# Study of the Relationship between Mode I Fracture Toughness and Rock Brittleness Indices
## 4 Discussion
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Reference** & **Parameter** & \(\sigma_{\rm t}\) **(MPa)** & \(\sigma_{\rm c}\) **(MPa)** & **E (GPa)** & \(\upsilon\) \\ \hline \multirow{4}{*}{This paper} & Mean & 9.42 & 125.88 & 41.31 & 0.21 \\ \cline{2-6}  & Range & 0.42 to 18.42 & 2 to 274.82 & 8.23 to 200.00 & 0.12 to 0.37 \\ \cline{2-6}  & Standard deviation & 3.92 & 65.11 & 32.31 & 0.06 \\ \cline{2-6}  & Skewness & \(-\)0.0230 & 0.4782 & 2.7206 & 0.5499 \\ \hline \multirow{4}{*}{[18]} & Mean & 11.8 & 141.79 & 44.13 & 0.25 \\ \cline{2-6}  & Range & 3.84 to 18.42 & 47.76 to 274.82 & 15.92 to 64.18 & 0.13 to 0.34 \\ \cline{2-6}  & Standard deviation & 4.76 & 65.58 & 15.91 & 0.06 \\ \cline{2-6}  & Skewness & \(-\)0.6026 & 0.452 & \(-\)0.3654 & \(-\)0.6731 \\ \hline \multirow{4}{*}{[69]} & Mean & 12.82 & 150.83 & ---- & ---- \\ \cline{2-6}  & Range & 5.9 to 17 & 57.2 to 264 & ---- & ---- \\ \cline{2-6}  & Standard deviation & 3.61 & 58.84 & ---- & ---- \\ \cline{2-6}  & Skewness & \(-\)0.8834 & 0.3376 & ---- & ---- \\ \hline \multirow{4}{*}{[24]} & Mean & 9.97 & 137.22 & 50.22 & ---- \\ \cline{2-6}  & Range & 2.3 to 17.6 & 32.3 to 224 & 9.9 to 78 & ---- \\ \cline{2-6}  & Standard deviation & 4.61 & 56.26 & 20.21 & ---- \\ \cline{2-6}  & Skewness & \(-\)0.1017 & \(-\)0.1939 & \(-\)0.6577 & ---- \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Descriptive statistics of the rock properties used in this paper. any considerable effect on crack behavior [33]. Hence, CB was used, in many studies, as a reference in comparison with other test methods. Figure 14: K\({}_{\rm{IC}}-\)rock brittleness (B4) relationships considering only CB test method. Figure 13: K\({}_{\rm{IC}}-\)rock brittleness (B3) relationships considering only CB test method. For Keochang Granite and Yeosan Marble, KIC was determined using CCNBD, SCB, BDT and chevron-notched SCB test methods. Similar values were reported between CB and CCNBD; however, the SCB results were incomparable with the remaining methods and [17]. Moreover, lower KIC values were obtained from CCNBD compared to those from CB and SR for the same rock type [31; 59]. These differences may be caused by various factors such as specimen geometry and loading type [59]. The SCB test usually produced KIC values lower than those using other test methods. The KIC of Kimachi sandstone obtained from CB was 35% higher than that from SCB [58]. A 36.4% lower KIC value from SCB was reported for Dazhou sandstone compared to that using CCNBD [70]. The main causes for the conservative results from SCB are the large FPZ size, compared to other methods [33; 70], and the unstable crack propagation [33]. It is believed that the notch length, in SCB samples, did not represent the critical crack length associated with the maximum load because fractures, in SCB tests, propagated before FPZ fully develops, i.e., unstable crack propagation occurred [58]. The unstable crack propagation was also reported by [54]. Furthermore, BDT results were compared with those obtained from CB for six Australian rocks. It was concluded that the results were close except for basalt, which they could not explain [71]. Similarly, it was argued that BDT was a viable KIC test method because its results were similar to CCNBD and it had simple sample preparations, i.e., no notch is needed, although a significant scatter in the BDT results was reported [17]. In contrast, BDT was found to be an improper test method in [33] due to the lack of a uniform load distribution in the sample, and the KIC calculation was based on the infinite plate assumption and the significant boundary effect on the fracture initiation and propagation. Furthermore, the KIC obtained from the same test method and rock can vary with the sample geometry and dimensions due to their effect on the formed FPZ in samples during loading. A linear positive correlation between the FPZ size and diameter of concrete SCB samples was reported in [72].