Issue 78

M. S ł owik et alii, Fracture and Structural Integrity, 78 (2026) 393-408; DOI: 10.3221/IGF-ESIS.78.23

to account for the length effect in splitting tensile strength tests conducted on cylinders of non-standard height. The conversion procedure was introduced to express all experimental results with respect to the standard specimen geometry (150 × 300 mm), thereby enabling a direct comparison between all investigated concrete series regardless of specimen length. The length effect appeared to be sensitive to aggregate type. Therefore, the first step of the analysis of concrete tensile strength results focused on statistical calculations for converting the results obtained on short-length cylindrical specimens to standard cylinders. After building the proper test data, the basic analysis was performed. The conversion of test results – from the length of 150 mm to 300 mm An analysis of tensile strength test results obtained from both standard (300 mm long) and short (150 mm long) cylindrical specimens was broadly discussed in [11]. Although a length effect was observed in the splitting tensile strength tests, it was not possible to establish a general relationship between the results for the two specimen lengths. It was found that the strength of the cement matrix was not significant, but on the contrary, the type of aggregate considerably affected the length effect. Therefore, a correlation analysis of the laboratory results for 150 mm and 300 mm long cylinders was carried out, taking into account the aggregate type. In order to find the conversion functions, the experimental results were grouped in two series (in which test results for concretes made of higher and weaker matrix were taken together): • concretes containing gravel aggregate, • concretes containing granite aggregate. Furthermore, the data were further divided within each group into two statistical subsets based on the length of the cylindrical specimens. The correlation coefficient was then determined using Statistica software (Statsoft, v.13.3) to evaluate the potential relationship between results obtained from cylinders with lengths of 150 mm and 300 mm. The outcomes of this analysis are presented in Fig. 6.

fct,sp15/30 (N, Dmax=16mm) = -0.8184 + 1.1222 * fct,sp15/15 Correlation coefficient: r = 0.98936

fct,sp15/30 (G, Dmax=16mm) = 0.77913 + 0.72799 * fct,sp15/15 Correlation coefficient: r = 0.95262

6

6

3

3

0

0

2 .2 2 .4 2 .6 2 .8 3 3 .2 3 .4 3 .6 3 .8 4 4 .2

3 .2 3 .4 3 .6 3 .8 4 4 .2 4 .4 4 .6

2 .4 2 .6 2 .8 3 3 .2 3 .4 3 .6 3 .8 4 4 .2 4 .4 4 .6 4 .8 5 5 .2 fct,sp15/15 (G, Dmax=16mm) 2 .8 3 fct,sp15/30 (G, Dmax=16mm)

fct,sp15/30 (N, Dmax=16mm)

2 .4 2 .6 2 .8 3 3 .2 3 .4 3 .6 3 .8 4 4 .2 4 .4 4 .6 fct,sp15/15 (N, Dmax=16mm) 1 .8 2

0

3

6

0

3

6

Figure 6: The scatter plots with correlation coefficients between splitting tensile strength obtained for short and long specimens: for gravel-based concrete, Dmax = 16mm (a), and for granite-based concrete, Dmax = 16mm (b). The correlation coefficient for both groups of samples exceeded 0.8 which suggested a high possibility of building correlation functions between results obtained for standard and short length specimens. The Multiple Regression Method was applied in the next step of the analysis. The splitting tensile strength tested on 150 mm long specimens was recognised as a good predictor for the splitting tensile strength tested on 300 mm long specimens for all groups. The models were built, in which the independent variable was the data of splitting tensile strength for short cylinders f ct,sp15/15 and the dependent variable was the data of splitting tensile strength for long cylinders f ct,sp15/30 . Two regression equations (Eqns. 5 and 6) were generated for the investigated experimental programme:  for concrete with gravel aggregate:

1.12 f  



(5)

f

0.82

ct

ct

,15/30

,15/15

 for concrete with granite aggregate:

400