# Study of the Relationship between Mode I Fracture Toughness and Rock Brittleness Indices
## 2 Materials and Methods
Rock brittleness was assessed using ten indices (Table 2), which were either based on strength parameters, i.e., Equations (1)-(4) and (9), or pre-peak elastic parameters, i.e., Equations (5)-(8), or both, i.e., Equation (10). In general, rock brittleness indices were chosen such that they can be estimated using rock properties common in most rock testing programs, i.e., UCS, TS, Young's modulus and Poisson's ratio. In this study, the considered brittleness indices (B1, B2, B3, B4, B9 and B10), in Table 2, were the same as those previously studied in [22; 23; 24]. In this way, the effect of considering additional KIC test methods, i.e., other than CB or SR, on the KIC--rock brittleness indices relationships could be investigated. Although strength-based indices B1, B2, B3 and B4 were used by many researchers due to their simplicity, they were criticized for not reflecting rock brittleness but rather the rock strength [42; 43]. Nonetheless, they, particularly indices B3 and B4, were used to assess the performance of different rock operations such as ornamental stone production rate [28], rock burst tendency [25; 26] and drilling operations [29; 30; 62]. Index B9 was proposed in [62] to assess the performance of drilling operations for thirty-two rocks from Turkey and Norway. It was concluded that B9 had good correlation with the drilling operation performance [62]. Moreover, Index \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Reference**} & \multirow{2}{*}{**Rock Type**} & \multirow{2}{*}{**Test Method**} & \(\mathbf{K_{IC}}\) & \(\mathbf{\sigma_{t}}\) & \(\mathbf{\sigma_{c}}\) & \(\mathbf{E}\) & \\  & & & (MPa\(\cdot\)m\({}^{0.5}\)) & (MPa) & (MPa) & (GPa) & \(\mathbf{\upsilon}\) \\ \hline \multirow{6}{*}{[10]} & Ankara andesite & SCB & 0.940 & 7.000 & 82.840 & 12.334 & 0.150 \\ \cline{2-7}  & Ankara andesite & CCNBD & 1.450 & 7.000 & 82.840 & 12.334 & 0.150 \\ \cline{2-7}  & Afyon marble & SCB & 0.560 & 5.130 & 52.320 & 34.294 & 0.120 \\ \cline{2-7}  & Afyon marble & CCNBD & 1.090 & 5.130 & 52.320 & 34.294 & 0.120 \\ \hline [51] & Fujian granite & SCB & 1.603 & 12.500 & 183.300 & 40.710 & 0.230 \\ \hline [52] & Fujian granite & CSTBD & 1.145 & 11.630 & 174.780 & 28.940 & 0.200 \\ \hline [53] & Fujian granite & SCB & 1.349 & 11.630 & 174.780 & 28.940 & 0.200 \\ \hline [54] & Bayan Sandstone & SCB & 0.441 & 2.850 & 43.110 & 12.240 & 0.170 \\ \hline \hline \end{tabular}  
* KIC: Mode I fracture toughness; \(\sigma_{t}\): Brazilian tensile strength; \(\sigma_{c}\): Uniaxial compressive strength; \(E\): Young’s modulus; \(\upsilon\): Poisson’s ratio; SectableB: Single Edge Crack Round Bar Bending; CSTBD: Cracked Straight Through Brazilian Disc; SNSRB: Straight Notched Short Rod Bend; BDT: Brazilian Disk Test.  
\end{table} 
Table 1: _Cont._B10 was proposed in [24] for KIC perdition when rocks with significant pre-fracture plastic deformation were considered. However, it was argued that it has no physical meaning in [43]. Elastic-based indices (B5, B6, B7 and B8) defined rock brittleness in terms of only pre-peak elastic parameters, i.e., Young's modulus and Poisson's ratio. They were mainly utilized in quantifying the brittleness of reservoirs, e.g., shale formations, in the oil and gas exploitation operations. These indices assumed that rocks with high Young's modulus and small Poisson's ratio would be more brittle. However, they showed contradicting results for different shale formations so it was recommended that they may not represent the brittleness of all shale rocks with the same accuracy [43].