## 4 Definition and Estimation of Brittleness Indexes
Mechanical parameters are measured through physical testing methods, such as hardness, strength, point-load, and penetration tests and tests regarding the inner frictional angle [6; 69]. Out of all 12 brittleness indexes reviewed by [PERSON] et al. [66] (2021), only a few (B\({}_{1}\), B\({}_{2}\), B\({}_{12}\), B\({}_{15-20}\), B\({}_{23}\), B\({}_{24}\), B\({}_{27}\), B\({}_{28}\), and B\({}_{30-34}\)) were based on hardness, strength, point-load testing, mineralogical composition, penetration tests, and inner frictional angle and can be used to determine the mechanical behavior of rock. Petrographic factors such as the grain area ratio, cement content, packing density, packing proximity, and feldspar percentage significantly influence brittleness in rocks [28]. [PERSON] et al. [70] (2023) also emphasized that petrographic properties, such as mineral composition, texture, grain size, and the presence of fractures, are crucial for evaluating the mechanical behavior of a rock and brittleness, which help to predict its tendency to fracture under stress. The brittleness index of norite is an important parameter that influences the intended or unintended rock failure process in mining, tunneling, and drilling operations. In hard rock tunnels, the brittle failure of surrounding rocks in the form of spalling and rock burst frequently occurs under high geo-stresses [71]. [PERSON] et al. [68] (2018) stated that various definitions and evaluation criteria for brittleness have been proposed to describe rock failure behavior, but their effectiveness and reliability remain unverified. Various brittleness indices (B1-B13) differ in how they incorporate mechanical parameters such as UCS, tensile strength, elastic modulus, and stress-strain behavior. Indices like B1-B5 are simple and widely used but rely solely on mechanical data, often ignoring petrographic influences [27]. Others, like B6-B9, integrate stress-strain characteristics and offer better insights into post-peak behavior, making them suitable for rocks showing brittle-ductile transitions [27]. For norite, indices that incorporate both strength ratios and deformation modulus, such as B7, B9, and B11, are more applicable due to norite's heterogeneous texture and mineral composition, which influence both stiffness and failure mode. Thus, more comprehensive models better capture norite's complex mechanical response, especially where altered minerals or grain size variability affect brittleness. As shown in Table 1, brittleness indices B\({}_{1}\) to B\({}_{13}\) are based on strength parameters, with index B\({}_{1}\) being the simplest, expressed as  
\[B_{1}=\sigma_{c}/\sigma_{t} \tag{4}\]  
\[B_{2}=\left(\sigma_{c}-\sigma_{t}\right)\ /\ \left(\sigma_{c}+\sigma_{t}\right) \tag{5}\]  
where \(\sigma_{c}\) and \(\sigma_{t}\) indicate the uniaxial compressive strength (UCS) and Brazilian tensile strength, respectively. Several researchers, such as [PERSON] [72] (1986), [PERSON] [73] (1991), [PERSON] and [PERSON] [74] (2007), and [PERSON] [75] (2015), have investigated these two brittleness indices (B\({}_{1}\) and B\({}_{2}\)) and concluded that they are commonly used to assess rock fragmentation efficiency. It is also believed that higher values of B\({}_{1}\) and B\({}_{2}\) indicate greater brittleness in the rock ([PERSON] and [PERSON] [76], 1974; [PERSON] [73], 1991; [PERSON] and [PERSON] [74], 2007; [PERSON] [77] (2014)), and there is also a possibility for predicting rock burst [78; 79; 80; 81]. B\({}_{1}\) and B\({}_{2}\) are simple indices to attain, and their simplicity makes them preferred by researchers and engineers. Nevertheless, there are limitations to the indices, for example, the rock fracture process is not reflected in the physical meaning of the two indices. Thus, B\({}_{1}\) is more appropriate to define rock strength than brittleness. Rocks with different \(\sigma_{c}\) and \(\sigma_{t}\) values may have the same B\({}_{1}\) value with a narrow difference range, which limits its effectiveness as a brittleness index [33].