## 4 Conclusions  
Using an orthogonal experimental design, this research systematically examines the impacts of the W/C ratio, SS substitution rate, and ceramsite substitution rate on the flowability and compressive strength of SSCFC. The optimal mixture ratio was identified through intuitive analysis, range analysis, and factor level evaluation. Multivariate regression models predicting SSCFC's flowability and compressive strength were developed through the PLSR methodology and rigorously validated. The experimental and analytical investigations yield the following key findings:  
1. The orthogonal experimental design revealed that the parameter combination of water-to-cement ratio (W/C = 0.4), SS substitution ratio (10%), and ceramsite substitution ratio (25%) optimizes SSCFC's performance, achieving peak compressive strength while maintaining acceptable workability characteristics.
2. Range analysis demonstrates the hierarchical influence of controlling factors on the compressive strength: W/C (most significant) > ceramicsite > SS. Compared to alternative parameter combinations, the optimized W/C ratio substantially increased the compressive strength by 78.4%. SS substitution contributed an 8.87% strength improvement, with ceramsite replacement providing an 18.18% enhancement.
3. The significance hierarchy for flowability control is as follows: SS > W/C > ceramsite. The SS dosage progressively reduces flowability: a 15.68% decline between 10 and  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Dependent Variable** & **One Principal Component** &
\begin{tabular}{c} **Two Principal** \\ **Components** \\ \end{tabular} \\ \hline Fluidity & 0.299 & 0.888 \\
7d compressive strength & 0.619 & 0.653 \\
14d compressive strength & 0.613 & 0.650 \\
28d compressive strength & 0.624 & 0.650 \\ \hline \hline \end{tabular}
\end{table}
Table 15: The R\({}^{2}\) of the partial least square regression model.  
15% substitution and 7.06% reduction at 15-20% replacement. Increasing the W/C ratio enhances flowability: a 14.33% gain when increasing from 0.4 to 0.45, followed by a 0.90% improvement in the 0.45-0.50 range. Ceramsite replacement moderately enhances flowability: a 0.92% increase at 20-25% replacement, escalating to a 8.91% improvement at a 25-30% dosage.
4. The inherent pressure gradient between foam lamellae interfaces and differential pressures among bubbles induce small bubbles to migrate toward larger ones, creating mechanically detrimental interconnected macro-pores. SS particles effectively fracture large bubbles into uniformly dispersed micro-bubbles through geometric wedging and compressive action, thereby significantly enhancing mechanical performance.
5. Multivariate regression models predicting the flowability and compressive strength of SSCFC were developed through PLSR analysis. Both models demonstrate predictive accuracies surpassing 65% for flowability and compressive strength parameters.  
Conceptualization, A.J. and T.-M.O.; methodology, A.J.; software, H.L.; validation, X.L., J.W. and S.Z.; formal analysis, H.L.; investigation, Y.C.; resources, A.J.; data curation, H.L. and X.L.; writing--original draft preparation, A.J. and H.L.; writing--review and editing, A.J.; visualization, T.-M.O.; supervision, A.J.; project administration, A.J.; funding acquisition, A.J. All authors have read and agreed to the published version of the manuscript. **Funding:** This work was supported by the Fundamental Research Funds for Universities of Xinjiang Uygur Autonomous Region (grant No. XJEDU2023Z003 ), National Natural Science Foundation of China (grant No. 52368051), and the Natural Science Foundation of Xinjiang Uygur Autonomous Region (grant No. 2022D01C685). The above-mentioned funders and their support are gratefully acknowledged.  
The original contributions presented in the study are included in the article; further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.