## 2 Materials and Methods  
RP was used as aggregate. It was collected in an industry, located in the municipality of Soledade--Rio Grande do Sul, Brazil, that processes rolled agate. The Portland cement (PC) (Cimpasso, Passo Fundo, RS, Brazil) V-ARI used complies with Brazilian standards NBR 5733 [39] and NBR 5737 [40], cements of initial high strength and sulfate tolerance, respectively. The physical and chemical properties of PC and RP are shown in Table 1.  
The granulometry of RP was conducted using a Cilas laser granulometer model 1190 (CILAS, ORLEANS, France), with an amplitude of measurement from 0.04 to 2500.00 \(\upmu\)m. The chemical composition of the RP was determined by X-ray fluorescence using PANalytical-MiniPal 4 equipment (PANalytical B.V., Almelo, Netherlands) [41]. X-ray diffraction was performed using a Siemens diffractometer model D-500 (Siemens, Monique, Germany), with a Cu anode, set at 40 kV and 17 mA. The 20 angle was varied from 10-80 degrees, with steps of 0.05 degrees. The foam-generating mixture consisted of Cocoamidopropyl Betaine (CPB) and Cocamide Diethanolamine (DEA) [42] in a ratio of 1:3 (one part CPB for two parts DEA). This mixture was diluted 1:70 (one part of mixture to sixty-nine of water) to make the pre-made foam. The foam was prepared by mechanical stirring. The density of the foam formed was 75 kg/m\({}^{3}\). The mortar was prepared by mixing the RP, water, cement, and the preformed foam. The constituents of the mortar were stirred by a mechanical stirrer until a homogeneous mass was formed. The AFCB was produced based on the procedures suggested by ASTM C796 and ASTM C869 [43; 44]. The designs of experiments to determine the properties of AFCB were developed using the complete factorial statistical method. The experimental design depended on two factors with three and four levels, i.e., the experiments were performed with water/cements (w/c) ratio of 1.08, 1.28, and 1.48; and a foam amount of 14%, 18%, 24% and 28% of the total solid mass (cement mass + RP mass). The amount of aggregate (RP) and binder (cement) were kept constant with equal proportion (1:1). Water levels were adjusted according to variations in the w/c rate. For example, when using 1.0 kg of cement, 1.0 kg of RP, 14% foam and a w/c ratio of 1.08, the amount of water should have been 0.80 kg. Table 2 shows an experimental matrix with 12 concrete traces. Three replicates for each response variable were made to avoid systematic errors. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multicolumn{10}{c}{**Physical Properties**} \\ \hline \multirow{3}{*}{**Materials**} & **Specific** & **Blaine** & \multicolumn{6}{c}{**Particle Size**} \\ \cline{3-10}  & **Gravity** & **Fineness** & **Pass in** & **D\({}_{\text{10\%}}\)** & **D\({}_{\text{50\%}}\)** & **D\({}_{\text{90\%}}\)** & **D\({}_{\text{average}}\)** & **pH Paste** \\  & **g/cm\({}^{3}\)** & **m\({}^{2}\)/kg** & **75 μm** & **Mm** & **μm** & **μm** & **μm** & **μm** \\ \hline Portland Cement (PC) & 3.1 & 430 & 0.5\% & 1.0 & 9.6 & 27.6 & 12.3 & 13.0 \\ Rolled Powder (PR) & 2.7 & 80 & 3.2\% & 2.8 & 31.4 & 151.5 & 57.6 & 8.2 \\ \hline \multicolumn{10}{c}{**Chemical Composition**} \\ \hline \multirow{2}{*}{**Materials**} & **Al\({}_{2}\)O\({}_{3}\)** & **CaO** & **CdO** & **SiO\({}_{2}\)** & **Fe\({}_{2}\)O\({}_{3}\)** & **Na\({}_{2}\)O** & **All** & **SO\({}_{3}\)** & **Loss on** \\  & **Al\({}_{2}\)O\({}_{3}\)** & **CaO** & **CdO** & **SiO\({}_{2}\)** & **Fe\({}_{2}\)O\({}_{3}\)** & **Na\({}_{2}\)O** & **Others** & **SO\({}_{3}\)** & **Ignition** \\ \hline Portland Cement (PC) & 3.1 & 60.6 & 4.3 & 18.9 & 0.5 & - & 13.0 & 2.0 & 2.9 \\ Rolled Powder (RP) & 1.2 & 0.4 & 0.1 & 92.2 & 1.1 & 0.1 & 0.1 & - & 3.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Physical and chemical properties of Portland Cement (PC) and Rolled Powder (PR).