## 2 Middle Rock Pillar Classification Index Analysis
### Mechanics Index
#### 2.4.2 Initial Stress State  
The second aspect that characterizes the mechanical state of the middle rock pillar is its initial stress state. The middle rock pillar is not only the carrier of the load in the small clear-distance tunnel but also the main part of the rock mass structure. The initial stress state is an important factor that cannot be ignored because it affects the stability of the rock mass and has a significant impact on the deformation and failure of the middle rock pillar.  
When the initial stress is medium or low, the stress and deformation characteristics after tunnel excavation are close to linear elasticity and viscoelasticity. When the initial stress is high or extremely high, the convergence deformation characteristics after tunnel excavation are close to elastoplasticity, plasticity, and viscoelasticity [12]. Under the condition that the rock hardness and integrity are maintained, the rock mass with high initial stress has worse stability. The index used to measure the initial stress state at home and abroad is usually expressed by the strength-stress ratio \(S\), as shown in Equation (3):  
\[S=R_{c}/\sigma_{\text{max}} \tag{3}\]  
where \(R_{c}\) is the uniaxial compressive strength of the rock (MPa), and \(\sigma_{\text{max}}\) is the maximum initial stress of the rock mass. \(\sigma_{\text{max}}=\gamma\)H (MPa), where \(\gamma\) is the surrounding rock unit weight and H is the buried depth of the surrounding rock.  
According to the strength stress ratio \(S\) of the surrounding rock, the stress state of the middle rock pillar can be quantitatively graded and evaluated, including extremely high, medium to high, and low stresses, as shown in Table 5.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Hardness**} & \multicolumn{3}{c}{**Hard Rock**} & \multicolumn{3}{c}{**Soft Rock**} \\ \cline{2-7}  & **Extremely Hard** & **Relatively Hard** & **General Hard** & **General Soft** & **Relatively Soft** & **Extremely Soft** \\ \hline \(R_{c}\) (MPa) & \(>\)120 & 70–120 & 30–70 & 15–30 & 5–15 & \(<\)5 \\ \hline \multirow{4}{*}{Representative rock} & \multirow{4}{*}{Unweathered granite, guertaite, sidiceous, limestone, etc.} & \multirow{4}{*}{Slightly weathered and weakly weathered marble, tuff, dolomite, magmatic rock, etc.} & Strongly & & \\  & & & weathered & extremely hard & Mudstone, coal, & \\ \cline{1-1} \cline{3-5}  & & & & rock, weakly & argillaceous & Completely \\ \cline{1-1} \cline{3-5}  & & & & weathered hard & cemented & \\ \cline{1-1} \cline{3-5}  & & & & rock, sandy & sandstone, & \\ \cline{1-1} \cline{3-5}  & & & & mudstone, & conglomerate, etc. & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Classification of the hardness of the middle rock pillar.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Initial Stress State of the Middle Rock pillar**} & \multicolumn{2}{c}{**Main Phenomenon**} & \multirow{2}{*}{**The Strength Stress Ratio S**} \\ \cline{2-2} \cline{4-4}  & **Hard Rock** & **Soft Rock** & \\ \hline \multirow{4}{*}{Extremely high stress} & \multicolumn{2}{c}{Excavation may cause rock bursts.} & The caking phenomenon of rock core. & \multirow{4}{*}{\(<\)4} \\  & & Many new fractures. & Sustained large displacement. & \\ \hline \multirow{4}{*}{Medium–High stress} & \multirow{2}{*}{
\begin{tabular}{c} Rock mass peeling and falling off of tunnel wall. \\ Poor cavern formation. \\ \end{tabular} } & Significant displacement of & \\  & & tunnel wall rock mass. & 4–8 \\ \cline{1-1} \cline{3-5}  & & & Persistent displacement. & \\ \hline \multirow{2}{*}{Low stress} & \multicolumn{2}{c}{Weak initial stress state.} & \multirow{2}{*}{\(>\)8} \\  & & The strength of rock mass is conducive to stability. & \\ \hline \hline \end{tabular}
\end{table}
Table 5: Classification of the initial stress state of the middle rock pillar.