## 1 Introduction
However, the raw materials used for coal gangue slurry filling are prepared by crushing pure gangue, which is significantly different from the properties of slurry containing a binder and aggregate. It is not easy to adjust and evaluate the fluidity and sedimentation performance of coal gangue slurry solely based on the ratio of several materials. There is an urgent need to assess and optimize the fluidity and sedimentation performance of gangue slurry. The fractal theory was founded by American mathematician [PERSON] in the 1970s [27, 28]. Fractal theory can quantify the complexity and fractal characteristics of particle systems, which is especially suitable for describing the non-uniform, complex, or nonlinear distribution of particle systems. Fractal theory has recently been utilized in the examination of coarse-grained soil, yielding several advancements in particle fragmentation [29, 30]. [PERSON] et al. [31] employed the box-counting approach to determine the fractal dimension of SEM images. They further explored the relationships between the fractal dimension and various properties, including compressive strength, pore structure, and hydraulic permeability. [PERSON] et al. [32] designed seven groups of recycled aggregate concrete slurry (RAC) with different fractal dimensions and investigated how the fractal dimension impacts the slump, compressive strength, and carbonation depth of recycled aggregate concrete (RAC) slurry. [PERSON] et al. [33] developed a model to describe the relationship between the fractal dimension of gangue aggregate gradation and rheological parameters. They also examined how the correlation between aggregate gradation and rheological parameters evolves. The above research proves that there is a correlation between the fractal dimension and rheological parameters of gangue slurry. Still, the research results cannot evaluate the fractal dimension of the fluidity and sedimentation performance of gangue slurry. Therefore, the purpose of this study is to establish the relationship between the fractal dimension of CSFMs and the flow performance and sedimentation performance, and to evaluate the flow performance and sedimentation performance by using the fractal dimension \(D\) of the slurry. In this paper, a new method for evaluating the flow performance and settlement performance of CSFMs based on the fractal dimension \(D\) is proposed, which aims to simplify the evaluation process and improve the accuracy of practical applications. The key innovations of this study are as follows. (1) By examining the mechanisms through which CSFMs impact the slump, expansion, bleeding rate, yield stress, and consistency coefficient under various fractal dimensions, an evaluation model for the flow performance of gangue filling slurry based on the fractal dimension is developed. (2) In terms of settlement performance, the dynamic settlement experiment was used to analyze the impact of the fractal dimension on the settlement behavior and stability of CSFMs, and an evaluation model is proposed to be established. (3) The optimum gradation range of CSFMs suitable for engineering is given by a synergistic evaluation of slurry flow performance and settlement performance. This study provides a new method for scientific CSFM performance evaluation and provides theoretical support and practical guidance for optimizing the filling process in mining engineering.