## 7 Conclusions  
1. The advantages and disadvantages of different approaches based on mineral composition, strain, stress, elastic parameter, and energy to determine the rock brittleness are summarized. Most brittleness indexes also fail to reflect some characteristics about the complete stress-strain curves. Therefore, it is necessary to propose a brittleness index that can simultaneously reflect the pre-peak and post-peak curve characteristics and capture the elastic and plastic deformation features during the rock failure process. (2) Considering the plastic deformation in pre-peak and failure energy in post-peak, an energy-based brittleness index is proposed in this study. The triaxial test data of red-bed sandstone and cyan sandstone under different conditions is used to evaluate the rock brittleness. For red-bed sandstone, both in the natural state and under saturated conditions, the brittleness index of red-bed sandstone decreases with increasing confining pressure. However, the brittleness of red-bed sandstone under saturated conditions is lower compared to its natural state. For cyan sandstone, the brittleness of cyan sandstone decreases with increasing confining pressure, and freezing-thawing action can reduce the brittleness of the rock. (3) To validate the rationality of the proposed brittleness index, three brittleness indexes, including stress-based, strain-based, and energy-based brittleness indexes, are selected to compare with the proposed brittleness index. For red-bed sandstone, the proposed brittleness index under natural conditions exhibits the maximum values at all confining pressures, with the lowest value observed for B7. The four brittleness indexes consistently characterize the brittleness of the red-bed sandstone under natural conditions. Under saturated conditions, the brittleness indexes exhibit different patterns of variation. For cyan sandstone, the three brittleness indexes--B7, B9, and Bnew--under natural conditions exhibit a similar trend in characterizing the brittleness of the cyan sandstone, while the trend of B17 is essentially opposite to the previous three indexes. Under freezing-thawing conditions, the variation patterns of the three brittleness indexes, B7, B9, and Bnew, are similar. Similarly, the trend of B17 is essentially opposite to that of the previous three indexes.  
Conceptualization, X.Y., T.W. and Y.G.; methodology, X.Y., T.W. and Y.G.; validation, T.W. and Y.G.; data curation, T.W.; writing--original draft preparation, X.Y., T.W. and Y.G.; writing--review and editing, X.Y., T.W. and W.J.; supervision, M.H.; project administration, Y.W.; funding acquisition, T.W. and M.H. All authors have read and agreed to the published version of the manuscript.  
The work was funded by the National Natural Science Foundation of China (No. 42002268); Science and technology program of Tibet Autonomous Region (XZ020202 YD0007C, XZ020301 YD0034C); Open Fund of Badong National Observation and Research Station of Geohazards (No. BNORSG-202204).  
Not applicable.  
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.  
Author [PERSON] was employed by the company Zhongguan Chenhua Petroleum Engineering Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.