## 4 Results and Analysis
### Analysis  
2.1 The Influence of Sand Layer Coefficient on the Maximum Development Height of Water-Conducting Fracture  
According to Table 4, when the mining height is 5 m and 3 m, the corresponding relationship curves between the sand layer coefficient of coal seam overburden and the maximum development height and fracture-mining ratio (N-MH-5m and N-MH-3m) of water-conducting fracture based on a numerical simulation test and the maximum development height and fracture-mining ratio (T-MH-5m and T-MH-5m) of water-conducting fracture based on the theory of rock fragmentation and expansion are drawn, as shown in Figures 5 and 6. The following can be seen from Table 4, Figures 5 and 6:  
Figure 5: The corresponding relationship curve between sand layer coefficient and the maximum development height of water-conducting fracture. (**a**) The sand–mud ratio is 6:4. (**b**) The sand–mud ratio is 8:2. Figure 6: Columnar diagram of the corresponding relationship between sand layer coefficient and fracture-mining ratio. (**a**) The sand–mud ratio is 6:4. (**b**) The sand–mud ratio is 8:2. Under the condition of a given sand-mud ratio, the maximum development height of a water-flowing fracture increases with the increase in the sand layer coefficient. That is to say, under the same buried depth, the more sandstone layers in the coal seam overburden, the greater the maximum development height of the water-flowing fracture. The numerical simulation results show that when the \"sand-mud ratio is 6:4 + mining height is 5 m\", the maximum development height of water-flowing fracture presents a three-stage change process of \"rapid increase-stable-slow increase\" with the change in sand layer coefficient. That is, when the sand layer coefficient is between 60-66.7%, the maximum development height of water-flowing fracture increases rapidly with the increase in sand layer coefficient, from 78.5 m to 97.6 m, with an average increase of 24.3%. When the sand layer coefficient is between 66.7% and 71.4%, the maximum development height of water-conducting fractures does not change much. When the sand layer coefficient is between 71.4% and 90.9%, the maximum development height of water-flowing fracture increases slowly with the increase in sand layer coefficient, from 99.1 m to 133.2 m, with an average increase of 10.5%. When the \"sand-mud ratio is 6:4 + mining height is 3 m\", the maximum development height of water-conducting fracture shows a two-stage change process of \"rapid increase-slow increase\" with the change in sand layer coefficient; that is, when the sand layer coefficient is between 60% and 71.4%, the maximum development height of water-conducting fracture increases rapidly with the increase in sand layer coefficient, from 48.0 m to 99.0 m, with an average increase of 43.99%. When the sand layer coefficient is between 71.4% and 90.9%, the maximum development height of a water-flowing fracture increases slowly with the increase in the sand layer coefficient, from 99.0 m to 134.2 m, with an average increase of 10.85%. Under the two conditions of \"sand-mud ratio of 6:4 + mining height of 5 m\" and \"sand-mud ratio of 6:4 + mining height of 3 m\", the distance between the bearing stratum and the coal seam increases from 75 m and 50 m to 135 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 6:4 + mining height is 5 m\", and the average error rate is only 3.1%.