## 2 Experimental Setup
### Mix Proportions Design  
In this experiment, the cementitious material was cement. Furthermore, the foam content was determined by the proportions of cementitious material, ceramics, and SS. The core objective of this study was to determine the optimal mix proportion for SSCFC. Extensive preliminary experiments and a literature review conducted by our team demonstrated that the W/C ratio, aggregate selection, and content ratios critically influence concrete performance. Consequently, the W/C ratio, SS replacement ratio, and ceramics substitution rate were selected as key variables to investigate mechanical property variations under different mix proportions, thereby identifying the optimal formulation. To reduce the experimental workload, an orthogonal experimental design was adopted. This method utilizes orthogonal arrays to systematically arrange and analyze tests across all factor levels. Representative test combinations were selected from all possibilities, with comprehensive analysis of test results enabling identification of the optimal combination [40]. The orthogonal design ensures \"uniform dispersion\" and \"orderly comparability\" of test points, allowing for a comprehensive evaluation of the factor significance hierarchy and optimal value determination. The orthogonal experimental design method was employed to investigate the effects of the W/C ratio, SS, and ceramicstic mass replacement ratios on the compressive strength performance of SSCFC. Therefore, the W/C ratio (Factor A), SS (Factor B), and ceramicstic (Factor C) were identified as the three critical factors in the orthogonal experimental design. The levels of each factor represent their reasonable operational values. In this study, three levels were assigned to each factor based on our research team's previous experimental experience and findings, as detailed in Table 4.  
To ensure scientific rationality and enable clearer evaluation of the effects of SS and ceramicstic on the foam concrete's performance, three control groups (Groups 10, 11, 12) were additionally designed with 0% steel slag powder and ceramicstic contents. The component proportions of SSCFC are detailed in Table 5. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Levels**} & \multicolumn{3}{c}{**Factors**} \\ \cline{2-4}  & **A (-)** & **B (wt.\%)** & **C (wt.\%)** \\ \hline
1 & 0.4 & 10 & 20 \\
2 & 0.45 & 15 & 25 \\
3 & 0.5 & 20 & 30 \\ \hline \hline \end{tabular} Note: B and C are the contents of SS and ceramicstic, respectively. A is the water–cement ratio, i.e., the ratio between water and cement. In addition, wt.% represents the mass of the materials.  
\end{table} 
Table 4: L9 (3\({}^{3}\)) orthogonal experimental array. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Foam Type** & **Density (kg/m\({}^{3}\))** & **Settlement Distance (mm)** & **Bleeding Volume (mL)** \\ \hline Plant protein foam & 55 & 2 & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Foam properties. The mixing ratio of foam concrete is calculated based on its target density and foam characteristics. To determine SSCFC formulations, the \"Solid Compatibility Product Method\" proposed by the University of Dundee (UK) was referenced, which essentially controls material dosages by regulating design proportions of components per unit volume [41; 42]. The specific equations are as follows:  
\[M_{D}=M_{C}+M_{W}+M_{F}+M_{T}+M_{G} \tag{1}\]  
\[1=\frac{M_{C}}{P_{C}}+\frac{M_{W}}{P_{W}}+\frac{M_{F}}{P_{F}}+\frac{M_{T}}{P_{ T}}+\frac{M_{G}}{P_{C}} \tag{2}\]  
where \(M_{D}\) represents the mass of 1 m\({}^{3}\) SSCFC (kg); \(M_{C}\) is the cement mass contained in 1 m\({}^{3}\) SSCFC (kg); \(M_{W}\) corresponds to the water content in 1 m\({}^{3}\) SSCFC (kg); \(M_{F}\) signifies the foam mass in 1 m\({}^{3}\) SSCFC (kg); \(M_{G}\) refers to the SS mass in 1 m\({}^{3}\) SSCFC (kg); and \(M_{T}\) indicates the ceramsite mass in 1 m\({}^{3}\) SSCFC (kg).