Effect of Size and Shape of Test Specimen on Compressive Strength of Concrete

INTRODUCTION

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 and Asia relies on the cube specimen. 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 characteristic compression strength of cylinders with a diameter of 150 mm (fck,cyl) or the characteristic compression strength of cubes with an edge length of 150 mm (fck,cube) at the age of 28 days forms the basis for the classification of normal-strength concrete (NSC) according to EN 206:2013. Retaining these specimen sizes as standard for high-strength concrete (HSC) beyond 75 MPa and UHPC may cause problems due to the high ultimate loads and limited capacity of present testing machines.

The two primary issues that arise when testing very high strength concrete specimens using the standard concrete compression test machines are the capacity of the testing machine and the preparation of the end of cylinders. Basically, the force supplied by a concrete compression machine is a definite value. For a normal strength concrete, say below 50MPa, the force applied by the compression machine on a standard cylinder/cube is sufficient to break the concrete cube. However, the determination of the compressive strength of a standard cylinder/cube made of very high strength concrete may be difficult, as it will exceed the capacity of normal testing machines. For example, if the designed concrete strength is 100MPa, the maximum force applied by the machine (about 2,000 kN), on a standard cylinder/cube may not be sufficient to crush the specimen. Hence,  smaller size cylinder/cubes (e.g., 100 mm × 100 mm × 100 mm or 70.5 mm × 70.5 mm × 70.5 mm size concrete cubes or cylinders with h/d [mm] = 200/100) may be used instead in order to crush the specimen with the same compression testing machine.

However, using test specimens with different shapes and sizes, other than the standard sizes specified in the codes may lead to the difficulty of correlation of compressive strength of concrete. The difficulty is basically caused by the different multi-axial compression stress-states depending on the slenderness of the test specimen (Bonzel, 1959). It has to be noted that even changing the specimen dimensions without changing the slenderness may influence the compressive strength. It has been found that the specimens with smaller dimensions (e.g., cube with a = 100 mm) have higher strengths than specimens with larger dimensions (e.g., cube with a = 150 mm). Thus, instead of purchasing a high load capacity testing machine, the simple solution to the first issue is to use smaller size specimens.

Regarding the second issue, instead of buying an expensive cylinder end grinding equipment, cube specimens could be used. The combination of these solutions, however, is not considered as standard practice in the concrete industry and may raise concerns about the accuracy and reliability of the test results.

PREVIOUS RESEARCH

Many studies have been conducted on this topic in the past 100 years. As early as 1925, Gonnerman, investigated the relationship between various cylinder and cube sizes on the compressive strength of concrete. For standard concrete mixes, at normal compressive strength levels, it was generally assumed that the cubes will have a higher compressive strength (up to 25%), but the difference will decrease at increasing strength levels. When comparing different sizes of specimens, researchers have demonstrated that, at normal strength levels, the smaller specimens tend to show higher compressive strengths. 

There have been a series of research efforts in the past 40 years focused on such issues. Nasser and Al-Manaseer, 1987, and Nasser and Kenyon, 1984, suggested that the 75 mm diameter cylinder results could be accepted as a standard compressive strength specimen. Day, 1994, compiled research results from 22 separate studies and performed statistical analyses on the relationship between 75, 100, and 150 mm cylinders. Issa et al., 2000, investigated the effect of 50 to 150 mm cylinders on the compressive strength of concrete. Aïtcin et al., 1994, investigated the effects of size and curing on cylinder compressive strength of normal and high-strength concretes up to 120 MPa. Mansur and Islam, 2002, investigated the relationship between cylinders and cubes of 100 and 150 mm size respectively and compressive strengths up to 100 MPa. The conclusions of these investigations are generally similar: As the specimen size increases, its compressive strength decreases. The strength of smaller cylinders and/ or cubes was slightly higher than the strength expressed by the 150 mm diameter cylinder, and that the strength differences decreased at higher compressive strengths. Also, the variation in the compressive strength increased with decreasing the specimen size. Graybeal and Davis,2008, conducted compressive strength tests on fifty-one, 75, and 100 mm cylinders and fifty-one, 70.7, and 100 mm cubes of ultra-high-performance fiber-reinforced concrete (UHPFRC) with strength ranging from 80 to 200 MPa. They found that the 76 mm cylinder as well as the 70.7 and 100 mm cubes could be acceptable alternatives to the standard 100 mm cylinder specimen. They recommended the 70.7 mm cube specimen for situations where machine capacity and/or cylinder end preparation are of concern.

A number of empirical models have also been constructed from the test results, such as Statistical Size effect, Fractal Size effect, Energetic Size effect, and Critical phase transition. A detailed study of previous research on these empirical models is presented by Talaat, et al., 2021.

