## 6 Discussion
### Application for the Rock Brittleness  
To further the rationality of the proposed brittleness indexes for different rock types, the datasets of uniaxial and triaxial tests on two rock types, including granite and coal specimen, are collected from the literature [26,27]. The brittleness for the two rock types  
Figure 10: Evolution process of the brittleness index \(BI_{\text{new}}\). is calculated using the proposed formula. Herein, the brittleness index B7 is selected to verify the accuracy of the proposed brittleness index, as shown in Figure 11, both B7 and Bnew have the same variation trend with the confining pressure, characterizing by gradual decline. Evidently, the Bnew conforms to the law of exponential decline, which better reflects the brittleness characteristics of the two rocks. Therefore, the proposed brittleness index can be used to evaluate the other rock types. A brittleness index is proposed in this study, which describes the characteristics of stress-strain curves at different stages by considering the pre-peak plastic deformation and post-peak failure energy of rock mass. This leads to the development of a new brittleness evaluation method that offers the following advantages: (a) Consideration of pre-peak plastic deformation: Traditional brittleness evaluation indices often overlook the pre-peak plastic deformation of rock mass. However, this method introduces a pre-peak brittleness index factor that fully takes into account the plastic deformation characteristics of rocks during the loading process. This aids in a more accurate assessment of rock brittleness. (b) Consideration of post-peak failure energy: The method also introduces a post-peak brittleness index factor, considering the total energy consumed by the rock mass during the post-peak failure process. This reflects the failure characteristics of rocks in the post-peak stage, providing more comprehensive information for evaluating rock brittleness. (c) Clear physical significance: The method is based on the analysis of stress-strain curve characteristics and provides a more physically meaningful approach to quantify rock brittleness through energy considerations. Compared to traditional empirical indices or simple parameters, this energy-based evaluation method better reflects the mechanical properties and engineering behavior of rocks. However, the method also has limitations and drawbacks, including requirement for experimental data support. The application of this method requires experimental testing to obtain relevant parameters such as stress-strain curves and failure energy of rocks. This may entail significant experimental workload and costs, and could be subject to limitations imposed by experimental conditions. Rock brittleness evaluation methods are essential tools in rock engineering, offering valuable information for a wide range of engineering applications [28]. This section aims to provide an overview of the engineering applications of these methods, emphasizing their importance in optimizing engineering designs, assessing stability, and predicting rock failure. The discussion also addresses the challenges associated with implementing these methods in practical engineering scenarios. (a) Optimization of Engineering Designs  
Rock brittleness evaluation methods are instrumental in the optimization of engineering designs, particularly in areas such as tunneling, mining, and geotechnical engineering. By assessing the brittleness characteristics of rocks, engineers can make informed decisions about support systems, excavation methods, and blasting techniques. This leads to more  
Figure 11: Application of the proposed brittleness index for different rock types: (a) Granite; (b) Coal specimen. efficient and cost-effective designs that minimize the risk of rock failures and ensure the long-term stability of structures. (b) Stability Analysis of Rock Structures The evaluation of rock brittleness is crucial for the stability analysis of rock structures, including slopes, foundations, and underground excavations.