## 2 Middle Rock Pillar Classification Index Analysis
### Physical Index
#### 2.3.1 Integrity  
The integrity of the middle rock pillar is affected by the cutting degree of the structure, size of the unit rock block, and combination state between the blocks, which depends on the density, number of groups, occurrence extension, openness, roughness, undulation, filling condition, and nature of the filling material of the structural plane. However, these factors can only reflect the integrity of the rock mass from different sides and to varying degrees. To comprehensively reflect the integrity of the rock mass, the commonly used description indices are the rock integrity coefficient \(K_{\rm v}\) and rock quality coefficient RQD [13].  
\(K_{\rm v}\) is the integrity coefficient of rock mass that is defined as the square of the ratio of the p-wave velocity of rock mass to that of rock, as shown in Equation (1):  
\[K_{\rm v}=\left(V_{pm}/V_{pr}\right)^{2} \tag{1}\]  
where \(V_{pr}\) is the p-wave velocity of rock (m/s) and V\({}_{pm}\) is the p-wave velocity of rock mass (m/s).  
Because the propagation velocity \(V_{pm}\) of the sound wave in the rock mass is related to the development degree of the rock mass structural plane, the shape of the structural plane, the nature of the filling material, water content, and other factors, \(V_{pr}\) is the wave velocity measured on the rock without the obvious structural plane, which can reflect the physical state of complete rock. \(K_{\rm v}\) determined according to \(V_{pr}\) and \(V_{pm}\) reflect the complete state of the rock mass, which is a relatively comprehensive quantitative physical index for comprehensively evaluating the integrity of the middle rock pillar. Table 1 shows the score division table proposed by the code compilation group of the Chinese Ministry of Railways and Ministry of Water Resources in the last 10 years [12]. The calculated score can be used to quantitatively assess the integrity of the middle rock pillar, which has been widely used.  
The rock quality coefficient RQD is also a quantitative physical index that can reflect the integrity state of the rock mass. This value represents the core acquisition rate with a length greater than 10 cm, as shown in Equation (2).  
\[\text{RQD}=\text{(Cumulative core length over 10 cm/Borehole length)}\times 100\% \tag{2}\]  
The rock core recovery rate and rock core length are strongly affected by the degree of rock fracture development, rock hardness, and rock mass homogeneity; that is, the RQD index reflects the degree of rock mass being cut by various structural planes. However, in terms of practical operation, although the RQD is a quantitative index, it is greatly affected by factors such as the inability to standardize and unify drilling machines and tools and  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Classification Basis**} & \multicolumn{5}{c}{**Integrity Degree (\(K_{\rm v}\))**} \\ \cline{2-6}  & \multicolumn{2}{c}{**Integrity**} & \multirow{2}{*}{**Relative Integrity**} & \multirow{2}{*}{**Relatively Broken**} & \multirow{2}{*}{**Broken**} \\ \cline{2-6}  & **Extremely Integrity** & & & & \\ \hline Classification of Tunnel Rock & \multirow{2}{*}{\(>\)0.85} & \multirow{2}{*}{0.85–0.65} & \multirow{2}{*}{0.65–0.45} & \multirow{2}{*}{0.45–0.25} & \multirow{2}{*}{\(<\)0.25} \\ Mass (Ministry of Railways) & & & & & \\ \hline Classification of Surrounding & \multirow{2}{*}{\(>\)0.75} & \multirow{2}{*}{0.75–0.45} & \multirow{2}{*}{0.45–0.2} & \multirow{2}{*}{\(<\)0.2} \\ Rock of Underground & & & & & \\ Engineering of Hydropower & & & & & \\ Station (Ministry of Water & & & & \\ Resources and Electric Power) & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Degree of integrity degree (\(K_{\rm v}\)).  
the lack of popularity of technology. Even the values obtained from the same rock mass vary greatly, therefore, it has not been widely used in China at present.