## 3 [PERSON]'s Extension Strain Criterion  
In its original form, the criterion given by [PERSON] [1] reads as follows: \"Fracture of a brittle rock will initiate when total tensile strain \(\varepsilon\) in the rock exceeds the critical value that \begin{table}
\begin{tabular}{l c c c c c c c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**Copression**} & \multicolumn{6}{c}{**Tension**} \\ \hline
**Sample** & \begin{tabular}{c} **Conf.** \\ \(\sigma_{2}=\sigma_{3}\) \\ \end{tabular} & **Density** & \
\begin{tabular}{c} **Long.** \\ **Wave** \\ **Vel.** \\ \end{tabular} & \(\sigma_{1}\) & \(\epsilon_{\text{Tc}}\) & \(\epsilon_{\text{Tc}}\) & **E** & \(\
u\) & **Sample** & **Density** &
\begin{tabular}{c} **Long.** \\ **Wave** \\ **Vel.** \\ \end{tabular} & \(\sigma_{\text{Tc}}\) & \(\epsilon_{\text{Tc}}\) \\ \hline  & **MPa** & **kg/m3** & **m/s** & **MPa** & **[-]** & **[-]** & **GPa** & **[-]** & & **kg/m3** & **m/s** & **MPa** & **[-]** \\ \hline p\_j\_1 & - & 2320.8 & 2565.8 & 71.15 & 0.0049 & \(-\)0.0041 & 16.33 & 0.35 & p\_r\_1 & 2270.66 & 2373.74 & 4.64 & \(-\)0.0026 \\ \hline p\_j\_2 & - & 2351.6 & 2511.1 & 65.68 & 0.0033 & \(-\)0.0030 & 14.30 & 0.33 & p\_r\_2 & 2378.14 & 2474.92 & 4.74 & \(-\)0.0026 \\ \hline p\_j\_3 & - & 2338.4 & 2468.4 & 76.30 & 0.0054 & \(-\)0.0034 & 16.92 & 0.24 & p\_r\_3 & 2289.07 & 2692.31 & 5.27 & \(-\)0.0028 \\ \hline p\_j\_4 & - & 2337.0 & 2555.6 & 71.53 & 0.0058 & \(-\)0.0037 & 15.40 & 0.26 & p\_r\_4 & 2266.47 & 2864.72 & 4.26 & \(-\)0.0021 \\ \hline p\_j\_5 & - & 2278.4 & 2543.3 & 62.50 & 0.0059 & \(-\)0.0036 & 13.03 & 0.21 & p\_r\_5 & 2344.97 & 2472.60 & 4.80 & \(-\)0.0028 \\ \hline Average & & 2325.2 & & 69.4 & 0.0051 & -0.0036 & 15.2 & 0.3 & & 2309.9 & 2575.7 & 4.7 & \(-\)0.0026 \\ \hline Stand. dev. & & 25.4 & & 4.8 & 0.0009 & 0.0004 & 1.4 & 0.1 & & 44.2 & 178.2 & 0.3 & 0.0002 \\ \hline p\_t\_1 & 2.5 & 2327.1 & 2611.84 & 74.54 & 0.0099 & \(-\)0.0050 & 9.10 & 0.20 & & & & & & \\ \hline p\_t\_2 & 5 & 2298.1 & 2569.44 & 91.10 & 0.0082 & \(-\)0.0047 & 12.68 & 0.26 & & & & & & \\ \hline p\_t\_3 & 5 & 2312.3 & 2392.64 & 115.00 & 0.0065 & \(-\)0.0036 & 25.38 & 0.20 & & & & & & \\ \hline p\_t\_4 & 10 & 2321.2 & 2516.13 & 158.50 & 0.0098 & \(-\)0.0039 & 23.16 & 0.28 & & & & & & \\ \hline p\_t\_5 & 10 & 2287.8 & 2363.64 & 161.17 & 0.0073 & \(-\)0.0055 & 26.24 & 0.30 & & & & & & \\ \hline p\_t\_6 & 15 & 2293.4 & 2392.64 & 176.21 & 0.0072 & \(-\)0.0047 & 29.79 & 0.25 & & & & & & \\ \hline p\_t\_7 & 15 & 2334.9 & 2600 & 172.07 & 0.0094 & \(-\)0.0058 & 23.43 & 0.27 & & & & & & \\ \hline Average & & 2310.7 & 2507.5 & & & & & & & & & & & \\ \hline Stand. dev. & & 16.7 & 99.2 & & & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary results of the uniaxial and triaxial compression tests and the Brazilian test. Figure 3: Rock block 0.5 m \(\times\) 0.5 m \(\times\) 0.5 taken from a Lubon tunnel (**a**) and longitudinal wave velocity histogram (**b**). Sandstone sample characteristics according to (**c**) the Brazilian test, (**d**) the unconfined compression test, and (**e**) the triaxial compression test. is characteristic of that type of rock\". According to this criterion, fracture initiates when the following condition in Equation (1) is met:  
\[\varepsilon\ \geq\ \varepsilon_{c}, \tag{1}\]  
where \(\varepsilon_{c}\) is the critical value of the extension strain. It should be noted that, in geochemical analyses of laboratory tests, the strains corresponding to compression are usually assumed to be positive while those corresponding to tension are assumed to be negative. As a consequence of that assumption, fracture will be initiated in a plane that is perpendicular to the direction of the extension strain, i.e., the direction of the least principal stress (\(\sigma_{1}>\sigma_{2}>\sigma_{3}\)). Importantly, [PERSON] suggests that the critical value of the extension strain should be determined based on the uniaxial compression tests of specimens and tracking the relationship between the radial strain (extension strain) and the axial strain.