The standard cylinder strength, is usually converted to standard cube strength, fck, by using the relation = 0.8 fck,. Neville, 1966, developed a relationship between the strength to the volume of specimen (V), lateral dimension (d), and height to lateral dimension (h/d) ratio, which agreed well with the test data, up to 600 mm diameter. According to him the coefficient K to convert cylinder strength to cube strength is

                                K= 0.76 + 0.2 log (f'c/20)                                                               (1)

DIFFICULTIES OF TESTING HIGH-STENGTH SPECIMEN AND CODES OF PRACTICES

From a practical standpoint, the compressive strength testing of a 150 mm cylinder of strength M80 to M 200 concretes may require both a 4500 kN compression machine and also grinding of the ends of a cylinder, thus making the testing a specialized task, which is possible only in some select testing laboratories (Graybeal and Davis, 2008).

According to Graybeal and Davis (2008) only two countries have design guidelines pertaining to the testing of high-strength concrete using smaller size specimens. The French specification (2002) suggests the use of either 70 or 110 mm cylinders to determine the compressive strength, whereas the Japanese specification (2004) suggests the use of 100 mm diameter cylinders. IS 1199(Part 5):2018 suggests that either cube (of size 150 mm) or cylinder specimens (diameter 150 mm, and length 300 mm) can be used for determining the compressive strength. IS 1199 (part 5) allows 100 mm cubes also to be tested as an alternative, provided the largest nominal size of aggregates does not exceed 20 mm. In addition, smaller cylinder test specimens are also allowed provided the cylinders have a minimum diameter to maximum nominal size of aggregate ratio of four. ACI 318-19 permits 100 × 200 mm or 150 × 300 mm test cylinders. As per the commentary to ACI 318-19, the average difference (Carino et al., 1994) between test results obtained by the two specimen sizes is not considered to be significant in design.

CONVERSION FACTORS FOR DIFFERENT SHAPES AND DIFFERENT CONCRETES

The pronounced effect of the height/diameter ratio and the cross-sectional dimension of test specimen on the compressive strength have been observed by several researchers. The difference in compressive strength of different sizes of specimens may be due to several factors such as St. Venant’s effect, size effect, or lateral restraint effect due to the platen of testing machines. The size effect is more predominant when small-scale models are used. 

Standard cubes have been found to have higher compressive strength than standard cylinders with height/diameter ratio of 2.0. The ratio of standard cylinder strength and standard cube strength is about 0.8-0.95; higher ratio is applicable for HSC. Similarly 100 × 200 mm cylinders exhibit 2-10 per cent higher strengths than 150 × 300 mm cylinders; the difference is less for higher strength concrete (Graybeal and Davis 2008). 

For Normal Strength Concrete (NSC) and High Strength Concrete (HSC), appropriate conversion factors have been established by several researchers (e.g., Bonzel, 1959; Walz, 1957, and Riedel and Leutbecher, 2017). Thus, the results obtained from different size specimens can be related to a reference cylinder with h/d (mm) = 300/150 and can be used as the basis for structural design [EN 1992-1-1:2004]. NSC cylinder with h/d [mm] = 300/150 typically reaches only about 82 % of the compressive strength of a cube with a = 150 mm and only about 75 % of the compressive strength of a cube with a = 100 mm. However, these factors increase for HSC and hence the difference in strength is smaller than that of NSC. 

Comparison of mean compressive strengths obtained from cylinders with d = 102 mm and cubes with a = 100 mm by Graybeal and Davis (2008) resulted in conversion factors for cylinder/cube strength ratio between 0.97 and 1.10 for the UHPC mixtures (see Table).

Conclusions

The compressive strength of concrete is an important parameter which is used in structural design, as all other strengths are expressed in terms of the compressive strength. National codes suggest determining the compressive strength based on tests conducted on standard size of cylinders (150 mm diameter and 300 mm depth) or cubes of side 150 mm. However, these codes do not suggest any correlation between the cube strength and the cylinder strength, although the cube strength is normally assumed to be 1.25 times the cylinder strength. Experiments have shown that the cylinder to cube strength ratio varies with the level of strength of concrete, with the difference narrowing for high strength concrete. The cylinder to cube strength ratio, suggested by the Eurocode 2 is not agreeing with actual tests as there is a large scatter in the results.

Keeping the above mentioned specimen sizes as standard for High-strength concrete (HSC) or Ultra high Performance concrete (UHPC) may cause problems due to the higher ultimate loads required to break the cubes/cylinders and the limited capacity of available testing machines. Hence smaller size cubes/cylinders are often used. Again, the correlation between these test results with the standard size cubes/cylinders are required as the values presented in codes as compressive strength belong to the standard cube/cylinder sizes. 

References

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