specimens. National codes and specifications in North America, France, Japan, Australia, and New Zealand define the cylinder as the standard specimen, whereas much of the remainder of Europe relies on the cube specimen.3,4 Around the world, cube and cylinder specimens of varying sizes are accepted as the standard representation of the compressive strength of concrete in a structural member.
The two primary issues that arise regarding the extension of standard concrete compression test methods to very high strength concretes are testing machine capacity and cylinder end preparation. Barring the purchase of high load capacity testing machines, the simple solution to the first issue is to use smaller specimens. Barring the purchase of expensive cylinder end grinding equipment, the simple solution to the second issue is to use cube specimens. The combination of these solutions, however, effectively moves away from standard practice in the concrete industry and raises concerns the about the accuracy and reliability of the test results.
Many studies going back over 80 years to Gonnerman5 have investigated the relationship between various cylinder and cube sizes on the compressive strength of concrete. For standard concrete mixture designs at normal compressive strength levels, it is normally assumed that cubes will relate a higher compressive strength (up to 25%), but the difference will decrease at increasing strength levels.4 When comparing different sizes of specimens, researchers have demonstrated that, at normal strength levels, the smaller specimens tend to present higher compressive strengths. This result has been theorized to be due to larger specimens having a greater likelihood of containing elements of low strength.4
There have been a series of research efforts in the last 25 years focused on similar issues to those addressed in the current research effort with what would now be considered high- strength concrete. Papers by Nasser and Al-Manaseer6 and Nasser and Kenyon7 pushed for an acceptance of the 76 mm (3 in.) diameter cylinder as a standard compressive strength specimen. Day8 compiled research results from 22 separate studies to perform statistical analyses on the relationship between 76, 102, and 152 mm (3, 4, and 6 in.) cylinders. Issa et al.9 investigated specimen size effects with 51 to 152 mm (2 to 6 in.) cylinders. Aïtcin et al.10 investigated cylinder strength results for concretes up to 120 MPa (17.5 ksi). Mansur and Islam11 investigated the relationship between cylinders and cubes of 100 and 150 mm (4 and 6 in.) minimum dimension and compressive strengths up to 100 MPa (14.5 ksi). The results of these investigations are generally similar in that the strength expressed by smaller cylinders and/ or cubes is expected to be slightly higher than the strength expressed by the 152 mm (6 in.) diameter cylinder, and that strength differences will decrease at higher compressive strength levels.
The present research effort is intended to extend the applicability of the previous research on this topic into the realm of the new advanced cementitious materials that have become commercially available in the last decade.12,13 These and other similar concretes are generally classified as ultra-high-performance fiber-reinforced concrete (UHPFRC), with very high compressive strengths, usable pre- and post- cracking tensile strengths, and significantly improved durability properties as compared with conventional concretes.
|Table 1—UHPFRC mixture design|
|Material||Mixture Design 1 amount, kg/m3||Mixture Design 2 amount, kg/m3||Mixture Design 3 amount, kg/m3|
|High-range water- reducing admixture||30||30||31|
*Premix is composed of the four succeeding items. Note: 1 lb/yd3 = 0.593 kg/m3.
|Table 2—Premix age, mixture design, curing, and testing age|
|Batch||Premix age at casting, months||Mixture design||Curing regime||Testing age, days|
From a practical standpoint, the compressive strength testing of a 152 mm (6 in.) cylinder composed of one of these concretes may require both a 4500 kN (1000 kip) compression machine and a cylinder end grinder, thus making the testing of this concrete a specialized task only possible in select testing laboratories. Using the compressive strength as a proxy for the development of other properties thus becomes more difficult and expensive.
Two countries currently have design guidelines pertaining to the structural use of this type of concrete. The French specification14 suggests the use of either 70 or 110 mm (2.75 or 4.3 in.) cylinders to determine the compressive strength, whereas the Japanese specification15 suggests the use of 100 mm (4 in.) diameter cylinders. In other parts of the world, 102 mm (4 in.) or larger least-dimensioned cylinders or cubes are required according to the relevant existing structural design specifications. In the U.S., 102 mm (4 in.) diameter cylinders are the accepted standard specimen size.
Only two previous studies have specifically investigated the use of smaller-dimensioned cubes to represent the compressive strength of 102 mm (4 in.) or larger cylinders in this very high compressive strength range. The data from these studies, one by the present author16 and one completed by Ahlborn and Kollmorgen,17 is included in the analysis performed on the data collected as part of the present study.
This paper investigates the relationship between the measured compressive strength of UHPFRC as expressed by three sizes of cylinder specimens and three sizes of cube specimens. Use of these types of concrete by the concrete industry at large will be hampered unless practical tests to accurately determine the compressive strength are developed. The research discussed herein focuses on determining the viability of using reduced-dimension cube specimens for the measurement of concrete compressive strength.
Six different cube and cylinder specimens were investigated. Fifty-one, 76, and 102 mm (2, 3, and 4 in.) cylinders were tested alongside 51, 70.7, and 100 mm (2, 2.78, and 4 in.) cube specimens. The compressive strength of the concrete tested ranged from 80 to 200 MPa (11.6 to 29 ksi).
