## 4 Conclusions  
Based on the fractal theory, this paper systematically studies the influence of the fractal dimension on the flow and sedimentation performance of CSFMs and establishes an evaluation model. The main conclusions are as follows:  
1. The fractal dimension has a significant effect on the slump, expansion, bleeding rate, yield stress, and consistency coefficient of CSFMs. With an increase in fractal dimension (\(D\)), the slump and expansion degree increase first and then decrease, and the bleeding rate decreases gradually. In contrast, an increase in the fine particle ratio will increase the consistency coefficient. Based on this, a CSFM flow performance evaluation model based on fractal dimensions is constructed, which provides a theoretical basis for optimizing the fluidity of slurry.
2. The influence of the fractal dimension on the sedimentation behavior and stability of CSFMs was revealed by dynamic sedimentation experiments and particle fractal distribution analysis. Studies have shown that the larger the fractal dimension (\(D\)), the slower the settling velocity of the slurry and the higher the stability. Based on the experimental results, a CSFM sedimentation performance evaluation model was established, which provided a new method for evaluating the sedimentation stability of slurry.
3. Through the collaborative evaluation and analysis of the flow characteristics and settlement performance of CSFMs, it is found that the CSFM with a fractal dimension (\(D\)) between 2.46 and 2.59 has the best balance between flow performance and settlement performance, which can ensure the reliability of long-distance transportation and construction quality.
4. The fractal theory can be used to evaluate the fluidity and sedimentation performance of CSFMs. By screening the particle size of gangue particles and calculating the fractal dimension, the complexity of particles and its influence on the filling performance of slurry can be accurately described. The fractal theory is easy to operate and suitable for the application of CSFMs in practical engineering.  
Conceptualization, X.S. and W.W.; software, B.Z.; validation, R.T.; formal analysis, W.W.; investigation, J.N.; data curation, Z.W.; writing--original draft, W.W.; writing--review and editing, Y.Z.; visualization, X.D.; supervision, R.T.; project administration, X.S.; funding acquisition, X.S. All authors have read and agreed to the published version of the manuscript.  
Figure 16: The relationship between the fractal dimension and flow and settlement performance.  
**Funding:** This research was supported by the National Natural Science Foundation of China under Grant Nos. 52400185 and the Key R & D plan of Shaami Province in 2023 under Grant Nos. 2023-LL-QY-02.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data will be made available on request.  
**Acknowledgments:** The authors express their sincere gratitude to [PERSON] and [PERSON] for their valuable suggestions and assistance during the preparation of this study. Their contributions were instrumental in refining the research methodology and enhancing the quality of the manuscript.  
**Conflicts of Interest:** The authors declare no conflicts of interest.