## 6 Conclusions  
1. The maximum development height of the water-flowing fracture in the overlying strata of the Yushenfu Coal Mine will increase with the increase in the sand layer coefficient; that is, under the same buried depth, the more sandstone layers in the overlying strata of the coal seam, the greater the maximum development height of the water-flowing fracture. This effect will show different change processes under different sand-mud ratio and mining thickness combination conditions. When the sand layer coefficient is greater than 67%, the increase in the number of sand layers in the overlying rock will eliminate the difference in the positive effect of different mining thicknesses on the maximum development height of the overlying rock water-flowing fracture.
2. The maximum development height of water-conducting fractures in the overlying strata of the study area will increase with the increase in sand-mud ratio; that is, under the same buried depth, the greater the total thickness of sandstone in the overlying strata of the coal seam, the greater the maximum development height of water-conducting fractures. The two methods together show that when the sand-mud ratio increases by 1%, the maximum development height of the water-conducting fracture increases by 1.56-2.40 m in the range of 60-90.9%; that is, the increase in the sand-mud ratio of the overlying strata of the coal seam will amplify the positive effect of the increase in the mining thickness on the maximum development height of the water-conducting fracture of the overlying strata.
3. Based on sand layer coefficient, sand-mud ratio, and mining thickness, the prediction model of maximum development height of a water-conducting fracture is constructed. It is verified by an example that the average absolute error rate between the calculated results of the model and the measured values is 7.17%, which is in line with the actual situation.
4. Based on the numerical simulation test and the theoretical calculation results of rock fragmentation, it is proposed that the effective area of water-preserved coal mining in the study area can be achieved by using the height-limited mining method and must conform to the coal seam overburden structure characteristics of'sand-mud ratio 6:4 and sand layer coefficient less than 70%' and'sand-mud ratio 8:2 and sand layer coefficient less than 80%'.  
S.S.: conceptualization, methodology, and writing--review and editing. H.R.: methodology, software drawing, data curation, writing--original draft, and experiment. J.W.: investigation, software drawing, and experiment. X.C.: investigation and writing--review and editing. R.N.: investigation and writing--review and editing; B.C.: writing--review and editing. All the authors reviewed the manuscript. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This paper is supported by the National Natural Science Foundation of China (41402308), the Key Research and Development Program of Shaanxi Province (2023-YBSF-458), and the Key Laboratory of Geological Guarantee for Coal Green Development of Shaanxi Province (DZBZ2022Z-03).  
**Data Availability Statement**: The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
**Conflicts of Interest**: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.