In North America, there is currently only one UHPFRC that is commercially available and as such, it was used in this research program. This high cement, high silica fume content concrete has an extremely low water-cement ratio (w/c) and uses a polycarboxylate-based high-range water- reducing admixture to obtain an acceptable workability. This concrete contains no coarse aggregate, with the largest nonfiber constituent being a fine (<600 micrometer diameter) sand. The mixture designs are provided in Table 1, with Mixture Design 1 being the standard mixture design, Mixture Design 2 being a modified design with higher water-cementitious material ratio (w/cm), and Mixture Design 3 being a modified version of Mixture Design 2 wherein the fiber reinforcement was eliminated. Mixture Designs 1 and 2 were internally reinforced at 2% by volume with 13 mm (0.5 in.) long, 0.2 mm (0.008 in.) diameter straight steel fiber reinforcement.
Fourteen sets of cylinder and cube specimens were fabricated in batches listed in Table 2. The range of compressive strengths over which the batches cover were obtained by fabricating the specimens at various ages after premix blending, by testing the concretes at various ages after casting, and through the application of different curing regimes to the cast concrete. All sets were fabricated between 1.5 and 12.5 months after premix blending and were tested between 3 and 28 days after fabrication. The curing regimes ranged from maintaining the specimens in a laboratory environment until testing to subjecting the specimens to 96 hours of 95 °C (203 °F) and 95% humidity conditions.
|Table 3—Fiber-reinforced cylinder and cube test results|
|Batch||Type||Size, mm||Compressive strength||95% confidence|
|Average, MPa||Standard deviation, MPa||Coefficient of variation||Lower, MPa||Upper, MPa|
Note: 1 in. = 25.4 mm; 1 ksi = 6.895 MPa.
|Table 4—Non-fiber-reinforced cylinder and cube test results|
|Batch||Type||Size. mm||Compressive strength||95% confidence|
|Average, MPa||Standard deviation, MPa||Coefficient of variation||Lower, MPa||Upper, MPa|
Note: 1 in. = 25.4 mm; 1 ksi = 6.895 MPa.
All supplemental curing conditions were initiated within 30 hours of casting.
All compression tests were completed in a 4450 kN (1000 kip) compression testing machine. The cylinders were tested according to ASTM C39, except that the initial rate of load application was increased to 1.0 MPa/second (150 psi/ second). The cubes were tested according to ASTM C109 with the same load rate modification. In all cases except one, six strength results were obtained for each specimen type from each batch of cylinders and cubes. The exception was the 51 mm (2 in.) cylinders in Batch QR, which only had five strength results.
The compressive strength results from the 503 cylinders and cubes tested in the study are presented in Tables 3 and 4. The results from the 11 batches containing fiber reinforcement are in Table 3, whereas the other three batches are in Table 4. The results from all 14 batches are presented graphically in Fig. 1. The batches have been arranged in this figure according to their compressive strength, with the average and the upper and lower 95% confidence interval of the compressive strength for each specimen type being shown. The compressive strengths covered (as observed from tests of 102 mm [4 in.] cylinders) ranged from 80 to 200 MPa (11.6 to 29.0 ksi).
A number of observations can be made based on these compressive strength results. First, the 70.7 and 51 mm (2.78 and 2 in.) cubes tend to show similar strengths with all of their confidence intervals overlapping, and their strengths tend to be at or above those exhibited by the other specimen types. Second, the 102 and 76 mm (4 and 3 in.) cylinders also tend to show similar strengths with all except one of their confidence intervals overlapping. Finally, the 51 mm (2 in.) cylinders tend to show similar or lower strengths as compared with all other specimen types.
Fig. 1—Compressive strength of cylinders and cubes tested in this study.
|Table 5—Coefficients for conversion of compressive strength results|
|Tested / Desired||76 mm diameter cylinder||102 mm diameter cylinder|
|100 mm cube||Multiply by 1.00 (R2 = 0.9672)||Multiply by 1.00 (R2 = 0.9791)|
|70.7 mm cube||Multiply by 0.94 (R2 = 0.9857)||Multiply by 0.93 (R2 = 0.9694)|
|51 mm cube||Multiply by 0.96 (R2 = 0.9541)||Multiply by 0.96 (R2 = 0.9472)|
|102 mm cylinder||Multiply by 1.01 (R2 = 0.9853)||—|
|76 mm cylinder||—||Multiply by 0.99 (R2 = 0.9839)|
|51 mm cylinder||Multiply by 1.08 (R2 = 0.9645)||Multiply by 1.07 (R2 = 0.9360)|
Note: 1 in. = 25.4 mm.
