Experimental investigations

The test program comprised the production and testing of 88 specimens each of fibre-free fine-grain and coarse-grain UHPFRC. The compressive strength, flexural tensile strength, splitting tensile strength and centric tensile strength were determined on the hardened concrete (Table 1). The compressive strength was tested on cubes with an edge length d = 100 mm (Cube100) and on cylinders with a diameter d = 100 mm and a height h = 200 mm (Cyl100). The splitting tensile strength test was also carried out on Cyl100 cylinders. Cylinders with a diameter and height of 50 mm each (Cyl50) were used for the non-standardized tensile tests. The bending tensile tests were carried out as 4-point tests on prisms with a width b = 100 mm and different cross-sectional heights h = 30, 40, 50, 70, 100, 150 and 200 mm (designated P30 to P200). The prisms were concreted horizontally approx. 2 cm higher and later cut to the nominal dimension using a concrete saw. This served to remove the edge zone on the filling side, which can have a slightly more porous structure, and to create a uniform cross-sectional geometry over the entire length of the test specimen. All test specimens were stored in a water basin until testing in order to counteract pre-damage caused by residual stresses as much as possible and to rule out the effects of a moisture gradient.

The average cylinder and cube compressive strength for series 1 was _fcm = 161.5 N/mm² and fcm_,cube = 174.4 N/mm² and for series 2 _fcm = 161.1 N/mm² and fcm_,cube = 174.1 N/mm². While the mean values of the compressive strengths of fine-grain and coarse-grain UHPFRC hardly differed, the centric tensile strength for the fine-grain UHPFRC was on average _fctm = 10.86 N/mm², around 17 % higher than the centric tensile strength of the coarse-grain UHPFRC of on average _fctm = 9.30 N/mm². The splitting tensile strengths of the fine-grain and coarse-grain UHPFRC also differed significantly at fctm_,sp = 11.53 and 8.56 N/mm². The mean values of the flexural tensile strength of fctm_,fl = 15.22 to 18.93 N/mm² for the fine-grain UHPFRC and fctm_,fl = 10.26 to 16.99 N/mm² for the coarse-grain UHPFRC were above the respective centric tensile strength _fctm and showed a clear influence of the cross-sectional height. At the same cross-section height, the coarse-grain UHPFRC also exhibited the lower strength compared to the fine-grain UHPFRC. The coefficients of variation were 1.1 to 4.5 % for the compressive strength, 6.7 and 7.7 % for the centric tensile strength, 4.8 and 8.0 % for the splitting tensile strength and 3.7 to 10.5 % for the flexural tensile strengths.

Correlation between compressive strength and centric tensile strength

To classify the centric tensile strengths _fctm determined in our own investigations, these are plotted in Figure 1 together with further data on fiber-free UHPFRC as a function of _fcm. The legend to Fig. 1 shows the specimen shape, the stress cross-section of the tensile specimen_Ac, the maximum grain diameter _Dmax and the type of post-treatment (NB) for each study or series. In addition to the test data, Eqs. (1) and (2) were evaluated, according to which the mean value of the centric tensile strength _fctm for normal strength concrete (NFB) and high strength concrete (HFB) can be calculated as a function of the compressive strength in accordance with EC 2 and fib Model Code 2010. The characteristic value of the concrete compressive strength was set at _fck = _fcm - 8 N/mm² in the evaluation of Eq. (1).

In addition to a wide range of results, it can be seen that the centric tensile strength of the concretes with _fcm between 145.0 and 209.1 N/mm² is almost invariably underestimated by Eq. (2). In some cases, the experimentally determined tensile strengths are more than twice the centric tensile strength predicted by Eq. (2). However, with two exceptions, the results lie within the quantiles of Eq. (1) for NFB. Furthermore, it is noticeable that tensile specimens with a small stress cross-section tend to provide higher tensile strengths than tensile specimens with a large stress cross-section. Exceptions are the own investigations and the study by Ma, which are in the upper range of tensile strengths despite large stress cross-sections. In both test series, the specimens were stored in water until testing (WL), while all other studies involved heat treatment (WB) or dry storage (room climate, RK). With the latter two forms of post-treatment, residual stresses due to a temperature or moisture gradient are more likely than with water storage. It can therefore be assumed that the observed influence of the stress cross-section on the tensile strength is primarily due to residual stresses.

Relationship between bending tensile strength and centric tensile strength

Figure 2 shows the relationship between bending tensile strength and centric tensile strength as a function of the cross-sectional height h. In addition to the results of our own investigations, the studies by Schultz-Cornelius and Fitik were also taken into account. Furthermore, the curves according to Eqs. (3) and (4), with which EC 2 and fib Model Code 2010 describe the relationship between the mean values of the centric tensile strength _fctm and the flexural tensile strength fctm_,fl.

Both the own test data and those from Schultz-Cornelius indicate a linear relationship between the ratio value fctm_,fl/fctm and the cross-section height h. However, the ratio values from Schultz-Corneliusare slightly higher than those from our own tests, which may be due to the different strength levels of the concretes in the two studies. The ratio values determined with the tensile strengths of the test specimens with small stress cross-section from Fitik fit in well with the own test data.

