## 5 Comparison of Brittleness Index with Other Existing Methods  
As shown in Figure 7, the changes in brittleness under different confining pressures for red-bed sandstone under saturated conditions and in its natural state were evaluated using B7, B9, and B17, which were compared to the brittleness evaluation method proposed in this study. Brittleness indexes B7 and B9 based on stress-strain parameters are selected to evaluate rock brittleness, while B17 is a brittleness index proposed based on energy parameters. The above three indexes have been validated by numerous cases, demonstrating their ability to evaluate rock brittleness [2; 10]. Therefore, the rationality of the proposed method is verified through various different definitions of brittleness indexes. Due to the different orders of magnitude of the various brittleness indexes, the brittleness indexes of each method were standardized to facilitate the presentation of their respective trends. In Figure 7, under natural conditions, the proposed brittleness index in this study exhibits the maximum values at all confining pressures, with the lowest value observed for B7. Furthermore, the magnitude of decrease in values for B7 and B9 diminishes as the confining pressure increases. 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. The values of the proposed brittleness index, in comparison with the other indexes, fall within the intermediate range, and their trends of change are generally consistent. Compared to B7 and B9, the advantages of the brittleness evaluation proposed in this study are as follows: the proposed method describes the stress-strain curve characteristics before and after the peak stress, and compared to B7 and B9, which use the stress increment after the peak stress and the slope of the curve to describe the brittleness of rock masses, the use of rock mass energy in this study for evaluating brittleness is more physically meaningful. This study argues that the stress growth rate and stress-strain rate only indicate the strength characteristics of the rock mass, without a direct relationship with  
Figure 6: The brittleness index of cyan sandstones: (**a**) Under natural condition; (**b**) Under freezing-thawing conditions. Figure 7: Comparison of the brittleness indexes for red-bed sandstones after normalization: (**a**) Under natural conditions; (**b**) Under saturated conditions. brittleness. However, analyzing the characteristics of rock mass failure from an energy perspective can better reflect the brittleness characteristics of the rock mass. Compared to the brittleness evaluation proposed in this study, B17 lacks the characteristics after the peak stress and uses the proportion of elastic energy to evaluate the brittleness of the rock mass, which would give an advantage to highly elastic rock masses. Therefore, the study suggests that if energy is used to evaluate the brittleness of rock masses, it should be based on the amount of energy consumed by the rock mass in overcoming friction and heat release. As shown in Figure 8, the changes in brittleness under different confining pressures for cyan sandstone under freezing-thawing conditions and in its natural state were evaluated using B7, B9, and B17, which were compared to the brittleness evaluation method proposed in this study. Due to the different orders of magnitude of the various brittleness indexes, the brittleness indexes of each method were standardized to facilitate the presentation of their respective trends. Under natural conditions, the three brittleness indexes, B7, B9, and Bnew, exhibit a similar trend in characterizing the brittleness of the cyan sandstone. They gradually decrease with increasing confining pressure, and the value of Bnew is larger than B9 and B7.