# Design Procedures for Sustainable Structural Concretes Using Wastes and Industrial By-Products
## 2 Experimental Program
### Materials
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Diameter (mm)** & **Length (mm)** & \
\begin{tabular}{c} **Developed** \\ **Length (mm)** \\ \end{tabular} & **Slenderness** &
\begin{tabular}{c} **Curvature** \\ **Index** \\ \end{tabular} \\ \hline Minimum & 0.1 & 5.0 & 19.0 & 45.5 & 0.1 \\ Maximum & 1.2 & 92.0 & 129.0 & 651.2 & 0.9 \\ Mode & 0.3 & 33.0 & 34.0 & 225.0 & 0.3 \\ Average & 0.3 & 33.2 & 53.3 & 199.0 & 0.4 \\ CoV & 0.448 & 0.411 & 0.358 & 0.392 & 0.529 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Geometric properties of RTSF. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **EAFS** & \multicolumn{3}{c}{**FA**} \\ \hline  & **XRF** & **XRF** & **EDS** & **XRD** \\ \hline Al\({}_{2}\)O\({}_{3}\) & 8.91 & 27.30 & 28.59 & 22.1 vitreous * \\ BaO & 0.15 & & & 3.65 & \\ C & & & 1.80 & \\ CaO & 26.73 & 2.36 & 1.80 & \\ Cl & 0.02 & & & \\ Cr\({}_{2}\)O\({}_{3}\) & 1.70 & & & & \\ CuO & 0.03 & & & & \\ Fe\({}_{2}\)O\({}_{3}\) & 32.33 & 8.19 & 6.86 & 4.8 vitreous * \\ K\({}_{2}\)O & 0.23 & 3.34 & 1.97 & \\ MgO & 4.27 & 1.42 & & \\ MnO & 3.25 & & & \\ Na\({}_{2}\)O & 0.30 & 0.99 & 1.78 & \\ Nb\({}_{2}\)O\({}_{5}\) & 0.02 & & & \\ P\({}_{2}\)O\({}_{5}\) & 0.51 & & & \\ SiO\({}_{2}\) & 20.29 & 49.12 & 56.83 & 28.7 vitreous * \\ SO\({}_{3}\) & 0.29 & 1.30 & & \\ SrO & 0.04 & & & \\ TiO\({}_{2}\) & 0.67 & 2.32 & & \\ V\({}_{2}\)O\({}_{5}\) & 0.14 & & & \\ WO\({}_{3}\) & 0.01 & & & \\ ZnO & 0.02 & & & \\ Other & & & & 15.4 vitreous * \\ Quartz & & & & 18.41 \\ Mullite & & & & 7.18 \\ Hematite & & & & 3.41 \\ Total crystalline phase * & & & & 29.00 \\ Total glassy phase & & & & 71.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Element composition of the EAFS and FA by XRF, SEM-EDS and XRD analysis [%]. ULFRC (Ultra-Lightweight Fiber Reinforced Concrete) and for ULC (Ultra-lightweight Concrete) the \(q\) values range between 0.32-0.35 [40; 41]. In this study the value of \(q\) was initially fixed to 0.35. However, in the course of the research, the value of \(q\) it has decreased to a minimum value of 0.15. Based on the modified equation of [PERSON] and [PERSON], [PERSON]. [32] established an optimized algorithm for optimizing concrete formulations. The algorithm adjusted the proportions of each individual material in the mixture, until an optimum fit between the composed mixture and the target curve was reached. To minimize the deviation between the target curve and the composed mixture the algorithm employed the residual sum of squares (\(RSS\)) at defined particle sizes based on the least squares method (LSM), as follows:  
\[RSS=\sum_{i=1}^{n}\left(P_{mix}\left(D_{i}^{i+1}\right)-P_{tar}\left(D_{i}^{i+ 1}\right)\right)^{2} \tag{2}\]  
where \(P_{mix}\) is the composed mix and the \(P_{tar}\) is the target grading calculated from Equation (2). With the purpose of reaching an optimal concrete design, this research made use of this algorithm. It should be noted that this algorithm is designed for optimization of the solid skeleton. Other variables such as SP, PL, and the \(w/p\) or \(w/c\) ratio must be defined by the technician considering the target properties including strength and its balance with the fresh properties. When choosing this methodology, only the solid skeleton formed by the aggregates was considered, the type of SP or PL and the type of fibers were not taken into account. However, some restrictions had to be imposed. Thus, based on the reference mixture REF1, the cement, water and SP amount were fixed in order to start the first iterations of mixtures. PL constituent was not added to the initial EAFS mixtures as it was not considered a relevant admixture. After the first design, using the previously mentioned algorithm with the predefined restrictions and a \(q\) value equal to 0.35, it was realized that \(w/p\) ratio value would be equal to 0.55. Then, the \(w/p\) ratio was kept constant. Initially, EAFS mixtures based on those predefined variables were made. In the first EAFS mixtures the limestone filler ingredient was considered as an addition.