## 3 Results and Discussion
### Hardened Concrete Properties
#### 3.2.3 Tensile Strength  
The relationship between the tensile strength ratios of BPW-containing concrete to control concrete and BPW percentages are shown in Figure 9.  
A quadratic equation is adopted to capture the optimal PP, yielding the maximum tensile strength. Figure 9 confirms that small addition of BPW can maintain tensile strength. However, there seems to be an optimal BPW percentage above which the tensile strength decreases. This behaviour can be attributed to the weaker bond strength between the cement paste and the BPW compared with the natural aggregate (Figure 7) [18; 40; 67]. It also can be observed that the impact of hybrid and hard BPW additions on the tensile strength is almost identical. Besides, although the addition of BPW decreases the tensile strength of concrete at higher percentages, hybrid and hard BPW's addition results in better tensile strength compared to soft BPW.  
Besides, most international codes propose a power relation between tensile and compressive strength (see, for example, ACI 363-R08 [68]). Figure 10 demonstrates the power relations found between tensile and compressive strength of different BPW-containing concrete.  
Figure 8: The compressive strength ratios versus the density ratios of BPW-containing concrete to control concrete.  
Figure 9: The tensile strength ratio of BPW-containing concrete to control concrete versus BPW percentages.  
The power relationship between tensile and compressive strength is not strongly dependent on the BPW type used in the mixtures based on Figure 10. Hence, a general relationship between the tensile and compressive strength of BPW-containing concrete is introduced in Figure 11 and Equation (1) as:  
\[\rm{f_{f(BPW)}=0.78~{}(f_{c}\text{~{}}^{*}(0.42))} \tag{1}\]  
Figure 11 illustrates the ratio of the predicted to experimental tensile strength results, where the predicted results are obtained using the relationship proposed by different international codes, tabulated in Table 3.  
Figure 10: The relation between the tensile strength and compressive strength of concrete containing different percentages and types of BPW.  
As can be seen, relationships proposed by ACI 363-R08 [68], ACI 318-14 [76], AS 3600-2018 [16], JCI [71], EC-2 [69] could predict the tensile strength of BPW-containing concrete within 15% of tolerance. Moreover, several formulae are proposed by other researchers to predict the tensile strength of plastic-containing concrete. The predicted tensile strength ratio, obtained from the proposed equations of other studies, to experimental results of BPW-containing concrete are listed in Table 3 and Figure 13.  
Figure 12: The ratio of predicted tensile strength from different standards for conventional concrete and experimental tensile strength results [16; 68; 69; 70; 71; 72; 73; 74; 75; 76; 77].  
Among all the predictive formulae, [PERSON] (coarse aggregate substitution) [35] and [PERSON] et al.'s [47] formulae could predict all three types of BPW-containing high-strength concrete within a reasonable tolerance of 15%. The other proposed formulae generally overestimate the tensile strength of BPW-containing high-strength concrete at low BPW percentages and underestimate it at higher percentages.