Correlation Analysis of Fiber-Reinforced Concrete Parameters

The correlation of all parameters with each other (pairwise correlation) can be seen in Fig. 1. Also, Fig. 2 illustrates the correlation between input parameters and the CS of SFRC.Figure 1

pair-wise correlation between variables.

Figure 2

Correlation between numeric variables.

The correlation coefficient ( $R$ ) is a statistical measure that shows the strength of the linear relationship between two sets of data. Equation (1) is the covariance between two variables ( $CO{V}_{\mathit{XY}}$ ) divided by their standard deviations ( ${\sigma }_X$ , ${\sigma }_Y$ ). $R$ shows the direction and strength of a two-variable relationship. The linear relationship between two variables is stronger if $R$ is close to + 1.00 or − 1.00. $$R_{\mathit{XY}}=\frac{CO{V}_{\mathit{XY}}}{{\sigma }_X{\sigma }_Y}$$
As can be seen in Fig. 2, it is obvious that the CS increased with increasing the SP (R = 0.792) followed by fly ash (R = 0.688) and C (R = 0.501). Whereas, it decreased by increasing the W/C ratio (R = − 0.786) followed by FA (R = − 0.521). However, the CS of SFRC was insignificantly influenced by D_MAX, CA, and properties of ISF (ISF, L/D_ISF). The same results are also reported by Kang et al.^{18 (link)}.