## 2 The Existing Methods for Determining Rock Brittleness  
Brittleness evaluation plays a significant role in assessing the mechanical behavior of rocks for various engineering applications [2]. This section aims to discuss the current state of the research of rock brittleness assessment and critically analyze the advantages and disadvantages of different approaches based on mineral composition, strain, stress, elastic parameter, and energy. Table 1 shows the existing methods for determining the rock brittleness. The stress-based approach defines rock brittleness in terms of stress levels at failure or the stress intensity required for crack propagation. This method allows for the assessment of the rock's resistance to fracturing under different loading conditions. The advantage of stress-based definitions is their direct relationship with fracture initiation and propagation. However, accurately determining stress levels in rocks can be challenging, particularly in heterogeneous formations. Definition of Brittleness Index based on Strain  
Another approach to evaluating rock brittleness is through strain-based definitions. This method focuses on quantifying the deformation characteristics of rocks under stress. By considering the strain at failure or the strain energy release, this approach provides insights into the rock's ability to undergo plastic deformation before failure. The advantage of strain-based definitions is their ability to capture the ductility or plasticity of rocks [17; 18]. However, their drawback lies in the complexity of strain measurements and the need for advanced testing equipment. Definition of Brittleness Index Based on Elastic Parameters  
Another approach involves defining brittleness indexes using elastic deformation parameters, such as Young's modulus and Poisson's ratio. These parameters reflect the rock's ability to undergo elastic deformation without fracturing. This approach provides a more direct connection to rock mechanics properties and can be determined through laboratory testing or empirical correlations. However, it neglects the influence of plastic deformation and post-peak behavior, limiting its ability to capture the complete brittleness spectrum. Definition of Brittleness Index based on Energy  
The energy-based definition of rock brittleness focuses on quantifying the fracture energy or the energy required to propagate cracks within rocks [19; 20; 21; 22]. This approach considers the relationship between the energy dissipated during fracture and the rock's brittleness characteristics. The advantage of energy-based definitions is their ability to capture the rock's fracture toughness and resistance to crack propagation. However, accurately measuring fracture energy necessitates sophisticated experimental setups and can be time-consuming. Definition of Brittleness Index based on Rock Mineral Composition  
One approach to defining rock brittleness is by considering the mineral composition. This method involves characterizing the rock's brittleness index based on the proportions and mechanical properties of its constituent minerals. The advantage of this approach is its ability to capture the influence of mineralogy on rock behavior. However, its major limitation lies in the difficulty of accurately quantifying the mineral composition and establishing consistent correlations between mineralogy and brittleness. Based on Figure 1, the shortcomings of the current brittleness evaluation method based on stress-strain curves can be identified. For lines 1 and 2, they exhibit the same stress drop after the peak but have different slopes before the peak. If only the post-peak portion of the stress-strain curve is considered, it would inevitably lead to the calculation of the same brittleness index. Clearly, this type of brittleness index is not suitable. For lines 1 and 3, they have the same slope before the peak but different peak strengths and different stress drops after the peak.