# Design Procedures for Sustainable Structural Concretes Using Wastes and Industrial By-Products
## 4 Discussion
### Mechanical Properties
#### 4.2.1 Compressive Behavior of EAFS Mixtures
2.2 Optimal Parameters for Designing EAFS Concrete Based on the Andreasen and Andersen Particle Packing Model  
Considering the results obtained when designing EAFS concrete mixtures adopting the modified Andreasen and Andersen particle packing model, it is important to further understand how the different design variables influenced the results obtained. Of particular interest are the percentage of EAFS aggregates added, the water/powder ratio, \(w/p\), and the distribution modulus, \(q\). As shown in Figure 14, for a \(q\) value of 0.35, as the percentage of EAFS increases, the characteristic compressive strength and elasticity modulus also increases. The reverse happens for high percentages of EAFS, where the characteristic compressive strength and elasticity modulus starts to decrease. The last may be justified, due to the decrease in paste compared to the amount of EAFS aggregates, which is not enough to obtain such a compact solid skeleton. As the \(q\) increases to 0.25, both the characteristic compressive strength and elasticity modulus increases substantially. Note that, despite the two EAFS3B and EAFS8B mixtures being very similar, the mixture EAFS3B has lower characteristic compressive strength and elasticity modulus. As the EAFS3B mixture has a greater variety of EAFS grain size fractions, the resulting paste had a higher amount of EAFS fines (<125 \(\upmu\)m) and less CEM and FA compared to the resulting paste of EAFS8B. The EAFS8B mixture has only two EAFS grain size fractions, which means that it has a lower amount of EAFS fines than in the EAFS3B mixture, and therefore, a paste that is richer in CEM and FA, making its solid skeleton stronger. On the other hand, if the value of \(q\) decreases by 0.20 or 0.15, the characteristic compressive strength and elasticity modulus will be approximately similar, independent of the EAFS amounts added. This means that an optimal value of \(q\) has been reached. This optimal value is lower than what was expected when using conventional aggregates (\(q\) = 0.30) perhaps due to the porous nature and angular shape of the EAFS aggregate particles, which appear to require a greater amount of paste [59; 60]. For mixtures with a \(q\) value equal to 0.20 it is verified what was explained above about the mixtures with higher EAFS grain size fractions having lower characteristic compressive strength and elasticity modulus because they have a paste with more EAFS powder fine particles. In this case, this happens for the mixtures EAFS5C (with higher grain size fractions of EAFS) and EAFS8C (with only two grain size fractions of EAFS), however, this difference is not so pronounced for a value of \(q\) equal to 0.20. From these findings it can be stated that there is an optimal value of \(q\) that depends on the EAFS percentage. This EAFS percentage comes from achieving a balance between the amount of EAFS particle size fineness in the EAFS mixture paste and EAFS aggregates. The higher the value of \(q\), the lower the amount of paste and the higher the amount of aggregates, and therefore, the lower the strength and the elasticity modulus. On the contrary, the smaller the value of \(q\), the greater the amount of paste present in the mixture and the smaller the amount of aggregates, which makes the solid skeleton more compact and stronger. However, if the value of \(q\) drops below 0.15, both the strength and the elasticity modulus have a decreasing tendency, that is, for a value of \(q\) that is too low there will be a large amount of paste for a small amount of aggregates, and therefore, these small amounts of aggregates are not enough to form a strong solid skeleton. The evolution of characteristic compressive strength, \(f_{ck}\), and average elasticity modulus at 28 days, \(E_{cm}\), for different \(q\) is represented in Figure 15. Based on designed EAFS mixtures it was possible to correlate the different distribution modulus with the characteristic compressive strength and elasticity modulus through a second-degree polynomial equation.