## 3 Determination of the Optimal Ratio of Cemented Crushed-Stone Slurry
### Cementation Factors of Crushed Stone Inside the Goaf  
To grasp the influences of water-cement ratio, crushed-stone particle size, and cement-sand ratio on the strength of the GCB, orthogonal experiments were performed. On the basis of the experimental results, sensitivity analysis was conducted on factors affecting the GCB specimens in the goal, so as to obtain the final optimal ratio of the grouting materials. 1. Orthogonal experimental design  
Considering the actual situation of mining enterprises, it was decided to choose ordinary silicate cement (cement type PO42.5) and tailing sand produced by the mine as the grouting materials. With reference to the previous experience of metal mine filling [25; 26], it was determined that the strength of the GCB in this experiment should range from 3 MPa to 6 MPa. Based on Equation (1) [27], the water-cement ratio is 3.5:1 when the strength of the GCB is 3 MPa and 2.5:1 when the strength is 6 MPa. Hence, the four levels of water-cement ratio in this experiment were finally set to be 2.5:1, 2.7:1, 2.9:1, and 3.1:1. \[W/B=\frac{\alpha_{a}f_{b}}{f_{cus*0}+\alpha_{a}\alpha_{b}f_{b}} \tag{1}\]  
where \(W/B\) is the water-cement ratio of concrete; \(\alpha_{a}\) and \(\alpha_{b}\) are the regression coefficients; \(f_{b}\) is the 28 d UCS of cementing material for cemented sand, MPa; and \(f_{cus*0}\) is the designed strength, MPa. To study how the crushed-stone particle size influences the strength of the GCB, 100 \(\times\) 100 \(\times\) 100 mm\({}^{3}\) cubes were selected as the specimen size. According to the Standard for Test Methods of Physical and Mechanical Properties of Concrete [28], when the cross-sectional size of the specimen is 100 \(\times\) 100 mm\({}^{2}\), the maximum particle size of aggregate is 31.5 mm. Accordingly, it was determined that the particle size of aggregate in this test lies in three ranges, i.e., \(<\)10 mm, 10-20 mm, and 20-30 mm. Based on field investigation, it was found that no obvious interval exists in the crushed-stone particle size in the goat, indicating that the distribution of crushed-stone particle size shows continuous grading. Under the condition of continuous grading, the crushed-stone particle size has an essential influence on the mechanical properties of the GCB. To reduce the adverse impact of difference in crushed-stone particle size between the engineering field and the laboratory test on the test results, photographs of crushed stone were taken at the sampling positions first. Next, the crushed-stone regions in the photographs were binarized with the aid of MATLAB (R2014b) (Figure 4) and subjected to fractal dimension identification. Eventually, according to the identification results, the mass ratios of crushed stone at the three particle size levels under different fractal dimensions were obtained in the light of [PERSON]'s theory [29]. With the above method, the following results were yielded: the fractal dimensions of crushed stone at the sampling positions lie between 0.62 and 0.65, mainly concentrated at 0.64, and those of crushed stone in this experiment are classified into four levels, i.e., 0.62, 0.63, 0.64, and 0.65. The smaller the cement-sand ratio of the grouting material, the higher the proportion of sand in the slurry, which is conducive to the strength and durability of the structure. In actual construction, selecting an appropriate cement-sand ratio plays a vital role in ensuring the quality of the project. With reference to the discussion and summary of the literature [30] regarding the existing grouting materials of metal mines in China, four levels of the cement-sand ratios in this experiment were determined, i.e., 1:4, 1:6, 1:8, and 1:10.