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This study presents a statistical analysis on the prediction of compressive strength of steel fiber reinforced self-compacting concrete (SFRSCC) based on pull-off test results using linear and nonlinear regression models. For this purpose, an extensive experimental program was conducted including different cement contents and aggregate sizes along with steel fiber contents of 0, 30, 50 and 80 kg/m³. 50 mm and 70 mm diameters aluminum and steel discs with different thicknesses were supplied. Moreover, the effect of partial core depth on pull-off strength was examined. In order to assess the SFRSCC characteristics which may be affected the pull-off test on SFRSCC, two levels of cement content of 400 and 500 kg/m³ were considered. The water/cement ratio (W/C) was kept constant at 0.45 for all the mixes studied. For each level, two maximum aggregate sizes of 10 and 20 mm containing steel fiber contents of 0, 30, 50 and 80 kg/m³ (Volume fractions, V_f , of 0, 0.38, 0.64 and 1%) were taken into account. The fresh properties are in the range of 600-700 mm for slump flow diameters, 2.2-3.5 s for T₅₀ and 550-620 mm for the J-ring test without segregation of aggregate near the edges of the spread-out (VSI of 1 and 1.5). Therefore, it can be stated that all concrete mixtures can be considered as SCC.
The effects of the SFRSCC properties and practical parameters of pull-off test are included in the proposed equations as dimensionless variables. The results showed that both linear and nonlinear regression models have high ability as a reliable tool for prediction of compressive strength of SFRSCC on the basis of pull-off testing so that about 80% of the variation in response value can be explained by the fitted models. Also, validation of the evolved models has been verified with the results obtained in the previous works. It has been demonstrated that the performance of the proposed models can be acceptable with reasonable accuracy. The linear models show the trend to overestimate the compressive strength.  By considering the results, 86% and 52% of the data are overestimated by linear models related to aluminum and steel discs, respectively. However, this behavior is less pronounced for nonlinear relationships so that the corresponding values are found to be 58% and 50%, respectively.
The validity of the derived models has been verified with the results obtained by Madandoust [8] and Long and Murray [9]. It can be derived that the performance of the introduced models may be acceptable with sensible degree of accuracy. According to the results, it is clear that there is not a considerable difference between the curves and also between the models, especially for higher values of pull-off test. However, it can be generally distinguished that the nonlinear models have slightly better performance compared to the linear models, especially for steel disc which is favorably close to the results obtained by Long and Murray [9].
 It should be stated that based on the large number of data and range of the variables used in this study, it may be possible to claim that the proposed models are robust with regard to the possibility of its use in various scenarios so that these models have no experience concerning to the unseen findings by others. Nevertheless, it must be borne in mind that different relationships may be expected to be reasonably developed for different types of concretes such as high-strength and lightweight.

Keywords: Self-compacting concrete, Steel fiber, Pull-off test, compressive strength, Regression models

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