## 2 The Existing Methods for Determining Rock Brittleness
If the brittleness index is calculated based on the pre-peak elastic modulus, it neglects the influence of the post-peak curve on rock brittleness. It is evident that this type of brittleness index is not appropriate. For lines 2 and 4, they have the same slope before the peak, the same stress drop after the peak, but different peak strengths. If only the post-peak portion of the stress-strain curve and the pre-peak elastic deformation are considered, it overlooks the influence of the rock's inherent peak strength. Clearly, this type of brittleness index is not suitable. For lines 3 and 4, they have different slopes before the peak, different stress drops after the peak, but the same peak strength and the same post-peak slope. Most brittleness indexes also fail to reflect this characteristic. 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. A Method to Evaluate the Brittleness in Consideration of Plastic Deformation in Pre-Peak and Failure Energy in Post-Peak  
In the evaluation of rock brittleness, it is essential to consider both pre-peak and post-peak stress-strain curves. This is because the behavior of rocks during the pre-peak and post-peak stages provides valuable insights into their brittleness characteristics. During the pre-peak stage, the rock undergoes elastic deformation and initial crack propagation. By analyzing the stress-strain curve in this stage, we can determine the elastic modulus, which represents the rock's stiffness and ability to withstand deformation without fracturing. The elastic modulus is a crucial parameter in defining the rock's brittleness, as a higher modulus indicates a more brittle behavior. The inclusion of pre-peak plastic deformation in the brittle evaluation method is necessitated by the recognition that rocks often exhibit significant ductility before reaching their peak strength. By quantifying the extent of plastic deformation prior to failure, this method captures the rock's ability to deform without fracturing. This information is essential for engineering design, as it helps identify potential failure modes and select appropriate mitigation measures. After reaching the peak stress, the rock experiences post-peak behavior characterized by progressive failure and plastic deformation. By examining the stress-strain curve in this stage, we can assess the extent of plastic deformation, energy absorption, and the ability to undergo ductile deformation. These parameters influence the rock's brittleness, as a higher degree of plastic deformation and energy absorption indicates a more ductile behavior. The consideration of post-peak failure energy in the brittle evaluation method is crucial as it provides insights into the rock's fracture toughness and energy dissipation capacity. By quantifying the energy required for crack propagation and failure, this approach can assess the rock's resistance to catastrophic failure and its ability to absorb and dissipate energy. Such information is vital for optimizing engineering designs and ensuring the stability of rock structures. Considering both pre-peak and post-peak stress-strain curves allows for a comprehensive evaluation of rock brittleness. It provides a holistic understanding of the rock's mechanical response to stress, including its initial stiffness, crack propagation, and ability to undergo plastic deformation. By analyzing the entire stress-strain curve, we can capture the complete spectrum of brittleness and understand the rock's failure mechanisms. Based on the definitions provided by existing scholars, this study considers brittleness and ductility as opposing characteristics [17; 18]. The strain occurring in the rock mass prior to failure can be divided into recoverable elastic strain and irrecoverable plastic strain induced by crack propagation.