## 6 Discussion  
### Rock Failure Mechanism from the Energy Evolution  
The transformation of rock brittleness and ductility depends on factors such as stress level, physical properties of the rock (including crack density and rock toughness), mechanical properties of the rock (including tensile strength and shear strength), and loading rate. These factors collectively determine the rock's failure behavior and mechanical response under stress. According to the proposed brittleness index in this study, during the evolution from absolute ductility to absolute brittleness, both pre-peak dissipated energy and post-peak fracture energy gradually decrease. As shown in Figure 10, two characteristic points exist in this process: the ductility characteristic point (E \(>-\) M = Q) and the moderate brittleness characteristic point (E = \(-\) M \(>\) Q). Based on these two characteristic points, the brittleness characteristics of the rock during the entire failure process can be classified as follows: absolute ductility (E \(>\) Q = M = 0), weak brittleness (E \(>-\) M \(>\) Q), strong brittleness (- M \(>\) E \(>\) Q), and extremely strong brittleness (E \(>\) M \(>\) Q).  
Figure 9: Comparison of the brittleness indexes for different rock types: (**a**) Red-bed sandstone under natural condition; (**b**) Red-bed sandstone under saturated condition; (**c**) Cyan sandstone under natural condition; (**d**) Cyan sandstone under freezing-thawing condition.  
The understanding of rock failure mechanisms is fundamental to evaluating rock brittleness and implementing appropriate engineering interventions [23,24]. This section focuses on elucidating the mechanisms of rock failure from the perspective of energy evolution. By examining energy redistribution, dissipation, and release during the progressive failure process, a comprehensive understanding of rock brittleness can be achieved. The discussion emphasizes the significance of energy-based analysis and its implications for engineering applications.  
Energy Redistribution during Rock Failure  
Rock failure is often accompanied by energy redistribution within the rock mass [25]. This redistribution occurs due to stress concentration and the initiation and propagation of cracks. Energy-based analysis allows for quantifying the redistribution of potential and kinetic energy, providing insights into the spatial and temporal evolution of failure. By understanding energy redistribution, engineers can anticipate potential failure zones, optimize support systems, and design effective reinforcement measures.  
Energy Dissipation during Rock Failure  
Energy dissipation plays a crucial role in rock failure processes. As cracks propagate and interact, energy is dissipated through various mechanisms, such as friction, micro-racking, and fracture surface roughness. Energy-based analysis enables the quantification of dissipated energy, helping to assess the brittleness of rocks. The measurement of energy dissipation provides valuable information for designing energy-absorbing structures and selecting suitable materials to enhance rock stability.  
Energy Release during Catastrophic Rock Failure  
Catastrophic failure events, such as rockbursts and collapses, involve the sudden release of stored energy. Energy-based analysis allows for understanding the magnitude and spatial distribution of released energy during such events. This information is crucial for assessing the potential impact on surrounding structures and developing effective hazard mitigation strategies. By quantifying energy release, engineers can optimize support systems, implement real-time monitoring, and design robust containment measures.