## 4 Results and Analysis
### Analysis
The numerical simulation results show that when the \"sand-mud ratio is 8:2 + mining height is 5 m\", the maximum development height of water-flowing fracture increases slowly and evenly with the change in sand layer coefficient; that is, when the sand layer coefficient increases from 60% to 90.9%, the maximum development height of water-flowing fracture increases slowly and evenly with the change in sand layer coefficient; that is, when the sand layer coefficient increases from 60% to 90.9%, the maximum development height of water-flowing fracture increases from 60% to 90.9%, the maximum development height of water-flowing fracture increases rapidly and evenly with the change in sand layer coefficient; that is, when the sand layer coefficient increases from 60% to 90.9%, the maximum development height of water-flowing fracture increases from 64.6 m to 178.2 m, with an average increase of 23.74%. Under the two conditions of \"sand-mud ratio of 8:2 + mining height of 5 m\" and \"sand-mud ratio of 8:2 + mining height of 3 m\", the distance between the bearing stratum and the coal seam increases from 120 m and 79.2 m to 180 m with the increase in sand layer coefficient, and the trend of the maximum development height of water-conducting fracture with the change in sand layer coefficient is consistent with the numerical simulation test results, which can be confirmed by each other. In particular, the two methods are highly consistent in identifying the maximum development height of water-conducting fractures when the sand-mud ratio is 8:2 + mining height is 5 m, and the average error rate is only 1.9%. It can be seen that the results of the theoretical calculation of rock fragmentation and the results of the numerical simulation test tend to be more consistent when the mining height and sand-mud ratio are large and tend to be more discrete when the mining height and sand-mud ratio are small. Based on the results of the two methods, combining the results of the two methods, the quantitative relationship between the maximum development height of water-conducting fractures and sand layer coefficient, sand-mud ratio, and mining thickness is shown in Equation (4). \[ \begin{split} H_{l}&=-11.76M^{2}-64.78x^{2}+0.07y^{2}+ 101.35M+319.50x-5.61y-251.04\\ R^{2}&=0.818\end{split}  \tag{4}\]  
where \(H_{l}\)--the maximum development height of water-conducting fracture, m; \(x\)--sandstone layer coefficient, %; \(y\)--sand-mud ratio; and \(M\)--height mining, m.
2. Under the condition of the same sand-mud ratio and the sand layer coefficient greater than 67%, the increase in the sand layer coefficient will eliminate the difference of the positive effect of different mining heights on the maximum development height of the overburden water-flowing fracture. The numerical simulation test results show that when the sand-mud ratio is 6:4 and the sand layer coefficient exceeds 71.4%, the maximum development height of the water-conducting fracture produced by 5 m and 3 m mining height is very small, only within 0.6 m. When the sand-mud ratio is 8:2 and the sand layer coefficient exceeds 83.3%, the maximum development height of water-conducting fractures produced by 5 m and 3 m mining heights is very small, only within 0.8 m. It can be seen that when the sand-mud ratio is 6:4 and the sand layer coefficient exceeds 72% or the sand-mud ratio is 8:2 and the sand layer coefficient exceeds 83%, the influence of mining height changes on the maximum development height of water-flowing fracture tends to disappear.