## 2 Experimental Design  
### Preparation of Paste Filling Material  
At present, there is no relevant experimental procedure standard for coal mine filling materials. Therefore, the experimental mainly referred to the 'Mortar basic performance test method standard' (JGJ/T70-2009) [14] and the 'Ordinary concrete mixture performance test method standard' (GB/T50080-2002) [15]. Coal mine filling paste is an ideal material with good fluidity, uniformity, and low water consumption. In the experiment, coal gangue was used as the main aggregate, which is rich in source, convenient for drawing materials, and low in price while reducing the harm caused by the stacking of gangue on the ground. Cement and gypsum are cementitious materials that can improve stability. They have a very important impact on the physical and mechanical properties of the paste before and after solidification. Water reducer, expansive agents, and fly ash are usually used as additives in experiments. In the experiment, coal gangue was used as the main aggregate, and cement and gypsum were used as cementitious materials to improve stability. Additives included the water reducer, expansion agent, and fly ash. The details of raw materials are as follows:  
(1) The natural coal gangue of a coal mine was sampled on site, and the filling aggregate with particle size less than 25 mm was prepared by hammer crushing, jaw crusher crushing, and vibrating screen screening. Coal gangue with particle size less than 25 mm acts as coarse aggregate. The chemical composition of coal gangue included SiO\({}_{2}\), Al\({}_{2}\)O\({}_{3}\), Fe\({}_{2}\)O\({}_{3}\), CaO, MgO, Na\({}_{2}\)O, K\({}_{2}\)O, SO\({}_{3}\), and P\({}_{2}\)O\({}_{5}\)[16]. (2) Ordinary Portland cement (P-O) was used as cement; its main components are clinker, gypsum (80-95%), and granulated blast furnace slag (5-20%). The bulk density is 300 kg/m\({}^{3}\), and the specific surface area is generally 300 m\({}^{2}\)/kg. The fineness requirement of cement is that the sieve residue of 80 \(\upmu\)m square hole sieve is not more than 10%, and the sieve residue of 45 \(\upmu\)m square hole sieve is not more than 30%. The initial setting time of ordinary Portland cement should not be less than 45 min, the final setting time should not be more than 600 min, and the water-cement ratio is 0.5. The main chemical compositions in cement included 3 CaO-SiO2 (C3S), 2 CaO-SiO2 (C2S), 3 CaO-Al2O3 (C3A), and 4 CaO-Al2O3-Fe2O3 (C4 AF) [17]. The measured 3 d strength was 18.96 MPa, and the 28 d strength was 44.59 MPa. The strength was higher than the theoretical strength. (3) The relative density of gypsum was 2.96 g/cm\({}^{3}\). The main component was CaSO4. The main parameters of gypsum are shown in Table 1[17]. (5) The expansion agent was used to limit the formation and development of cracks, effectively improve the impermeability of the paste, and improve the stability of the entire goat. The parameters are shown in Table 3.  
In this experiment, five groups of coal mine filling materials with different proportions were tested. The content of expansive agent in the filling materials was used as an invariant. Using the method of single variable control contrast test, the contents of coal gangue were the same in each group, but the contents of expansive agent, water, fly ash, gypsum, cement, and water-reducing agent were appropriately increased. The filling paste was prepared by manual mixing. The compositions of qualified filling materials are shown in Table 5. \begin{table}
\begin{tabular}{c c c c c} \hline
**Fineness (0.2 mm) Sieve Residue** & **Break Off Strength** & **Compressive** & **The Initial Setting** & **Final Setting Time** \\
**Percentage (\%)** & **(MPa)** & **Strength (MPa)** & **Time (min)** & **(min)** \\ \hline
10.0 & 2.1 & 3.9 & \(\geq\)6 & \(\leq\)30 \\ \hline \end{tabular}
\end{table} 
Table 1: Performance parameter table of gypsum.