## 7 Conclusions  
This paper uses elastic thin plates and rheological theory to build the physical model of the bauxite protective roof-pillar bearing structure and gives the calculation formula of the stand-up time of the bearing structure. The following conclusions can be obtained from this study:  
1. Taking the protective roof-pillar bearing structure in the goat of bauxite mine as the research object, based on the elastic sheet theory and rheological theory and considering the interaction of roof or pillar, a physical model of the protective roof-pillar bearing structure is constructed to solve the problem. The stand-up time \(T\) is used as the index to consider the bearing capacity of the goat bearing structure and the calculation method of the stand-up time of the bearing structure is given.
2. The stand-up time (\(T\)) of the bearing structure in the goat of bauxite is mainly affected by the thickness of the protective roof (\(h\)), the uniform surface force coefficient (\(\lambda\)) of pillar, the span of the goat (\(2n\)) and the thickness of the overlying rock layer (\(H\)). 1. When other factors remain unchanged, \(T\) is positively correlated with \(h\), which increases with the increase of \(h\). When \(h\) is within the range of 0.3-0.4 m, the bearing capacity of the bearing structure reaches the limit state. 2. When other factors remain unchanged, \(T\) is positively correlated with \(\lambda\) which increases with the increase of \(\lambda\) and the increasing speed is gradually accelerated. When \(\lambda\) is in the range of 0.3-0.4, the bearing capacity of the bearing structure reaches the limit state. 3. When other factors remain unchanged, \(T\) is negatively correlated with \(2n\) which decreases with the increase of \(2n\) and the decreasing speed slows down gradually. When \(2n\) is greater than 60.0 m, the bearing capacity of the bearing structure reaches the limit state. 4. When other factors remain unchanged, \(T\) is negatively correlated with \(H\) and decreases with \(H\) increasing and the decreasing speed slows down gradually. When \(H\) comes 90.0 m, the bearing capacity of the structure reaches the limit state.
3. The engineering application shows that the goat bearing structure in case 1 is within stand-up time range and the goat is basically stable. In case 2, the goat bearing structure loses its bearing capacity and the goaf has become unstable and collapsed. The results of theoretical calculation are basically consistent with those of engineering examples, which verifies the scientific nature of the calculation results of load-bearing mechanics model.
* Taking the bauxite mine in Shanxi Province studied in this paper as an example, a proposed range of goaf structural parameters is given in consideration of economic benefits and production safety. Under the condition that the thickness of the overlaying rock and soil layer is 50 m, the thickness of the protective roof is 0.5 m, the uniform surface force coefficient of pillars is 0.5 and the goaf span is 30 m. Such a scheme is relatively safe and reliable.  
Conceptualization, L.J.; Methodology, W.L.; Validation, L.J.; Investigation, W.L.; Resources, L.J.; Data curation, W.L.; Writing--original draft, W.L.; Supervision, L.J.; Project administration, L.J. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Natural Science Foundation of China (Grant No. 51974135).  
Not applicable.  
Most of the analysis and resulting data during this study are included in this manuscript, and all of the data are available from the corresponding authors upon reasonable request.  
Sincere thanks to the related engineers at the Shanxi Senze Energy Technology Group Co., Ltd. for their substantial support and help in field measurements and engineering detection.  
The authors declare no conflict of interest.