## 5 Conclusions  
The paper experimentally studied the changes in dynamic stress-strain of fine sandstone under different temperatures (18-100 \({}^{\circ}\)C), axial static loads (1-9 MPa), bullet incidence velocities, or strain rates, and analyzed the changes in physical properties and surface displacement fields of fine sandstone. A one-dimensional stress state dynamic stress-strain constitutive model of fine sandstone was established and verified. The main conclusions are as follows:  
1. The increase in temperature and axial static load leads to an increase in the dynamic peak stress of coal bearing fine sandstone. When the temperature changes from 18 degrees to 100 \({}^{\circ}\)C, the dynamic peak stress increases by 103.7%. When the axial static load changes from 1 MPa to 9 MPa, the dynamic peak stress increases by 39.7%. Within the temperature range studied in this article (18-100 \({}^{\circ}\)C), the dynamic peak stress and peak strain of fine sandstone are positively correlated with strain rate or  
Figure 11: Comparison between true and fitting stress of fine sandstone at different temperatures.  
bullet incidence velocity. At a temperature of 18 \({}^{\circ}\)C, when the strain rate changes from 53.1 s\({}^{-1}\) to 137.4 s\({}^{-1}\), the dynamic peak stress increases by 215.6%. When the temperature is 40 \({}^{\circ}\)C and the strain rate changes from 47.1 s\({}^{-1}\) to 107.5 s\({}^{-1}\), the dynamic peak stress increases by 60.3%. When the temperature is 60 \({}^{\circ}\)C and the strain rate changes from 53.1 s\({}^{-1}\) to 140.9 s\({}^{-1}\), the dynamic peak stress increases by 117.6%. When the temperature is 80 \({}^{\circ}\)C and the strain rate changes from 49.1 s\({}^{-1}\) to 87.9 s\({}^{-1}\), the dynamic peak stress increases by 46.3%. When the temperature is 100 \({}^{\circ}\)C and the strain rate changes from 50.2 s\({}^{-1}\) to 114.4 s\({}^{-1}\), the dynamic peak stress increases by 55.6%.
2. The influence of external experimental parameters on the dynamic mechanical properties of fine sandstone was analyzed, and it was found that the dynamic stress, strain, temperature, axial static load, strain rate, or bullet incidence velocity of fine sandstone exhibit a polynomial relationship, with a determination coefficient greater than 0.9.
3. The main components of this group of fine sandstone are quartz, sodium feldspar, muscovite, and kaolinite. The continuous effect of temperature causes free water to precipitate from muscovite and kaolinite, increasing the friction force between fine sandstone particles and improving their macroscopic bearing capacity.
4. Based on [PERSON]'s effective stress principle, rock mechanics strength theory, and statistical damage theory, a dynamic stress constitutive model of fine sandstone under a one-dimensional stress state was established. The values of model parameters were theoretically determined, and the model was validated through dynamic stress change curves of fine sandstone at different temperatures.  
Conceptualization, E.Z.; methodology, E.Z. and E.W.; software, H.C.; validation, H.C.; formal analysis, E.Z.; investigation, E.Z.; resources, H.C.; data curation, H.C.; writing-original draft preparation, E.Z.; writing-review and editing, H.C.; visualization, H.C.; supervision, E.Z.; project administration, E.Z.; funding acquisition, E.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (52004267, 51934007), and Basic Research Project of Xuzhou City, China (Grant No. KC22001).  
Not applicable.  
Data Availability StatementData available on request due to privacy.  
The authors declare no conflict of interest.