## 1 Introduction  
The evaluation of rock brittleness holds significant research significance in the field of academic studies [1; 2]. Understanding the brittleness characteristics of rocks is crucial for various applications, such as geotechnical engineering, rock mechanics, and petroleum reservoir characterization [3; 4]. Evaluating rock brittleness helps in predicting rock failure behavior, designing safe and stable structures, optimizing drilling and hydraulic fracturing operations, and assessing the potential for induced seismicity [5; 6; 7].  
Currently, numerous studies have been conducted to investigate rock brittleness evaluation methods [2]. These studies have proposed various approaches, includingempirical indexes, laboratory testing, and numerical modeling techniques [2,3,8]. Empirical indexes often rely on simple parameters, such as the ratio of compressive to tensile strength or the strength ratio index, to estimate rock brittleness [9,10]. Laboratory testing involves conducting experiments, such as uniaxial or triaxial compression tests, to analyze the stress-strain behavior and failure patterns of rocks [11, 12, 13]. Numerical modeling techniques utilize advanced computational methods, such as finite element analysis or discrete element modeling, to simulate rock behavior and predict brittleness. Brittleness indexes based on mineral composition vary with the classification criteria of brittle minerals and do not consider the influence of rock diagenesis and strength components on rock brittleness [1,3,14]. Although brittleness indexes based on mechanical properties take into account the influence of rock mass strength characteristics, they are not suitable for evaluating the brittleness characteristics of different types of rocks and complex stress conditions in the rock mass [5,6]. Brittleness indexes based on the characteristics of the complete stress-strain curve can reflect the influence of crack propagation on rock failure deformation during the rock's damage process but fail to explain the strength evolution process of the rock [7,12]. Brittleness indexes based on hardness testing are primarily used for the brittleness evaluation of homogeneous materials, and the heterogeneity and anisotropy of rocks inevitably result in significant deviations in brittleness evaluation in such cases [7]. Despite the progress made in rock brittleness evaluation, challenges still exist. The complex nature of rock behavior, including heterogeneity, anisotropy, and nonlinear stress-strain relationships, poses difficulties in accurately assessing brittleness [15,16]. Additionally, the lack of standardized brittleness evaluation criteria and the need for integrating multiple parameters for comprehensive assessments remain areas of active research.  
In light of these research gaps, this study aims to contribute to the field of rock brittleness evaluation by proposing a novel method that incorporates energy considerations into the assessment. By analyzing the stress-strain curve characteristics before and after the peak stress, this method provides a more physically meaningful approach to quantifying rock brittleness. The findings of this study will enhance our understanding of rock failure mechanisms and provide valuable insights for engineering and geoscience applications.