## 6 Conclusions  
1. The optimal ratio of the gypsum-mixed sandstone-like material is 7.5% river sand, 17.5% quartz sand, 58.3% \(\alpha\)-high-strength gypsum powder, and 16.7% water, respectively. Performance testing experiment have verified that the physical parameters of sandstone in a certain proportion can be simulated well, and the damage pattern is basically the same.
2. The curves were cut into two parts by a HDR of 1.2, and the \(R^{2}\) of the fitting parameters is greater than 0.9. The UCS displayed a changing trend that is M shaped, and the maximum value is obtained at a HDR of 0.6\(\sim\)1, although it does not monotonically decrease as the HDR increases. The peak strains show a W-shaped pattern in contrast to the UCS, which indicates that the stronger the gypsum-like material, the lower the peak strain. And when the HDR is less than 1, specimen damage shows X cross cracks and an increasing number of cracks. Mechanical analysis and numerical simulation results show that the main reason for the difference between UCS and previous studies is the generation of the EFE at a HDR of 0.6-1, which restricts the lateral deformation of the specimen and shows an effect of circumferential pressure, therefore increasing the ability of the specimen to resist deformation.
3. The UCS of the specimens at each SR stage shows roughly the same phased pattern of variation: first a decrease and then an increase. The rapid loading speed prevents cracks within the specimen so that they do not penetrate and converge in time, reducing the degree of destruction of the specimen, and thus increasing the ability of the specimen to resist external loading. For 50 mm\(\cdot\)min\({}^{-1}\), under the action of the EFE, the very fast rate results in multiple X-damage new cracks, but not complete fusion with the primary cracks, and the lateral deformation at the end of the specimen is also limited. The power consumed \(W_{\tau}\) through the EFE significantly increases in 50 mm\(\cdot\)min\({}^{-1}\). Accordingly, its UCS value increases significantly.
4. Both experiments and numerical simulations have confirmed that the SE and LR did have an influence on the physical parameters of the sandstone-like specimens. By mechanical analysis, the EFE was generated during the loading process with a HDR of 0.6-1 and during dynamic loading phases, which was the root cause of the SE and the LR. Meanwhile, the results also showed that the power consumed as a result of the EFE increased as the HDR of the specimen decreased and the LR increased, which reduced the actual amount of energy transferred inside the specimen. In order to accurately obtain the physical parameters of real coal and rock and effectively avoid engineering disasters, the influence of the EFE should be mitigated as far as possible.  
Y.G., formal analysis, methodology, and writing--original draft; J.B., conceptualization, writing--review and editing, supervision, and funding acquisition; Y.L., visualization and writing--review and editing; X.Z., conceptualization; L.T., conceptualization; Z.F., investigation and methodology. All authors have read and agreed to the published version of this manuscript.  
The research described in this paper was financially supported by the National Natural Science Foundation of China (No. 52074239); the National Natural Science Foundation of China (No. 51927807); the Graduate Innovation Program of China University of Mining and Technology (2024 WLJCRCZL027); and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (SJCX24_1412).  
Not applicable.  
Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.  
The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.  
The authors would like to thank the editor and reviewers for their constructive suggestions.  
The authors declare that they have no conflicts of interest regarding the publication of this paper.