It can be stated that the experimentally determined ratio values fctm_,fl/fctm are almost without exception overestimated by equation (4). Equation (3) tends to predict fctm_,fl/fctm too low for small cross-sectional heights and too high for larger cross-sectional heights, so that an adjustment of the approach based on the experimental data appears necessary. In order to decide to what extent a different treatment of fine-grain and coarse-grain UHPFRC is expedient, a regression analysis was carried out for the data sets of our own investigations. A linear relationship between the ratio value fctm_,fl/fctm and the cross-section height h was assumed (see above). If the evaluation is carried out separately for each of the seven data sets of the fine-grain and coarse-grain UHPFRC, coefficients of determination R²of 79.3 % and 97.2 % are obtained (Fig. 3). If the 14 data sets of both concretes are considered as part of a single population, the goodness of fit of R²= 81.0 % is worse than for the coarse-grain UHPFRC alone. In view of the limited sample size, it nevertheless appears justified not to differentiate between fine-grain and coarse-grain UHPFRC in the mathematical determination of the flexural tensile strength for the time being. In Figure 3, the error indicator indicates the smallest and largest individual values of the ratio fct_,fl/fctm of a prism size. The approach proposed here for the mathematical determination of the flexural tensile strength of UHPFRC is based on the red regression line in Fig. 3.

In Eq. (5), _fctm is the mean value of the centric tensile strength of the fine-grain or coarse-grain UHPFRC and h is the cross-sectional height of the component or specimen in mm.

Summary of results and conclusions

For the same compressive strength, coarse-grain UHPFRC tends to have a lower centric tensile strength than fine-grain UHPFRC. This may be due to the greater differences in stiffness in the microstructure of the coarse-grain UHPFRC or to residual stresses due to shrinkage restraint caused by the coarse aggregate.

The type of post-treatment has an influence on the centric tensile strength of the UHPFRC. Specimens that are subjected to heat treatment or dry storage tend to have a lower tensile strength than specimens that are stored in water until testing. The reduction in strength, which Ma states to be around 25 %, is obviously dependent on the cross-sectional size. Specimens with a very small cross-sectional size achieve high tensile strengths despite heat treatment or dry storage. The centric tensile strength decreases as the cross-sectional size increases. It is assumed that the reduction in strength is caused by residual stresses due to a temperature or moisture gradient. It is also possible that the proportion of unconnected edge in the total cross-sectional area of the tensile specimen (porous edge zone on the filling side) influences the tensile strength.

The equation from EC 2, with which the mean tensile strength _fctm for HFB can be calculated as a function of the mean cylindrical compressive strength _fcm, sometimes significantly underestimates the centric tensile strengths determined experimentally for UHPFRC. This approach is therefore not suitable for concretes with _fcm ≥ 150 N/mm². Better agreement between experimental and calculated tensile strength is achieved with the equation from EC 2 that applies to NFB. The test results of almost all studies - regardless of whether fine-grain or coarse-grain UHPFRC - lie within the quantiles of this approach. Test specimens with a large cross-sectional size that have undergone post-treatment by heat treatment or dry storage are at the lower end of this spectrum.

The difference between centric tensile strength and splitting tensile strength is small for UHPFRC. Therefore, the approach _fctm = fctm_,sp is recommended.

The flexural tensile strength of UHPFRC decreases approximately linearly with increasing cross-section height. The approach from fib Model Code 2010 overestimates fctm_,fl almost without exception, while the approach from EC 2 tends to underestimate the flexural tensile strength for small cross-section heights and tends to overestimate it for larger cross-section heights. The more rapidly decreasing ratio value fctm_,fl/fctm compared to NFB and HFB with increasing cross-section height h can be attributed to the greater brittleness (lower specific fracture energy) of UHPFRC.

Based on the results of our own investigations and data from the studies by Schultz-Cornelius and Fitik, an approach for determining the flexural tensile strength is proposed which provides for a linear dependence of the ratio value fctm_,fl/fctm on the cross-sectional height h. With this approach, fctm_,fl/fctm can assume a maximum value of 1.9 and becomes 1.0 for cross-section heights h ≥ 270 mm. Different treatment of fine-grain and coarse-grain UHPFRC does not currently appear justified in view of the data situation and the limited sample size.

Publications

LEUTBECHER, T.; SCHULLER, J., 2025. Axial and flexural tensile strength of thin members made of ultra-high-performance concrete | Tensile and flexural tensile strength of thin load-bearing elements made of ultra-high-performance concrete. In: Congress documents 69th BetonTage: Rethinking sustainability. Ulm, March 11-13, 2025 Concrete Plant and Precast Technology. 91(3), 88. ISSN 0373-4331

SCHULLER, J.; LEUTBECHER, T., 2024. Influence of cross-section height on the flexural strength of ultra-high performance concrete. Beton- und Stahlbetonbau. 119(4), 242-252. doi:10.1002/best.202300095
Supporting Information: Data S1. Results of the strength tests

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