## 4 Statistical Evaluation of Results
### Correlation between Tensile and Compressive Strengths  
Figure 16 denotes the relationship between the compressive strength (\(f_{cm}\)) and splitting-test tensile strength (\(f_{sp}\)) of PPFRC. It can be observed that the splitting-test tensile strength increased with the compressive strength. After 28 days of measurements, the splitting-test tensile strength ranged from 2.75 to 3.45 MPa. Previous studies [23; 54; 56; 59; 60; 63; 64; 65; 66; 67; 68] have demonstrated that the split tensile strength of PPFRC after 28 days was in the range of 1.56 to 5.60 MPa. The tensile-strength values measured through the splitting test were within the typical strength range. The splitting-test tensile strength of PPFRC at 28 days was within 6.09-8.43% of the compressive strength. Generally, the splitting-test tensile strength of regular concrete is within 8.00% to 14.00% [52; 69; 70; 71]. However, previous studies have indicated that splitting-test tensile strengths range from 6.78% to 13.30% of compressive strength for PPFRC. Although the 6.09% value was out of range, this value matched the type of concrete with the highest compressive strength. All the other values were within the typical values for PPFRC. Furthermore, the split tensile strength/compressive strength ratio decreased as the compressive strength increased. This trend was reported by [PERSON] [72]  
Figure 15: Correlation and contour graphs between the mechanical strengths (\(f_{cm}\), \(f_{sp}\) and \(f_{r}\) ) of PPFRC and fiber variables (\(l\)/\(d\) and \(V_{f}\) ). in regular-weight concretes, Caldarone [70], and Dewar [73] for high-strength concretes, and [71] for lightweight concretes. According to these studies, the splitting-test strength at low compressive strengths is approximately 10%, whereas, for high strengths, this value is reduced by up to 5%. This trend was also observed in the present study results, as shown in Figure 17.  
The regression equations between the splitting-test tensile strength and modulus of rupture were generated from the general expression of the form shown in Equation (8) [70]. Other authors and standards widely use this general expression [74]. \[f_{t}=a\ f_{cm}\ ^{b} \tag{8}\]  
where \(f_{t}\) is the tensile strength, and \(f_{cm}\) is the compressive strength. Finally, \(a\) and \(b\) are constants. According to [PERSON] [69], the splitting-test tensile strength is estimated as 0.4 to 0.7 times the square root of the compressive strength. Therefore, the proposed Equation (9) based on the results of this experimental study denotes a nonlinear exponential relationship between the splitting-test and compressive strengths, as shown below:  
\[f_{sp}=0.46\ \sqrt{f_{cm}} \tag{9}\]  
where \(f_{sp}\) is the splitting-test tensile strength, and \(f_{cm}\) is the uniaxial compressive strength, both in MPa. Figure 18 denotes the comparison of the experimental values of the splitting-test tensile strength calculated using several equations given by [PERSON] [75] for regular  
Figure 16: Relationship between the splitting-test tensile strength and compressive strength of PPFRC. Figure 17: Relationship between the split strength/compressive strength ratio (\(y\)-axis) and compressive strength (\(x\)-axis) of PPFRC. weight concretes in Equation (10), [PERSON] and [PERSON] (2012) for concretes with PP macrofibers with compressive strengths between 30 and 40 MPa in Equation (11), [PERSON] and [PERSON] ([PERSON] and [PERSON], 2013) for self-compacting concretes with PP macrofibers between 45 and 50 MPa in Equation (12), [PERSON] et al. (2016) for high-strength lightweight concrete with PP fibers between 40 and 46 MPa in Equation (13) and [PERSON] et al. (2017) for palm-shell reinforced concrete with PP fibers in Equation (14).