Cylinder vs. cube conversion.
Ultra-High-Performance Concrete (UHPC) is a concrete class initially developed in the 1990s. UHPC contains no coarse aggregates. When fibers are used in UHPC, it is called Ultra-High-Performance Fiber Reinforced Concrete (UHPFRC) and offers increased strength and durability. The compressive strength of UHPC may have values exceeding 21,750 psi (Graybeal&Davis, 2008). It has been found by researchers, especially at the Kassel Universität, Germany, that UHPC can be designed to reach compressive strengths up to 36,250 psi. In addition to its high compressive strength, UHPC offers enhancements of high strength concrete (HSC) such as very high tensile strength (over 2175 psi) and flexural strength (over 7250 psi), very high ductility, very high durability to freeze-thaw cycles, chloride penetration, abrasion resistance, and carbonation. These enhanced properties will result in the overall improved performance of structures using this material, thus increasing construction safety, providing longer service life, and lower maintenance costs.
However, the exceptionally high compression strength of UHPC and UHPFRC will pose issues regarding their strength in laboratory testing. These issues are the limited capacity of compression testing machines and the surface preparation requirement for testing cylinder specimens. The issue of using high-load capacity testing machines could be solved using small specimens (e.g., cylinders with h/d [in] = 8/4 or cubes with side a = 4 inches).The use of cubes also eliminates the problem of the surface preparation requirement of cylinders. Generally, cylinder specimens are used in the USA, Canada, France, Australia, and New Zealand. However, cubes are commonly used in the UK, Europe, India, and Singapore. For standard concrete and HSC, the concrete compressive strength test results from cube specimens are generally higher than cylinders specimens due to the h/d ratio of 2 of standard cylinders (Subramanian, 2013). Usually, the compressive strength of concrete cylinder specimens is considered to have 0.8-0.85 times the compressive strength of cube specimens.
Cube vs. Cylinder Strength Conversion Factors for NSC and HSC
For NSC and HSC, appropriate conversion factors have been established by several researchers in order to relate results obtained from different specimen sizes to a reference size of cylinder or cube (generally cylinder with h/d [in] = 12/6) that forms the basis for structural design (EN 1992-1-1:2004). As shown in Figure 1, an NSC cylinder with h/d [in] = 12/6 typically reaches only about 82% of the compressive strength of a 6-inch cube and only about 75% of the compressive strength of a 4-inch cube. These factors increase for HSC, i.e., the difference in test results obtained from specimens with different slenderness is smaller than for NSC. This effect may be attributed to the minor increase in concrete compressive strength of HSC due to the multi-axial compression stress state (Riedel &Leutbecher, 2017).
Cube vs. Cylinder Strength of UHPC and UHPFRC Specimen
The French guidelines NF P 18-470-2016 propose using cylinder specimens with a 2.8 or 4.4 inches diameter to determine the compressive strength of UHPC and UHPFRC. In contrast, the Japanese guidelines propose a diameter of 4 inches. In other countries, such as the USA, a diameter of 4 inches is accepted. The French Standard classifies UHPC using six strength classes, defined using the characteristic compressive strength obtained from cylinders with h/d = 8.8/4.4 inches or 4-inch cubes, assuming a difference of 2175 psi between cylinder and cube strength as indicative value. This results in ratios between cylinder compressive strength and cube compressive strength of 0.90 (fck,cyl/fck,cube = 18,850/21,025 psi) up to about 0.94 (fck,cyl/fck,cube = 36,250/38,425 psi).
Graybeal and Davis (2008) evaluated 14 compression tests on HSC and UHPC mixtures using premixes without coarse aggregate with compressive strengths between 11,600 and 29,000 psi. Methods of producing, curing, preparing, and testing UHPC are based on the findings of a large-scale research program investigating commercially available UHPC premixes (Graybeal,2006). Each series included three sizes of cylinders (d = 2, 3, and 4 inches) with a slenderness of h/d = 2 and three sizes of cubes (a = 2, 2.78, and 4 inches). Most of the series were heat-treated, and some were cured in air. The cube specimens were tested with unground-loaded faces. Comparison of mean compressive strengths obtained from 4-inch diameter cylinders (fcyl) and 4-inch cubes (fcu) resulted in conversion factors fcyl/fcu between 0.97 and 1.10 for the UHPC mixtures, i.e., in most cases, the compressive strength obtained from cylinders was higher than the compressive strength obtained from cubes. Especially the UHPC mixtures without fibers showed a high standard deviation of up to 2175 psi, so the scattering of test results superimposed the impact of the different shapes and sizes.
