## 4 Definition and Estimation of Brittleness Indexes  
One of the most important mechanical properties of rocks is their brittleness. In rock mechanics, a key property for assessing how a rock fractures are through its brittleness,  
Figure 10: The effect of intermediate principal stress on the propagation law of internal fractures in rock: **(a)** the initial direction of internal cracks is parallel to \(\sigma_{2}\); **(b)** the initial direction of internal cracks is perpendicular to \(\sigma_{2}\)[55]. which is influenced by factors such as mineral composition, fluid content, and the complexity of the microstructure [61]. The brittleness of a rock depends on mechanical properties such as the unconfined compressive strength (UCS), Young's modulus, and Poisson's ratio [62]. [PERSON] and [PERSON] [63] (2004) stated that there are many researchers who have explored various methods for determining brittleness indexes. Unfortunately, there is no universally accepted standardized method or concept for measuring or characterizing the brittleness of rocks [64; 65]. Despite the fact that brittleness is significant in many different engineering fields, many researchers noted that there is currently no standardized technique for measuring or quantifying the brittleness indices of different rocks [66; 67; 68; 6; 33; 61; 6]. The method used to quantify the brittleness index could vary based on the type of rock, its material characteristics, and the specific objectives or requirements of the project [62]. Researchers have proposed various methods to quantify the brittleness index, considering factors like stress and strain, mineral composition, and the strength of different rocks, with the reliability of each index varying depending on the specific task at hand. A compilation of 80 brittleness indices that are publicly available in the rock mechanics literature reveals that these indices are not generally relevant across fields, and they are treated differently based on rock fracture behavior. Additionally, the term \"brittleness\" is often misrepresented, with many empirically derived indices lacking a theoretical basis and not accurately reflecting rock brittleness [66]. Table 1 categorizes mechanical and petrographic brittleness indices into two groups based on their assessment approaches in this study. The first group uses rock strength parameters from standard tests for brittleness, while the second group uses rock mineral constituent analysis for brittleness. [PERSON] et al. [66] (2021) outlined that, since 1967, numerous brittleness indices have been developed for various purposes in rock mechanics, classified into two groups, which are stress-strain and mineralogical parameters. These groups are further subdivided into 12 categories based on different parameters or measurement methods. These categories are summarized in Table 1, each offering a unique perspective on the fracture or failure tendency of a material under stress. \begin{table}
\begin{tabular}{c c} \hline
**Brittleness Indices** & **Measurement Parameter** \\ \hline B1 to B13 & Strength parameters \\ \hline B14 to B40 & Stress–strain curve \\ \hline B41 to B47 & Elastic parameters \\ \hline B48 to B55 & Mineral composition \\ \hline B56 to B62 & Conversional well logging \\ \hline B63 to B65 & Angle of internal friction \\ \hline B66 to B73 & Indentation test \\ \hline B74 to B75 & Fine content \\ \hline B76 to B77 & Consolidation characteristics \\ \hline B78 & Point load test \\ \hline B79 & Pulling test \\ \hline B80 & Micro-scratch test \\ \hline \end{tabular}
\end{table} 
Table 1: A summary of brittleness indices and the parameters used for their measurements (obtained from [PERSON] et al. [66] (2021). )Table 1 presents the brittleness indices used for specific parameters, with the main focus of this review paper being the comparison of the mechanical and petrographic characteristics of norite.