Table 1 The calculation formula for the brittleness, toughness and hardness of rock.

\({B_1}=\frac{{{\sigma _{\text{c}}}}}{{{\sigma _{\text{t}}}}}\)

\(\begin{aligned} Y' = & - 1.297 + 9.516 \times \frac{S}{{2R}} - \left( {0.47 + 16.457 \times \frac{S}{{2R}}} \right) \\ & \;\;\; \times \frac{a}{R} + \left( {1.071 + 34.401 \times \frac{S}{{2R}}} \right) \times \left( {\frac{a}{R}} \right)^{2} \\ \end{aligned}\)

\(HI=\frac{{{P_{\hbox{max} }}}}{d}\)

\({B_2}=\frac{{{\sigma _{\text{c}}} - {\sigma _{\text{t}}}}}{{{\sigma _{\text{c}}}+{\sigma _{\text{t}}}}}\)

\(K_{{IC}} = Y^{\prime} \times \max \left( {\frac{a}{R},\frac{S}{{2R}}} \right) \times \frac{{P\sqrt {\pi a} }}{{2RT}}\)

\({B_3}=\sqrt {\frac{{{\sigma _{\text{c}}} \times {\sigma _{\text{t}}}}}{2}}\)

\({K_{{\text{IIC}}}}=7.74 \times {10^{ - 2}}{P_{\hbox{max} }} - 1.8 \times {10^{ - 3}}{P_{\text{c}}}\)