Fládr et al. (2013) investigated the relation of compressive strengths of different-sized cubes made with fiber-reinforced HSC and UHPC using mixtures with coarse aggregate. 4-inch and 6-inch cubes with compressive strengths between 14,500 and 26,100 psi were tested in 7 series. For converting 4-inch cube strength to 6-inch cube strength, a factor between 0.85 and 0.99 was obtained by comparing the mean compressive strengths. However, standard deviations of test results of up to 1740 psi might make these results unreliable to accept the impact of specimen size.
Kusumawardaningsih et al. (2015) tested UHPC and UHPFRC 4-inch diameter by 6-inch tall cylinders and 4-inch cube specimens. UHPC and UHPFRC specimens used had to mean compressive strengths of 23,987 psi (for UHPC, using cube specimens) and 26,975 psi (for UHPC, using cylinder specimens), 26,540 psi (for UHPFRC with 1% fibers, using cube specimens) and 27,400 psi (for UHPFRC with 1% fibers, using cylinder specimens), and 26,430 psi(for UHPFRC with 2% fibers, using cube specimens) and 26,970 psi (for UHPFRC with 2% fibers, using cylinder specimens). The UHPC specimens that contained no fibers experienced sudden explosive and brittle failures, whereas failures of UHPFRC specimens were ductile and were due to the rupture of fibers.
The mean compressive strength conversion ratio between cube and cylinder specimens was found to be: 0.89 (for UHPC), 0.99 (for UHPFRC 1%), and 1.0 (for UHPFRC 2%), respectively. Similarly, the mean compressive strength conversion ratio between cylinder and cube specimens was found to be: 1.12 (for UHPC), 1.01 (for UHPFRC 1%), and 1.0 (for UHPFRC 2%), respectively. These ratios of UHPFRC with 1% fiber and 2% fiber, respectively, are somewhat closer to the conversion ratio found by Riedel and Leutbecher, 2017, Table 1, and as suggested by AMPA (2010), which is 0.95. This finding is interesting as it is opposite to the conversion factors normally used for NSC and HSC, which indicate that cube specimens produce higher concrete compressive strength, as the h/d ratio of standard cubes is less than cylinders. Also, other researchers found that the shape effect of compressive strengths decreases as the specimen size increases. Additionally, for HSC, the difference in compressive strengths between cylinders and cubes more rapidly disappeared than that of NSC (Yi et al., 2006)
According to Dr. Satish Jain, who owns a UHPC/UHFRC plant in India, 2-inch (50 mm) cubes should be sufficient for all internal testing and initial R&D purposes. Using 4-inch (100 mm) cubes for final tests is better, as suggested by the Swiss standards, SIA 2052-2016. According to ASTM C1856-17, the compressive strength of 4-inch UHPC cubes can be used to predict the compressive strength of 3 × 6-inch (75 × 150 mm) UHPC cylinders with an accuracy of +/− 10 percent. The loading rate shall be 145 psi/sec (1 MPa/sec).
Suggested Equation to Predict Strength
Neville(2012) suggested the following L’Hermite’s equation to convert cylinder compressive strength to cube compressive strength of concrete:
Where R is the conversion factor, as shown below:
The above equation has been found to predict the cube or cylinder compressive strengths if one of the values is determined or known, particularly for Normal Strength Concrete (NSC) or High Strength Concrete (HSC), with values ranging from 2900 to 14,500 psi (20 to 100 MPa).
For UHPC and UHFRC, the following modified conversion factor is suggested by the author:
A comparison of the proposed equation with the experimental results is given in Table 2.
Summary and Conclusions
Ultra-High-Performance Concrete (UHPC)and Ultra-High-Performance Fiber-Reinforced Concrete (UHPFRC)are increasingly used due to their increased strength and durability advantages. Available compression testing machines cannot be used to test standard 6-inch diameter and 12-inch high cylinder or 6-inch cube specimens, as their capacity will be exceeded. This problem could be solved using small specimens (e.g., cylinders with h/d [in] = 8/4 or cubes of 4 inches).The use of cubes also eliminates the problem of the surface preparation requirement of cylinders. Several researchers have tested UHPC and UHPFRC cylinders of 4-inch diameter and 8-inch tall, and 4-inch cube specimens. Some of these results have been presented. A new equation to convert cylinder compressive strength to cube compressive strength has been suggested. This equation has been compared with the available experimental results and found to give satisfactory results; for UHPC and UHPFRC, the cube and cylinder strengths are almost the same.■
References
AMPA (2010), Druckfestigkeitfactor, AmtlicheMaterialprüfanstalt für das Bauwesen, Kassel Universität, Germany.
ASTM C1856/C1856M-17, Standard Practice for Fabricating and Testing Specimens of Ultra-High Performance Concrete, ASTM International, 4 pp.
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