## 4 Discussion and Conclusions  
Characterizing the floor failure will be helpful in practice to improve the safety of coal mining above the underlying aquifers. With respect to the effects of mining and hydraulic pressures as well as strata dip, mechanical models were proposed to comparatively investigate the vertical failure ranges and water inrush risk of the horizontal and the inclined floors after excavation. Then, these models were confirmed by numerically simulating the failure characteristics of coal seam floors above the aquifers. The detailed conclusions of the current study can be drawn as the following:  
1. The results of theoretical calculation and numerical simulation exhibit good agreement regarding the ranges of vertical failure of the horizontal and inclined floors. The characteristic of the horizontal floor after coal mining conforms to an approximately \"inverted saddle\" shape, and shows geometric symmetry along the inclination. Compared with the horizontal floor, the damage zone at the lower end of the inclined stratum presents a wider and deeper range than the upper end.
2. The possibility of groundwater inrush through the sides of the goat is relatively higher for both the horizontal and inclined seam floors, with their theoretical maximum failure depths roughly 12 m, 15 m (the upper part) and 12.5 m (the lower part). The distribution of the vertical failure ranges is generally consistent with water inrush zoning on the key strata. For example, the damage zones of the remaining waterproof layers, such as zones 1, 2 and 3, are dominantly concentrated near the model boundaries under the mined-out area. The ordering of these zones in terms of water-inrush risk from the horizontal and inclined impermeable layer is R(H2) = R(H3) > R(H1) and R(I2) > R(I1) > R(I3), respectively. Therefore, effective countermeasures such as goat filling and floor grouting should be implemented within areas of high risk after coal excavation.
3. The proposed analytical models are beneficial to a comparative analysis of the failure modes and instability between horizontal and inclined floors. The representation of the fracturing process of the floor rock mass was limited. However, the presented mechanical models reveal the theoretical mechanism inducing the frequent occurrence of inrush disasters at the stope floor close to the rear goat or the coal wall. Thus, the study results can provide some valuable references for assessing and managing water-related hazards in deep underground engineering.  
Conceptualization, C.Z. and W.S.; methodology, C.Z. and W.S.; software, C.Z.; validation, C.Z. and W.S.; formal analysis, C.Z. and W.S.; investigation, C.Z. and W.S.; data curation, C.Z. and W.S.; writing--original draft preparation, C.Z. and W.S.; writing--review and editing, W.S. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.  
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy concerns.  
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.