## 3 Results and Discussion
### Hardened Concrete Properties
#### 3.2.4 Modulus of Elasticity  
The modulus of elasticity ratio of BPW-containing to control concrete versus BPW percentages is shown in Figure 14.  
According to the figure, the modulus of elasticity is gradually decreased by the addition of BPW. This phenomenon can be related to the lower modulus of elasticity of BPW compared with aggregate and cement paste. The weaker ITZ can also be another contributing factor for the decline in the concrete's modulus of elasticity after adding more BPW (Figure 7) [18]. Hence, hybrid and hard BPW addition could better maintain the modulus of elasticity due to their higher modulus of elasticity than the soft BPW. Figure 13: The ratio of predicted tensile strength from other studies for normal strength BPW-containing concrete, and experimental results [39; 50; 51; 52; 53; 54; 55]. Moreover, to better understand the behaviour of BPW-containing concrete, the relations between the modulus of elasticity ratio and the density ratio and the compressive strength of BPW-containing concrete to control concrete are investigated and illustrated in Figure 15a, b, respectively. Figure 14: The modulus of elasticity ratio of BPW-containing concrete to control concrete versus BPW percentages. Figure 15: The modulus of elasticity ratio vs: (**a**) The density ratio of BPW-containing concrete to control concrete, (**b**) the 28-day compressive strength. As expected, the modulus of elasticity decreases by a decrease in the density. It is clear from the figure that the higher the compressive strength, the higher the modulus of elasticity. The relations between the modulus of elasticity and the compressive strength are almost similar and follow the same trend. Hence, to reach simpler formulae and easier engineering interpretations, a general equation for the BPW-containing concrete is introduced with reasonable accuracy, as shown in Figure 16 and Equation (2). As can be seen, the modus of elasticity and the compressive strength of concrete containing BPW follow a power relationship, as suggested in most renowned international codes for conventional concrete. \[\text{E}=2469.5\;(\text{f}_{\text{c}})^{*}(0.6526) \tag{2}\]  
In which both E and f\({}_{\text{c}}\) are in MPa. Afterwards, different international codes were investigated to compare the results and investigate if they are still suitable for designing the BPW-containing concrete. In this regard, Figure 17 demonstrates the ratio of predicted modulus of elasticity obtained from the equations proposed by different international codes and the experimental modulus of elasticity results of this study (Table 3). Figure 16: The relation between modulus of elasticity and compressive strength of BPW-containing concrete and correction factors for each type of BPW. It can be concluded that except for JCI [71], EHE [82], NBR 6118 [78], and TS-500 [79], other codes [68; 69; 72; 73; 74; 76; 81; 82; 84] could predict the modulus of elasticity of the BPW-containing concrete within the range of 15% tolerance. Some codes also introduced an equation predicting modulus of elasticity from the compressive strength and the conventional concrete's unit weight (Table 3). Figure 18 illustrates the ratio of the predicted and the experimental modulus of elasticity values for concrete containing different percentages of BPW. As can be seen, ACI 363 [68], NS 3473 [81], and CSA [74] codes can predict the modulus of elasticity of BPW-containing concrete with an error of less than 15%. AS 3600 [16] predictions also fall in a reasonable range, except regarding concrete containing 9% of soft BPW. Figure 17: The ratio of predicted modulus of elasticity by the compressive strength from different design codes for conventional concrete and experimental modulus of elasticity results [16; 68; 71; 72; 73; 74; 78; 79; 80; 81; 82; 83]. [PERSON]'s [35] formula regarding fine-aggregate partial substitution with  
Polyvinyl chloride (PVC) aggregate could predict the modulus of elasticity of all three types of BPW-containing high-strength concrete within a reasonable tolerance.