The coefficient of variation information presented in Tables 3 and 4 and displayed in Fig. 2 are indicative of the dispersion that was observed in the test results. The coefficients of variation from similar tests conducted in both Graybeal16 and Ahlborn and Kollmorgen17 are also presented in the figure. ASTM C39 indicates that the expected coefficient of variation for 100 mm (4 in.) cylinders tested at a single laboratory is 3.2%. Forty percent of specimen sets tested in this program displayed coefficients of variation above 3.2%. From the largest to smallest dimension, the median coefficients of variation for the cylinder sets tested in the three studies were 2.7, 3.8, and 5.5%. For the three sets of cubes, the values were 2.8, 2.8, and 3.3%. Cylinders in general, and 51 mm (2 in.) diameter cylinders in particular, make up a larger percentage of the specimen sets with higher coefficients of variation. Also, the results from batches that did not contain fiber reinforcement tended to display higher coefficients of variation.
The test results presented previously demonstrate that, with the possible exception of the 51 mm (2 in.) cylinder specimens, these six specimen types tend to relate similar compressive strength results for individual batches of UHPFRC. As the 76 and 102 mm (3 and 4 in.) diameter cylinders are frequently used to relate the compressive strength of concretes in the 140 to 200 MPa (20 to 30 ksi) range, these types of specimens were used as a references to which the compressive strength results of the specimen types were compared. Figures 3 through 7 plot the results of this study along with the results obtained in Graybeal16 and Ahlborn and Kollmorgen17 as compared with the 76 mm (3 in.) cylinders. The 95% confidence interval is shown for each specimen set, and the nonfiber reinforced specimens from the present study are distinguished from the remainder of the test results.
Fig. 2—Coefficient of variation results. (Note: 1 mm = 0.039 in.)
Fig. 3—Comparison of 100 mm (4 in.) cube and 76 mm (3 in.) cylinder results.
Fig. 4—Comparison of 70.7 mm (2.78 in.) cube and 76 mm (3 in.) cylinder results.
Fig. 5—Comparison of 51 mm (2 in.) cube and 76 mm (3 in.) cylinder results.
Fig. 6—Comparison of 102 mm (4 in.) cylinder and 76 mm (3 in.) cylinder results.
Fig. 7—Comparison of 51 mm (2 in.) cylinder and 76 mm (3 in.) cylinder results.
In the five plots, the least-squared best-fit line for the relationship between the compressive strength of the 102 mm (4 in.) cylinders (fc', 102 mm cylinder), the 51 mm (2 in.) cylinders (fc', 51 mm cylinder), the 102 mm (4 in.) cubes (fc',100 mm cube), the 70.7 mm (2.78 in.) cubes (fc',70.7 mm cube), and the 51 mm (2 in.) cubes (fc',51 mm cube) and the compressive strength of the 76 mm (3 in.) cylinders (fc',76 mm cylinder) is displayed. These least-squares fit lines were forced through the origin and are only displayed over the range of data for which they were calculated. The data from all three studies was included in the linear estimation process.
Table 5 presents the least-squares fit linear estimation of the conversion coefficients for relating strengths to the two cylinder diameters. The R2 values are also presented. These results demonstrate that the 102 mm (4 in.) diameter cylinders, the 76 mm (3 in.) diameter cylinders, and the 102 mm (4 in.) cubes exhibit similar strengths and reasonable correlations. The highest correlation is exhibited by the relationship between the 70.7 mm (2.78 in.) cubes and the 76 mm (3 in.) cylinders, where a factor of 0.94 converts the earlier into the latter. Finally, the 51 mm (2 in.) cylinders and cubes both exhibit lesser correlations.
Based on the results of this experimental investigation of the compressive strength exhibited by various size cylinders and cubes, the following conclusions are drawn:
The research was funded by the Federal Highway Administration. The author gratefully acknowledges this support. The publication of this article does not necessarily indicate approval or endorsement of the findings, opinions, conclusions, or recommendations either inferred or specifically expressed herein by the Federal Highway Administration or the U.S. Government.
|fc',51 mm cube||= compressive strength of 51 mm (2 in.) cube|
|fc',70.7 mm cube||= compressive strength of 70.7 mm (2.78 in.) cube|
|fc',100 mm cube||= compressive strength of 100 mm (4 in.) cube|
|fc', 51 mm cylinder||= compressive strength of 51 mm (2 in.) cylinder|
|fc',76 mm cylinder||= compressive strength of 76 mm (3 in.) cylinder|
|fc', 102 mm cylinder||= compressive strength of 102 mm (4 in.) cylinder|
ACI Materials Journal, V. 105, No. 6, November-December 2008.
MS No. M-2007-416 received December 21, 2007, and reviewed under Institute publication policies. Copyright © 2008, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including authors’ closure, if any, will be published in the September- October 2009 ACI Materials Journal if the discussion is received by June 1, 2009.
Benjamin Graybeal is a Research Structural Engineer at the Federal Highway Administration at the Turner-Fairbank Highway Research Center, McLean, VA. He received his BS and MS from Lehigh University, Bethlehem, PA, and his PhD from the University of Maryland, College Park, MD. His research interests include the structural application of advanced cementitious materials, concrete material characterization, experimental evaluation of highway bridge structures, and nondestructive evaluation techniques.
Marshall Davis is a Research Assistant with Professional Service Industries, Inc., at the Turner-Fairbank Highway Research Center. He received his BS from Radford University, Radford, VA. His research interests include concrete material characterization.